Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm

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} div.type-section h2 { font-size: 20px; line-height: 26px; font-weight: 300; } div.type-section h3 { margin-left: 15px; margin-bottom: 0px; font-weight: 300; } .journal-tabs .tab-title.active a { } </style> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/slick.css?f38b2db10e01b157?1740558760"> <meta name="title" content="Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm"> <meta name="description" content="This paper introduces a novel physical-inspired metaheuristic algorithm called “Light Spectrum Optimizer (LSO)” for continuous optimization problems. The inspiration for the proposed algorithm is the light dispersions with different angles while passing through rain droplets, causing the meteorological phenomenon of the colorful rainbow spectrum. In order to validate the proposed algorithm, three different experiments are conducted. First, LSO is tested on solving CEC 2005, and the obtained results are compared with a wide range of well-regarded metaheuristics. In the second experiment, LSO is used for solving four CEC competitions in single objective optimization benchmarks (CEC2014, CEC2017, CEC2020, and CEC2022), and its results are compared with eleven well-established and recently-published optimizers, named grey wolf optimizer (GWO), whale optimization algorithm (WOA), and salp swarm algorithm (SSA), evolutionary algorithms like differential evolution (DE), and recently-published optimizers including gradient-based optimizer (GBO), artificial gorilla troops optimizer (GTO), Runge–Kutta method (RUN) beyond the metaphor, African vultures optimization algorithm (AVOA), equilibrium optimizer (EO), grey wolf optimizer (GWO), Reptile Search Algorithm (RSA), and slime mold algorithm (SMA). In addition, several engineering design problems are solved, and the results are compared with many algorithms from the literature. The experimental results with the statistical analysis demonstrate the merits and highly superior performance of the proposed LSO algorithm." > <link rel="image_src" href="https://pub.mdpi-res.com/img/journals/mathematics-logo.png?8600e93ff98dbf14" > <meta name="dc.title" content="Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm"> <meta name="dc.creator" content="Mohamed Abdel-Basset"> <meta name="dc.creator" content="Reda Mohamed"> <meta name="dc.creator" content="Karam M. Sallam"> <meta name="dc.creator" content="Ripon K. Chakrabortty"> <meta name="dc.type" content="Article"> <meta name="dc.source" content="Mathematics 2022, Vol. 10, Page 3466"> <meta name="dc.date" content="2022-09-23"> <meta name ="dc.identifier" content="10.3390/math10193466"> <meta name="dc.publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="dc.rights" content="http://creativecommons.org/licenses/by/3.0/"> <meta name="dc.format" content="application/pdf" > <meta name="dc.language" content="en" > <meta name="dc.description" content="This paper introduces a novel physical-inspired metaheuristic algorithm called “Light Spectrum Optimizer (LSO)” for continuous optimization problems. The inspiration for the proposed algorithm is the light dispersions with different angles while passing through rain droplets, causing the meteorological phenomenon of the colorful rainbow spectrum. In order to validate the proposed algorithm, three different experiments are conducted. First, LSO is tested on solving CEC 2005, and the obtained results are compared with a wide range of well-regarded metaheuristics. In the second experiment, LSO is used for solving four CEC competitions in single objective optimization benchmarks (CEC2014, CEC2017, CEC2020, and CEC2022), and its results are compared with eleven well-established and recently-published optimizers, named grey wolf optimizer (GWO), whale optimization algorithm (WOA), and salp swarm algorithm (SSA), evolutionary algorithms like differential evolution (DE), and recently-published optimizers including gradient-based optimizer (GBO), artificial gorilla troops optimizer (GTO), Runge–Kutta method (RUN) beyond the metaphor, African vultures optimization algorithm (AVOA), equilibrium optimizer (EO), grey wolf optimizer (GWO), Reptile Search Algorithm (RSA), and slime mold algorithm (SMA). In addition, several engineering design problems are solved, and the results are compared with many algorithms from the literature. The experimental results with the statistical analysis demonstrate the merits and highly superior performance of the proposed LSO algorithm." > <meta name="dc.subject" content="metaheuristic" > <meta name="dc.subject" content="optimization" > <meta name="dc.subject" content="physics-based algorithm" > <meta name="dc.subject" content="Light Spectrum Optimizer" > <meta name ="prism.issn" content="2227-7390"> <meta name ="prism.publicationName" content="Mathematics"> <meta name ="prism.publicationDate" content="2022-09-23"> <meta name ="prism.volume" content="10"> <meta name ="prism.number" content="19"> <meta name ="prism.section" content="Article" > <meta name ="prism.startingPage" content="3466" > <meta name="citation_issn" content="2227-7390"> <meta name="citation_journal_title" content="Mathematics"> <meta name="citation_publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="citation_title" content="Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm"> <meta name="citation_publication_date" content="2022/1"> <meta name="citation_online_date" content="2022/09/23"> <meta name="citation_volume" content="10"> <meta name="citation_issue" content="19"> <meta name="citation_firstpage" content="3466"> <meta name="citation_author" content="Abdel-Basset, Mohamed"> <meta name="citation_author" content="Mohamed, Reda"> <meta name="citation_author" content="Sallam, Karam M."> <meta name="citation_author" content="Chakrabortty, Ripon K."> <meta name="citation_doi" content="10.3390/math10193466"> <meta name="citation_id" content="mdpi-math10193466"> <meta name="citation_abstract_html_url" content="https://www.mdpi.com/2227-7390/10/19/3466"> <meta name="citation_pdf_url" content="https://www.mdpi.com/2227-7390/10/19/3466/pdf?version=1665578111"> <link rel="alternate" type="application/pdf" title="PDF Full-Text" href="https://www.mdpi.com/2227-7390/10/19/3466/pdf?version=1665578111"> <meta name="fulltext_pdf" content="https://www.mdpi.com/2227-7390/10/19/3466/pdf?version=1665578111"> <meta name="citation_fulltext_html_url" content="https://www.mdpi.com/2227-7390/10/19/3466/htm"> <link rel="alternate" type="text/html" title="HTML Full-Text" href="https://www.mdpi.com/2227-7390/10/19/3466/htm"> <meta name="fulltext_html" content="https://www.mdpi.com/2227-7390/10/19/3466/htm"> <link rel="alternate" type="text/xml" title="XML Full-Text" href="https://www.mdpi.com/2227-7390/10/19/3466/xml"> <meta name="fulltext_xml" content="https://www.mdpi.com/2227-7390/10/19/3466/xml"> <meta name="citation_xml_url" content="https://www.mdpi.com/2227-7390/10/19/3466/xml"> <meta name="twitter:card" content="summary" /> <meta name="twitter:site" content="@MDPIOpenAccess" /> <meta name="twitter:image" content="https://pub.mdpi-res.com/img/journals/mathematics-logo-social.png?8600e93ff98dbf14" /> <meta property="fb:app_id" content="131189377574"/> <meta property="og:site_name" content="MDPI"/> <meta property="og:type" content="article"/> <meta property="og:url" content="https://www.mdpi.com/2227-7390/10/19/3466" /> <meta property="og:title" content="Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm" /> <meta property="og:description" content="This paper introduces a novel physical-inspired metaheuristic algorithm called “Light Spectrum Optimizer (LSO)” for continuous optimization problems. The inspiration for the proposed algorithm is the light dispersions with different angles while passing through rain droplets, causing the meteorological phenomenon of the colorful rainbow spectrum. In order to validate the proposed algorithm, three different experiments are conducted. First, LSO is tested on solving CEC 2005, and the obtained results are compared with a wide range of well-regarded metaheuristics. In the second experiment, LSO is used for solving four CEC competitions in single objective optimization benchmarks (CEC2014, CEC2017, CEC2020, and CEC2022), and its results are compared with eleven well-established and recently-published optimizers, named grey wolf optimizer (GWO), whale optimization algorithm (WOA), and salp swarm algorithm (SSA), evolutionary algorithms like differential evolution (DE), and recently-published optimizers including gradient-based optimizer (GBO), artificial gorilla troops optimizer (GTO), Runge–Kutta method (RUN) beyond the metaphor, African vultures optimization algorithm (AVOA), equilibrium optimizer (EO), grey wolf optimizer (GWO), Reptile Search Algorithm (RSA), and slime mold algorithm (SMA). In addition, several engineering design problems are solved, and the results are compared with many algorithms from the literature. The experimental results with the statistical analysis demonstrate the merits and highly superior performance of the proposed LSO algorithm." /> <meta property="og:image" content="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g001-550.jpg?1665578216" /> <link rel="alternate" type="application/rss+xml" title="MDPI Publishing - Latest articles" href="https://www.mdpi.com/rss"> <meta name="google-site-verification" content="PxTlsg7z2S00aHroktQd57fxygEjMiNHydKn3txhvwY"> <meta name="facebook-domain-verification" content="mcoq8dtq6sb2hf7z29j8w515jjoof7" /> <script id="usercentrics-cmp" src="https://web.cmp.usercentrics.eu/ui/loader.js" data-ruleset-id="PbAnaGk92sB5Cc" async></script>  <script> window.dataLayer = window.dataLayer || []; function gtag() { dataLayer.push(arguments); } gtag('consent', 'default', { 'ad_user_data': 'denied', 'ad_personalization': 'denied', 'ad_storage': 'denied', 'analytics_storage': 'denied', 'wait_for_update': 500, }); 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<div class="art-authors hypothesis_container"> by <span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop9027328' data-options='is_hover:true, hover_timeout:5000'> Mohamed Abdel-Basset</div><div id="profile-card-drop9027328" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/profiles/373987/thumb/Mohamed_Abdel-Basset.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Mohamed Abdel-Basset</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a href="https://sciprofiles.com/profile/373987?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name" class="button button--color-inversed" target="_blank"> SciProfiles </a><a 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Chakrabortty</div><div id="profile-card-drop9027331" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/profiles/2143153/thumb/Ripon_K_Chakrabortty.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Ripon K. 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margin-left: 3px; max-width: 13px !important; height: auto; top: -5px;"></a></span> </div> <div class="nrm"></div> <span style="display:block; height:6px;"></span> <div></div> <div style="margin: 5px 0 15px 0;" class="hypothesis_container"> <div class="art-affiliations"> <div class="affiliation "> <div class="affiliation-item"><sup>1</sup></div> <div class="affiliation-name ">Faculty of Computers and Informatics, Zagazig University, Zagazig 44519, Sharqiyah, Egypt</div> </div> <div class="affiliation "> <div class="affiliation-item"><sup>2</sup></div> <div class="affiliation-name ">School of Engineering and IT, UNSW Canberra at ADFA 2600, Campbell, ACT 2610, Australia</div> </div> <div class="affiliation"> <div class="affiliation-item"><sup>*</sup></div> <div class="affiliation-name ">Author to whom correspondence should be addressed. </div> </div> </div> </div> <div class="bib-identity" style="margin-bottom: 10px;"> <em>Mathematics</em> <b>2022</b>, <em>10</em>(19), 3466; <a href="https://doi.org/10.3390/math10193466">https://doi.org/10.3390/math10193466</a> </div> <div class="pubhistory" style="font-weight: bold; padding-bottom: 10px;"> <span style="display: inline-block">Submission received: 2 August 2022</span> / <span style="display: inline-block">Revised: 12 September 2022</span> / <span style="display: inline-block">Accepted: 17 September 2022</span> / <span style="display: inline-block">Published: 23 September 2022</span> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/mathematics/special_issues/Advanced_Metaheuristic_Algorithms ">Metaheuristic Algorithms</a>)<br/> </div> <div class="highlight-box1"> <div class="download"> <a class="button button--color-inversed button--drop-down" data-dropdown="drop-download-922967" aria-controls="drop-supplementary-922967" aria-expanded="false"> Download <i class="material-icons">keyboard_arrow_down</i> </a> <div id="drop-download-922967" class="f-dropdown label__btn__dropdown label__btn__dropdown--button" data-dropdown-content aria-hidden="true" tabindex="-1"> <a class="UD_ArticlePDF" href="/2227-7390/10/19/3466/pdf?version=1665578111" data-name="Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm" data-journal="mathematics">Download PDF</a> <br/> <a id="js-pdf-with-cover-access-captcha" href="#" data-target="/2227-7390/10/19/3466/pdf-with-cover" class="accessCaptcha">Download PDF with Cover</a> <br/> <a id="js-xml-access-captcha" href="#" data-target="/2227-7390/10/19/3466/xml" class="accessCaptcha">Download XML</a> <br/> <a href="/2227-7390/10/19/3466/epub" id="epub_link">Download Epub</a> <br/> </div> <div class="js-browse-figures" style="display: inline-block;"> <a href="#" class="button button--color-inversed margin-bottom-10 openpopupgallery UI_BrowseArticleFigures" data-target='article-popup' data-counterslink = "https://www.mdpi.com/2227-7390/10/19/3466/browse" >Browse Figures</a> </div> <div id="article-popup" class="popupgallery" style="display: inline; line-height: 200%"> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g001.png?1665578215" title=" <strong>Figure 1</strong><br/> <p>Categories of metaheuristic algorithms.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g002.png?1665578176" title=" <strong>Figure 2</strong><br/> <p>Light dispersion and colors of rainbow.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g003.png?1665578214" title=" <strong>Figure 3</strong><br/> <p>Light dispersion and colors of rainbow and vector form of refraction and reflection in rainbow.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g004.png?1665578183" title=" <strong>Figure 4</strong><br/> <p>The behavior of the inverse incomplete gamma function with respect to <inline-formula><mml:math id="mm436"><mml:semantics><mml:mi>a</mml:mi></mml:semantics></mml:math></inline-formula> values.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g005.png?1665578186" title=" <strong>Figure 5</strong><br/> <p>Tracing F’s values versus R<sub>1</sub> for an individual over 9 independent runs: The red points indicate that <inline-formula><mml:math id="mm437"><mml:semantics><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>&lt;</mml:mo><mml:msup><mml:mi>F</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula>; and the blue points indicate that <inline-formula><mml:math id="mm438"><mml:semantics><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>&gt;</mml:mo><mml:msup><mml:mi>F</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:semantics></mml:math></inline-formula>.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g006.png?1665578216" title=" <strong>Figure 6</strong><br/> <p>Flowchart of LSO.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g007.png?1665578224" title=" <strong>Figure 7</strong><br/> <p>Depiction of exploration and exploitation stages of the proposed algorithm (LSO). (<bold>a</bold>) Exploitation phase. (<bold>b</bold>) Exploration phase.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008a.png?1665578192" title=" <strong>Figure 8</strong><br/> <p>Sensitivity analysis of LSO. (<bold>a</bold>) Tuning the parameter P<sub>h</sub> over F58. (<bold>b</bold>) Tuning the parameter P<sub>h</sub> over F57. (<bold>c</bold>) Tuning the parameter <bold><italic>β</italic></bold> over F58. (<bold>d</bold>) Tuning the parameter <bold><italic>β</italic></bold> over F57. (<bold>e</bold>) Tuning the parameter <bold><italic>β</italic></bold> over F58 in terms of convergence speed. (<bold>f</bold>) Tuning the parameter P<sub>e</sub> over F58. (<bold>g</bold>) Tuning the parameter P<sub>e</sub> over F57. (<bold>h</bold>) Adjusting the parameter P<sub>s</sub> over F58. (<bold>i</bold>) Adjusting the parameter P<sub>s</sub> over F57.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008b.png?1665578202" title=" <strong>Figure 8 Cont.</strong><br/> <p>Sensitivity analysis of LSO. (<bold>a</bold>) Tuning the parameter P<sub>h</sub> over F58. (<bold>b</bold>) Tuning the parameter P<sub>h</sub> over F57. (<bold>c</bold>) Tuning the parameter <bold><italic>β</italic></bold> over F58. (<bold>d</bold>) Tuning the parameter <bold><italic>β</italic></bold> over F57. (<bold>e</bold>) Tuning the parameter <bold><italic>β</italic></bold> over F58 in terms of convergence speed. (<bold>f</bold>) Tuning the parameter P<sub>e</sub> over F58. (<bold>g</bold>) Tuning the parameter P<sub>e</sub> over F57. (<bold>h</bold>) Adjusting the parameter P<sub>s</sub> over F58. (<bold>i</bold>) Adjusting the parameter P<sub>s</sub> over F57.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g009.png?1665578218" title=" <strong>Figure 9</strong><br/> <p>Average rank of each optimizer on all CEC2014.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g010.png?1665578208" title=" <strong>Figure 10</strong><br/> <p>Average SD of each optimizer on all CEC2014.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g011.png?1665578205" title=" <strong>Figure 11</strong><br/> <p>Average rank on all CEC2017 test functions.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g012.png?1665578206" title=" <strong>Figure 12</strong><br/> <p>Average SD of each optimizer on all CEC2017.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g013.png?1665578221" title=" <strong>Figure 13</strong><br/> <p>Average rank of each optimizer on all CEC2020.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g014.png?1665578227" title=" <strong>Figure 14</strong><br/> <p>Average SD of each optimizer on all CEC2020.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g015.png?1665578198" title=" <strong>Figure 15</strong><br/> <p>Average rank of each optimizer on all CEC2022.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g016.png?1665578223" title=" <strong>Figure 16</strong><br/> <p>Average SD of each optimizer on all CEC2022.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017a.png?1665578220" title=" <strong>Figure 17</strong><br/> <p>Depiction of averaged convergence speed among algorithms on some test functions. (<bold>a</bold>) F51 (Unimodal), (<bold>b</bold>) F52 (Unimodal), (<bold>c</bold>) F53 (Multimodal), (<bold>d</bold>) F54 (Multimodal), (<bold>e</bold>) F55 (Multimodal), (<bold>f</bold>) F56 (Multimodal), (<bold>g</bold>) F57 (Multimodal), (<bold>h</bold>) F59 (Multimodal), (<bold>i</bold>) F60 (Multimodal), (<bold>j</bold>) F61 (Multimodal), (<bold>k</bold>) F62 (Hybrid), (<bold>l</bold>) F63 (Hybrid), (<bold>m</bold>) F65 (Hybrid), (<bold>n</bold>) F64 (Hybrid), (<bold>o</bold>) F73 (Composition), (<bold>p</bold>) F75 (Composition), (<bold>q</bold>) F77 (Composition), and (<bold>r</bold>) F78 (Composition).</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017b.png?1665578189" title=" <strong>Figure 17 Cont.</strong><br/> <p>Depiction of averaged convergence speed among algorithms on some test functions. (<bold>a</bold>) F51 (Unimodal), (<bold>b</bold>) F52 (Unimodal), (<bold>c</bold>) F53 (Multimodal), (<bold>d</bold>) F54 (Multimodal), (<bold>e</bold>) F55 (Multimodal), (<bold>f</bold>) F56 (Multimodal), (<bold>g</bold>) F57 (Multimodal), (<bold>h</bold>) F59 (Multimodal), (<bold>i</bold>) F60 (Multimodal), (<bold>j</bold>) F61 (Multimodal), (<bold>k</bold>) F62 (Hybrid), (<bold>l</bold>) F63 (Hybrid), (<bold>m</bold>) F65 (Hybrid), (<bold>n</bold>) F64 (Hybrid), (<bold>o</bold>) F73 (Composition), (<bold>p</bold>) F75 (Composition), (<bold>q</bold>) F77 (Composition), and (<bold>r</bold>) F78 (Composition).</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017c.png?1665578179" title=" <strong>Figure 17 Cont.</strong><br/> <p>Depiction of averaged convergence speed among algorithms on some test functions. (<bold>a</bold>) F51 (Unimodal), (<bold>b</bold>) F52 (Unimodal), (<bold>c</bold>) F53 (Multimodal), (<bold>d</bold>) F54 (Multimodal), (<bold>e</bold>) F55 (Multimodal), (<bold>f</bold>) F56 (Multimodal), (<bold>g</bold>) F57 (Multimodal), (<bold>h</bold>) F59 (Multimodal), (<bold>i</bold>) F60 (Multimodal), (<bold>j</bold>) F61 (Multimodal), (<bold>k</bold>) F62 (Hybrid), (<bold>l</bold>) F63 (Hybrid), (<bold>m</bold>) F65 (Hybrid), (<bold>n</bold>) F64 (Hybrid), (<bold>o</bold>) F73 (Composition), (<bold>p</bold>) F75 (Composition), (<bold>q</bold>) F77 (Composition), and (<bold>r</bold>) F78 (Composition).</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017d.png?1665578224" title=" <strong>Figure 17 Cont.</strong><br/> <p>Depiction of averaged convergence speed among algorithms on some test functions. (<bold>a</bold>) F51 (Unimodal), (<bold>b</bold>) F52 (Unimodal), (<bold>c</bold>) F53 (Multimodal), (<bold>d</bold>) F54 (Multimodal), (<bold>e</bold>) F55 (Multimodal), (<bold>f</bold>) F56 (Multimodal), (<bold>g</bold>) F57 (Multimodal), (<bold>h</bold>) F59 (Multimodal), (<bold>i</bold>) F60 (Multimodal), (<bold>j</bold>) F61 (Multimodal), (<bold>k</bold>) F62 (Hybrid), (<bold>l</bold>) F63 (Hybrid), (<bold>m</bold>) F65 (Hybrid), (<bold>n</bold>) F64 (Hybrid), (<bold>o</bold>) F73 (Composition), (<bold>p</bold>) F75 (Composition), (<bold>q</bold>) F77 (Composition), and (<bold>r</bold>) F78 (Composition).</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018a.png?1665578210" title=" <strong>Figure 18</strong><br/> <p>Diversity, convergence curve, average fitness history, trajectory, and search history.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018b.png?1665578212" title=" <strong>Figure 18 Cont.</strong><br/> <p>Diversity, convergence curve, average fitness history, trajectory, and search history.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g019.png?1665578222" title=" <strong>Figure 19</strong><br/> <p>Comparison among algorithms in terms of CPU time.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g020.png?1665578181" title=" <strong>Figure 20</strong><br/> <p>Tuning the parameter P<sub>s</sub> over tension spring design.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g021.png?1665578199" title=" <strong>Figure 21</strong><br/> <p>Tension/compression spring design problem. (<bold>a</bold>) Structure. (<bold>b</bold>) Convergence curve.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g022.png?1665578184" title=" <strong>Figure 22</strong><br/> <p>Weld beam design problem. (<bold>a</bold>) Structure. (<bold>b</bold>) Convergence curve.</p> "> </a> <a href="https://pub.mdpi-res.com/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g023.png?1665578200" title=" <strong>Figure 23</strong><br/> <p>Pressure vessel design problem. (<bold>a</bold>) Structure. (<bold>b</bold>) Convergence curve.</p> "> </a> </div> <a class="button button--color-inversed" href="/2227-7390/10/19/3466/notes">Versions Notes</a> </div> </div> <div class="responsive-moving-container small hidden" data-id="article-counters" style="margin-top: 15px;"></div> <div class="html-dynamic"> <section> <div class="art-abstract art-abstract-new in-tab hypothesis_container"> <p> <div><section class="html-abstract" id="html-abstract"> <h2 id="html-abstract-title">Abstract</h2><b>:</b> <div class="html-p">This paper introduces a novel physical-inspired metaheuristic algorithm called “Light Spectrum Optimizer (LSO)” for continuous optimization problems. The inspiration for the proposed algorithm is the light dispersions with different angles while passing through rain droplets, causing the meteorological phenomenon of the colorful rainbow spectrum. In order to validate the proposed algorithm, three different experiments are conducted. First, LSO is tested on solving CEC 2005, and the obtained results are compared with a wide range of well-regarded metaheuristics. In the second experiment, LSO is used for solving four CEC competitions in single objective optimization benchmarks (CEC2014, CEC2017, CEC2020, and CEC2022), and its results are compared with eleven well-established and recently-published optimizers, named grey wolf optimizer (GWO), whale optimization algorithm (WOA), and salp swarm algorithm (SSA), evolutionary algorithms like differential evolution (DE), and recently-published optimizers including gradient-based optimizer (GBO), artificial gorilla troops optimizer (GTO), Runge–Kutta method (RUN) beyond the metaphor, African vultures optimization algorithm (AVOA), equilibrium optimizer (EO), grey wolf optimizer (GWO), Reptile Search Algorithm (RSA), and slime mold algorithm (SMA). In addition, several engineering design problems are solved, and the results are compared with many algorithms from the literature. The experimental results with the statistical analysis demonstrate the merits and highly superior performance of the proposed LSO algorithm.</div> </section> <div id="html-keywords"> <div class="html-gwd-group"><div id="html-keywords-title">Keywords: </div><a href="/search?q=metaheuristic">metaheuristic</a>; <a href="/search?q=optimization">optimization</a>; <a href="/search?q=physics-based+algorithm">physics-based algorithm</a>; <a href="/search?q=Light+Spectrum+Optimizer">Light Spectrum Optimizer</a></div> <div class="html-gwd-group"><div id="html-keywords-title">MSC:</div> 68-04; 68Q25; 68T20; 68W25; 68W40; 68W50</div> <div> </div> </div> </div> </p> </div> </section> </div> <div class="hypothesis_container"> <ul class="menu html-nav" data-prev-node="#html-quick-links-title"> </ul> <div class="html-body"> <section id='sec1-mathematics-10-03466' type='intro'><h2 data-nested='1'> 1. Introduction</h2><div class='html-p'>The practical implications of metaheuristic algorithms have been widely spread, especially in the last few years. The reason behind this is the rapidity, high-quality solutions, and problem-independent characteristics of metaheuristics [<a href="#B1-mathematics-10-03466" class="html-bibr">1</a>,<a href="#B2-mathematics-10-03466" class="html-bibr">2</a>,<a href="#B3-mathematics-10-03466" class="html-bibr">3</a>,<a href="#B4-mathematics-10-03466" class="html-bibr">4</a>,<a href="#B5-mathematics-10-03466" class="html-bibr">5</a>]. Unfortunately, no metaheuristics can efficiently solve all types of optimization problems. Consequently, a significant number of metaheuristics have been proposed from time to time, aiming to find efficient metaheuristics that are proper for various types of optimization problems. In particular, metaheuristics depend on the progress or movement behavior of a specified phenomenon or creature. By simulating such a progress or movement style, a metaheuristic can invade the search space of a problem as the environment of the simulated phenomenon or creature.</div><div class='html-p'>Metaheuristics depend on two search mechanisms while trying to find the best solution to the given problem. The first mechanism is exploration, which invades the unvisited search area. The second mechanism is exploitation, which searches around the found best solution [<a href="#B6-mathematics-10-03466" class="html-bibr">6</a>]. The main factor of any metaheuristic success is balancing these two mechanisms. In particular, using more exploration makes metaheuristics unable to reach the global best solution. Alternatively, using more exploitation may lead to trapping into the local optima. In general, metaheuristics’ searching mechanisms have stemmed from natural phenomena or the behavior of creatures.</div><div class='html-p'>Metaheuristics can be categorized based on their metaphors into seven main categories [<a href="#B7-mathematics-10-03466" class="html-bibr">7</a>,<a href="#B8-mathematics-10-03466" class="html-bibr">8</a>,<a href="#B9-mathematics-10-03466" class="html-bibr">9</a>,<a href="#B10-mathematics-10-03466" class="html-bibr">10</a>,<a href="#B11-mathematics-10-03466" class="html-bibr">11</a>]: evolution-based, swarm-based, physics-based, human-based, chemistry-based, math-based, and others (See <a href="#mathematics-10-03466-f001" class="html-fig">Figure 1</a>). Evolution-based metaheuristics mimic the natural evolution process, which consists of select, crossover, and mutation processes such as genetic algorithm (GA) [<a href="#B12-mathematics-10-03466" class="html-bibr">12</a>], genetic programming (GP) [<a href="#B13-mathematics-10-03466" class="html-bibr">13</a>], evolution strategy (ES) [<a href="#B14-mathematics-10-03466" class="html-bibr">14</a>], probability-based incremental learning (PBIL) [<a href="#B15-mathematics-10-03466" class="html-bibr">15</a>], and differential evolution (DE) [<a href="#B16-mathematics-10-03466" class="html-bibr">16</a>].</div><div class='html-p'>The second category, referred to as swarm-based algorithms, imitates the social behavior of swarms, birds, insects, and animal groups [<a href="#B17-mathematics-10-03466" class="html-bibr">17</a>]. Some of the well-established and recently-published algorithms in this category are particle swarm optimization (PSO) [<a href="#B18-mathematics-10-03466" class="html-bibr">18</a>], cuckoo search (CS) algorithm [<a href="#B19-mathematics-10-03466" class="html-bibr">19</a>], flower pollination algorithm (FPA) [<a href="#B20-mathematics-10-03466" class="html-bibr">20</a>], marine predators algorithm (MPA) [<a href="#B21-mathematics-10-03466" class="html-bibr">21</a>], Harris hawks optimization (HHO) [<a href="#B22-mathematics-10-03466" class="html-bibr">22</a>], salp swarm algorithm (SSA) [<a href="#B23-mathematics-10-03466" class="html-bibr">23</a>], red fox optimizer (RFO) [<a href="#B24-mathematics-10-03466" class="html-bibr">24</a>], duck swarm algorithm [<a href="#B25-mathematics-10-03466" class="html-bibr">25</a>], chameleon swarm algorithm [<a href="#B26-mathematics-10-03466" class="html-bibr">26</a>], artificial gorilla troops optimizer [<a href="#B27-mathematics-10-03466" class="html-bibr">27</a>], cat optimization algorithm [<a href="#B28-mathematics-10-03466" class="html-bibr">28</a>], donkey and smuggler optimization algorithm [<a href="#B29-mathematics-10-03466" class="html-bibr">29</a>], krill herd algorithm [<a href="#B30-mathematics-10-03466" class="html-bibr">30</a>], elephant herding optimization [<a href="#B31-mathematics-10-03466" class="html-bibr">31</a>], wolf pack search algorithm [<a href="#B32-mathematics-10-03466" class="html-bibr">32</a>], hunting search [<a href="#B33-mathematics-10-03466" class="html-bibr">33</a>], monkey search [<a href="#B34-mathematics-10-03466" class="html-bibr">34</a>], chicken swarm optimization [<a href="#B35-mathematics-10-03466" class="html-bibr">35</a>], horse herd optimization algorithm (HOA) [<a href="#B36-mathematics-10-03466" class="html-bibr">36</a>], moth search (MS) algorithm [<a href="#B37-mathematics-10-03466" class="html-bibr">37</a>], earthworm optimization algorithm (EWA) [<a href="#B38-mathematics-10-03466" class="html-bibr">38</a>], monarch butterfly optimization (MBO) [<a href="#B39-mathematics-10-03466" class="html-bibr">39</a>], slime mold algorithm (SMA) [<a href="#B40-mathematics-10-03466" class="html-bibr">40</a>] and whale optimization algorithm (WOA) [<a href="#B41-mathematics-10-03466" class="html-bibr">41</a>]. In general, swarm-based metaheuristics have some advantages over evolution-based ones. In particular, a swarm-based metaheuristics search in a cumulative form preserves the information of subsequent search iterations. On the other hand, evolution-based metaheuristics ignore previous search information once the new population is generated. Additionally, evolution-based metaheuristics usually need more parameters than swarm-based metaheuristics. This makes swarm-based metaheuristics more applicable than evolution-based metaheuristics in most cases.</div><div class='html-p'>The third category of metaheuristics is human-based algorithms, which mimic human behaviors and human interactions in societies. The most popular algorithms belonging to this category are teaching–learning-based Optimization (TLBO) [<a href="#B42-mathematics-10-03466" class="html-bibr">42</a>], harmony search (HS) [<a href="#B43-mathematics-10-03466" class="html-bibr">43</a>], past present future (PPF) [<a href="#B44-mathematics-10-03466" class="html-bibr">44</a>], political optimizer (PO) [<a href="#B45-mathematics-10-03466" class="html-bibr">45</a>], brain storm optimization (BSO) [<a href="#B46-mathematics-10-03466" class="html-bibr">46</a>], exchange market algorithm (EMA) [<a href="#B47-mathematics-10-03466" class="html-bibr">47</a>], league championship algorithm (LCA) [<a href="#B48-mathematics-10-03466" class="html-bibr">48</a>], poor and rich optimization algorithm [<a href="#B49-mathematics-10-03466" class="html-bibr">49</a>], driving training-based optimization [<a href="#B50-mathematics-10-03466" class="html-bibr">50</a>], gaining–sharing knowledge-based algorithm (GSK) [<a href="#B51-mathematics-10-03466" class="html-bibr">51</a>], imperialist competitive algorithm (ICA) [<a href="#B52-mathematics-10-03466" class="html-bibr">52</a>], and soccer league competition (SLC) [<a href="#B53-mathematics-10-03466" class="html-bibr">53</a>].</div><div class='html-p'>The fourth category is physics-based algorithms, which are inspired by physical laws, such as inertia, electromagnetic force, gravitational force, and so on. In this category, the algorithms are based on physical principles to enable the search agents to interact and navigate the optimization problems’ search space to reach the near-optimal solution. This category includes several algorithms like simulated annealing (SA) [<a href="#B54-mathematics-10-03466" class="html-bibr">54</a>], gravitational search algorithm (GSA) [<a href="#B55-mathematics-10-03466" class="html-bibr">55</a>], charged system search (CSS) [<a href="#B56-mathematics-10-03466" class="html-bibr">56</a>], big-bang big-crunch (BBBC) [<a href="#B57-mathematics-10-03466" class="html-bibr">57</a>], artificial physics algorithm (APA) [<a href="#B58-mathematics-10-03466" class="html-bibr">58</a>], galaxy-based search algorithm (GbSA) [<a href="#B59-mathematics-10-03466" class="html-bibr">59</a>], black hole (BH) algorithm [<a href="#B60-mathematics-10-03466" class="html-bibr">60</a>], river formation dynamics (RFD) algorithm [<a href="#B61-mathematics-10-03466" class="html-bibr">61</a>], henry gas solubility optimization (HGSO) algorithm [<a href="#B62-mathematics-10-03466" class="html-bibr">62</a>], curved space optimization (CSO) [<a href="#B63-mathematics-10-03466" class="html-bibr">63</a>], central force optimization (CFO) [<a href="#B64-mathematics-10-03466" class="html-bibr">64</a>], water cycle algorithm (WCA) [<a href="#B65-mathematics-10-03466" class="html-bibr">65</a>], water waves optimization (WWO) [<a href="#B66-mathematics-10-03466" class="html-bibr">66</a>], ray optimization (RO) algorithm [<a href="#B67-mathematics-10-03466" class="html-bibr">67</a>], gravitational local search algorithm (GLSA) [<a href="#B68-mathematics-10-03466" class="html-bibr">68</a>], small-world optimization algorithm (SWOA) [<a href="#B69-mathematics-10-03466" class="html-bibr">69</a>], multi-verse optimizer (MVO) [<a href="#B70-mathematics-10-03466" class="html-bibr">70</a>], intelligent water drops (IWD) algorithm [<a href="#B71-mathematics-10-03466" class="html-bibr">71</a>], integrated radiation algorithm (IRA) [<a href="#B72-mathematics-10-03466" class="html-bibr">72</a>], space gravitational algorithm (SGA) [<a href="#B73-mathematics-10-03466" class="html-bibr">73</a>], ion motion algorithm (IMA) [<a href="#B74-mathematics-10-03466" class="html-bibr">74</a>], electromagnetism-like algorithm (EMA) [<a href="#B75-mathematics-10-03466" class="html-bibr">75</a>], equilibrium optimizer (EO) [<a href="#B76-mathematics-10-03466" class="html-bibr">76</a>], light ray optimization (LRO) [<a href="#B77-mathematics-10-03466" class="html-bibr">77</a>], and Archimedes optimization algorithm (AOA) [<a href="#B78-mathematics-10-03466" class="html-bibr">78</a>]. Both light ray optimization (LRO) [<a href="#B77-mathematics-10-03466" class="html-bibr">77</a>] and ray optimization (RO) [<a href="#B67-mathematics-10-03466" class="html-bibr">67</a>] simulate the reflection and refraction of the light rays, respectively, when transferred from a medium to a darker one, which is completely different from the proposed algorithm, referred to as Light Spectrum Optimizer (LSO), as illustrated later.</div><div class='html-p'>The chemistry-based metaheuristic algorithms in the fifth category are inspired by mimicking certain chemical laws; some of those algorithms are gases Brownian motion optimization (GBMO) [<a href="#B79-mathematics-10-03466" class="html-bibr">79</a>], artificial chemical reaction optimization algorithm (ACROA) [<a href="#B80-mathematics-10-03466" class="html-bibr">80</a>], and several others [<a href="#B81-mathematics-10-03466" class="html-bibr">81</a>]. The sixth category, called math-based metaheuristics, is based on presenting metaheuristic algorithms inspired by simulating certain mathematics functions like the golden sine algorithm (GSA) [<a href="#B82-mathematics-10-03466" class="html-bibr">82</a>], base optimization algorithm (BOA) [<a href="#B83-mathematics-10-03466" class="html-bibr">83</a>], and sine–cosine algorithm [<a href="#B84-mathematics-10-03466" class="html-bibr">84</a>]. <a href="#mathematics-10-03466-t001" class="html-table">Table 1</a> presents the category and inspiration of some of the recently-published metaheuristic algorithms―specifically published over the last three years.</div><div class='html-p'>The last category (Others) includes all the metaheuristic algorithms, which has not been inspired by the behaviors of creatures or natural phenomena, such as adaptive large neighborhood search technique (ALNS) [<a href="#B85-mathematics-10-03466" class="html-bibr">85</a>], large neighborhood search (LNS) [<a href="#B86-mathematics-10-03466" class="html-bibr">86</a>,<a href="#B87-mathematics-10-03466" class="html-bibr">87</a>], and greedy randomized adaptive search procedure (GRASP) [<a href="#B88-mathematics-10-03466" class="html-bibr">88</a>,<a href="#B89-mathematics-10-03466" class="html-bibr">89</a>]. For example, the large neighborhood search technique is a metaheuristic algorithm based on improving an initial solution using destroy and repair operators.</div><div class="html-table-wrap" id="mathematics-10-03466-t001"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t001'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t001"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 1.</b> Classification and inspiration of some recently-published metaheuristic algorithms. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t001" > <div class="html-caption" ><b>Table 1.</b> Classification and inspiration of some recently-published metaheuristic algorithms.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Algorithm</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Inspiration</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Category</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Year</th></tr></thead><tbody ><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Starling murmuration optimizer (SMO) [<a href="#B90-mathematics-10-03466" class="html-bibr">90</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Starlings’ behaviors</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Snake optimizer (SO) [<a href="#B91-mathematics-10-03466" class="html-bibr">91</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Mating behavior of snakes</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Reptile Search Algorithm (RSA) [<a href="#B92-mathematics-10-03466" class="html-bibr">92</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Hunting behavior of Crocodiles</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Archerfish hunting optimizer (AHO) [<a href="#B93-mathematics-10-03466" class="html-bibr">93</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Jumping behaviors of the archerfish</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Water optimization algorithm (WAO) [<a href="#B94-mathematics-10-03466" class="html-bibr">94</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Chemical and physical properties of water molecules</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Physics-based<br>Chemistry-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Ebola optimization search algorithm (EOSA) [<a href="#B95-mathematics-10-03466" class="html-bibr">95</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Propagation mechanism of the Ebola virus disease</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Others </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Beluga whale optimization (BWO) [<a href="#B96-mathematics-10-03466" class="html-bibr">96</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Behaviors of beluga whales</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >White Shark Optimizer (WSO)</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Behaviors of great white sharks</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Aphid–Ant Mutualism (AAM) [<a href="#B97-mathematics-10-03466" class="html-bibr">97</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >The relationship between aphids and ants species is called Mutualism</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Circle Search Algorithm (CSA) [<a href="#B98-mathematics-10-03466" class="html-bibr">98</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Geometrical features of circles</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Math-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Pelican optimization algorithm (POA) [<a href="#B99-mathematics-10-03466" class="html-bibr">99</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >The behavior of pelicans during hunting</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Sheep flock optimization algorithm (SFOA) [<a href="#B100-mathematics-10-03466" class="html-bibr">100</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Shepherd and sheep behaviors in the pasture</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Gannet optimization algorithm (GOA) [<a href="#B101-mathematics-10-03466" class="html-bibr">101</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Behaviors of gannets during foraging</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Prairie dog optimization (PDO) [<a href="#B102-mathematics-10-03466" class="html-bibr">102</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >The behavior of the prairie dogs</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Driving Training-Based Optimization (DTBO) [<a href="#B50-mathematics-10-03466" class="html-bibr">50</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >The human activity of driving training</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Human-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Stock exchange trading optimization (SETO) [<a href="#B103-mathematics-10-03466" class="html-bibr">103</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >The behavior of traders and stock price changes</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Human-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2022</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Archimedes optimization algorithm (AOA) [<a href="#B78-mathematics-10-03466" class="html-bibr">78</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Archimedes law</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Physics-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2021</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Golden eagle optimizer (GEO) [<a href="#B104-mathematics-10-03466" class="html-bibr">104</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Golden eagles’ hunting process</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2021</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Heap-based optimizer (HBO) [<a href="#B105-mathematics-10-03466" class="html-bibr">105</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Corporate rank hierarchy</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Human-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2021</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >African vultures optimization algorithm (AVOA) [<a href="#B106-mathematics-10-03466" class="html-bibr">106</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >African vultures’ lifestyle</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2021</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Artificial gorilla troops optimizer (GTO) [<a href="#B27-mathematics-10-03466" class="html-bibr">27</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Gorilla troops’ social intelligence</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2021</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Quantum-based avian navigation optimizer algorithm (QANA) [<a href="#B107-mathematics-10-03466" class="html-bibr">107</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Migratory birds’ navigation behaviors</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Evolution-based<br>(Based DE)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2021</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Colony predation algorithm (CPA) [<a href="#B108-mathematics-10-03466" class="html-bibr">108</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Corporate predation of animals</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2021</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Lévy flight distribution (LFD) [<a href="#B42-mathematics-10-03466" class="html-bibr">42</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Lévy flight random walk</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Physics-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2020</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Political Optimizer (PO) [<a href="#B45-mathematics-10-03466" class="html-bibr">45</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Multi-phased process of politics</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Human-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2020</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Marine predators algorithm (MPA) [<a href="#B21-mathematics-10-03466" class="html-bibr">21</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Foraging strategy in the ocean between predators and prey</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Swarm-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2020</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Equilibrium optimizer (EO) [<a href="#B76-mathematics-10-03466" class="html-bibr">76</a>]</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Mass balance models</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Physics-based</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2020</td></tr></tbody> </table> </div><div class='html-p'>Over the last few decades, several metaheuristic algorithms have been proposed, but unfortunately, most of these algorithms are not able to adapt themselves when tackling several optimization problems with various characteristics. Therefore, this paper proposes a novel physical-based metaheuristic algorithm called Light Spectrum Optimizer (LSO) for global optimization over a continuous search space. This novel metaheuristic is inspired by the sunlight ray dispersion while passing through the rain droplets causing the sparkle rainbow phenomenon. In particular, the mathematical formulation of the sunlight ray’s reflection, refraction, and dispersion can be efficiently utilized for presenting a variety in the updating process to preserve the population diversity, in addition to accelerating the convergence speed when applied to different optimization problems. Experimentally, LSO is extensively assessed using several mathematical benchmarks like CEC2005, CEC2014, CEC2017, CEC2020, and CEC2022 to reveal its performance compared to several well-established metaheuristic algorithms. In addition, LSO is employed to solve some engineering design problems to further affirm its efficiency. The main advantages of the proposed metaheuristic are:</div><div class='html-p'><dl class='html-bullet'><dt id=''>➢</dt><dd><div class='html-p'>Simple representation.</div></dd><dt id=''>➢</dt><dd><div class='html-p'>Robustness.</div></dd><dt id=''>➢</dt><dd><div class='html-p'>Balancing between exploration and exploitation.</div></dd><dt id=''>➢</dt><dd><div class='html-p'>High-quality solutions.</div></dd><dt id=''>➢</dt><dd><div class='html-p'>Swarm intelligence powerfulness.</div></dd><dt id=''>➢</dt><dd><div class='html-p'>Low computational complexity.</div></dd><dt id=''>➢</dt><dd><div class='html-p'>High scalability.</div></dd></dl></div><div class='html-p'>These advantages are proved with three different validating experiments that include several optimization problems with various characteristics. Besides, LSO is compared with many other optimization algorithms, and the results are analyzed with the appropriate statistical tests. The experimental findings affirm the superiority of LSO compared to all the other rival algorithms. Finally, the main contributions of this study are listed as follows:</div><div class='html-p'><ul class='html-bullet'><li><div class='html-p'>Proposing a novel physical-based metaheuristic algorithm called Light Spectrum Optimizer (LSO), inspired by the sparkle rainbow phenomenon caused by passing sunlight rays through the rain droplets.</div></li><li><div class='html-p'>Validating LSO using four challengeable mathematical benchmarks like CEC2014, CEC2017, CEC2020, and CEC2022, as well as several engineering design problems.</div></li><li><div class='html-p'>The experimental findings, along with the Wilcoxon rank-sum test as a statistical test, illustrate the merits and highly superior performance of the proposed LSO algorithm</div></li></ul></div><div class='html-p'>The remainder of this work is organized as follows. <a href="#sec2-mathematics-10-03466" class="html-sec">Section 2</a> gives the background illustration of the inspiration and the mathematical modelling of the rainbow phenomenon. <a href="#sec3-mathematics-10-03466" class="html-sec">Section 3</a> explains the mathematical formulation and the searching procedure of LSO. In <a href="#sec4-mathematics-10-03466" class="html-sec">Section 4</a>, various experiments are done on the CEC2005, CEC2014, CEC2017, CEC2020, and CEC2022 benchmarks, and their experimental results are analyzed with the proper statistical analysis. Additionally, LSO sensitivity is presented. In <a href="#sec5-mathematics-10-03466" class="html-sec">Section 5</a>, popular engineering design problems are solved with LSO.</div></section><section id='sec2-mathematics-10-03466' type=''><h2 data-nested='1'> 2. Background</h2><div class='html-p'>Rainbow is one of the most fabulous metrological wonders. From the physical perspective, it is a half-circle of spectrum colors created by dispersion and internal reflection of sunlight rays that hit spherical rain droplets [<a href="#B109-mathematics-10-03466" class="html-bibr">109</a>]. When a white ray hits a water droplet, it changes its direction by refracting and reflecting inside and outside the droplet (sometimes more than once) [<a href="#B110-mathematics-10-03466" class="html-bibr">110</a>]. In other words, the rainbow is formed by light rays’ refraction, reflection, and dispersion through water droplets. </div><div class='html-p'>According to Descartes’s laws [<a href="#B111-mathematics-10-03466" class="html-bibr">111</a>,<a href="#B112-mathematics-10-03466" class="html-bibr">112</a>], refraction occurs when the light rays travel from one material to another with a different refractive index. When light rays hit the outer surface of a droplet, some light rays reflect away from the droplet while the others are refracted. The refracted light rays hit the inner surface of a droplet, causing another reflection and refracting away from the droplet with different angles, which causes the white sunlight to be dispersed into its seven spectral colors: red, orange, yellow, green, blue, indigo, and violet, as depicted in <a href="#mathematics-10-03466-f002" class="html-fig">Figure 2</a>. These spectral colors, differs according to the angles of deviations, which range from 40° (violet) to 42° (red) [<a href="#B113-mathematics-10-03466" class="html-bibr">113</a>,<a href="#B114-mathematics-10-03466" class="html-bibr">114</a>] (See <a href="#mathematics-10-03466-f002" class="html-fig">Figure 2</a>).</div><div class='html-p'>Mathematically, the refraction and reflection of the rainbow spectrum have been illustrated by Snell’s laws. Snell’s law said that the ratio between the sines of the incident and refracted angles is equal to the ratio between the refractive indices of air and water, as [<a href="#B115-mathematics-10-03466" class="html-bibr">115</a>]:<div class='html-disp-formula-info' id='FD1-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mfrac> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>θ</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </mfrac> </mrow> </semantics></math> </div> <div class='l'> <label >(1)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> </mrow> </semantics></math> is the incident angle, <math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is the refracted angle, <math display='inline'><semantics> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is the refractive index of water, and <math display='inline'><semantics> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </semantics></math> is the refractive index of air.</div><div class='html-p'>In this work, Snell’s law is used in its vector form. As shown in <a href="#mathematics-10-03466-f003" class="html-fig">Figure 3</a>, all normal, incidents, refracted, and reflected rays are converted to vectors. The mathematical formulation of the refracted ray can be expressed as [<a href="#B116-mathematics-10-03466" class="html-bibr">116</a>]:<div class='html-disp-formula-info' id='FD2-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>k</mi> </mfrac> <mrow> <mo>[</mo> <mrow> <msub> <mi>L</mi> <mn>0</mn> </msub> <mo>−</mo> <msub> <mi>n</mi> <mi>A</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>n</mi> <mi>A</mi> </msub> <mo>·</mo> <msub> <mi>L</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>−</mo> <msub> <mi>n</mi> <mi>A</mi> </msub> <msup> <mrow> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>−</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> </mfrac> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>n</mi> <mi>A</mi> </msub> <mo>·</mo> <msub> <mi>L</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>]</mo> </mrow> </mrow> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </semantics></math> </div> <div class='l'> <label >(2)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </semantics></math> is the refracted light ray, <math display='inline'><semantics> <mi>k</mi> </semantics></math> is the refractive index of the droplet, <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mn>0</mn> </msub> </mrow> </semantics></math> is the incident light ray, and <math display='inline'><semantics> <mrow> <msub> <mi>n</mi> <mi>A</mi> </msub> </mrow> </semantics></math> is the normal line at the point of incidence. Meanwhile, the inner reflected ray can be formulated as:<div class='html-disp-formula-info' id='FD3-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>−</mo> <mn>2</mn> <msub> <mi>n</mi> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>n</mi> <mi>B</mi> </msub> <mo>·</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(3)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is the inner reflected light ray and <math display='inline'><semantics> <mrow> <msub> <mi>n</mi> <mi>B</mi> </msub> </mrow> </semantics></math> is the normal line at the point of inner reflection. Finally, the outer refracted ray is expressed as:<div class='html-disp-formula-info' id='FD4-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> <mo>=</mo> <mi>k</mi> <mrow> <mo>[</mo> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>n</mi> <mi>C</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>n</mi> <mi>C</mi> </msub> <mo>·</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mi>C</mi> </msub> <msup> <mrow> <mrow> <mo stretchy="false">[</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>k</mi> <mn>2</mn> </msup> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>n</mi> <mi>C</mi> </msub> <mo>·</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo stretchy="false">]</mo> </mrow> </mrow> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </semantics></math> </div> <div class='l'> <label >(4)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> </mrow> </semantics></math> is the outer refracted light ray and <math display='inline'><semantics> <mrow> <msub> <mi>n</mi> <mi>C</mi> </msub> </mrow> </semantics></math> is the normal line at the point of outer refraction.</div></section><section id='sec3-mathematics-10-03466' type=''><h2 data-nested='1'> 3. Light Spectrum Optimizer (LSO)</h2><div class='html-p'>As discussed before, the rainbow spectrum rays are caused by colorful light dispersion. In this paper, the proposed algorithm takes its inspiration from this metrological phenomenon. In particular, LSO is based on the following assumptions: </div><div class='html-p'><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>Each colorful ray represents a candidate solution.</div></dd><dt id=''>(2)</dt><dd><div class='html-p'>The dispersion of light rays ranges from 40° to 42° or have a refractive index that varies between <math display='inline'><semantics> <mrow> <msup> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>d</mi> </mrow> </msup> <mo>=</mo> <mn>1.331</mn> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <msup> <mi>k</mi> <mrow> <mi>v</mi> <mi>i</mi> <mi>o</mi> <mi>l</mi> <mi>e</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>1.344</mn> </mrow> </semantics></math>.</div></dd><dt id=''>(3)</dt><dd><div class='html-p'>The population of light rays has a global best solution, which is the best dispersion reached so far.</div></dd><dt id=''>(4)</dt><dd><div class='html-p'>The refraction and reflection (inner or outer) are randomly controlled.</div></dd><dt id=''>(5)</dt><dd><div class='html-p'>The current solution’s fitness value controls a colorful rainbow curve’s first and second scattering phases compared to the best so-far solution’s fitness. Suppose the fitness value between them is so close. In that case, the algorithm will apply the first scattering phase to exploit the regions around the current solution because it might be so close to the near-optimal solution. Otherwise, the second phase will be applied to help the proposed algorithm avoid getting stuck in the regions of the best-so-far solution because it might be local minima.</div></dd></dl></div><div class='html-p'>Next, the detailed mathematical formulation of LSO will be discussed.</div><section id='sec3dot1-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 3.1. Initialization Step</h4><div class='html-p'>The search process of LSO begins with the random initialization of the initial population of white lights as:<div class='html-disp-formula-info' id='FD5-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mn>0</mn> </msup> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mi>l</mi> <mi>b</mi> <mo>+</mo> <mi>R</mi> <msub> <mi>V</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <mi>u</mi> <mi>b</mi> <mo>−</mo> <mi>l</mi> <mi>b</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(5)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mn>0</mn> </msup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> is the initial solution, <math display='inline'><semantics> <mrow> <mi>R</mi> <msub> <mi>V</mi> <mn>1</mn> </msub> </mrow> </semantics></math> is a vector of uniform random numbers generated between <math display='inline'><semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mo> </mo> <mn>1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics></math> with a length equal to the given problem dimension (d), and <math display='inline'><semantics> <mrow> <mi>l</mi> <mi>b</mi> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mi>u</mi> <mi>b</mi> </mrow> </semantics></math> are the lower and upper bounds of the search space, respectively. After that, the generated initial solutions are evaluated in order to determine the global and personal best solutions.</div></section><section id='sec3dot2-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 3.2. Colorful Dispersion of Light Rays</h4><div class='html-p'>In this subsection, we discuss the mathematical formulation of rainbow spectrum directions, colorful rays scattering, and the exploration and exploitation mechanisms of LSO.</div><section id='sec3dot2dot1-mathematics-10-03466' type=''><h4 class='' data-nested='3'> 3.2.1. The Direction of Rainbow Spectrums</h4><div class='html-p'>After the initialization, the normal vector of inner refraction <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, inner reflection <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>B</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, and outer refraction <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> are calculated as:<div class='html-disp-formula-info' id='FD6-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>r</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> <mo> </mo> <mrow> <mo>(</mo> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>r</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </semantics></math> </div> <div class='l'> <label >(6)</label> </div> </div><div class='html-disp-formula-info' id='FD7-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>B</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>p</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> <mo> </mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </mfrac> </mrow> </semantics></math> </div> <div class='l'> <label >(7)</label> </div> </div><div class='html-disp-formula-info' id='FD8-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> <mo> </mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </mfrac> </mrow> </semantics></math> </div> <div class='l'> <label >(8)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>r</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> is a randomly selected solution from the current population at iteration <math display='inline'><semantics> <mi>t</mi> </semantics></math>, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>p</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> is the current solution at iteration <math display='inline'><semantics> <mi>t</mi> </semantics></math>, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> is the global best solution ever founded, and <math display='inline'><semantics> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> <mrow> <mo>(</mo> <mo>.</mo> <mo>)</mo> </mrow> </mrow> </semantics></math> indicates the normalized value of a vector and computed according to the following formula:<div class='html-disp-formula-info' id='FD9-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> <mrow> <mo stretchy="false">(</mo> <mover accent="true"> <mi>x</mi> <mo>→</mo> </mover> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>d</mi> </munderover> </mstyle> <msubsup> <mi>x</mi> <mi>j</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mrow> </semantics></math> </div> <div class='l'> <label >(9)</label> </div> </div> where <span class='html-italic'>d</span> stands for the number of dimensions in an optimization problem. <math display='inline'><semantics> <mover accent="true"> <mi>x</mi> <mo>→</mo> </mover> </semantics></math> is the input vector to the <math display='inline'><semantics> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> </mrow> </semantics></math> function to normalize it. <math display='inline'><semantics> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> </semantics></math> is the jth dimension in the input vector <math display='inline'><semantics> <mover accent="true"> <mi>x</mi> <mo>→</mo> </mover> </semantics></math>. For the incident light ray, it is calculated as follows:<div class='html-disp-formula-info' id='FD10-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>X</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mi>i</mi> <mi>N</mi> </msubsup> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mi>N</mi> </mfrac> </mrow> </semantics></math> </div> <div class='l'> <label >(10)</label> </div> </div><div class='html-disp-formula-info' id='FD11-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msub> <mi>X</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> <mo> </mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>X</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </semantics></math> </div> <div class='l'> <label >(11)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> is the incident light ray, <math display='inline'><semantics> <mrow> <msub> <mi>X</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> is the mean of the current population of solutions <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mi>N</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>, and <math display='inline'><semantics> <mi>N</mi> </semantics></math> is the population size.</div><div class='html-p'>Then, the vectors of inner and outer refracted and reflected light rays are calculated as:<div class='html-disp-formula-info' id='FD12-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mi>k</mi> <mi>r</mi> </msup> </mrow> </mfrac> <mrow> <mo stretchy="false">[</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>·</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> <mo stretchy="false">]</mo> </mrow> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <msup> <mrow> <mrow> <mo>|</mo> <mrow> <mn>1</mn> <mo>−</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msup> <mi>k</mi> <mi>r</mi> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msup> <mi>k</mi> <mi>r</mi> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <msup> <mrow> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>·</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </semantics></math> </div> <div class='l'> <label >(12)</label> </div> </div><div class='html-disp-formula-info' id='FD13-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mn>2</mn> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>B</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>·</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>B</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(13)</label> </div> </div><div class='html-disp-formula-info' id='FD14-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <msup> <mi>k</mi> <mi>r</mi> </msup> <mrow> <mo stretchy="false">[</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>·</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> <mo stretchy="false">]</mo> </mrow> <mo>+</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <msup> <mrow> <mrow> <mo stretchy="false">|</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msup> <mi>k</mi> <mi>r</mi> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msup> <mi>k</mi> <mi>r</mi> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>·</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </semantics></math> </div> <div class='l'> <label >(14)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> are the inner refracted, inner reflected, and outer refracted light rays, respectively. <math display='inline'><semantics> <mrow> <msup> <mi>k</mi> <mi>r</mi> </msup> </mrow> </semantics></math> stands for the refractive index, which is updated randomly between <math display='inline'><semantics> <mrow> <msup> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>d</mi> </mrow> </msup> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <msup> <mi>k</mi> <mrow> <mi>v</mi> <mi>i</mi> <mi>o</mi> <mi>l</mi> <mi>e</mi> <mi>t</mi> </mrow> </msup> </mrow> </semantics></math> to define a random spectrum color as:<div class='html-disp-formula-info' id='FD15-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msup> <mi>k</mi> <mi>r</mi> </msup> <mo>=</mo> <msup> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>d</mi> </mrow> </msup> <mo>+</mo> <mi>R</mi> <msub> <mi>V</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <msup> <mi>k</mi> <mrow> <mi>v</mi> <mi>i</mi> <mi>o</mi> <mi>l</mi> <mi>e</mi> <mi>t</mi> </mrow> </msup> <mo>−</mo> <msup> <mi>k</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>d</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(15)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mi>R</mi> <msub> <mi>V</mi> <mn>1</mn> </msub> </mrow> </semantics></math> is a uniform random number generated randomly between <math display='inline'><semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mo> </mo> <mn>1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics></math>.</div><div class='html-p'><a href="#mathematics-10-03466-t002" class="html-table">Table 2</a> presents a numerical example to illustrate the vectors with six dimensions generated by the previously described equations with noting that the vectors <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>r</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>p</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> presented at the same table are randomly generated between 100 and −100. The values of the inner refracted and inner reflected are obvious from this table. Outer refracted vectors could not be employed alone to update the individuals, which have to be ranged between 100 and −100 because the change rate in the updated solutions will be so low. Hence, many function evaluations will be consumed to reach better solutions. Therefore, the equations described in the next section are adapted to deal with this problem by extensively encouraging the exploration operator of the newly-proposed algorithm.</div></section><section id='sec3dot2dot2-mathematics-10-03466' type=''><h4 class='' data-nested='3'> 3.2.2. Generating New Colorful Ray: Exploration Mechanism</h4><div class='html-p'>After the calculation of the rays’ directions, we calculate the candidate solutions according to the value of a randomly generated probability between 0 and 1, referred to as <math display='inline'><semantics> <mi>p</mi> </semantics></math>. In particular, if the value of <math display='inline'><semantics> <mi>p</mi> </semantics></math> is lower than a number generated randomly between 0 and 1, then the new candidate solution will be calculated as:<div class='html-disp-formula-info' id='FD16-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>+</mo> <mi>ϵ</mi> <mi>R</mi> <msubsup> <mi>V</mi> <mn>1</mn> <mi>n</mi> </msubsup> <mi>G</mi> <mi>I</mi> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> <mo>×</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(16)</label> </div> </div></div><div class='html-p'>Otherwise, the new candidate solution will be calculated as:<div class='html-disp-formula-info' id='FD17-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>+</mo> <mi>ϵ</mi> <mi>R</mi> <msubsup> <mi>V</mi> <mn>2</mn> <mi>n</mi> </msubsup> <mi>G</mi> <mi>I</mi> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> <mo>×</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>3</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>4</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(17)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> is the newly generated candidate solution, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> is the current candidate solution at iteration <math display='inline'><semantics> <mi>t</mi> </semantics></math>. <math display='inline'><semantics> <mrow> <mi>r</mi> <mn>1</mn> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mi>r</mi> <mn>2</mn> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mi>r</mi> <mn>3</mn> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <mi>r</mi> <mn>4</mn> </mrow> </semantics></math> are indices of four solutions selected randomly from the current population. <math display='inline'><semantics> <mrow> <mi>R</mi> <msubsup> <mi>V</mi> <mn>1</mn> <mi>n</mi> </msubsup> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mi>R</mi> <msubsup> <mi>V</mi> <mn>2</mn> <mi>n</mi> </msubsup> </mrow> </semantics></math> are vectors of uniform random numbers that are generated between <math display='inline'><semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mo> </mo> <mn>1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics></math>. <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math> is a scaling factor that is calculated using (18). <math display='inline'><semantics> <mrow> <mi>G</mi> <mi>I</mi> </mrow> </semantics></math> is an adaptive control factor based on the inverse incomplete gamma function and computed according to (19). <div class='html-disp-formula-info' id='FD18-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>ϵ</mi> <mo>=</mo> <mi>a</mi> <mo>×</mo> <mi>R</mi> <msubsup> <mi>V</mi> <mn>3</mn> <mi>n</mi> </msubsup> </mrow> </semantics></math> </div> <div class='l'> <label >(18)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mi>R</mi> <msubsup> <mi>V</mi> <mn>3</mn> <mi>n</mi> </msubsup> </mrow> </semantics></math> a vector of normally distributed random numbers with a mean equal to zero and a standard deviation equal to one, and <math display='inline'><semantics> <mi>a</mi> </semantics></math> is an adaptive parameter that can be calculated using (20). <div class='html-disp-formula-info' id='FD19-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>G</mi> <mi>I</mi> <mo>=</mo> <mi>a</mi> <mo>×</mo> <msup> <mi>r</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>×</mo> <msup> <mi>P</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>,</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(19)</label> </div> </div></div><div class='html-p'><math display='inline'><semantics> <mrow> <mi>G</mi> <mi>I</mi> </mrow> </semantics></math> is an adaptive control factor. <math display='inline'><semantics> <mi>r</mi> </semantics></math> is a uniform random number between <math display='inline'><semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mo> </mo> <mn>1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics></math> that is inversed to promote the exploration operator throughout the optimization process because inversing any random value will generate a new decimal number greater than 1, which might take the current solution to far away regions within the search space for finding a better solution. <math display='inline'><semantics> <mrow> <msup> <mi>P</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> is the inverse incomplete gamma function for the corresponding value of <math display='inline'><semantics> <mi>a</mi> </semantics></math>. <div class='html-disp-formula-info' id='FD20-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi mathvariant="normal">A</mi> <mo>=</mo> <msub> <mrow> <mi>RV</mi> </mrow> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mfrac> <mi>t</mi> <mrow> <mi>T</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(20)</label> </div> </div>where <math display='inline'><semantics> <mi>t</mi> </semantics></math> is the current iteration number, <math display='inline'><semantics> <mrow> <mi>R</mi> <msub> <mi>V</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is a scalar numerical value of uniform random numbers generated between <math display='inline'><semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mo> </mo> <mn>1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <mi>T</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </semantics></math> is the maximum number of function evaluations.</div><div class='html-p'>When the input numbers are greater than 0.5, this inverse incomplete gamma function generates high numerical values starting from almost 0.8 and ending at nearly 5.5, as described in <a href="#mathematics-10-03466-f004" class="html-fig">Figure 4</a>; otherwise, it generates decimal values down to 0. When the input numbers to this function are high, it will encourage the exploration operator. However, the highly-generated value might take the updated solutions out of the search boundary, and hence the algorithm might be converted into a randomization process because the boundary checking method will move those infeasible solutions back again into the search space. Therefore, the factor, a, described before in (20), is modeled with the inverse incomplete gamma values to reduce their magnitude and avoid the randomization process when the input values are high. Both the inverse function and factor <span class='html-italic'>a</span> decrease gradually with increasing the current iteration, and hence the optimization process will be gradually converted from the exploration operator into the exploitation that might lead to falling into local minima. Therefore, to support the exploration operator throughout the optimization process, the inverse of a number generated randomly between 0 and 1 will be modeled with both the inverse function and factor <span class='html-italic'>a</span> as defined in (19).</div></section><section id='sec3dot2dot3-mathematics-10-03466' type=''><h4 class='' data-nested='3'> 3.2.3. Colorful Rays Scattering: Exploitation Mechanism</h4><div class='html-p'>This phase helps to scatter the rays in the direction of the best-so-far solution, the current solution, and a solution selected randomly from the current population to improve its exploitation operator. At the start, the algorithm will scatter the rays around the current solution to exploit the region around it to reach better outcomes. However, this might reduce the convergence speed of LSO, so an additional step size applied with a predefined probability <math display='inline'><semantics> <mi>β</mi> </semantics></math> is integrated to move the current solution in the direction of the best-so-far solution to overcome this problem. The mathematical model of scattering around the current solution is as follows:<div class='html-disp-formula-info' id='FD21-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>+</mo> <mi>R</mi> <msub> <mi>V</mi> <mn>3</mn> </msub> <mo>×</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mi>R</mi> <msubsup> <mi>V</mi> <mn>4</mn> <mi>n</mi> </msubsup> <mo>×</mo> <mo stretchy="false">(</mo> <mi>R</mi> <mo><</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mo>×</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(21)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> is the best-so-far solution, and <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> are two solutions selected randomly from the current population. <math display='inline'><semantics> <mrow> <mi>R</mi> <msub> <mi>V</mi> <mn>3</mn> </msub> </mrow> </semantics></math> includes a number selected randomly at the interval of 0 and 1. <math display='inline'><semantics> <mrow> <mi>R</mi> <msubsup> <mi>V</mi> <mn>4</mn> <mi>n</mi> </msubsup> </mrow> </semantics></math> is a vector including numbers generated randomly between 0 and 1. The second scattering phase is based on generating rays in a new position based on the best-so-far solution and the current solution according to the following formula:<div class='html-disp-formula-info' id='FD22-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mn>2</mn> <mo> </mo> <mi>cos</mi> <mrow> <mo stretchy="false">(</mo> <mrow> <mi>π</mi> <mo>×</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(22)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </semantics></math> is a randomly generated numerical value at the interval of 0 and 1. <math display='inline'><semantics> <mi>π</mi> </semantics></math> indicates the ratio of the perimeter of a circle to its diameter. Exchanging between the first and second scattering phases is achieved based on a predefined probability <span class='html-italic'>P<sub>e</sub></span> as shown in the following formula:<div class='html-disp-formula-info' id='FD23-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mtable columnalign="right"> <mtr> <mtd> <mi>E</mi> <mi>q</mi> <mo>.</mo> <mo> </mo> <mrow> <mo>(</mo> <mrow> <mn>21</mn> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mi>i</mi> <mi>f</mi> <mo> </mo> <mi>R</mi> <mo><</mo> <msub> <mi>P</mi> <mi>e</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mi>E</mi> <mi>q</mi> <mo>.</mo> <mo> </mo> <mrow> <mo>(</mo> <mrow> <mn>22</mn> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mi>O</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>i</mi> <mi>s</mi> <mi>e</mi> </mtd> </mtr> </mtable> </mrow> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(23)</label> </div> </div> where <math display='inline'><semantics> <mi>R</mi> </semantics></math> is a number generated randomly between 0 and 1. The last scattering phase is based on generating a new solution according to a solution selected randomly from the population and the current solution according to the following formula:<div class='html-disp-formula-info' id='FD24-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mrow> <mi>r</mi> <mn>1</mn> </mrow> <mi>p</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> <mo>+</mo> <mrow> <mo>|</mo> <mrow> <mi>R</mi> <msub> <mi>V</mi> <mn>5</mn> </msub> </mrow> <mo>|</mo> </mrow> <mo>×</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>−</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mn>3</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mover accent="true"> <mi>U</mi> <mo>→</mo> </mover> <mo>+</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mover accent="true"> <mi>U</mi> <mo>→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> <mo>×</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mi>t</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> </div> <div class='l'> <label >(24)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mi>R</mi> <msub> <mi>V</mi> <mn>5</mn> </msub> </mrow> </semantics></math> is a scalar value of normally distributed random numbers with a mean equal to zero and a standard deviation equal to one, and <math display='inline'><semantics> <mover accent="true"> <mi>U</mi> <mo>→</mo> </mover> </semantics></math> is a vector including random values of 0 and 1. <math display='inline'><semantics> <mrow> <mrow> <mo>|</mo> <mo>…</mo> <mo>|</mo> </mrow> </mrow> </semantics></math> is the absolute symbol, which converts the negative values into positive ones and returns the positive numbers as passed. Exchanging between Equations (23) and (24) is based on computing the difference between the fitness value of each solution and that of the best-so-far solution and normalizing this difference between 0 and 1 according to (25). If this difference is less than a threshold value <math display='inline'><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> </mrow> </semantics></math> generated randomly between 0 and 1, (23) will be applied; otherwise, (24) is applied. Our hypothesis is based herein computing the probabilistic fitness value using (25) to determine how far the current light ray is close to the best-so-far light ray. If the probabilistic fitness value for the ith light ray is smaller than <math display='inline'><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> </mrow> </semantics></math>, it is preferable to scatter this light ray in the same direction as the best-so-far solution. Our proposed algorithm suggests this hypothesis to maximize its performance when dealing with any optimization problem that needs a high-exploitation operator to accelerate the convergence speed and save computational costs. <div class='html-disp-formula-info' id='FD25-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msup> <mi>F</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mfrac> <mrow> <mi>F</mi> <mo>−</mo> <msub> <mi>F</mi> <mi>b</mi> </msub> </mrow> <mrow> <msub> <mi>F</mi> <mi>b</mi> </msub> <mo>−</mo> <msub> <mi>F</mi> <mi>w</mi> </msub> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(25)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mi>F</mi> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <msub> <mi>F</mi> <mi>b</mi> </msub> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <msub> <mi>F</mi> <mi>w</mi> </msub> </mrow> </semantics></math> indicate the fitness values of the current solution, best-so-far solution, and worst solution, respectively. However, the probability of applying (23) when the value of <math display='inline'><semantics> <msup> <mi>F</mi> <mo>′</mo> </msup> </semantics></math> is high is a little. For example, <a href="#mathematics-10-03466-f005" class="html-fig">Figure 5</a> has tracked the values of <math display='inline'><semantics> <msup> <mi>F</mi> <mo>′</mo> </msup> </semantics></math> for an agent and the random number R<sub>1</sub> during the optimization process of a test function; this figure shows that the <math display='inline'><semantics> <msup> <mi>F</mi> <mo>′</mo> </msup> </semantics></math> values are nearly greater than <math display='inline'><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> </mrow> </semantics></math> for most of the optimization process, as shown by red points that are much greater than the blue points in the 9 subgraphs depicted in <a href="#mathematics-10-03466-f005" class="html-fig">Figure 5</a>, and thus the chance of firing the first and second scattering stages is so low when relying solely on factor F′. Therefore, exchanging between (23) and (24) is also applied with a predefined probability <span class='html-italic'>P<sub>s</sub></span> to further promote the first and second scattering stages for accelerating convergence toward the best-so-far solution. Finally, exchanging between these two equations is formulated in the following formula:<div class='html-disp-formula-info' id='FD26-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mtable columnalign="right"> <mtr> <mtd> <mi>E</mi> <mi>q</mi> <mo>.</mo> <mo> </mo> <mrow> <mo>(</mo> <mrow> <mn>23</mn> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mi>i</mi> <mi>f</mi> <mo> </mo> <mi>R</mi> <mrow> <mo><</mo> <mrow> <msub> <mi>P</mi> <mi>s</mi> </msub> <mo> </mo> </mrow> <mo>|</mo> </mrow> <mo> </mo> <msup> <mi>F</mi> <mo>′</mo> </msup> <mo><</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>E</mi> <mi>q</mi> <mo>.</mo> <mo> </mo> <mrow> <mo>(</mo> <mrow> <mn>24</mn> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mi>O</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>i</mi> <mi>s</mi> <mi>e</mi> </mtd> </mtr> </mtable> </mrow> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(26)</label> </div> </div> where <math display='inline'><semantics> <mi>R</mi> </semantics></math> and <math display='inline'><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> </mrow> </semantics></math> are numbers generated randomly between 0 and 1.</div></section></section><section id='sec3dot3-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 3.3. LSO Pseudocode</h4><div class='html-p'>The pseudocode of the proposed algorithm is stated in Algorithm 1, and the same steps are depicted in <a href="#mathematics-10-03466-f006" class="html-fig">Figure 6</a>. Some solutions might go outside the problem’s search space. Thus, they have to be returned back into the search space to find feasible solutions to the problem. There are two common ways to convert the infeasible solutions, which go outside the search space to feasible ones; the first one is based on setting the lower bound to the dimensions, which are smaller, and setting the upper bound to these, which are higher; while the second one is based on generating new random values within the search boundaries of the dimensions, which go outside the search space of the problem. Within our proposed algorithm, we make hybridization between these two methods to improve the convergence rate by the first and the exploration by the second. This hybridization is achieved based on a predefined probability <span class='html-italic'>P<sub>h</sub></span>, which is estimated within the experiments section. <table class='html-array_table'><tbody ><tr ><td colspan='2' align='left' valign='middle' style='border-top:solid thin' class='html-align-left' ><b>Algorithm 1: LSO Pseudo-Code</b></td></tr><tr ><td colspan='2' align='left' valign='middle' style='border-top:solid thin' class='html-align-left' ><b>Input</b>: Population size of light rays <math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">N</mi> </mrow> </semantics></math>, problem Number of Iterations <math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> </semantics></math></td></tr><tr ><td colspan='2' align='left' valign='middle' class='html-align-left' ><b>Output</b>: The best light dispersion <math display='inline'><semantics> <mrow> <msup> <mi mathvariant="bold-italic">x</mi> <mo>*</mo> </msup> </mrow> </semantics></math> and its fitness<br>Generate initial random population of light rays <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mi mathvariant="bold-italic">i</mi> </msub> <mo> </mo> <mo> </mo> <mo stretchy="false">(</mo> <mi mathvariant="bold-italic">i</mi> <mo>=</mo> <mn mathvariant="bold">1</mn> <mo>,</mo> <mn mathvariant="bold">2</mn> <mo>,</mo> <mn mathvariant="bold">3</mn> <mo>,</mo> <mo> </mo> <mo>…</mo> <mo>,</mo> <mo> </mo> <mi mathvariant="bold-italic">N</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math></td></tr><tr ><td colspan='2' align='left' valign='middle' class='html-align-left' >t = 0</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>1</b></td><td align='left' valign='middle' class='html-align-left' > <b>While</b> (<math display='inline'><semantics> <mrow> <mi>t</mi> <mo><</mo> <mi>T</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </semantics></math>)</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>2</b></td><td align='left' valign='middle' class='html-align-left' > <span class='html-italic'><b>for</b></span> each light ray</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>3</b></td><td align='left' valign='middle' class='html-align-left' > evaluate the fitness value </td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>4</b></td><td align='left' valign='middle' class='html-align-left' > t = t + 1</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>5</b></td><td align='left' valign='middle' class='html-align-left' > keep the current global best <math display='inline'><semantics> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>6</b></td><td align='left' valign='middle' class='html-align-left' > Update the current solution if the updated solution is better.</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>7</b></td><td align='left' valign='middle' class='html-align-left' > determine normal lines <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>B</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, & <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>8</b></td><td align='left' valign='middle' class='html-align-left' > determine direction vectors <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, & <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>9</b></td><td align='left' valign='middle' class='html-align-left' > update the refractive index <math display='inline'><semantics> <mrow> <msup> <mi>k</mi> <mi>r</mi> </msup> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>10</b></td><td align='left' valign='middle' class='html-align-left' > update <math display='inline'><semantics> <mi>a</mi> </semantics></math>, <math display='inline'><semantics> <mi>ϵ</mi> </semantics></math>, and <math display='inline'><semantics> <mrow> <mi>G</mi> <mi>I</mi> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>11</b></td><td align='left' valign='middle' class='html-align-left' > Generate two random numbers: <math display='inline'><semantics> <mi>p</mi> </semantics></math>, <math display='inline'><semantics> <mi>q</mi> </semantics></math> between 0 and 1</td></tr><tr ><td colspan='2' align='center' valign='middle' class='html-align-center' ><b><span class='html-italic'>%%%%Generating new ColorFul ray: Exploration phase</span></b></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>12</b></td><td align='left' valign='middle' class='html-align-left' > if <math display='inline'><semantics> <mrow> <mi>p</mi> <mo>≤</mo> <mi>q</mi> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>13</b></td><td align='left' valign='middle' class='html-align-left' > update the next light dispersion using Equation (16)</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>14</b></td><td align='left' valign='middle' class='html-align-left' > <span class='html-italic'><b>Else</b></span></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>15</b></td><td align='left' valign='middle' class='html-align-left' > update the next light dispersion using Equation (17)</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>16</b></td><td align='left' valign='middle' class='html-align-left' > <span class='html-italic'><b>end if</b></span></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>17</b></td><td align='left' valign='middle' class='html-align-left' > evaluate the fitness value</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>18</b></td><td align='left' valign='middle' class='html-align-left' > t = t + 1</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>19</b></td><td align='left' valign='middle' class='html-align-left' > keep the current global best <math display='inline'><semantics> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>20</b></td><td align='left' valign='middle' class='html-align-left' > Update the current solution if the updated solution is better.</td></tr><tr ><td colspan='2' align='center' valign='middle' class='html-align-center' ><b><span class='html-italic'>%%%%Scattering phase: exploitation phase</span></b></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>21</b></td><td align='left' valign='middle' class='html-align-left' > Update the next light dispersion using Equation (26)</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>22</b></td><td align='left' valign='middle' class='html-align-left' > <span class='html-italic'><b>end for</b></span></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>23</b></td><td align='left' valign='middle' class='html-align-left' > <span class='html-italic'><b>end while</b></span></td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>24</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' > <span class='html-italic'><b>Return</b></span> <math display='inline'><semantics> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> </semantics></math></td></tr></tbody></table></div></section><section id='sec3dot4-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 3.4. Searching Behavior and Complexity of LSO</h4><div class='html-p'>In this section, we will discuss the searching schema of LSO and its computational complexity.</div><dl class='html-alpha-upper'><dt id=''>A.</dt><dd><div class='html-p'>Searching behavior of LSO</div></dd></dl><div class='html-p'>As discussed before, LSO reciprocates the methods of finding the next solution through the use of <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>r</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>p</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math>. In other words, <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> is calculated according to a randomly selected solution, which ensures the exploration of the search space. Meanwhile, the calculation of <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>B</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> and <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math> depends on the global and personal best solutions, respectively. This preserves the exploitation of the search space. Another exploitation consolidation is preserved by the usage of the inverse incomplete gamma function [<a href="#B117-mathematics-10-03466" class="html-bibr">117</a>], which can be expressed as follows:<div class='html-disp-formula-info' id='FD27-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>j</mi> <mo>=</mo> <msup> <mi>P</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mi>y</mi> <mo>,</mo> <mi>w</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(27)</label> </div> </div><div class='html-disp-formula-info' id='FD28-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mi>P</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mo>,</mo> <mi>w</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi mathvariant="sans-serif">Γ</mi> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∫</mo> </mstyle> <mn>0</mn> <mi>z</mi> </munderover> </mstyle> <msup> <mi>t</mi> <mrow> <mi>w</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mo>−</mo> <mi>t</mi> </mrow> </msup> <mi>d</mi> <mi>t</mi> </mrow> </semantics></math> </div> <div class='l'> <label >(28)</label> </div> </div> where <math display='inline'><semantics> <mi>w</mi> </semantics></math> is a scaling factor that is greater than or equal 0.</div><div class='html-p'><a href="#mathematics-10-03466-f007" class="html-fig">Figure 7</a> depicts the LSO’s exploration and exploitation operators to illustrate the behavior of LSO experimentally. This figure is plotted by displaying the search core of an individual during the exploration and exploitation phases for the first two dimensions (<math display='inline'><semantics> <mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo> </mo> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo> </mo> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </semantics></math>. From this figure, specifically <a href="#mathematics-10-03466-f007" class="html-fig">Figure 7</a>a, which depicts the LSO’s exploitation operator, it is obvious that this operator focuses its search toward a specific region, often the best-so-far region, to explore the solutions around and inside this region in the hope of reaching better solutions in a lower number of function evaluations. On the other side, <a href="#mathematics-10-03466-f007" class="html-fig">Figure 7</a>b pictures the exploration behavior of LSO to show how far LSO could reach; this figure shows that the individuals within the optimization process try to attack different regions, far from the current, within the search space of the optimization process for reaching the most promising region, which is attacked using the exploitation operator discussed formerly. </div><div class='html-p'><dl class='html-alpha-upper'><dt id=''>B.</dt><dd><div class='html-p'>Space and Time Complexity </div><div class='html-p'><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>LSO Space Complexity</div><div class='html-p'>The space complexity of any metaheuristic can be defined as the maximum space required during the search process. The big O notation of LSO space complexity can be stated as <math display='inline'><semantics> <mrow> <mi>O</mi> <mrow> <mo>(</mo> <mrow> <mi>N</mi> <mo>×</mo> <mi>d</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>, where <math display='inline'><semantics> <mi>N</mi> </semantics></math> is the number of search agents, and <math display='inline'><semantics> <mi>d</mi> </semantics></math> is the dimension of the given optimization problem.</div></dd><dt id=''>(2)</dt><dd><div class='html-p'>LSO Time Complexity</div><div class='html-p'>The time complexity of LSO is analyzed in this study using asymptotic analysis, which could analyze the performance of an algorithm based on the input size. Other than the input, all the other operations, like the exploration and exploitation operators, are considered constant. There are three asymptotic notations: big-O, omega, and theta, which are commonly used to analyze the running time complexity of an algorithm. The big-O notation is considered in this study to analyze the time complexity of LSO because it expresses the upper bound of the running time required by LSO for reaching the outcomes.</div></dd></dl></div></dd></dl></div><div class='html-p'>The time complexity of any metaheuristic depends on the required time for each step of the algorithm, like generating the initial population, updating candidate solutions, etc. Thus, the total time complexity is the sum of all such time measures. The time complexity of LSO results from three main algorithm steps:</div><div class='html-p'><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>Generation of the initial population.</div></dd><dt id=''>(2)</dt><dd><div class='html-p'>Calculation of candidate solutions.</div></dd><dt id=''>(3)</dt><dd><div class='html-p'>Evaluation of candidate solutions.</div></dd></dl></div><div class='html-p'>The first initialization step has a time complexity equal to <math display='inline'><semantics> <mrow> <mi>O</mi> <mrow> <mo>(</mo> <mrow> <mi>N</mi> <mo>×</mo> <mi>d</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>. The candidate solutions calculation has a time complexity <math display='inline'><semantics> <mrow> <mi>O</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>×</mo> <mi>N</mi> <mo>×</mo> <mi>d</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>, which includes the evaluation of the generated solutions and updating the current best solution, Where <math display='inline'><semantics> <mrow> <mi>T</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </semantics></math> is the maximum number of search iterations. So, the total time complexity of LSO in big-O is <math display='inline'><semantics> <mrow> <mi>O</mi> <mrow> <mo>(</mo> <mrow> <mi>N</mi> <mo>×</mo> <mi>d</mi> <mo>×</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>, which is confirmed in detail in <a href="#mathematics-10-03466-t003" class="html-table">Table 3</a>.</div></section><section id='sec3dot5-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 3.5. Difference between LSO, RO, and LRO</h4><div class='html-p'>This section compares the proposed algorithm to two other metaheuristic algorithms inspired by light reflection and refraction to demonstrate that LSO is completely different from those algorithms in terms of inspiration, formulation of candidate solutions, and the variation of the updating process, as illustrated in <a href="#mathematics-10-03466-t004" class="html-table">Table 4</a>.</div></section></section><section id='sec4-mathematics-10-03466' type=''><h2 data-nested='1'> 4. Experimental Results and Discussions</h2><div class='html-p'>In this section, we investigate the efficiency of LSO by different benchmarks, including CEC2005, CEC2014, CEC2017, CEC2020, and CEC2022. In addition, the sensitivity and scalability analyses of the proposed algorithm are introduced in this section.</div><section id='sec4dot1-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.1. Benchmarks and Compared Optimizers</h4><div class='html-p'>We first validate the efficiency of LSO by solving 20 classical benchmarks CEC2005 that were selected from [<a href="#B118-mathematics-10-03466" class="html-bibr">118</a>,<a href="#B119-mathematics-10-03466" class="html-bibr">119</a>,<a href="#B120-mathematics-10-03466" class="html-bibr">120</a>]. The selected benchmarks consist of three classes: uni-modal, multi-modal, and fixed-dimension multi-modal. Both unimodal and multimodal functions of CEC2005 are solved in 100 dimensions. <a href="#app1-mathematics-10-03466" class="html-app">Appendix A</a> <a href="#mathematics-10-03466-t0A1" class="html-table">Table A1</a>, <a href="#mathematics-10-03466-t0A2" class="html-table">Table A2</a>, <a href="#mathematics-10-03466-t0A3" class="html-table">Table A3</a>, <a href="#mathematics-10-03466-t0A4" class="html-table">Table A4</a>, <a href="#mathematics-10-03466-t0A5" class="html-table">Table A5</a>, <a href="#mathematics-10-03466-t0A6" class="html-table">Table A6</a> and <a href="#mathematics-10-03466-t0A7" class="html-table">Table A7</a> shows the characteristics of these three classes, which are mathematical formulations of benchmarks, dimension (D), boundaries of the search space (B), and the global optimal solution (OS). Furthermore, the proposed algorithm is tested on solving challengeable benchmarks like CEC2014, CEC2017, CEC2020, and CEC2020, which are described in <a href="#app1-mathematics-10-03466" class="html-app">Appendix A</a> <a href="#mathematics-10-03466-t0A1" class="html-table">Table A1</a>, <a href="#mathematics-10-03466-t0A2" class="html-table">Table A2</a>, <a href="#mathematics-10-03466-t0A3" class="html-table">Table A3</a>, <a href="#mathematics-10-03466-t0A4" class="html-table">Table A4</a>, <a href="#mathematics-10-03466-t0A5" class="html-table">Table A5</a>, <a href="#mathematics-10-03466-t0A6" class="html-table">Table A6</a> and <a href="#mathematics-10-03466-t0A7" class="html-table">Table A7</a>. The dimensions of these challengeable benchmarks are set to 10. In addition, the Wilcoxon test [<a href="#B121-mathematics-10-03466" class="html-bibr">121</a>] is performed to analyze both algorithms’ performance during the 30 runs with a 5% significance level.</div><div class='html-p'>The experimental results of LSO are compared with highly-cited state-of-the-art optimization algorithms like grey wolf optimizer (GWO) [<a href="#B122-mathematics-10-03466" class="html-bibr">122</a>], whale optimization algorithm (WOA) [<a href="#B123-mathematics-10-03466" class="html-bibr">123</a>], and salp swarm algorithm (SSA) [<a href="#B23-mathematics-10-03466" class="html-bibr">23</a>], evolutionary algorithms like differential evolution (DE), and recently-published optimizers including gradient-based optimizer (GBO) [<a href="#B124-mathematics-10-03466" class="html-bibr">124</a>], artificial gorilla troops optimizer (GTO) [<a href="#B27-mathematics-10-03466" class="html-bibr">27</a>], Runge–Kutta method (RUN) beyond the metaphor [<a href="#B125-mathematics-10-03466" class="html-bibr">125</a>], African vultures optimization algorithm (AVOA) [<a href="#B106-mathematics-10-03466" class="html-bibr">106</a>], equilibrium optimizer (EO) [<a href="#B76-mathematics-10-03466" class="html-bibr">76</a>], grey wolf optimizer (GWO) [<a href="#B122-mathematics-10-03466" class="html-bibr">122</a>], reptile search algorithm (RSA) [<a href="#B92-mathematics-10-03466" class="html-bibr">92</a>], and slime mold algorithm (SMA) [<a href="#B40-mathematics-10-03466" class="html-bibr">40</a>]. Both comparisons are based on standard deviation (SD), an average of fitness values (Avr), and rank. All the algorithms are coded in MATLAB<sup>©</sup> 2019. All experiments are performed on a 64-bit operating system with a 2.60 GHz CPU and 32 GB RAM. For a fair comparison, each algorithm runs for 25 independent times, the maximum number of function evaluations and population size are of 50,000 and 20, respectively (These parameters are constant within our experiments for all validated benchmarks). The other algorithms’ parameters are kept as standard. The used parameters are given in <a href="#mathematics-10-03466-t005" class="html-table">Table 5</a>.</div></section><section id='sec4dot2-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.2. Sensitivity Analysis of LSO</h4><div class='html-p'>Extensive experiments have been done to perform a sensitivity analysis of four controlling parameters found in LSO, which are <span class='html-italic'>P<sub>e</sub></span>, <span class='html-italic'>P<sub>s</sub></span>, <span class='html-italic'>P<sub>h</sub></span>, and <span class='html-italic'>β</span>. For each parameter of these, extensive experiments have been done using different values for each one to solve two test functions: F57 and F58, and the obtained outcomes, are depicted in <a href="#mathematics-10-03466-f008" class="html-fig">Figure 8</a>. This figure shows that the most effective values of these four parameters: <span class='html-italic'>P<sub>e</sub></span>, <span class='html-italic'>P<sub>s</sub></span>, <span class='html-italic'>P<sub>h</sub></span>, and <span class='html-italic'>β</span>, for two observed test functions are of 0.9, 0.05, 0.4, and 0.05, respectively.</div><div class='html-p'>The first investigated parameter is <span class='html-italic'>P<sub>h</sub></span> (responsible for the tradeoff between two boundary checking methods to improve the LSO’s searchability), which is analyzed in <a href="#mathematics-10-03466-f008" class="html-fig">Figure 8</a>a,b using various randomly-picked values between 0 and 1.0. These figures show that LSO could reach the optimal value for the test function: F58 when <span class='html-italic'>P<sub>h</sub></span> = 0.4. Based on that, this value is assigned to <span class='html-italic'>P<sub>h</sub></span> within the experiments conducted in this study.</div><div class='html-p'>For the parameter <span class='html-italic'>β</span> (responsible for improving the convergence speed of LSO), <a href="#mathematics-10-03466-f008" class="html-fig">Figure 8</a>c,d depicts the performance of LSO under various randomly-picked values between 0 and 0.6 for this parameter over two test problems: F57 and F58. According to this figure, over F57, on one side, the performance of LSO is substantially improved with increasing the value of this parameter even reaching 0.3, and then the performance again deteriorated. On the other side, over F58, LSO has poor performance when increasing the value of this parameter. Therefore, we found that the best value for the parameter <span class='html-italic'>β</span> that will be substantially suitable for most test functions is 0.05, since LSO under this value could reach the optimal value for the test problem: F58. It is worth mentioning that this parameter is responsible for accelerating the convergence speed of LSO to reach the near-optimal solution in as low a number of function evaluations as possible. Therefore, an additional experiment has been conducted in this section to depict the convergence speed of LSO under various values for the parameter <span class='html-italic'>β</span> over F58 (see <a href="#mathematics-10-03466-f008" class="html-fig">Figure 8</a>e). <a href="#mathematics-10-03466-f008" class="html-fig">Figure 8</a>e further affirms that the best value for this parameter is 0.05.</div><div class='html-p'>The third parameter is <span class='html-italic'>P<sub>e</sub></span>, employed in LSO to exchange between the first and second scattering phases. <a href="#mathematics-10-03466-f008" class="html-fig">Figure 8</a>f,g compare the influence of various values for this parameter over the test functions: F57 and F58. According to these figures, the best value for this parameter is 0.9, since LSO under this value could reach 900 and 805.9 for F58 and F57, respectively. Regarding the parameter <span class='html-italic'>P<sub>s</sub></span>, which is employed to further promote the first and second scattering stages for improving the exploitation operator of LSO, <a href="#mathematics-10-03466-f008" class="html-fig">Figure 8</a>h,i were presented to report the influence of various values for this parameter; these values range between 0 and 0.6. Inspecting these figures shows that LSO reaches the top performance when <span class='html-italic'>P<sub>s</sub></span> has a value of 0.05 over two investigated test functions: F57 and F58.</div></section><section id='sec4dot3-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.3. Evaluation of Exploitation and Exploration Operators</h4><div class='html-p'>The class of Uni-modal benchmarks has only one global optimal solution. This feature allows testing and validating a metaheuristic’s exploitation capabilities. <a href="#mathematics-10-03466-t006" class="html-table">Table 6</a> and <a href="#mathematics-10-03466-t007" class="html-table">Table 7</a> show that LSO is competitive with some other comparators for F1, F2, and F3. For F3 and F5, LSO has inferior performance compared to some of the recently-published rival algorithms. In general, LSO proves that it has a competitive exploitation operator. Multi-modal classes can efficiently discover the exploration of metaheuristics, as they have many optimal solutions. As observed in <a href="#mathematics-10-03466-t006" class="html-table">Table 6</a>, LSO is able to reach the optimal solution for 13 benchmarks, especially fixed-dimension ones, including F11-F20. In addition, LSO is competitive with the other comparators for F6-F8. To affirm the difference between the outcomes produced by LSO and those of the rival algorithms, the Wilcoxon rank-sum test is employed to compute the <span class='html-italic'>p</span>-values, which determine that there is a difference when its value is less than 5%; otherwise, there is no difference. <a href="#mathematics-10-03466-t007" class="html-table">Table 7</a> introduces the <span class='html-italic'>p</span>-values on unimodal and multimodal test functions between LSO and each rival algorithm. These values clarify that there are differences between the outcomes of LSO and most rival algorithms on most test functions. NaN in this table indicates that the independent outcomes of LSO and the corresponding optimizer are the same. As a result, the results and discussion is given herein assure the prosperity of LSO’s exploration and exploitation capabilities.</div></section><section id='sec4dot4-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.4. LSO for Challengeable CEC2014</h4><div class='html-p'>Additional validation is carried out on the CEC-2014 test suite in order to ensure that the proposed and other methods perform in accordance with expectations. With the help of this collection of test functions, you can determine whether or not an algorithm has the ability to explore, escape from local minima, and exploit. The test functions are divided into four categories: unimodal, multimodal, hybrid, and composition. The test suite’s characteristics are described in greater detail in <a href="#app1-mathematics-10-03466" class="html-app">Appendix A</a> <a href="#mathematics-10-03466-t0A1" class="html-table">Table A1</a>, <a href="#mathematics-10-03466-t0A2" class="html-table">Table A2</a>, <a href="#mathematics-10-03466-t0A3" class="html-table">Table A3</a>, <a href="#mathematics-10-03466-t0A4" class="html-table">Table A4</a>, <a href="#mathematics-10-03466-t0A5" class="html-table">Table A5</a>, <a href="#mathematics-10-03466-t0A6" class="html-table">Table A6</a> and <a href="#mathematics-10-03466-t0A7" class="html-table">Table A7</a>. The dimensions taken into consideration within our experiments are all ten. <a href="#mathematics-10-03466-t008" class="html-table">Table 8</a> shows the average and standard deviation values and the rank metric obtained by rival optimizers and others on CEC2014. Inspecting this table demonstrates that LSO could rank first for 23 out of 30 test functions, while its performance for the other test functions is competitive with some of the other optimizers. The average of rank values presented in <a href="#mathematics-10-03466-t008" class="html-table">Table 8</a> for each test function to show the best-performance order of the algorithms is computed and displayed in <a href="#mathematics-10-03466-f009" class="html-fig">Figure 9</a>. This figure shows the superior performance of LSO because it could come in the first rank with a value of 1.7, followed by DE with a value of 4.4, while RSA is the worst performing one.</div><div class='html-p'>In terms of the standard deviation, <a href="#mathematics-10-03466-f010" class="html-fig">Figure 10</a> displays the average SD values of 25 independent runs for each CEC-2014 test function; this figure discloses that the outcomes obtained by LSO within these independent runs are substantially similar since it could reach less average SD of 23, while RSA has the worst average SD. Finally, the Wilcoxon rank-sum statistical test is employed to show the difference between the outcomes of LSO and each rival algorithm; this test relies on two hypotheses: the null hypothesis, indicating that there is no difference, and the alternative one, indicating that there is difference between the outcomes of each pair of algorithms. This test determines the accepted hypothesis based on the confidence level and <span class='html-italic'>p</span>-value returned after comparing the outcomes of each pair of algorithms. Within our experiments, the confidence level is 0.05. The obtained <span class='html-italic'>p</span>-value between LSO and each rival algorithm is presented in <a href="#mathematics-10-03466-t009" class="html-table">Table 9</a>. The majority of <span class='html-italic'>p</span>-values presented in this table is less than 5%, which notifies us that the alternative hypothesis is accepted; hence, the outcome of LSO is different from those of the other compared algorithms.</div></section><section id='sec4dot5-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.5. LSO for Challengeable CEC2017</h4><div class='html-p'>This section compares the performance of LSO and other optimizers using the CEC2017 test suite to further validate the performance of LSO against the comparators for more challenging mathematical test functions [<a href="#B126-mathematics-10-03466" class="html-bibr">126</a>]. CEC2017 is composed of four mathematical function families: unimodal (F51–F52), multimodal (F53–F59), composition (F60–F69), and hybrid (F70–F79). As previously described, unimodal test functions are preferable for evaluating the exploitation operator of optimization algorithms because they involve only one global best solution, and multimodal test functions contain multiple local optimal solutions, which makes them particularly well-suited for evaluating the exploration operator of newly proposed optimizers; while composition and hybrid test functions have been designed to evaluate the optimization algorithms’ ability to escape out of local optima. The dimension of this benchmark is set to 10 within the conducted experiments in this section. <a href="#app1-mathematics-10-03466" class="html-app">Appendix A</a> <a href="#mathematics-10-03466-t0A1" class="html-table">Table A1</a>, <a href="#mathematics-10-03466-t0A2" class="html-table">Table A2</a>, <a href="#mathematics-10-03466-t0A3" class="html-table">Table A3</a>, <a href="#mathematics-10-03466-t0A4" class="html-table">Table A4</a>, <a href="#mathematics-10-03466-t0A5" class="html-table">Table A5</a>, <a href="#mathematics-10-03466-t0A6" class="html-table">Table A6</a> and <a href="#mathematics-10-03466-t0A7" class="html-table">Table A7</a> contains the characteristics of the CEC2017 benchmark.</div><div class='html-p'><a href="#mathematics-10-03466-t010" class="html-table">Table 10</a> shows the Avr, SD, and Rank values of 25 independent findings obtained by this suite’s proposed and rival optimizers. According to this table, LSO comes in the first rank compared to all optimizers for unimodal, multimodal, composition and hybrid test functions since it could reach better Avr and SD for all test functions. <a href="#mathematics-10-03466-f011" class="html-fig">Figure 11</a> and <a href="#mathematics-10-03466-f012" class="html-fig">Figure 12</a> display the average of the rank and standard deviation values presented in <a href="#mathematics-10-03466-t010" class="html-table">Table 10</a> for all test functions for each algorithm. According to these figures, LSO is the best since it occupies the 1st rank with a value of 1 and has the lowest standard deviation of 32, while RSA is the worst.</div><div class='html-p'>The Wilcoxon rank-sum test is used to determine the difference between the outcomes of LSO and these of each rival optimizer on CEC2017 test functions. Wilcoxon rank-sum test demonstrates a significant difference between the outcomes of LSO with the rival algorithms, as the <span class='html-italic'>p</span>-values in <a href="#mathematics-10-03466-t011" class="html-table">Table 11</a> support the alternative hypothesis. Ultimately, LSO is a strong optimizer, as demonstrated by its ability to defeat GBO, RUN, GTO, AVOA, SMA, RSA, and EO, which are the most recently published optimizers, as well as four highly-cited metaheuristic algorithms such as WOA, GWO, SSA, and DE.</div></section><section id='sec4dot6-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.6. LSO for Challengeable CEC2020</h4><div class='html-p'>During this section, additional testing is carried out on the CEC-2020 test suite to determine whether the proposed has stable performance for more challenging test functions. An algorithm’s ability to explore, exploit, and stay away from local minima can be evaluated using this suite, which consists of ten test functions and is divided into four categories: unimodal, multimodal, hybrid, and compositional. The characteristics of this suite are shown in <a href="#app1-mathematics-10-03466" class="html-app">Appendix A</a> <a href="#mathematics-10-03466-t0A1" class="html-table">Table A1</a>, <a href="#mathematics-10-03466-t0A2" class="html-table">Table A2</a>, <a href="#mathematics-10-03466-t0A3" class="html-table">Table A3</a>, <a href="#mathematics-10-03466-t0A4" class="html-table">Table A4</a>, <a href="#mathematics-10-03466-t0A5" class="html-table">Table A5</a>, <a href="#mathematics-10-03466-t0A6" class="html-table">Table A6</a> and <a href="#mathematics-10-03466-t0A7" class="html-table">Table A7</a>. LSO has superior performance for all test functions found in the CEC-2020 test suite except for F83, as evidenced by the Avr, rank, and SD values presented in <a href="#mathematics-10-03466-t012" class="html-table">Table 12</a> and obtained after analyzing the results of 25 independent runs. <a href="#mathematics-10-03466-f013" class="html-fig">Figure 13</a> and <a href="#mathematics-10-03466-f014" class="html-fig">Figure 14</a> show the average of the rank values and SD on all test functions of CEC2020. According to these figures, LSO is the best because it is ranked first with a value of 1.7 and has the lowest standard deviation of 38, whereas RSA is the worst because it is ranked last with a value of 12. Finally, the Wilcoxon rank-sum test is used to determine the difference between the results of LSO and those of each rival optimizer on this suite. The Wilcoxon rank-sum test results demonstrate a statistically significant difference between the outcomes of LSO and the rival algorithms for most test functions, as evidenced by the <span class='html-italic'>p</span>-values in <a href="#mathematics-10-03466-t013" class="html-table">Table 13</a>, which support the alternative hypothesis. As an added bonus, in this section, we present additional experimental evidence that LSO belongs to the strong optimizers.</div></section><section id='sec4dot7-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.7. LSO for Challengeable CEC2022</h4><div class='html-p'>The proposed and other methods are tested again on the CEC2022 test suite. This test suite contains 12 test functions divided into unimodal, multimodal, hybrid, and compositional. The properties of this test suite are also listed in <a href="#app1-mathematics-10-03466" class="html-app">Appendix A</a> (<a href="#mathematics-10-03466-t0A1" class="html-table">Table A1</a>, <a href="#mathematics-10-03466-t0A2" class="html-table">Table A2</a>, <a href="#mathematics-10-03466-t0A3" class="html-table">Table A3</a>, <a href="#mathematics-10-03466-t0A4" class="html-table">Table A4</a>, <a href="#mathematics-10-03466-t0A5" class="html-table">Table A5</a>, <a href="#mathematics-10-03466-t0A6" class="html-table">Table A6</a> and <a href="#mathematics-10-03466-t0A7" class="html-table">Table A7</a>), and their dimensions in the conducted experiments are 10. <a href="#mathematics-10-03466-t014" class="html-table">Table 14</a> shows the Avr, rank, and SD for 25 independent runs, demonstrating LSO’s superior performance for 9 out of 12 test functions of the CEC-2022 test suite. The average of the rank values and standard deviation on all test functions of CEC2022 are depicted in <a href="#mathematics-10-03466-f015" class="html-fig">Figure 15</a> and <a href="#mathematics-10-03466-f016" class="html-fig">Figure 16</a>. These figures show that LSO is the best because it is ranked first with a value of 1.6 and has the lowest standard deviation of 12, whereas RSA is the worst because it is ranked last with a value of 12 and has the highest standard deviation. In the end, the Wilcoxon rank-sum test is used to determine whether there is a significant difference between the results of LSO and those of each rival optimizer on this suite of problems. For most test functions, the Wilcoxon rank-sum test results demonstrate a statistically significant difference between the outcomes of LSO and the rival algorithms, as demonstrated by the <span class='html-italic'>p</span>-values in <a href="#mathematics-10-03466-t015" class="html-table">Table 15</a>. This section further affirms that LSO belongs to the category of highly-performed optimizers.</div></section><section id='sec4dot8-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.8. The Overall Effectiveness of the Proposed Algorithm</h4><div class='html-p'>In the previous sections, LSO has been separately assessed using five mathematical benchmarks: CEC2005, CEC2014, CEC2017, CEC2020, and CEC2022, and compared with twenty-two well-established metaheuristic algorithms, but the overall performance of LSO over all benchmarks has to be elaborated. Therefore, this section is presented to compare the overall performance of LSO and the other algorithms over all the test functions of each benchmark and all benchmarks. The average rank values and SD values of each benchmark are computed and reported in <a href="#mathematics-10-03466-t016" class="html-table">Table 16</a>. This table also indicates the overall effectiveness of the proposed algorithm and other rival algorithms using an additional metric known as overall effectiveness (OE) and computed according to the following formula [<a href="#B127-mathematics-10-03466" class="html-bibr">127</a>]:<div class='html-disp-formula-info' id='FD29-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>OE</mi> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mo>%</mo> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mrow> <msup> <mi mathvariant="normal">N</mi> <mo>′</mo> </msup> </mrow> <mo>−</mo> <msub> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">i</mi> </msub> </mrow> <mrow> <msup> <mi mathvariant="normal">N</mi> <mo>′</mo> </msup> </mrow> </mfrac> </mrow> </semantics></math> </div> <div class='l'> <label >(29)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msup> <mi mathvariant="normal">N</mi> <mo>′</mo> </msup> </mrow> </semantics></math> denotes the total number of test functions, and <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">i</mi> </msub> </mrow> </semantics></math> denotes the number of test functions in which the i-th algorithm is a loser. Inspecting this table reveals that the proposed algorithm could be superior in terms of SD, rank, and OE for four challengeable benchmarks, and competitive regarding rank and superior regarding SD and OE for the remaining benchmark. The average of the rank values, OE values, and SD values of each algorithm across all benchmarks are computed and reported in the last rows of <a href="#mathematics-10-03466-t016" class="html-table">Table 16</a>, respectively, to measure the overall effectiveness of each algorithm across all benchmarks. According to those rows, LSO ranks first for all indicators, with a significant difference from the nearest well-performed algorithm. The LSO’s strong performance due to the variation of the search process enables the algorithm to have a strong exploration and exploitation operator during the optimization process to help aid in preserving the population diversity, avoiding being stuck in local optima, accelerating the convergence towards the best-so-far solution. It is worth noting that both the inverse incomplete gamma function and the inverse random number are capable of preserving population diversity as well as avoiding becoming stuck in local minima due to their ability to generate significant numbers that aid in jumping the current solution to far away regions within the search space throughout the optimization process. On the other hand, three different scattering stages provide a variation in the exploitation operator to the LSO for rapidly reaching the near-optimal solution for various optimization problems of varying difficulty.</div></section><section id='sec4dot9-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.9. Convergence Curve</h4><div class='html-p'><a href="#mathematics-10-03466-f017" class="html-fig">Figure 17</a> compares the convergence rates of LSO and competing algorithms to show how they differ in terms of reaching the near-optimal solution in less number function evaluations. This figure illustrates that all LSO convergence curves exhibit an accelerated reducing pattern within the various stages of the optimization process for four families of test functions (unimodal, multimodal, composition, and hybrid). The LSO optimizer is significantly faster than any of the other competing algorithms, as shown by the convergence curves in <a href="#mathematics-10-03466-f017" class="html-fig">Figure 17</a>. Exploration and exploitation operators of LSO can work together in harmony, which prevents stagnation in local minima and speeds up convergence in the right direction to the most promising regions.</div></section><section id='sec4dot10-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.10. Qualitative Analysis</h4><div class='html-p'>The following metrics are used to evaluate the LSO performance during optimization: diversity, convergence curve, average fitness value, trajectory in the first dimension, and search history. The diversity metric shows how far apart an individual is on average from other individuals in the population; the convergence curve depicts the best-fitting value that was obtained within each iteration; the average fitness value represents the average of all individuals’ fitness values throughout each iteration; the trajectory curve shows how a solution’s first dimension changes over time as it progresses through the optimization process; and search history shows how a solution’s position changed during the optimization process.</div><div class='html-p'>The diversity metric shown in the second column of <a href="#mathematics-10-03466-f018" class="html-fig">Figure 18</a> is computed by summing the difference mean between the positions of each two solutions in the population according to the following formula:<div class='html-disp-formula-info' id='FD30-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>ℵ</mi> <mo>=</mo> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>j</mi> <mo>=</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <mfrac> <mrow> <mrow> <mo stretchy="false">(</mo> <mrow> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>d</mi> </msubsup> <mrow> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> <mi>d</mi> </mfrac> </mrow> </semantics></math> </div> <div class='l'> <label >(30)</label> </div> </div> where <span class='html-italic'>d</span> indicates the number of dimensions, <span class='html-italic'>N</span> stands for the population size, <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mrow> <mi mathvariant="bold-italic">i</mi> <mo>,</mo> <mi mathvariant="bold-italic">k</mi> </mrow> </msub> </mrow> </semantics></math> indicate the <span class='html-italic'>k</span>th dimension in the <span class='html-italic'>i</span>th and <span class='html-italic'>j</span>th solutions such that <math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">j</mi> <mo>></mo> <mi mathvariant="bold-italic">i</mi> </mrow> </semantics></math>. Observing <a href="#mathematics-10-03466-f018" class="html-fig">Figure 18</a> shows that the diversity metric of LSO is decreasing over time, indicating that LSO’s optimization process is gradually shifting from exploration to exploitation. LSO’s performance initially started to explore most regions in the search space to avoid stagnation into local minima and then shifted gradually to the exploitation operator to reduce diversity quickly during the second half of the optimization process to accelerate the convergence toward the most promising region discovered thus far.</div><div class='html-p'>The LSO convergence curves show an accelerated reducing pattern on a variety of test functions during the latter half of the optimization process when population diversity is reduced. The exploratory phase is largely transformed into the exploitative phase, as illustrated in the third column of <a href="#mathematics-10-03466-f018" class="html-fig">Figure 18</a>. At the beginning of the optimization process, LSO convergence is slow to avoid becoming stuck in local minima. Then, it is highly improved in the second half of the optimization process.</div><div class='html-p'>The depiction of average fitness history in <a href="#mathematics-10-03466-f018" class="html-fig">Figure 18</a> shows that LSO’s competitiveness has decreased over time due to all solutions focusing on exploiting the regions around the best-so-far solution, and as a result, the fitness values of all solutions are nearly moved towards the same region which involves the best-so-far solution. <a href="#mathematics-10-03466-f018" class="html-fig">Figure 18</a> also depicts the trajectory of LSO’s search for the optimal position of the first dimension as it gradually explores all aspects of the search space, as depicted in <a href="#mathematics-10-03466-f018" class="html-fig">Figure 18</a>. Because of the need to find a better solution in a short period of time, the exploratory approach is being replaced by an exploitative approach that restricts the scope of the search to a single aspect of it. As can be seen from the LSO’s trajectory curve, the optimization process begins with an exploratory trend before moving to an exploitation trend in search of better outcomes before coming to an end.</div><div class='html-p'>In the final column of <a href="#mathematics-10-03466-f018" class="html-fig">Figure 18</a>, the history of LSO positions is depicted. The search history is investigated by depicting the search core followed by LSO’s solutions within the whole optimization process for the first two dimensions: <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mn>1</mn> </msub> <msub> <mrow> <mrow> <mtext> </mtext> <mi>and</mi> <mtext> </mtext> <mi mathvariant="normal">X</mi> </mrow> </mrow> <mn>2</mn> </msub> </mrow> </semantics></math> of an optimization problem. The same pattern is followed for the other dimensions. As can be seen in this preceding column, LSO does not follow a consistent pattern for all test functions. Consider F21 as an example: to find an optimal solution for this problem, LSO first explores the entire search space before narrowing its focus to the range 0–50. The search history graph shows that LSO’s performance is more dispersed for the multimodal and composition test functions, while its performance for the unimodal test function is more concentrated around the optimum points.</div></section><section id='sec4dot11-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 4.11. Computational Cost</h4><div class='html-p'>The average computational cost consumed by each algorithm on the investigated test functions is shown in <a href="#mathematics-10-03466-f019" class="html-fig">Figure 19</a>. The graph shows that the CPU time for all algorithms is nearly the same, except RSA and SMA, which take a long time, and WOA, which takes less than half the time required by the rest. LSO is thus far superior in terms of the convergence speed and the quality of the obtained outcomes, with a negligible difference in CPU time.</div></section></section><section id='sec5-mathematics-10-03466' type=''><h2 data-nested='1'> 5. LSO for Engineering Design Problems</h2><div class='html-p'>In section, LSO is applied to solve three constrained engineering benchmarks, including Tension/Compression Spring Design Optimization Problem, Welded Beam Design Problem, and Pressure Vessel Design Problem. The best values found by LSO during 25 runs are compared with many optimization algorithms. For compared the algorithms’ parameters settings, all parameters are left as the defaults suggested by the authors. The parameters of LSO are kept as mentioned in <a href="#mathematics-10-03466-t005" class="html-table">Table 5</a>, except for Ps, which substantially affect the performance of LSO based on the nature of the solved problems. Therefore, an extensive experiment has been done under various values for this parameter, and the obtained outcomes are depicted in <a href="#mathematics-10-03466-f020" class="html-fig">Figure 20</a>. This figure shows that the performance of LSO is maximized when <span class='html-italic'>P<sub>s</sub></span> = 0.6. In addition to all rival algorithms used in the previous comparisons, five recently-published metaheuristic algorithms known as political optimizer (PO) [<a href="#B45-mathematics-10-03466" class="html-bibr">45</a>], continuous-state cellular automata algorithm (CCAA) [<a href="#B128-mathematics-10-03466" class="html-bibr">128</a>], snake optimizer (SO) [<a href="#B91-mathematics-10-03466" class="html-bibr">91</a>], beluga whale optimization (BWO), [<a href="#B96-mathematics-10-03466" class="html-bibr">96</a>] and driving training-based optimization (DTBO) [<a href="#B50-mathematics-10-03466" class="html-bibr">50</a>] are added in the next experiments to further show the superiority of LSO when tackling the real-world optimization problems, such as engineering design problems. Additionally, LSO is compared to some of the state-of-the-art optimizers proposed for each constrained engineering benchmark according to the cited results.</div><div class='html-p'>Engineering design problems are characterized by many different constraints. In order to handle this type of constraint, we employ penalty-based constraint handling techniques with LSO. There are several methods for handling constraints of optimization problems based on the penalty function. In this work, we choose to implement the Death Penalty method (the rejection of infeasible solutions method) [<a href="#B129-mathematics-10-03466" class="html-bibr">129</a>], in which the infeasible solutions are rejected and regenerated. So, the infeasible solution is automatically omitted from the candidate solutions. The main advantage of the Death Penalty method is its simple implementation and low computational complexity.</div><section id='sec5dot1-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 5.1. Tension/Compression Spring Design Optimization Problem</h4><div class='html-p'>The main objective of the tension/compression spring design optimization problem is to find the minimum volume <math display='inline'><semantics> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> of a coil spring under compression undergoing constraints of minimum deflection, shear stress, surge frequency, and limits on outside diameter and design variables (See <a href="#mathematics-10-03466-f021" class="html-fig">Figure 21</a>a). Mathematically, the problem can be formulated as [<a href="#B130-mathematics-10-03466" class="html-bibr">130</a>]:<div class='html-disp-formula-info' id='FD31-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>min</mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD32-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <msub> <mi>g</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mfrac> <mrow> <msubsup> <mi>x</mi> <mn>2</mn> <mn>3</mn> </msubsup> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> <mrow> <mn>71785</mn> <mo> </mo> <msubsup> <mi>x</mi> <mn>1</mn> <mn>4</mn> </msubsup> </mrow> </mfrac> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD33-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mn>4</mn> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msubsup> <mi>x</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mrow> <mo>(</mo> <mrow> <mn>12566</mn> <mo> </mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>5108</mn> <mo> </mo> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>−</mo> <mn>1</mn> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> <label >(31)</label> </div> </div><div class='html-disp-formula-info' id='FD34-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mfrac> <mrow> <mn>140.45</mn> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> <mrow> <msubsup> <mi>x</mi> <mn>2</mn> <mn>2</mn> </msubsup> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </mfrac> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD35-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mn>3</mn> </mfrac> <mo>−</mo> <mn>1</mn> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD36-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mn>0.05</mn> <mo>≤</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>≤</mo> <mn>2</mn> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mn>0.25</mn> <mo>≤</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>≤</mo> <mn>1.3</mn> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mn>2</mn> <mo>≤</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>≤</mo> <mn>15</mn> <mo>,</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </semantics></math> is the wire diameter, <math display='inline'><semantics> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is the mean coil diameter, and <math display='inline'><semantics> <mrow> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> is the length or number of coils.</div><div class='html-p'>LSO is compared with 14 additional algorithms (mathematical techniques or metaheuristics) selected from various literature including evolution strategies (ES) [<a href="#B131-mathematics-10-03466" class="html-bibr">131</a>], gravitational search algorithm (GSA) [<a href="#B55-mathematics-10-03466" class="html-bibr">55</a>], Tabu search (TS) [<a href="#B132-mathematics-10-03466" class="html-bibr">132</a>], swarm strategy [<a href="#B133-mathematics-10-03466" class="html-bibr">133</a>], unified particle swarm optimization (UPSO) [<a href="#B134-mathematics-10-03466" class="html-bibr">134</a>], cultural algorithms (CA) [<a href="#B132-mathematics-10-03466" class="html-bibr">132</a>], two-point adaptive nonlinear approximations-3 (TANA-3) [<a href="#B135-mathematics-10-03466" class="html-bibr">135</a>], particle swarm optimization (PSO) [<a href="#B136-mathematics-10-03466" class="html-bibr">136</a>], ant colony optimization (ACO) [<a href="#B137-mathematics-10-03466" class="html-bibr">137</a>], genetic algorithm (GA) [<a href="#B138-mathematics-10-03466" class="html-bibr">138</a>], quantum evolutionary algorithm (QEA) [<a href="#B137-mathematics-10-03466" class="html-bibr">137</a>], ray optimization (RO) [<a href="#B67-mathematics-10-03466" class="html-bibr">67</a>], probability collectives (PC) [<a href="#B139-mathematics-10-03466" class="html-bibr">139</a>], social interaction genetic algorithm (SIGA) [<a href="#B140-mathematics-10-03466" class="html-bibr">140</a>], and parallel genetic algorithm with social interaction (PSIGA) [<a href="#B138-mathematics-10-03466" class="html-bibr">138</a>]. <a href="#mathematics-10-03466-t017" class="html-table">Table 17</a> shows the results obtained by LSO for tension/compression spring design optimization problem. As shown, LSO is better able to reach minimum values than others. <a href="#mathematics-10-03466-f021" class="html-fig">Figure 21</a>b shows the convergence speed of LSO.</div></section><section id='sec5dot2-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 5.2. Welded Beam Design Problem</h4><div class='html-p'>The problem of designing welded beams can be defined as finding the feasible dimensions of a welded beam <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="normal">x</mi> <mn>1</mn> </msub> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="normal">x</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="normal">x</mi> <mn>3</mn> </msub> </mrow> </semantics></math>, and <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="normal">x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> (which are the thickness of weld, length of the clamped bar, the height of the bar, and thickness of the bar, respectively) that minimize the total manufacturing cost <math display='inline'><semantics> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> subject to a set of constraints. <a href="#mathematics-10-03466-f022" class="html-fig">Figure 22</a>a shows a representation of the weld beam design problem. Mathematically, the problem can be formulated as the following [<a href="#B130-mathematics-10-03466" class="html-bibr">130</a>]:<div class='html-disp-formula-info' id='FD39-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo> </mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1.10471</mn> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>0.04811</mn> <msub> <mi>x</mi> <mn>3</mn> </msub> <msub> <mi>x</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mrow> <mi>L</mi> <mo>+</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD40-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>τ</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>τ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD41-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD42-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>σ</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>σ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD43-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD44-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.10471</mn> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>−</mo> <mn>0.04811</mn> <msub> <mi>x</mi> <mn>3</mn> </msub> <msub> <mi>x</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mrow> <mi>L</mi> <mo>+</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mn>5</mn> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD45-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>5</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.125</mn> <mo>−</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD46-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>6</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>δ</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>δ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD47-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>7</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>P</mi> <mo>−</mo> <msub> <mi>P</mi> <mi>C</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> <label >(32)</label> </div> </div><div class='html-disp-formula-info' id='FD48-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>τ</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <msup> <mi>τ</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msup> <mi>τ</mi> <mo>′</mo> </msup> <msup> <mi>τ</mi> <mo>″</mo> </msup> <mfrac> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> <mrow> <mn>2</mn> <mi>R</mi> </mrow> </mfrac> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <msup> <mi>τ</mi> <mo>″</mo> </msup> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <msup> <mi>τ</mi> <mo>′</mo> </msup> <mo>=</mo> <mfrac> <mi>P</mi> <mrow> <msqrt> <mn>2</mn> </msqrt> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <msup> <mi>τ</mi> <mo>″</mo> </msup> <mo>=</mo> <mfrac> <mrow> <mi>M</mi> <mi>R</mi> </mrow> <mi>J</mi> </mfrac> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD51-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>M</mi> <mo>=</mo> <mi>P</mi> <mrow> <mo stretchy="false">(</mo> <mrow> <mi>L</mi> <mo>+</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mi>R</mi> <mo>=</mo> <msqrt> <mrow> <mfrac> <mrow> <msubsup> <mi>x</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> <mn>4</mn> </mfrac> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>,</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD53-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>2</mn> </msqrt> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <msubsup> <mi>x</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> <mrow> <mn>12</mn> </mrow> </mfrac> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD54-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>σ</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>6</mn> <mi>P</mi> <mi>L</mi> </mrow> <mrow> <msubsup> <mi>x</mi> <mn>3</mn> <mn>2</mn> </msubsup> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mi>δ</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <mi>P</mi> <msup> <mi>L</mi> <mn>3</mn> </msup> </mrow> <mrow> <mi>E</mi> <msubsup> <mi>x</mi> <mn>3</mn> <mn>3</mn> </msubsup> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD56-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>4.013</mn> <mi>E</mi> <mroot> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <msubsup> <mi>x</mi> <mn>3</mn> <mn>2</mn> </msubsup> <msubsup> <mi>x</mi> <mn>4</mn> <mn>6</mn> </msubsup> </mrow> <mrow> <mn>36</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo> </mo> </mroot> </mrow> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> <mrow> <mn>2</mn> <mi>L</mi> </mrow> </mfrac> <msqrt> <mrow> <mfrac> <mi>E</mi> <mrow> <mn>4</mn> <mi>G</mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD57-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>P</mi> <mo>=</mo> <mn>6000</mn> <mo> </mo> <mi>lb</mi> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mi>L</mi> <mo>=</mo> <mn>14</mn> <mo> </mo> <mi>in</mi> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mi>E</mi> <mo>=</mo> <mn>30</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mn>6</mn> </msup> <mo> </mo> <mi>psi</mi> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mi>G</mi> <mo>=</mo> <mn>12</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mn>6</mn> </msup> <mo> </mo> <mi>psi</mi> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD61-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <msub> <mi>τ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>13600</mn> <mo> </mo> <mi>psi</mi> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <msub> <mi>σ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>30000</mn> <mo> </mo> <mi>psi</mi> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <msub> <mi>δ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>0.25</mn> <mo> </mo> <mi>in</mi> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD64-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mn>0.1</mn> <mo>≤</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>≤</mo> <mn>2</mn> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mn>0.1</mn> <mo>≤</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>≤</mo> <mn>10</mn> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mo> </mo> <mn>0.1</mn> <mo>≤</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>≤</mo> <mn>10</mn> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mn>0.1</mn> <mo>≤</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> <mo>≤</mo> <mn>2</mn> <mo>,</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div> where <math display='inline'><semantics> <mi>τ</mi> </semantics></math> is shear stress, <math display='inline'><semantics> <mrow> <mi>σ</mi> </mrow> </semantics></math> is the bending stress, <math display='inline'><semantics> <mrow> <msub> <mi>P</mi> <mi>C</mi> </msub> </mrow> </semantics></math> is the buckling load, and <math display='inline'><semantics> <mi>δ</mi> </semantics></math> is the end deflection.</div><div class='html-p'>The proposed algorithm is compared with nine additional algorithms from the literature including hybrid and improved ones, which are RO [<a href="#B67-mathematics-10-03466" class="html-bibr">67</a>], WOA [<a href="#B41-mathematics-10-03466" class="html-bibr">41</a>], HS [<a href="#B141-mathematics-10-03466" class="html-bibr">141</a>], hybrid charged system search and particle swarm optimization (PSO) algorithms I (CSS&PSO I) [<a href="#B136-mathematics-10-03466" class="html-bibr">136</a>], hybrid charged system search and particle swarm optimization (PSO) algorithms II (CSS&PSO II) [<a href="#B136-mathematics-10-03466" class="html-bibr">136</a>], particle swarm optimization algorithm with struggle selection (PSOStr) [<a href="#B140-mathematics-10-03466" class="html-bibr">140</a>], RO [<a href="#B67-mathematics-10-03466" class="html-bibr">67</a>], firefly algorithm (FA) [<a href="#B142-mathematics-10-03466" class="html-bibr">142</a>], differential evolution with dynamic stochastic selection (DE) [<a href="#B143-mathematics-10-03466" class="html-bibr">143</a>], and hybrid artificial immune system and genetic algorithm (AIS-GA). As shown in <a href="#mathematics-10-03466-t018" class="html-table">Table 18</a>, on one side, LSO has a competitive result comparing to GBO, GTO, EO, and DE, and superior in terms of the convergence speed as shown in <a href="#mathematics-10-03466-f022" class="html-fig">Figure 22</a>b. On the other side, LSO is superior to all the other optimizers.</div></section><section id='sec5dot3-mathematics-10-03466' type=''><h4 class='html-italic' data-nested='2'> 5.3. Pressure Vessel Design Problem</h4><div class='html-p'>The problem of pressure vessel design can be described as minimizing the total fabrication cost of a cylindrical pressure vessel with the consideration of optimization constraints. The mathematical formulation of the problem can be expressed as [<a href="#B41-mathematics-10-03466" class="html-bibr">41</a>]:<div class='html-disp-formula-info' id='FD68-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo> </mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.6224</mn> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>3</mn> </msub> <msub> <mi>x</mi> <mn>4</mn> </msub> <mo>+</mo> <mn>1.7781</mn> <msub> <mi>x</mi> <mn>2</mn> </msub> <msubsup> <mi>x</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3.1661</mn> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msub> <mi>x</mi> <mn>4</mn> </msub> <mo>+</mo> <mn>19.84</mn> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD69-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <msub> <mi>g</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <mn>0.0193</mn> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>≤</mo> <mn>0</mn> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD70-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <mn>0.00954</mn> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>≤</mo> <mn>0</mn> <mo> </mo> <mo> </mo> </mrow> </semantics></math> </div> <div class='l'> <label >(33)</label> </div> </div><div class='html-disp-formula-info' id='FD71-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>g</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mi>π</mi> <msubsup> <mi>x</mi> <mn>3</mn> <mn>2</mn> </msubsup> <msub> <mi>x</mi> <mn>4</mn> </msub> <mo>−</mo> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> <mi>π</mi> <msubsup> <mi>x</mi> <mn>3</mn> <mn>3</mn> </msubsup> <mo>+</mo> <mn>1296000</mn> <mo>≤</mo> <mn>0</mn> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD72-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mo> </mo> <msub> <mi>g</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> <mo>−</mo> <mn>240</mn> <mo>≤</mo> <mn>0</mn> <mo> </mo> <mo> </mo> </mrow> </semantics></math> </div> <div class='l'> </div> </div><div class='html-disp-formula-info' id='FD73-mathematics-10-03466'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mo> </mo> <mn>0</mn> <mo>≤</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mo> </mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>≤</mo> <mn>99</mn> </mrow> <mrow> <mo>,</mo> <mtext> </mtext> <mn>10</mn> <mo>≤</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>,</mo> <mo> </mo> <msub> <mi>x</mi> <mn>4</mn> </msub> <mo>≤</mo> <mn>200</mn> <mo>,</mo> </mrow> </mrow> </semantics></math> </div> <div class='l'> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </semantics></math> is the shell thickness, <math display='inline'><semantics> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is the head thickness, <math display='inline'><semantics> <mrow> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> is the inner radius, and <math display='inline'><semantics> <mrow> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> is the cylindrical section length (without the head), as shown in <a href="#mathematics-10-03466-f023" class="html-fig">Figure 23</a>a.</div><div class='html-p'>For the problem of pressure vessel design, the proposed algorithm is compared with 16 metaheuristics and mathematical methods, including Harris Hawks optimization (HHO) [<a href="#B22-mathematics-10-03466" class="html-bibr">22</a>], grey wolf optimizer (GWO) [<a href="#B122-mathematics-10-03466" class="html-bibr">122</a>], hybrid particle swarm optimization with a feasibility-based rule (HPSO) [<a href="#B144-mathematics-10-03466" class="html-bibr">144</a>], Gaussian quantum-behaved particle swarm optimization (G-QPSO) [<a href="#B145-mathematics-10-03466" class="html-bibr">145</a>], water evaporation optimization (WEO) [<a href="#B146-mathematics-10-03466" class="html-bibr">146</a>], bat algorithm (BA) [<a href="#B147-mathematics-10-03466" class="html-bibr">147</a>], MFO [<a href="#B148-mathematics-10-03466" class="html-bibr">148</a>], charged system search (CSS) [<a href="#B56-mathematics-10-03466" class="html-bibr">56</a>], multimembered evolution strategy (ESs) [<a href="#B149-mathematics-10-03466" class="html-bibr">149</a>], genetic algorithm for design and optimization of composite laminates (BIANCA) [<a href="#B150-mathematics-10-03466" class="html-bibr">150</a>], modified differential evolution (MDDE) [<a href="#B151-mathematics-10-03466" class="html-bibr">151</a>], differential evolution with level comparison (DELC) [<a href="#B152-mathematics-10-03466" class="html-bibr">152</a>], WOA [<a href="#B41-mathematics-10-03466" class="html-bibr">41</a>], niched-pareto genetic algorithm (NPGA) [<a href="#B153-mathematics-10-03466" class="html-bibr">153</a>], Lagrangian multiplier [<a href="#B41-mathematics-10-03466" class="html-bibr">41</a>], and branch-bound [<a href="#B41-mathematics-10-03466" class="html-bibr">41</a>]. As observed from <a href="#mathematics-10-03466-t019" class="html-table">Table 19</a>, LSO significantly reaches the best results for the given problem compared to other algorithms except for DE and GTO, which have competitive performance for the best result, but LSO is superior for the average convergence speed as shown in <a href="#mathematics-10-03466-f023" class="html-fig">Figure 23</a>b.</div></section></section><section id='sec6-mathematics-10-03466' type='conclusions'><h2 data-nested='1'> 6. Conclusions</h2><div class='html-p'>In this work, a novel LSO metaheuristic algorithm is introduced that is inspired by sunlight dispersion through a water droplet, causing the rainbow phenomenon. The proposed algorithm is tested on several selected benchmarks. For CEC2005 benchmarks, LSO significantly performs well, especially for fixed dimensional multi-model functions. This indicates that LSO has high exploration capabilities. In addition, the sensitivity analysis of LSO parameters shows that the selected values of the parameters are the best. Finally, for CEC2020, CEC2017, CEC2022, and CEC2014, LSO has a superior performance compared to several well-established and recently published metaheuristic algorithms like DE, WOA, SMA, EO, GWO, GTO, GBO, RSA, SSA, RUN, and AVOA, which have been selected in our comparison due to their stability and recent publication compared to some of the other optimization algorithms like MBO, EWA, EHO, MS, HGS, CPA, and HHO proposed for tackling the same benchmarks. This indicates that LSO has a good balance between exploration and exploitation. LSO has competitive results for engineering design problems compared to other algorithms, even for improved and hybrid metaheuristics. For future work, we suggest developing the binary and multi-objective versions of LSO. In addition, several enhancements can be proposed for LSO by using fuzzy controllers or chaotic maps for defining LSO controlling probabilities and the hybridization with other algorithms. Finally, we suggest using LSO for solving recent real-life optimization problems such as sensor allocation problems, smart management of the power grid, and smart routing of vehicles.</div></section> </div> <div class="html-back"> <section class='html-notes'><h2 >Author Contributions</h2><div class='html-p'>Conceptualization, M.A.-B. and R.M.; methodology, M.A.-B., R.M. and K.M.S.; software, M.A.-B. and R.M.; validation, M.A.-B., R.M., R.K.C. and K.M.S.; formal analysis, M.A.-B., R.M., R.K.C. and K.M.S.; investigation, M.A.-B., R.M., R.K.C. and K.M.S.; data curation, M.A.-B., R.M., R.K.C. and K.M.S.; writing—original draft preparation, M.A.-B. and R.M.; writing—review and editing M.A.-B., R.M., R.K.C. and K.M.S.; visualization, M.A.-B., R.M., R.K.C. and K.M.S.; supervision, M.A.-B. and R.K.C.; funding acquisition, R.K.C. All authors have read and agreed to the published version of the manuscript. </div></section><section class='html-notes'><h2>Funding</h2><div class='html-p'>This research received no external funding.</div></section><section class='html-notes'><h2 >Data Availability Statement</h2><div class='html-p'>The code used in this paper can be obtained from this publicly accessible platform: <a href='https://drive.matlab.com/sharing/633c724c-9b52-4145-beba-c9e49f9df42e' target='_blank' rel="noopener noreferrer">https://drive.matlab.com/sharing/633c724c-9b52-4145-beba-c9e49f9df42e</a> (accessed on 9 January 2022).</div></section><section id='html-ack' class='html-ack'><h2 >Acknowledgments</h2><div class='html-p'>We would like to thank the Editor and anonymous reviewers for their thorough comments, which have helped us improve the manuscript—also, special thanks to Seyedali Mirjalili for his excellent suggestions and comments.</div></section><section class='html-notes'><h2 >Conflicts of Interest</h2><div class='html-p'>The authors declare no conflict of interest.</div></section><section id='html-glossary'><h2 >Nomenclature</h2><table class='html-array_table'><tbody ><tr ><td colspan='2' align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Nomenclature of symbols used in this study</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mi mathvariant="bold-italic">θ</mi> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Angle of reflection or refraction</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">k</mi> <mo>∈</mo> <mi>ℝ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Refractive index of a medium</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi mathvariant="bold-italic">L</mi> <mi mathvariant="bold-italic">i</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">i</mi> <mo>=</mo> <mn mathvariant="bold">0</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn mathvariant="bold">3</mn> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' ><math display='inline'><semantics> <mrow> <msup> <mi>i</mi> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> refracted or reflected light ray</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi mathvariant="bold-italic">n</mi> <mi mathvariant="bold-italic">s</mi> </msub> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Normal line at a point <math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">s</mi> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">p</mi> <mo>∈</mo> <mrow> <mo>[</mo> <mrow> <mn mathvariant="bold">0</mn> <mo>,</mo> <mo> </mo> <mn mathvariant="bold">1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Controlling probability of inner and outer reflection and refraction</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">q</mi> <mo>∈</mo> <mrow> <mo>[</mo> <mrow> <mn mathvariant="bold">0</mn> <mo>,</mo> <mo> </mo> <mn mathvariant="bold">1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Controlling probability of the first scattering phase</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">z</mi> <mo>∈</mo> <mrow> <mo>[</mo> <mrow> <mn mathvariant="bold">0</mn> <mo>,</mo> <mo> </mo> <mn mathvariant="bold">1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Controlling probability of the second scattering phase</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">t</mi> <mo>∈</mo> <mi>ℕ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Iteration number</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msup> <mi mathvariant="bold-italic">x</mi> <mn mathvariant="bold">0</mn> </msup> </mrow> <mo stretchy="true">→</mo> </mover> <mo>∈</mo> <mi>ℝ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Initial candidate solution</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>∈</mo> <mi>ℕ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Population size</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">d</mi> <mo>∈</mo> <mi>ℕ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Problem dimension</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">l</mi> <mi mathvariant="bold-italic">b</mi> <mo>∈</mo> <mi>ℝ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Lower bound of the search space</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">u</mi> <mi mathvariant="bold-italic">b</mi> <mo>∈</mo> <mi>ℝ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Upper bound of the search space</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">R</mi> <mi mathvariant="bold-italic">V</mi> <mo>∈</mo> <mrow> <mo>[</mo> <mrow> <mn mathvariant="bold">0</mn> <mo>,</mo> <mo> </mo> <mn mathvariant="bold">1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Vector of uniform random numbers</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mi mathvariant="bold-italic">t</mi> </msub> </mrow> <mo stretchy="true">→</mo> </mover> <mo>∈</mo> <mi>ℝ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Candidate solution at iteration <math display='inline'><semantics> <mrow> <mi>t</mi> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">w</mi> <mo>∈</mo> <mrow> <mo>[</mo> <mrow> <mn mathvariant="bold">0</mn> <mo>,</mo> <mo> </mo> <mo>∞</mo> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Scaling factor</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">G</mi> <mi mathvariant="bold-italic">I</mi> <mo>∈</mo> <mi>ℝ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Scaling factor</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">ϵ</mi> <mo>∈</mo> <mi>ℝ</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' class='html-align-left' >Scaling factor</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">g</mi> <mi mathvariant="bold-italic">i</mi> <mi mathvariant="bold-italic">n</mi> <mi mathvariant="bold-italic">v</mi> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Inverse incomplete gamma function</td></tr></tbody></table></section><section><section id='app1-mathematics-10-03466' type=''><h2 data-nested='1'> Appendix A</h2><div class="html-table-wrap" id="mathematics-10-03466-t0A1"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t0A1'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t0A1"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table A1.</b> Description of uni-modal benchmark functions. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t0A1" > <div class="html-caption" ><b>Table A1.</b> Description of uni-modal benchmark functions.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >ID</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Benchmark</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >D</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Domain</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Global Opt.</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >F1</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>100</mn> <mo>,</mo> <mn>100</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F2</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <mrow> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mo>|</mo> </mrow> <mo>+</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∏</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mo> </mo> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>10</mn> <mo>,</mo> <mn>10</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F3</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>j</mi> <mo>−</mo> <mn>1</mn> </mrow> <mi>i</mi> </msubsup> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>100</mn> <mo>,</mo> <mn>100</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F4</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>m</mi> <mi>a</mi> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>{</mo> <mrow> <mrow> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mo>|</mo> </mrow> <mo>,</mo> <mo> </mo> <mn>1</mn> <mo>≤</mo> <mi>i</mi> <mo>≤</mo> <mi>n</mi> </mrow> <mo>}</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>100</mn> <mo>,</mo> <mn>100</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F5</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mn>5</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> </mstyle> <mrow> <mo>[</mo> <mrow> <mn>100</mn> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >100</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>30</mn> <mo>,</mo> <mn>30</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t0A2"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t0A2'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t0A2"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table A2.</b> Description of multi-modal benchmark functions. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t0A2" > <div class="html-caption" ><b>Table A2.</b> Description of multi-modal benchmark functions.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >ID</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Benchmark</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >D</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Domain</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Global Opt.</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >F6</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mn>6</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <mrow> <mo>[</mo> <mrow> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>−</mo> <mn>10</mn> <mi>cos</mi> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi mathvariant="sans-serif">π</mi> <msub> <mi>x</mi> <mi mathvariant="normal">i</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>10</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td valign='middle' align='center' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>5.12</mn> <mo>,</mo> <mn>5.12</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F7</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mn>7</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>20</mn> <msup> <mi>e</mi> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>0.2</mn> <msqrt> <mrow> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mrow> <mo>)</mo> </mrow> </mrow> </msup> <mo>−</mo> <msup> <mi>e</mi> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi mathvariant="sans-serif">π</mi> <msub> <mi>x</mi> <mi mathvariant="normal">i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </msup> <mo>+</mo> <mn>20</mn> <mo>+</mo> <mi>e</mi> </mrow> </semantics> </math></td><td valign='middle' align='center' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>32</mn> <mo>,</mo> <mn>32</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F8</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mn>8</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>4000</mn> </mrow> </mfrac> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>−</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∏</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <mi>cos</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mrow> <msqrt> <mi>i</mi> </msqrt> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> </mrow> </semantics> </math></td><td valign='middle' align='center' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>600</mn> <mo>,</mo> <mn>600</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F9</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mtable columnalign="left"> <mtr> <mtd> <msub> <mi>f</mi> <mn>9</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>π</mi> <mi>n</mi> </mfrac> <mrow> <mo>{</mo> <mrow> <mn>10</mn> <mi>sin</mi> <mrow> <mo>(</mo> <mrow> <mi>π</mi> <msub> <mi>y</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> </mstyle> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>10</mn> <mi>s</mi> <mi>i</mi> <msup> <mi>n</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mrow> <mi>π</mi> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mspace width="80pt"/> <mo>+</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <mi>u</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mo> </mo> <mn>100</mn> <mo>,</mo> <mo> </mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </semantics> </math><br><math display='inline'> <semantics> <mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mn>4</mn> </mfrac> </mrow> </semantics> </math><math display='inline'> <semantics> <mrow> <mo>,</mo> <mtext> </mtext> <mi>u</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>s</mi> <mo>,</mo> <mo> </mo> <mi>l</mi> <mo>,</mo> <mo> </mo> <mi>v</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mtable> <mtr> <mtd> <mrow> <mi>l</mi> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>−</mo> <mi>s</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mi>v</mi> </msup> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>></mo> <mi>s</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo> </mo> <mo>−</mo> <mi>s</mi> <mo><</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo><</mo> <mi>s</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>l</mi> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>−</mo> <mi>s</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mi>v</mi> </msup> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo><</mo> <mo>−</mo> <mi>s</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mrow> </mrow> </semantics> </math></td><td valign='middle' align='center' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>50</mn> <mo>,</mo> <mn>50</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F10</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mtable columnalign="left"> <mtr> <mtd> <msub> <mi>f</mi> <mrow> <mn>10</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.1</mn> <mo stretchy="true">{</mo> <mrow> <mi>s</mi> <mi>i</mi> <msup> <mi>n</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mi>π</mi> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mo>+</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>s</mi> <mi>i</mi> <msup> <mi>n</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mi>π</mi> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>s</mi> <mi>i</mi> <msup> <mi>n</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>π</mi> <msub> <mi>x</mi> <mi>n</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mo>+</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> </mstyle> <mi>u</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mo> </mo> <mn>100</mn> <mo>,</mo> <mo> </mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> <mo stretchy="true">}</mo> </mtd> </mtr> </mtable> </mrow> </semantics> </math></td><td valign='middle' style='border-bottom:solid thin' align='center' class='html-align-center' >100</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>1.28</mn> <mo>,</mo> <mn>1.28</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mn>0</mn> </semantics> </math></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t0A3"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t0A3'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t0A3"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table A3.</b> Fixed-dimension multi-modal benchmark. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t0A3" > <div class="html-caption" ><b>Table A3.</b> Fixed-dimension multi-modal benchmark.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >ID</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Benchmark</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >D</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Domain</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Global Opt.</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >F11</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mn>11</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mrow> <mn>500</mn> </mrow> </mfrac> <mo>+</mo> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mn>25</mn> </mrow> </msubsup> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mo>+</mo> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>−</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mn>6</mn> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >2</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>65</mn> <mo>,</mo> <mn>65</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>1</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F12</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mn>12</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mn>11</mn> </mrow> </munderover> </mstyle> <msup> <mrow> <mrow> <mo>[</mo> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>−</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>b</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msubsup> <mi>b</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>5</mn> <mo>,</mo> <mn>5</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mn>0.00030</mn> </mrow> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F13</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mn>13</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>4</mn> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>−</mo> <mn>2.1</mn> <msubsup> <mi>x</mi> <mn>1</mn> <mn>4</mn> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <msubsup> <mi>x</mi> <mn>1</mn> <mn>6</mn> </msubsup> <mo>+</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <mn>4</mn> <msubsup> <mi>x</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mn>4</mn> <msubsup> <mi>x</mi> <mn>2</mn> <mn>4</mn> </msubsup> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >2</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>5</mn> <mo>,</mo> <mn>5</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mo>−</mo> <mn>1.0316</mn> </mrow> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F14</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mn>14</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <mfrac> <mrow> <mn>5.1</mn> </mrow> <mrow> <mn>4</mn> <msup> <mi>π</mi> <mn>2</mn> </msup> </mrow> </mfrac> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mfrac> <mn>5</mn> <mi>π</mi> </mfrac> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mn>10</mn> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mfrac> <mn>1</mn> <mrow> <mn>8</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>cos</mi> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <mn>10</mn> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >2</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>5</mn> <mo>,</mo> <mn>5</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mn>0.39789</mn> </mrow> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F15</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mtable columnalign="left"> <mtr> <mtd> <msub> <mi>f</mi> <mrow> <mn>15</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo stretchy="false">[</mo> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mrow> <mn>19</mn> <mo>−</mo> <mn>14</mn> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <mn>3</mn> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>−</mo> <mn>14</mn> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>6</mn> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>3</mn> <msubsup> <mi>x</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> <mo stretchy="false">]</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext> </mtext> <mo>×</mo> <mrow> <mo stretchy="false">[</mo> <mrow> <mn>30</mn> <mo>+</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>−</mo> <mn>3</mn> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mn>18</mn> <mo>−</mo> <mn>32</mn> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <mn>12</mn> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mn>48</mn> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>−</mo> <mn>36</mn> <msub> <mi>x</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>27</mn> <msubsup> <mi>x</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> <mo stretchy="false">]</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >2</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mn>3</mn> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F16</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mn>16</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> </mstyle> <msub> <mi>c</mi> <mi>i</mi> </msub> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>6</mn> </msubsup> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>−</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >3</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>3</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mo>−</mo> <mn>3.86</mn> </mrow> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F17</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mn>17</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>4</mn> </munderover> </mstyle> <msub> <mi>c</mi> <mi>i</mi> </msub> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>−</mo> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >6</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mo>−</mo> <mn>3.32</mn> </mrow> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F18</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mn>18</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>5</mn> </munderover> </mstyle> <msup> <mrow> <mrow> <mo>[</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>−</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>−</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> </mrow> <mo>]</mo> </mrow> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>10</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mo>−</mo> <mn>10.1532</mn> </mrow> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F19</td><td align='left' valign='middle' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mn>19</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>7</mn> </munderover> </mstyle> <msup> <mrow> <mrow> <mo>[</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>−</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>−</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> </mrow> <mo>]</mo> </mrow> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>10</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mo>−</mo> <mn>10.4028</mn> </mrow> </semantics> </math></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F20</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><math display='inline'> <semantics> <mrow> <msub> <mi>f</mi> <mrow> <mn>20</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mstyle displaystyle="true"> <munderover> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mn>10</mn> </mrow> </munderover> </mstyle> <msup> <mrow> <mrow> <mo>[</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>−</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>−</mo> <msub> <mi>a</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> </mrow> <mo>]</mo> </mrow> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mrow> <mo>[</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>10</mn> </mrow> <mo>]</mo> </mrow> </mrow> </semantics> </math></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mo>−</mo> <mn>10.5363</mn> </mrow> </semantics> </math></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t0A4"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t0A4'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t0A4"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table A4.</b> Description of CEC-2014 benchmark. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t0A4" > <div class="html-caption" ><b>Table A4.</b> Description of CEC-2014 benchmark.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Type</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >ID</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Functions</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Global Opt.</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Domain</th></tr></thead><tbody ><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal<br>function</td><td align='center' valign='middle' class='html-align-center' >F21 (CF1)</td><td valign='middle' align='left' class='html-align-left' >Rotated High Conditioned Elliptic Function</td><td align='center' valign='middle' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F22 (CF2)</td><td valign='middle' align='left' class='html-align-left' >Rotated Bent Cigar Function</td><td align='center' valign='middle' class='html-align-center' >200</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F23 (CF3)</td><td valign='middle' style='border-bottom:solid thin' align='left' class='html-align-left' >Rotated Discus Function</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >300</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='13' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Simple multimodal<br>Test functions</td><td align='center' valign='middle' class='html-align-center' >F24 (CF4)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated Rosenbrock’s Function</td><td align='center' valign='middle' class='html-align-center' >400</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F25 (CF5)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated Ackley’s Function</td><td align='center' valign='middle' class='html-align-center' >500</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F26 (CF6)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated Weierstrass Function</td><td align='center' valign='middle' class='html-align-center' >600</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F27 (CF7)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated Griewank’s Function</td><td align='center' valign='middle' class='html-align-center' >700</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F28 (CF8)</td><td valign='middle' align='left' class='html-align-left' >Shifted Rastrigin’s Function</td><td align='center' valign='middle' class='html-align-center' >800</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F29 (CF9)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated Rastrigin’s Function</td><td align='center' valign='middle' class='html-align-center' >900</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F30 (CF10)</td><td valign='middle' align='left' class='html-align-left' >Shifted Schwefel’s Function</td><td align='center' valign='middle' class='html-align-center' >1000</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F31 (CF11)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated Schwefel’s Function</td><td align='center' valign='middle' class='html-align-center' >1100</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F32 (CF12)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated Katsuura Function</td><td align='center' valign='middle' class='html-align-center' >1200</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F33 (CF13)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated HappyCat Function</td><td align='center' valign='middle' class='html-align-center' >1300</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F34 (CF14)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated HGBat Function</td><td align='center' valign='middle' class='html-align-center' >1400</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F35 (CF15)</td><td valign='middle' align='left' class='html-align-left' >Shifted and Rotated Expanded Griewank’s plus Rosenbrock’s Function</td><td align='center' valign='middle' class='html-align-center' >1500</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F36 (CF16)</td><td valign='middle' style='border-bottom:solid thin' align='left' class='html-align-left' >Shifted and Rotated Expanded Scaffer’s F6 Function</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1600</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='6' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid test functions</td><td align='center' valign='middle' class='html-align-center' >F37 (CF17)</td><td valign='middle' align='left' class='html-align-left' >Hybrid Function 1</td><td align='center' valign='middle' class='html-align-center' >1700</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F38 (CF18)</td><td valign='middle' align='left' class='html-align-left' >Hybrid Function 2</td><td align='center' valign='middle' class='html-align-center' >1800</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F39 (CF19)</td><td valign='middle' align='left' class='html-align-left' >Hybrid Function 3</td><td align='center' valign='middle' class='html-align-center' >1900</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F40 (CF20)</td><td valign='middle' align='left' class='html-align-left' >Hybrid Function 4</td><td align='center' valign='middle' class='html-align-center' >2000</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F41 (CF17)</td><td valign='middle' align='left' class='html-align-left' >Hybrid Function 5</td><td align='center' valign='middle' class='html-align-center' >2100</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F42 (CF18)</td><td valign='middle' style='border-bottom:solid thin' align='left' class='html-align-left' >Hybrid Function 6</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2200</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='8' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition test functions</td><td align='center' valign='middle' class='html-align-center' >F43 (CF23)</td><td valign='middle' align='left' class='html-align-left' >Composition Function 1</td><td align='center' valign='middle' class='html-align-center' >2300</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F44 (CF24)</td><td valign='middle' align='left' class='html-align-left' >Composition Function 2</td><td align='center' valign='middle' class='html-align-center' >2400</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F45 (CF25)</td><td valign='middle' align='left' class='html-align-left' >Composition Function 3</td><td align='center' valign='middle' class='html-align-center' >2500</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F46 (CF26)</td><td valign='middle' align='left' class='html-align-left' >Composition Function 4</td><td align='center' valign='middle' class='html-align-center' >2600</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F47 (CF27)</td><td valign='middle' align='left' class='html-align-left' >Composition Function 5</td><td align='center' valign='middle' class='html-align-center' >2700</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F48 (CF28)</td><td valign='middle' align='left' class='html-align-left' >Composition Function 6</td><td align='center' valign='middle' class='html-align-center' >2800</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F49 (CF29)</td><td valign='middle' align='left' class='html-align-left' >Composition Function 7</td><td align='center' valign='middle' class='html-align-center' >2900</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F50 (CF30)</td><td valign='middle' style='border-bottom:solid thin' align='left' class='html-align-left' >Composition Function 8</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3000</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t0A5"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t0A5'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t0A5"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table A5.</b> Description of CEC-2017 benchmark. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t0A5" > <div class="html-caption" ><b>Table A5.</b> Description of CEC-2017 benchmark.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Type</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >ID</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Functions</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Global Opt.</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Domain</th></tr></thead><tbody ><tr ><td rowspan='2' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal<br>function</td><td align='center' valign='middle' class='html-align-center' >F51 (CF1)</td><td align='left' valign='middle' class='html-align-left' >Shifted and Rotated Bent Cigar Function</td><td align='center' valign='middle' class='html-align-center' >100</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F52 (CF3)</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Shifted and Rotated Zakharov Function</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >300</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='7' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Simple multimodal<br>Test functions</td><td align='center' valign='middle' class='html-align-center' >F53 (CF4)</td><td align='left' valign='middle' class='html-align-left' >Shifted and Rotated Rosenbrock’s Function</td><td align='center' valign='middle' class='html-align-center' >400</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F54 (CF5)</td><td align='left' valign='middle' class='html-align-left' >Shifted and Rotated Rastrigin’s Function</td><td align='center' valign='middle' class='html-align-center' >500</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F55 (CF6)</td><td align='left' valign='middle' class='html-align-left' >Shifted and Rotated Expanded Scaffer’s Function</td><td align='center' valign='middle' class='html-align-center' >600</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F56 (CF7)</td><td align='left' valign='middle' class='html-align-left' >Shifted and Rotated Lunacek Bi_Rastrigin Function</td><td align='center' valign='middle' class='html-align-center' >700</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F57 (CF8)</td><td align='left' valign='middle' class='html-align-left' >Shifted and Rotated Non-Continuous Rastrigin’s Function</td><td align='center' valign='middle' class='html-align-center' >800</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F58 (CF9)</td><td align='left' valign='middle' class='html-align-left' >Shifted and Rotated Levy Function</td><td align='center' valign='middle' class='html-align-center' >900</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F59 (CF10)</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Shifted and Rotated Schwefel’s Function</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1000</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='10' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid test functions</td><td align='center' valign='middle' class='html-align-center' >F60 (CF11)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 1</td><td align='center' valign='middle' class='html-align-center' >1100</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F61 (CF12)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 2</td><td align='center' valign='middle' class='html-align-center' >1200</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F62 (CF13)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 3</td><td align='center' valign='middle' class='html-align-center' >1300</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F63 (CF14)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 4</td><td align='center' valign='middle' class='html-align-center' >1400</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F64 (CF15)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 5</td><td align='center' valign='middle' class='html-align-center' >1500</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F65 (CF16)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 6</td><td align='center' valign='middle' class='html-align-center' >1600</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F66 (CF17)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 7</td><td align='center' valign='middle' class='html-align-center' >1700</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F67 (CF18)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 8</td><td align='center' valign='middle' class='html-align-center' >1800</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F68 (CF19)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 9</td><td align='center' valign='middle' class='html-align-center' >1900</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F69 (CF20)</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Hybrid Function 10</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2000</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='10' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition test functions</td><td align='center' valign='middle' class='html-align-center' >F70 (CF21)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 1</td><td align='center' valign='middle' class='html-align-center' >2100</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F71 (CF22)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 2</td><td align='center' valign='middle' class='html-align-center' >2200</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F72 (CF23)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 3</td><td align='center' valign='middle' class='html-align-center' >2300</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F73 (CF24)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 4</td><td align='center' valign='middle' class='html-align-center' >2400</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F74 (CF25)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 5</td><td align='center' valign='middle' class='html-align-center' >2500</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F75 (CF26)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 6</td><td align='center' valign='middle' class='html-align-center' >2600</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F76 (CF27)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 7</td><td align='center' valign='middle' class='html-align-center' >2700</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F77 (CF28)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 8</td><td align='center' valign='middle' class='html-align-center' >2800</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F78 (CF29)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 9</td><td align='center' valign='middle' class='html-align-center' >2900</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F79 (CF30)</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Composition Function 10</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3000</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t0A6"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t0A6'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t0A6"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table A6.</b> Description of CEC2020 benchmarks. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t0A6" > <div class="html-caption" ><b>Table A6.</b> Description of CEC2020 benchmarks.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Type</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >ID</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Functions</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Global Opt.</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Domain</th></tr></thead><tbody ><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F80 (CF1)</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Shifted and Rotated Bent Cigar Function</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >100</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='2' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >multimodal</td><td align='center' valign='middle' class='html-align-center' >F81 (CF2)</td><td align='left' valign='middle' class='html-align-left' >Shifted and Rotated Lunacek Bi_Rastrigin Function</td><td align='center' valign='middle' class='html-align-center' >700</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F82 (CF3)</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Hybrid Function 1</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1100</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='4' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid</td><td align='center' valign='middle' class='html-align-center' >F83 (CF4)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 2</td><td align='center' valign='middle' class='html-align-center' >1700</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F84 (CF5)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 3</td><td align='center' valign='middle' class='html-align-center' >1900</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F85 (CF6)</td><td align='left' valign='middle' class='html-align-left' >Hybrid Function 4</td><td align='center' valign='middle' class='html-align-center' >2100</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F86 (CF7)</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Hybrid Function 5</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1600</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition</td><td align='center' valign='middle' class='html-align-center' >F87 (CF8)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 1</td><td align='center' valign='middle' class='html-align-center' >2200</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F88 (CF9)</td><td align='left' valign='middle' class='html-align-left' >Composition Function 2</td><td align='center' valign='middle' class='html-align-center' >2400</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F89 (CF10)</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Composition Function 3</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2500</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t0A7"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t0A7'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t0A7"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table A7.</b> Description of CEC2022 benchmark. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t0A7" > <div class="html-caption" ><b>Table A7.</b> Description of CEC2022 benchmark.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Type</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >No.</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Functions</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Global Opt.</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Domain</th></tr></thead><tbody ><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal function</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F90</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Shifted and full Rotated Zakharov Function </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >300</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='3' align='center' valign='middle' class='html-align-center' >Basic functions</td><td align='center' valign='middle' class='html-align-center' >F91</td><td align='left' valign='middle' class='html-align-left' >Shifted and full Rotated Rosenbrock’s Function </td><td align='center' valign='middle' class='html-align-center' >400</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F92</td><td align='left' valign='middle' class='html-align-left' >Shifted and full Rotated Expanded Schaffer’s f6 Function </td><td align='center' valign='middle' class='html-align-center' >600</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F93</td><td align='left' valign='middle' class='html-align-left' >Shifted and full Rotated Non-continuous Rastrigin’s Function </td><td align='center' valign='middle' class='html-align-center' >800</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F94</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Shifted and Rotated Levy Function</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >900</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid functions</td><td align='center' valign='middle' class='html-align-center' >F95</td><td align='left' valign='middle' class='html-align-left' >Hybrid function 1 (N = 3)</td><td align='center' valign='middle' class='html-align-center' >1800</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F96</td><td align='left' valign='middle' class='html-align-left' >Hybrid function 2 (N = 6)</td><td align='center' valign='middle' class='html-align-center' >2000</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F97</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Hybrid function 3 (N = 5)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2200</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr><tr ><td rowspan='4' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composite functions</td><td align='center' valign='middle' class='html-align-center' >F98</td><td align='left' valign='middle' class='html-align-left' >Composite function 1 (N = 5)</td><td align='center' valign='middle' class='html-align-center' >2300</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F99</td><td align='left' valign='middle' class='html-align-left' >Composite function 2 (N = 4)</td><td align='center' valign='middle' class='html-align-center' >2400</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F100</td><td align='left' valign='middle' class='html-align-left' >Composite function 3 (N = 5)</td><td align='center' valign='middle' class='html-align-center' >2600</td><td align='center' valign='middle' class='html-align-center' >[−100,100]</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F101</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Composite function 4 (N = 6)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2700</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[−100,100]</td></tr></tbody> </table> </div></section></section><section id='html-references_list'><h2>References</h2><ol class='html-xxx'><li id='B1-mathematics-10-03466' class='html-x' data-content='1.'>Fausto, F.; Reyna-Orta, A.; Cuevas, E.; Andrade, Á.G.; Perez-Cisneros, M. 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data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g001.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g001.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g001-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f001"></a> </div> </div> <div class="html-fig_description"> <b>Figure 1.</b> Categories of metaheuristic algorithms.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f001" > <div class="html-caption" > <b>Figure 1.</b> Categories of metaheuristic algorithms.</div> <div class="html-img"><img alt="Mathematics 10 03466 g001" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g001.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g001.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g001.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f002"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f002"> <img alt="Mathematics 10 03466 g002 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g002.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g002.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g002-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f002"></a> </div> </div> <div class="html-fig_description"> <b>Figure 2.</b> Light dispersion and colors of rainbow.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f002" > <div class="html-caption" > <b>Figure 2.</b> Light dispersion and colors of rainbow.</div> <div class="html-img"><img alt="Mathematics 10 03466 g002" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g002.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g002.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g002.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f003"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f003"> <img alt="Mathematics 10 03466 g003 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g003.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g003.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g003-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f003"></a> </div> </div> <div class="html-fig_description"> <b>Figure 3.</b> Light dispersion and colors of rainbow and vector form of refraction and reflection in rainbow.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f003" > <div class="html-caption" > <b>Figure 3.</b> Light dispersion and colors of rainbow and vector form of refraction and reflection in rainbow.</div> <div class="html-img"><img alt="Mathematics 10 03466 g003" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g003.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g003.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g003.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f004"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f004"> <img alt="Mathematics 10 03466 g004 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g004.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g004.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g004-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f004"></a> </div> </div> <div class="html-fig_description"> <b>Figure 4.</b> The behavior of the inverse incomplete gamma function with respect to <math display='inline'><semantics> <mi>a</mi> </semantics></math> values.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f004" > <div class="html-caption" > <b>Figure 4.</b> The behavior of the inverse incomplete gamma function with respect to <math display='inline'><semantics> <mi>a</mi> </semantics></math> values.</div> <div class="html-img"><img alt="Mathematics 10 03466 g004" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g004.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g004.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g004.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f005"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f005"> <img alt="Mathematics 10 03466 g005 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g005.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g005.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g005-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f005"></a> </div> </div> <div class="html-fig_description"> <b>Figure 5.</b> Tracing F’s values versus R<sub>1</sub> for an individual over 9 independent runs: The red points indicate that <math display='inline'><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo><</mo> <msup> <mi>F</mi> <mo>′</mo> </msup> </mrow> </semantics></math>; and the blue points indicate that <math display='inline'><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>></mo> <msup> <mi>F</mi> <mo>′</mo> </msup> </mrow> </semantics></math>.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f005" > <div class="html-caption" > <b>Figure 5.</b> Tracing F’s values versus R<sub>1</sub> for an individual over 9 independent runs: The red points indicate that <math display='inline'><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo><</mo> <msup> <mi>F</mi> <mo>′</mo> </msup> </mrow> </semantics></math>; and the blue points indicate that <math display='inline'><semantics> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>></mo> <msup> <mi>F</mi> <mo>′</mo> </msup> </mrow> </semantics></math>.</div> <div class="html-img"><img alt="Mathematics 10 03466 g005" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g005.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g005.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g005.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f006"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f006"> <img alt="Mathematics 10 03466 g006 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g006.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g006.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g006-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f006"></a> </div> </div> <div class="html-fig_description"> <b>Figure 6.</b> Flowchart of LSO.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f006" > <div class="html-caption" > <b>Figure 6.</b> Flowchart of LSO.</div> <div class="html-img"><img alt="Mathematics 10 03466 g006" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g006.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g006.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g006.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f007"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f007"> <img alt="Mathematics 10 03466 g007 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g007.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g007.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g007-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f007"></a> </div> </div> <div class="html-fig_description"> <b>Figure 7.</b> Depiction of exploration and exploitation stages of the proposed algorithm (LSO). (<b>a</b>) Exploitation phase. (<b>b</b>) Exploration phase.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f007" > <div class="html-caption" > <b>Figure 7.</b> Depiction of exploration and exploitation stages of the proposed algorithm (LSO). (<b>a</b>) Exploitation phase. (<b>b</b>) Exploration phase.</div> <div class="html-img"><img alt="Mathematics 10 03466 g007" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g007.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g007.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g007.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f008"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f008"> <img alt="Mathematics 10 03466 g008a 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008a.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008a.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008a-550.jpg" /><img alt="Mathematics 10 03466 g008b 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008b.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008b.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008b-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f008"></a> </div> </div> <div class="html-fig_description"> <b>Figure 8.</b> Sensitivity analysis of LSO. (<b>a</b>) Tuning the parameter P<sub>h</sub> over F58. (<b>b</b>) Tuning the parameter P<sub>h</sub> over F57. (<b>c</b>) Tuning the parameter <b><span class='html-italic'>β</span></b> over F58. (<b>d</b>) Tuning the parameter <b><span class='html-italic'>β</span></b> over F57. (<b>e</b>) Tuning the parameter <b><span class='html-italic'>β</span></b> over F58 in terms of convergence speed. (<b>f</b>) Tuning the parameter P<sub>e</sub> over F58. (<b>g</b>) Tuning the parameter P<sub>e</sub> over F57. (<b>h</b>) Adjusting the parameter P<sub>s</sub> over F58. (<b>i</b>) Adjusting the parameter P<sub>s</sub> over F57.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f008" > <div class="html-caption" > <b>Figure 8.</b> Sensitivity analysis of LSO. (<b>a</b>) Tuning the parameter P<sub>h</sub> over F58. (<b>b</b>) Tuning the parameter P<sub>h</sub> over F57. (<b>c</b>) Tuning the parameter <b><span class='html-italic'>β</span></b> over F58. (<b>d</b>) Tuning the parameter <b><span class='html-italic'>β</span></b> over F57. (<b>e</b>) Tuning the parameter <b><span class='html-italic'>β</span></b> over F58 in terms of convergence speed. (<b>f</b>) Tuning the parameter P<sub>e</sub> over F58. (<b>g</b>) Tuning the parameter P<sub>e</sub> over F57. (<b>h</b>) Adjusting the parameter P<sub>s</sub> over F58. (<b>i</b>) Adjusting the parameter P<sub>s</sub> over F57.</div> <div class="html-img"><img alt="Mathematics 10 03466 g008a" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008a.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008a.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008a.png" /><img alt="Mathematics 10 03466 g008b" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008b.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008b.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g008b.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f009"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f009"> <img alt="Mathematics 10 03466 g009 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g009.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g009.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g009-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f009"></a> </div> </div> <div class="html-fig_description"> <b>Figure 9.</b> Average rank of each optimizer on all CEC2014.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f009" > <div class="html-caption" > <b>Figure 9.</b> Average rank of each optimizer on all CEC2014.</div> <div class="html-img"><img alt="Mathematics 10 03466 g009" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g009.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g009.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g009.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f010"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f010"> <img alt="Mathematics 10 03466 g010 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g010.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g010.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g010-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f010"></a> </div> </div> <div class="html-fig_description"> <b>Figure 10.</b> Average SD of each optimizer on all CEC2014.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f010" > <div class="html-caption" > <b>Figure 10.</b> Average SD of each optimizer on all CEC2014.</div> <div class="html-img"><img alt="Mathematics 10 03466 g010" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g010.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g010.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g010.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f011"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f011"> <img alt="Mathematics 10 03466 g011 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g011.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g011.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g011-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f011"></a> </div> </div> <div class="html-fig_description"> <b>Figure 11.</b> Average rank on all CEC2017 test functions.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f011" > <div class="html-caption" > <b>Figure 11.</b> Average rank on all CEC2017 test functions.</div> <div class="html-img"><img alt="Mathematics 10 03466 g011" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g011.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g011.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g011.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f012"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f012"> <img alt="Mathematics 10 03466 g012 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g012.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g012.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g012-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f012"></a> </div> </div> <div class="html-fig_description"> <b>Figure 12.</b> Average SD of each optimizer on all CEC2017.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f012" > <div class="html-caption" > <b>Figure 12.</b> Average SD of each optimizer on all CEC2017.</div> <div class="html-img"><img alt="Mathematics 10 03466 g012" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g012.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g012.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g012.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f013"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f013"> <img alt="Mathematics 10 03466 g013 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g013.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g013.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g013-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f013"></a> </div> </div> <div class="html-fig_description"> <b>Figure 13.</b> Average rank of each optimizer on all CEC2020.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f013" > <div class="html-caption" > <b>Figure 13.</b> Average rank of each optimizer on all CEC2020.</div> <div class="html-img"><img alt="Mathematics 10 03466 g013" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g013.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g013.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g013.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f014"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f014"> <img alt="Mathematics 10 03466 g014 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g014.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g014.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g014-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f014"></a> </div> </div> <div class="html-fig_description"> <b>Figure 14.</b> Average SD of each optimizer on all CEC2020.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f014" > <div class="html-caption" > <b>Figure 14.</b> Average SD of each optimizer on all CEC2020.</div> <div class="html-img"><img alt="Mathematics 10 03466 g014" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g014.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g014.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g014.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f015"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f015"> <img alt="Mathematics 10 03466 g015 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g015.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g015.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g015-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f015"></a> </div> </div> <div class="html-fig_description"> <b>Figure 15.</b> Average rank of each optimizer on all CEC2022.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f015" > <div class="html-caption" > <b>Figure 15.</b> Average rank of each optimizer on all CEC2022.</div> <div class="html-img"><img alt="Mathematics 10 03466 g015" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g015.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g015.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g015.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f016"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f016"> <img alt="Mathematics 10 03466 g016 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g016.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g016.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g016-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f016"></a> </div> </div> <div class="html-fig_description"> <b>Figure 16.</b> Average SD of each optimizer on all CEC2022.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f016" > <div class="html-caption" > <b>Figure 16.</b> Average SD of each optimizer on all CEC2022.</div> <div class="html-img"><img alt="Mathematics 10 03466 g016" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g016.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g016.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g016.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f017"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f017"> <img alt="Mathematics 10 03466 g017a 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017a.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017a.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017a-550.jpg" /><img alt="Mathematics 10 03466 g017b 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017b.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017b.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017b-550.jpg" /><img alt="Mathematics 10 03466 g017c 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017c.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017c.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017c-550.jpg" /><img alt="Mathematics 10 03466 g017d 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017d.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017d.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017d-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f017"></a> </div> </div> <div class="html-fig_description"> <b>Figure 17.</b> Depiction of averaged convergence speed among algorithms on some test functions. (<b>a</b>) F51 (Unimodal), (<b>b</b>) F52 (Unimodal), (<b>c</b>) F53 (Multimodal), (<b>d</b>) F54 (Multimodal), (<b>e</b>) F55 (Multimodal), (<b>f</b>) F56 (Multimodal), (<b>g</b>) F57 (Multimodal), (<b>h</b>) F59 (Multimodal), (<b>i</b>) F60 (Multimodal), (<b>j</b>) F61 (Multimodal), (<b>k</b>) F62 (Hybrid), (<b>l</b>) F63 (Hybrid), (<b>m</b>) F65 (Hybrid), (<b>n</b>) F64 (Hybrid), (<b>o</b>) F73 (Composition), (<b>p</b>) F75 (Composition), (<b>q</b>) F77 (Composition), and (<b>r</b>) F78 (Composition).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f017" > <div class="html-caption" > <b>Figure 17.</b> Depiction of averaged convergence speed among algorithms on some test functions. (<b>a</b>) F51 (Unimodal), (<b>b</b>) F52 (Unimodal), (<b>c</b>) F53 (Multimodal), (<b>d</b>) F54 (Multimodal), (<b>e</b>) F55 (Multimodal), (<b>f</b>) F56 (Multimodal), (<b>g</b>) F57 (Multimodal), (<b>h</b>) F59 (Multimodal), (<b>i</b>) F60 (Multimodal), (<b>j</b>) F61 (Multimodal), (<b>k</b>) F62 (Hybrid), (<b>l</b>) F63 (Hybrid), (<b>m</b>) F65 (Hybrid), (<b>n</b>) F64 (Hybrid), (<b>o</b>) F73 (Composition), (<b>p</b>) F75 (Composition), (<b>q</b>) F77 (Composition), and (<b>r</b>) F78 (Composition).</div> <div class="html-img"><img alt="Mathematics 10 03466 g017a" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017a.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017a.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017a.png" /><img alt="Mathematics 10 03466 g017b" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017b.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017b.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017b.png" /><img alt="Mathematics 10 03466 g017c" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017c.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017c.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017c.png" /><img alt="Mathematics 10 03466 g017d" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017d.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017d.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g017d.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f018"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f018"> <img alt="Mathematics 10 03466 g018a 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018a.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018a.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018a-550.jpg" /><img alt="Mathematics 10 03466 g018b 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018b.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018b.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018b-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f018"></a> </div> </div> <div class="html-fig_description"> <b>Figure 18.</b> Diversity, convergence curve, average fitness history, trajectory, and search history.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f018" > <div class="html-caption" > <b>Figure 18.</b> Diversity, convergence curve, average fitness history, trajectory, and search history.</div> <div class="html-img"><img alt="Mathematics 10 03466 g018a" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018a.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018a.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018a.png" /><img alt="Mathematics 10 03466 g018b" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018b.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018b.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g018b.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f019"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f019"> <img alt="Mathematics 10 03466 g019 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g019.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g019.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g019-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f019"></a> </div> </div> <div class="html-fig_description"> <b>Figure 19.</b> Comparison among algorithms in terms of CPU time.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f019" > <div class="html-caption" > <b>Figure 19.</b> Comparison among algorithms in terms of CPU time.</div> <div class="html-img"><img alt="Mathematics 10 03466 g019" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g019.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g019.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g019.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f020"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f020"> <img alt="Mathematics 10 03466 g020 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g020.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g020.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g020-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f020"></a> </div> </div> <div class="html-fig_description"> <b>Figure 20.</b> Tuning the parameter P<sub>s</sub> over tension spring design.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f020" > <div class="html-caption" > <b>Figure 20.</b> Tuning the parameter P<sub>s</sub> over tension spring design.</div> <div class="html-img"><img alt="Mathematics 10 03466 g020" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g020.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g020.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g020.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f021"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f021"> <img alt="Mathematics 10 03466 g021 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g021.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g021.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g021-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f021"></a> </div> </div> <div class="html-fig_description"> <b>Figure 21.</b> Tension/compression spring design problem. (<b>a</b>) Structure. (<b>b</b>) Convergence curve.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f021" > <div class="html-caption" > <b>Figure 21.</b> Tension/compression spring design problem. (<b>a</b>) Structure. (<b>b</b>) Convergence curve.</div> <div class="html-img"><img alt="Mathematics 10 03466 g021" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g021.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g021.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g021.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f022"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f022"> <img alt="Mathematics 10 03466 g022 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g022.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g022.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g022-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f022"></a> </div> </div> <div class="html-fig_description"> <b>Figure 22.</b> Weld beam design problem. (<b>a</b>) Structure. (<b>b</b>) Convergence curve.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f022" > <div class="html-caption" > <b>Figure 22.</b> Weld beam design problem. (<b>a</b>) Structure. (<b>b</b>) Convergence curve.</div> <div class="html-img"><img alt="Mathematics 10 03466 g022" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g022.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g022.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g022.png" /></div> </div><div class="html-fig-wrap" id="mathematics-10-03466-f023"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f023"> <img alt="Mathematics 10 03466 g023 550" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g023.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g023.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g023-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#fig_body_display_mathematics-10-03466-f023"></a> </div> </div> <div class="html-fig_description"> <b>Figure 23.</b> Pressure vessel design problem. (<b>a</b>) Structure. (<b>b</b>) Convergence curve.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_mathematics-10-03466-f023" > <div class="html-caption" > <b>Figure 23.</b> Pressure vessel design problem. (<b>a</b>) Structure. (<b>b</b>) Convergence curve.</div> <div class="html-img"><img alt="Mathematics 10 03466 g023" data-large="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g023.png" data-original="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g023.png" data-lsrc="/mathematics/mathematics-10-03466/article_deploy/html/images/mathematics-10-03466-g023.png" /></div> </div><div class="html-table-wrap" id="mathematics-10-03466-t002"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t002'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t002"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 2.</b> An illustrative numerical example to the results generated according to Equations (6)–(14). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t002" > <div class="html-caption" ><b>Table 2.</b> An illustrative numerical example to the results generated according to Equations (6)–(14).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' > </th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>1</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>2</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>3</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>4</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>5</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>6</mn> </msub> </mrow> </mstyle> </semantics> </math></th></tr></thead><tbody ><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>r</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >61.4064</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−77.7085</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−91.5639</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−70.6667</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−41.4573</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−58.8625</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msubsup> <mi>x</mi> <mi>t</mi> <mi>p</mi> </msubsup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−33.8424</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >85.3758</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−13.0301</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−37.5489</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >62.1643</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >39.1392</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−2.2651</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >25.3057</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >76.0485</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >45.3216</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−75.5683</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−80.4718</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1006</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.1273</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.1500</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.1157</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0679</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0964</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>B</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0622</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1569</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0239</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0690</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1143</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0719</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0047</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0529</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1590</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0947</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.1580</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.1682</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0090</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0972</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0282</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0217</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0122</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0749</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0989</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1893</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1586</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0900</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0532</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0325</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0765</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1327</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1672</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1149</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0119</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.0066</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics> </math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.1054</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.2106</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.3229</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.2128</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0823</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >−0.0959</td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t003"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t003'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t003"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 3.</b> Execution time of each line in the proposed algorithm according to using the asymptotic analysis. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t003" > <div class="html-caption" ><b>Table 3.</b> Execution time of each line in the proposed algorithm according to using the asymptotic analysis.</div> <table > <thead ><tr ><th colspan='2' align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Algorithm 1: LSO Pseudo-Code</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Execution Time for Each Line</th></tr></thead><tbody ><tr ><td colspan='2' align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>Input</b>: Population size of light rays <math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">N</mi> </mrow> </semantics></math>, problem Number of Iterations <math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> </semantics></math></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >One execution time for each input. This line contains 3 inputs, and the total execution time will be equal to <b>3</b></td></tr><tr ><td colspan='2' align='left' valign='middle' class='html-align-left' ><b>Output</b>: The best light dispersion <math display='inline'><semantics> <mrow> <msup> <mi mathvariant="bold-italic">x</mi> <mo mathvariant="bold">*</mo> </msup> </mrow> </semantics></math> and its fitness<br>Generate an initial random population of light rays <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mi mathvariant="bold-italic">i</mi> </msub> <mo> </mo> <mo> </mo> <mo stretchy="false">(</mo> <mi mathvariant="bold-italic">i</mi> <mo>=</mo> <mn mathvariant="bold">1</mn> <mo>,</mo> <mn mathvariant="bold">2</mn> <mo>,</mo> <mn mathvariant="bold">3</mn> <mo>,</mo> <mo> </mo> <mo>…</mo> <mo>,</mo> <mo> </mo> <mi mathvariant="bold-italic">N</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math></td><td align='left' valign='middle' class='html-align-left' ><dl class='html-bullet'><dt id=''>-</dt><dd><div class='html-p'>The output will be returned one time, so the execution time of this line will be 1</div></dd><dt id=''>-</dt><dd><div class='html-p'>Regarding the initialization, this stage will initialize <span class='html-italic'>d</span> dimensions for N solutions, so the time complexity will be <math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math></div></dd></dl></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>1</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>While</b> <math display='inline'><semantics> <mrow> <mtext> </mtext> <mo>(</mo> <mi>t</mi> <mo><</mo> <mi>T</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </semantics></math>)</td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >This line will be executed <math display='inline'><semantics> <mrow> <mi>T</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </semantics></math> times</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>2</b></td><td align='left' valign='middle' class='html-align-left' > <b><span class='html-italic'>for</span></b> each light ray <math display='inline'><semantics> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mi mathvariant="bold-italic">i</mi> </msub> <mo> </mo> <mo stretchy="false">(</mo> <mi mathvariant="bold-italic">i</mi> <mo>=</mo> <mn mathvariant="bold">1</mn> <mo>,</mo> <mn mathvariant="bold">2</mn> <mo>,</mo> <mn mathvariant="bold">3</mn> <mo>,</mo> <mo> </mo> <mo>…</mo> <mo>,</mo> <mo> </mo> <mi mathvariant="bold-italic">N</mi> </mrow> </semantics></math>)</td><td align='left' valign='middle' class='html-align-left' ><b><span class='html-italic'>Executed N times multiplied by</span></b> <math display='inline'><semantics> <mrow> <mi>T</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </semantics></math>, <span class='html-italic'>which</span> <math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>3</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > evaluate the fitness value </td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> since the objective function will observe each dimension in the updated solution</td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>4</b></td><td align='left' valign='middle' class='html-align-left' > t = t + 1</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>5</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > keep the current global best <math display='inline'><semantics> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> </semantics></math></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>6</b></td><td align='left' valign='middle' class='html-align-left' > Update the current solution if the updated solution is better.</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>7</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > determine normal lines <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math><math display='inline'><semantics> <mrow> <mo>,</mo> <mtext> </mtext> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>B</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math><math display='inline'><semantics> <mrow> <mo>,</mo> <mo> </mo> <mo>&</mo> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mn mathvariant="bold">3</mn> <mo>×</mo> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> <mo>=</mo> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math><b>|3 here indicates the number of generated vectors</b></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>8</b></td><td align='left' valign='middle' class='html-align-left' > determine direction vectors <math display='inline'><semantics> <mrow> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>0</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math><math display='inline'><semantics> <mrow> <mo>,</mo> <mtext> </mtext> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math><math display='inline'><semantics> <mrow> <mo> </mo> <mo>,</mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math><math display='inline'><semantics> <mrow> <mo>,</mo> <mtext> </mtext> <mo>&</mo> <mo> </mo> <mover accent="true"> <mrow> <msub> <mi>x</mi> <mrow> <mi>L</mi> <mn>3</mn> </mrow> </msub> </mrow> <mo stretchy="true">→</mo> </mover> </mrow> </semantics></math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mn mathvariant="bold">3</mn> <mo>×</mo> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> <mo>=</mo> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math><b>|3 here indicates the number of generated direction vectors</b></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>9</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > update the refractive index <math display='inline'><semantics> <mrow> <msup> <mi>k</mi> <mi>r</mi> </msup> </mrow> </semantics></math></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>10</b></td><td align='left' valign='middle' class='html-align-left' > update <math display='inline'><semantics> <mrow> <mrow> <mi>a</mi> </mrow> <mo>,</mo> <mtext> </mtext> <mi>ϵ</mi> <mo>,</mo> <mtext> </mtext> <mo>&</mo> <mtext> </mtext> <mi>G</mi> <mi>I</mi> </mrow> </semantics></math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>11</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > Generate two random numbers: <math display='inline'><semantics> <mrow> <mi>p</mi> </mrow> </semantics></math><math display='inline'><semantics> <mo>,</mo> <mtext> </mtext> <mi>q</mi> </semantics></math> between 0 and 1</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td colspan='2' align='center' valign='middle' class='html-align-center' ><b><span class='html-italic'>%%%%Generating new ColorFul ray: Exploration phase</span></b></td><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>Comments not implemented</span></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>12</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > <span class='html-italic'><b>if</b></span><math display='inline'><semantics> <mrow> <mo> </mo> <mi>p</mi> <mo>≤</mo> <mi>q</mi> </mrow> </semantics></math></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>13</b></td><td align='left' valign='middle' class='html-align-left' > update the next light dispersion using Equation (16)</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>14</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > Else</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>15</b></td><td align='left' valign='middle' class='html-align-left' > update the next light dispersion using Equation (17)</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>16</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > <span class='html-italic'><b>end if</b></span></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>17</b></td><td align='left' valign='middle' class='html-align-left' > evaluate the fitness value</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>18</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > t = t + 1</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>19</b></td><td align='left' valign='middle' class='html-align-left' > keep the current global best <math display='inline'><semantics> <mrow> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> </semantics></math></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>20</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > Update the current solution if the updated solution is better.</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td colspan='2' align='center' valign='middle' class='html-align-center' ><b><span class='html-italic'>%%%%Scattering phase: exploitation phase</span></b></td><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>Comments not implemented</span></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>21</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > Update the next light dispersion using Equation (25)</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>22</b></td><td align='left' valign='middle' class='html-align-left' > <span class='html-italic'><b>end for</b></span></td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>23</b></td><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><span class='html-italic'><b>end while</b></span></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math></td></tr><tr ><td align='left' valign='middle' class='html-align-left' ><b>24</b></td><td align='left' valign='middle' class='html-align-left' ><b><span class='html-italic'>Return</span></b> <math display='inline'><semantics> <mrow> <mo> </mo> <msup> <mi>x</mi> <mo>*</mo> </msup> </mrow> </semantics></math></td><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'><b>1 time</b></span></td></tr><tr ><td align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' > </td><td colspan='2' align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' ><b>By Summing the execution time of all lines, it is obvious that the highest growth rate is</b> <math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>. <b>Hence, the time omplexity of LSO is</b><math display='inline'><semantics> <mrow> <mi mathvariant="bold-italic">O</mi> <mrow> <mo>(</mo> <mrow> <mi mathvariant="bold-italic">N</mi> <mo>×</mo> <mi mathvariant="bold-italic">d</mi> <mo>×</mo> <mi mathvariant="bold-italic">T</mi> <mi mathvariant="bold-italic">max</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math><b>since it has the highest growth rate</b></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t004"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t004'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t004"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 4.</b> Comparison between LSO, RO, and LRO. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t004" > <div class="html-caption" ><b>Table 4.</b> Comparison between LSO, RO, and LRO.</div> <table > <thead ><tr ><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Characteristics</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >LSO</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >RO</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >LRO</th></tr></thead><tbody ><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Inspiration</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Simulating the light movement and orientation in the rainbow metrological phenomenon.</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Simulating Snell’s light refraction law when light transfers from a lighter medium to a darker medium.</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Simulating the light’s reflection and refraction.</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Formulation </td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >LSO mainly depends on the vector representation of the rainbow and its intersperse in the sky.</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >The formulation of RO depends on the general Snell’s law of light ray transformation from a medium to a darker one to ray tracing in 2-dimensional and 3-dimensional spaces.</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >The updating of candidate solutions depends on the division of a search space into grid cells and then considering these cells as reflection and refraction points.</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Variation </td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><dl class='html-bullet'><dt id=''>-</dt><dd><div class='html-p'>Variations in the updating process enable it to overcome several optimization problems of varying difficulty.</div></dd><dt id=''>-</dt><dd><div class='html-p'>Having a strong exploration operator due to employing both the inverse incomplete gamma function and the inverse random number in an effective way.</div></dd><dt id=''>-</dt><dd><div class='html-p'>Enjoying in strong exploitation operator aiding in exploiting the regions around the current solution, the best-so-far solution, and solutions selected randomly from the population.</div></dd></dl></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><dl class='html-bullet'><dt id=''>-</dt><dd><div class='html-p'>Having a weak exploration operator due to its inability to find the optimal solution for most fixed-dimensional multimodal optimization problems with many local minima necessitates using a strong exploration operator. On the contrary, our proposed algorithm can solve all fixed-dimensional multimodal problems.</div></dd><dt id=''>-</dt><dd><div class='html-p'>Its performance for some unimodal problems requiring a strong exploitation operator is subpar.</div></dd></dl></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><dl class='html-bullet'><dt id=''>-</dt><dd><div class='html-p'>Its updating process is limited due to its reliance solely on refraction and reflection.</div></dd><dt id=''>-</dt><dd><div class='html-p'>Slower convergence speed than LSO due to the weakness of its exploitation operator.</div></dd></dl></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t005"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t005'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t005"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 5.</b> Parameters of the compared algorithms. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t005" > <div class="html-caption" ><b>Table 5.</b> Parameters of the compared algorithms.</div> <table > <thead ><tr ><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Algorithms</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Parameters</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Value</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Algorithms</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Parameters</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Value</th></tr></thead><tbody ><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>GWO (2014)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Convergence constant <span class='html-italic'>a</span><br><span class='html-italic'>N</span></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Decreases Linearly from 2 to 0<br>20</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>SMA (2020)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><span class='html-italic'>z</span><br><span class='html-italic'>N</span></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.03<br>20</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>WOA (2017)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Convergence constant <span class='html-italic'>a</span><br>Spiral factor <span class='html-italic'>b</span><br><span class='html-italic'>N</span></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Decreases Linearly from 2 to 0<br>1<br>20</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>GTO (2021)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><span class='html-italic'>p</span><br><span class='html-italic'>Beta</span><br><span class='html-italic'>w</span><br><span class='html-italic'>N</span></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.03<br>3<br>8<br>20</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>EO (2020)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><span class='html-italic'>a</span><sub>1</sub><br><span class='html-italic'>a</span><sub>2</sub><br><span class='html-italic'>V</span><br><span class='html-italic'>GP</span><br><span class='html-italic'>N</span></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >2<br>1<br>1<br>0.5<br>20</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>AVOA (2021)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><math display='inline'> <semantics> <mrow> <mi>Alpha</mi> <mtext> </mtext> <mo>(</mo> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </semantics> </math><br><math display='inline'> <semantics> <mrow> <mi>Beta</mi> <mtext> </mtext> <mo>(</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics> </math><br><math display='inline'> <semantics> <mrow> <mi>Gamma</mi> <mtext> </mtext> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> </semantics> </math><br><math display='inline'> <semantics> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> </mrow> </semantics> </math><br><math display='inline'> <semantics> <mrow> <msub> <mi>P</mi> <mn>2</mn> </msub> </mrow> </semantics> </math><br><math display='inline'> <semantics> <mrow> <msub> <mi>P</mi> <mn>3</mn> </msub> </mrow> </semantics> </math><br><span class='html-italic'>N</span></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.8<br>0.2<br>2.5<br>0.6<br>0.4<br>0.6<br>20</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>RUN (2021)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><span class='html-italic'>a</span><br><span class='html-italic'>b</span><br><span class='html-italic'>N</span></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >20<br>12<br>20</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>RSA (2022)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Alpha<br>Beta<br>N</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.1<br>0.1<br>20</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>GBO(2020)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >pr<br><math display='inline'><semantics> <mrow> <msub> <mi>β</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math><br><math display='inline'><semantics> <mrow> <msub> <mi>β</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math><br>N</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >0.5<br>0.2<br>1.2<br>20</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>DE</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><br>Crossover rate<br>Scaling factor<br>N</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><br>0.5<br>0.5<br>20</td></tr><tr ><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' ><b>SSA (2017)</b></td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >c1<br>N</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Decreases from 2 to 0<br>20</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' > </td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' > </td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' > </td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t006"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t006'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t006"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 6.</b> Avr and SD of CEC2005 for 25 independent runs (The bolded value is the best overall). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t006" > <div class="html-caption" ><b>Table 6.</b> Avr and SD of CEC2005 for 25 independent runs (The bolded value is the best overall).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >F</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Index</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >LSO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F1</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >4.27 × 10<sup>−7</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.5 × 10<sup>−145</sup></td><td align='center' valign='middle' class='html-align-center' >3.90 × 10<sup>−70</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.20 × 10<sup>−3</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >7.68 × 10<sup>−8</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >7.4 × 10<sup>−145</sup></td><td align='center' valign='middle' class='html-align-center' >7.34 × 10<sup>−70</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.75 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F2</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.94 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.6 × 10<sup>−283</sup></td><td align='center' valign='middle' class='html-align-center' >1.5 × 10<sup>−238</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.58 × 10<sup>−84</sup></td><td align='center' valign='middle' class='html-align-center' >1.33 × 10<sup>−41</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.70 × 10<sup>−5</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.20 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.02 × 10<sup>−83</sup></td><td align='center' valign='middle' class='html-align-center' >1.04 × 10<sup>−41</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.57 × 10<sup>−5</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F3</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.92 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >7.25 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.63 × 10<sup>−10</sup></td><td align='center' valign='middle' class='html-align-center' >8.42 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.44 × 10<sup>5</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.24 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.42 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.01 × 10<sup>−9</sup></td><td align='center' valign='middle' class='html-align-center' >3.97 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.81 × 10<sup>4</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F4</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.22 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >3.9 × 10<sup>−253</sup></td><td align='center' valign='middle' class='html-align-center' >1.3 × 10<sup>−196</sup></td><td align='center' valign='middle' class='html-align-center' >7.78 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.87 × 10<sup>−16</sup></td><td align='center' valign='middle' class='html-align-center' >2.72 × 10<sup>−8</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >9.59 × 10<sup>1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.81 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.30 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.57 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >1.26 × 10<sup>−7</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.17 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F5</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >9.70 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >3.85 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >9.31 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >9.65 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >9.74 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >8.30 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >1.03 × 10<sup>−5</sup></td><td align='center' valign='middle' class='html-align-center' >9.43 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >9.76 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >9.90 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.88 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.66 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >6.18 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.25 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >2.49 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.12 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >6.96 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.14 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >1.35 × 10<sup>−5</sup></td><td align='center' valign='middle' class='html-align-center' >9.49 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >6.38 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >0.00 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.87 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >5.76 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >High-dimensional multimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F6</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.33 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >7.57 × 10<sup>2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >5.60 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.26 × 10<sup>1</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>1</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F7</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>8.88 × 10<sup>−16</sup></b></td><td align='center' valign='middle' class='html-align-center' >5.71 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>8.88 × 10<sup>−16</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>8.88 × 10<sup>−16</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.14 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' ><b>8.88 × 10<sup>−16</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>8.88 × 10<sup>−16</sup></b></td><td align='center' valign='middle' class='html-align-center' >5.63 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >2.61 × 10<sup>−14</sup></td><td align='center' valign='middle' class='html-align-center' ><b>8.88 × 10<sup>−16</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>8.88 × 10<sup>−16</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.23 × 10<sup>−4</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.30 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.72 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.70 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >3.41 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.05 × 10<sup>−4</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F8</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >9.68 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >6.37 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.31 × 10<sup>−4</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >5.56 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.49 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.80 × 10<sup>−3</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F9</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >4.67 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >1.52 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.25 × 10<sup>−6</sup></td><td align='center' valign='middle' class='html-align-center' >1.95 × 10<sup>−6</sup></td><td align='center' valign='middle' class='html-align-center' >9.70 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >8.72 × 10<sup>−7</sup></td><td align='center' valign='middle' class='html-align-center' ><b>5.07 × 10<sup>−9</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.85 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >2.91 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.33 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >6.83 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >1.59 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >1.91 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >2.95 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.11 × 10<sup>−6</sup></td><td align='center' valign='middle' class='html-align-center' >6.52 × 10<sup>−6</sup></td><td align='center' valign='middle' class='html-align-center' >3.24 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >1.14 × 10<sup>−6</sup></td><td align='center' valign='middle' class='html-align-center' ><b>2.63 × 10<sup>−9</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.79 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >7.27 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >0.00 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.08 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >6.68 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F10</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >8.42 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.66 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >1.87 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.11 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.50 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >3.95 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' ><b>3.05 × 10<sup>−9</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.70 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >6.55 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.72 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >5.29 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >2.54 × 10<sup>4</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >1.47 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.71 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >2.63 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.15 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >5.79 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >2.03 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' ><b>4.10 × 10<sup>−9</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.05 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >4.13 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >8.77 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >5.86 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >6.44 × 10<sup>4</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Fixed-dimensional multimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F11</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>9.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>9.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>9.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' >4.63 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.24 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>9.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.06 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.06 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >5.76 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >4.47 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>9.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.23 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.24 × 10<sup>−16</sup></td><td align='center' valign='middle' class='html-align-center' >4.12 × 10<sup>−17</sup></td><td align='center' valign='middle' class='html-align-center' >3.84 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.49 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.62 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.62 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.64 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >3.30 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >8.55 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >9.59 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F12</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>3.07 × 10<sup>−4</sup></b></td><td align='center' valign='middle' class='html-align-center' >8.50 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >4.30 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >7.04 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >6.30 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >5.52 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >3.08 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >4.38 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >6.32 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >1.58 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >4.82 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >2.68 × 10<sup>−3</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>2.01 × 10<sup>−19</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.64 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >3.17 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >4.62 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >3.47 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >4.12 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >4.17 × 10<sup>−8</sup></td><td align='center' valign='middle' class='html-align-center' >8.13 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >9.35 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >1.03 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >2.95 × 10<sup>−4</sup></td><td align='center' valign='middle' class='html-align-center' >6.01 × 10<sup>−3</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F13</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.03 × 10<sup>0</sup></b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >6.78 × 10<sup>−16</sup></td><td align='center' valign='middle' class='html-align-center' >3.72 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >6.78 × 10<sup>−16</sup></td><td align='center' valign='middle' class='html-align-center' >2.05 × 10<sup>−13</sup></td><td align='center' valign='middle' class='html-align-center' >5.36 × 10<sup>−12</sup></td><td align='center' valign='middle' class='html-align-center' >6.52 × 10<sup>−16</sup></td><td align='center' valign='middle' class='html-align-center' ><b>5.13 × 10<sup>−16</sup></b></td><td align='center' valign='middle' class='html-align-center' >6.39 × 10<sup>−16</sup></td><td align='center' valign='middle' class='html-align-center' >8.86 × 10<sup>−10</sup></td><td align='center' valign='middle' class='html-align-center' >1.59 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >1.72 × 10<sup>−11</sup></td><td align='center' valign='middle' class='html-align-center' >6.78 × 10<sup>−16</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F14</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' >4.18 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.98 × 10<sup>−1</sup></b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.70 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >0.00 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.17 × 10<sup>−11</sup></td><td align='center' valign='middle' class='html-align-center' >3.58 × 10<sup>−7</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >5.93 × 10<sup>−8</sup></td><td align='center' valign='middle' class='html-align-center' >4.66 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.82 × 10<sup>−9</sup></td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F15</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.00 × 10<sup>0</sup></b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>1.31 × 10<sup>−15</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.94 × 10<sup>−14</sup></td><td align='center' valign='middle' class='html-align-center' >1.40 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >1.43 × 10<sup>−13</sup></td><td align='center' valign='middle' class='html-align-center' >1.63 × 10<sup>−5</sup></td><td align='center' valign='middle' class='html-align-center' >1.33 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >5.67 × 10<sup>−8</sup></td><td align='center' valign='middle' class='html-align-center' >1.39 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >3.76 × 10<sup>−6</sup></td><td align='center' valign='middle' class='html-align-center' >5.55 × 10<sup>−5</sup></td><td align='center' valign='middle' class='html-align-center' >2.27 × 10<sup>−13</sup></td><td align='center' valign='middle' class='html-align-center' >1.83 × 10<sup>−15</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F16</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >−3.80 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−3.86 × 10<sup>0</sup></b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>2.71 × 10<sup>−15</sup></b></td><td align='center' valign='middle' class='html-align-center' >5.11 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >2.71 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >4.64 × 10<sup>−6</sup></td><td align='center' valign='middle' class='html-align-center' >2.98 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >2.59 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >2.20 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >2.00 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >2.79 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >5.08 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.64 × 10<sup>−9</sup></td><td align='center' valign='middle' class='html-align-center' ><b>2.71 × 10<sup>−15</sup></b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F17</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>−3.32 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >−3.07 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−3.27 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−3.24 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−2.71 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−3.07 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−3.07 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−3.24 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−3.19 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−1.74 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−3.03 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−3.12 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>1.32 × 10<sup>−15</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.57 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >6.62 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >7.38 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >4.14 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >2.49 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.31 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >8.05 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >1.19 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >5.78 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.05 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.01 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F18</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>−1.02 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' >−5.12 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−7.36 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−6.31 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−4.51 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−7.44 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−7.25 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−7.18 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−7.36 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−4.79 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−6.37 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−3.64 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>7.23 × 10<sup>−15</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.16 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.44 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.47 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.33 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.48 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.84 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >3.20 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >3.50 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.60 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >2.53 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.28 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F19</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>−1.04 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' >−9.27 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−8.63 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>−1.04 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' >−9.38 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>−1.04 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.04 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' >−1.00 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >−1.00 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >−5.09 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>−1.04 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' >−9.35 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >1.48 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >2.35 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.55 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >6.54 × 10<sup>−10</sup></td><td align='center' valign='middle' class='html-align-center' >2.36 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>7.38 × 10<sup>−16</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.14 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >1.34 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.35 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >8.85 × 10<sup>−7</sup></td><td align='center' valign='middle' class='html-align-center' >1.91 × 10<sup>−5</sup></td><td align='center' valign='middle' class='html-align-center' >2.42 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F20</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>−1.05 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' >−9.74 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−8.91 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >−1.04 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >−9.23 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>−1.05 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>−1.05 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' >−1.00 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >−1.04 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >−5.13 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' ><b>−1.05 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' >−9.16 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>1.81 × 10<sup>−15</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.10 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.52 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.87 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >2.42 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.06 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >3.32 × 10<sup>−15</sup></td><td align='center' valign='middle' class='html-align-center' >1.65 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.87 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.85 × 10<sup>−6</sup></td><td align='center' valign='middle' class='html-align-center' >1.91 × 10<sup>−5</sup></td><td align='center' valign='middle' class='html-align-center' >2.80 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t007"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t007'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t007"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 7.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC2005 test suite (F1–F20). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t007" > <div class="html-caption" ><b>Table 7.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC2005 test suite (F1–F20).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Fun</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SCA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RFO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th></tr></thead><tbody ><tr ><td colspan='12' align='center' valign='middle' class='html-align-center' >Unimodal</td></tr><tr ><td align='center' valign='middle' style='border-top:solid thin' class='html-align-center' >F1</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F2</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F3</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.75 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.37 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.37 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.26 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.37 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.37 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.61 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.61 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.37 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.37 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.26 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F4</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F5</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.56 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.53 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.51 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.97 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.44 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.17 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' class='html-align-center' >High-dimensional multimodal</td></tr><tr ><td align='center' valign='middle' style='border-top:solid thin' class='html-align-center' >F6</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >5.69 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >3.47 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >5.57 × 10<sup>−10</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F7</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.11 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.56 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.52 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.38 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.79 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.87 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.32 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.88 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F8</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.64 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.74 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.89 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.69 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.05 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F9</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F10</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.75 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.37 × 10<sup>−13</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.73 × 10<sup>−13</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' class='html-align-center' >Fixed-dimensional multimodal</td></tr><tr ><td align='center' valign='middle' style='border-top:solid thin' class='html-align-center' >F11</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F12</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.20 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.46 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−10</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F13</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.92 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.33 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.57 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.10 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.15 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F14</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>−13</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.52 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.19 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.61 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.58 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.33 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.55 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.28 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.43 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.97 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.89 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.58 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.55 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.69 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.23 × 10<sup>−5</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F16</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.19 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.18 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.47 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.09 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F17</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.15 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.66 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.43 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.70 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.46 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.46 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.11 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.46 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.24 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.46 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.46 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.46 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.30 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F19</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.54 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.67 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.15 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F20</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.44 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.62 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.15 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.90 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.46 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.21 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.16 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.44 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.88 × 10<sup>−5</sup></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t008"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t008'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t008"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 8.</b> Avr and SD of CEC2014 for 25 independent runs (The bolded value is the best overall). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t008" > <div class="html-caption" ><b>Table 8.</b> Avr and SD of CEC2014 for 25 independent runs (The bolded value is the best overall).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >F</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Index</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >LSO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F21</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1.00 × 10<sup>2</sup></b></td><td align='center' valign='middle' class='html-align-center' >5.29 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.73 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.29 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >8.21 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >2.81 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.87 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >5.06 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >5.03 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >1.32 × 10<sup>8</sup></td><td align='center' valign='middle' class='html-align-center' >1.53 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >3.05 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>7.09 × 10<sup>−11</sup></b></td><td align='center' valign='middle' class='html-align-center' >5.03 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >2.04 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.11 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >6.51 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >3.88 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.12 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >6.63 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >3.43 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >8.55 × 10<sup>7</sup></td><td align='center' valign='middle' class='html-align-center' >4.14 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >7.78 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F22</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>200.00</b></td><td align='center' valign='middle' class='html-align-center' >3802.99</td><td align='center' valign='middle' class='html-align-center' >272.45</td><td align='center' valign='middle' class='html-align-center' >4382.91</td><td align='center' valign='middle' class='html-align-center' >940,880.88</td><td align='center' valign='middle' class='html-align-center' >557.78</td><td align='center' valign='middle' class='html-align-center' >3404.48</td><td align='center' valign='middle' class='html-align-center' >1.30 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >5.69 × 10<sup>7</sup></td><td align='center' valign='middle' class='html-align-center' >7.09 × 10<sup>9</sup></td><td align='center' valign='middle' class='html-align-center' >5.94 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >7.20 × 10<sup>2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>4.22 × 10<sup>−14</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.65 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.30 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5.25 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >7.23 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >8.18 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >3.67 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.65 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >2.88 × 10<sup>8</sup></td><td align='center' valign='middle' class='html-align-center' >1.99 × 10<sup>9</sup></td><td align='center' valign='middle' class='html-align-center' >3.99 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >2.07 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F23</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>300.00</b></td><td align='center' valign='middle' class='html-align-center' >3450.21</td><td align='center' valign='middle' class='html-align-center' >314.70</td><td align='center' valign='middle' class='html-align-center' >1401.82</td><td align='center' valign='middle' class='html-align-center' >43,769.75</td><td align='center' valign='middle' class='html-align-center' >315.07</td><td align='center' valign='middle' class='html-align-center' >1571.60</td><td align='center' valign='middle' class='html-align-center' >426.51</td><td align='center' valign='middle' class='html-align-center' >7388.05</td><td align='center' valign='middle' class='html-align-center' >8368.14</td><td align='center' valign='middle' class='html-align-center' >2407.10</td><td align='center' valign='middle' class='html-align-center' >301.79</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >2845.55</td><td align='center' valign='middle' class='html-align-center' >21.18</td><td align='center' valign='middle' class='html-align-center' >566.37</td><td align='center' valign='middle' class='html-align-center' >28,043.51</td><td align='center' valign='middle' class='html-align-center' >50.45</td><td align='center' valign='middle' class='html-align-center' >1128.64</td><td align='center' valign='middle' class='html-align-center' >203.06</td><td align='center' valign='middle' class='html-align-center' >4648.72</td><td align='center' valign='middle' class='html-align-center' >2959.58</td><td align='center' valign='middle' class='html-align-center' >1895.90</td><td align='center' valign='middle' class='html-align-center' >9.80</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Multimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F24</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>405.36</b></td><td align='center' valign='middle' class='html-align-center' >425.87</td><td align='center' valign='middle' class='html-align-center' >424.51</td><td align='center' valign='middle' class='html-align-center' >416.08</td><td align='center' valign='middle' class='html-align-center' >438.61</td><td align='center' valign='middle' class='html-align-center' >419.47</td><td align='center' valign='middle' class='html-align-center' >419.49</td><td align='center' valign='middle' class='html-align-center' >423.67</td><td align='center' valign='middle' class='html-align-center' >434.97</td><td align='center' valign='middle' class='html-align-center' >1735.39</td><td align='center' valign='middle' class='html-align-center' >424.29</td><td align='center' valign='middle' class='html-align-center' >425.97</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>11.85</b></td><td align='center' valign='middle' class='html-align-center' >15.12</td><td align='center' valign='middle' class='html-align-center' >15.98</td><td align='center' valign='middle' class='html-align-center' >15.73</td><td align='center' valign='middle' class='html-align-center' >22.17</td><td align='center' valign='middle' class='html-align-center' >16.71</td><td align='center' valign='middle' class='html-align-center' >17.93</td><td align='center' valign='middle' class='html-align-center' >16.02</td><td align='center' valign='middle' class='html-align-center' >18.96</td><td align='center' valign='middle' class='html-align-center' >992.19</td><td align='center' valign='middle' class='html-align-center' >15.13</td><td align='center' valign='middle' class='html-align-center' >14.33</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F25</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >520.03</td><td align='center' valign='middle' class='html-align-center' >520.04</td><td align='center' valign='middle' class='html-align-center' >520.07</td><td align='center' valign='middle' class='html-align-center' >520.09</td><td align='center' valign='middle' class='html-align-center' >520.14</td><td align='center' valign='middle' class='html-align-center' >520.11</td><td align='center' valign='middle' class='html-align-center' >520.06</td><td align='center' valign='middle' class='html-align-center' >520.11</td><td align='center' valign='middle' class='html-align-center' >520.42</td><td align='center' valign='middle' class='html-align-center' >520.43</td><td align='center' valign='middle' class='html-align-center' ><b>519.43</b></td><td align='center' valign='middle' class='html-align-center' >520.21</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >1.18 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >8.81 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >9.18 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >1.06 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >9.39 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >7.89 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >7.39 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >7.25 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >0.08</td><td align='center' valign='middle' class='html-align-center' >0.08</td><td align='center' valign='middle' class='html-align-center' ><b>3.66</b></td><td align='center' valign='middle' class='html-align-center' >0.06</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F26</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>600.32</b></td><td align='center' valign='middle' class='html-align-center' >603.66</td><td align='center' valign='middle' class='html-align-center' >604.32</td><td align='center' valign='middle' class='html-align-center' >605.49</td><td align='center' valign='middle' class='html-align-center' >607.99</td><td align='center' valign='middle' class='html-align-center' >605.26</td><td align='center' valign='middle' class='html-align-center' >605.99</td><td align='center' valign='middle' class='html-align-center' >601.51</td><td align='center' valign='middle' class='html-align-center' >6.02 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >609.69</td><td align='center' valign='middle' class='html-align-center' >604.19</td><td align='center' valign='middle' class='html-align-center' >600.84</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.61</b></td><td align='center' valign='middle' class='html-align-center' >1.59</td><td align='center' valign='middle' class='html-align-center' >1.65</td><td align='center' valign='middle' class='html-align-center' >1.14</td><td align='center' valign='middle' class='html-align-center' >1.76</td><td align='center' valign='middle' class='html-align-center' >1.53</td><td align='center' valign='middle' class='html-align-center' >1.48</td><td align='center' valign='middle' class='html-align-center' >1.21</td><td align='center' valign='middle' class='html-align-center' >1.16 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >0.80</td><td align='center' valign='middle' class='html-align-center' >1.24</td><td align='center' valign='middle' class='html-align-center' >0.83</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F27</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>700.02</b></td><td align='center' valign='middle' class='html-align-center' >700.26</td><td align='center' valign='middle' class='html-align-center' >700.17</td><td align='center' valign='middle' class='html-align-center' >700.35</td><td align='center' valign='middle' class='html-align-center' >701.09</td><td align='center' valign='middle' class='html-align-center' >700.29</td><td align='center' valign='middle' class='html-align-center' >700.41</td><td align='center' valign='middle' class='html-align-center' >700.05</td><td align='center' valign='middle' class='html-align-center' >701.20</td><td align='center' valign='middle' class='html-align-center' >795.27</td><td align='center' valign='middle' class='html-align-center' >700.24</td><td align='center' valign='middle' class='html-align-center' >700.08</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.01</b></td><td align='center' valign='middle' class='html-align-center' >0.10</td><td align='center' valign='middle' class='html-align-center' >0.08</td><td align='center' valign='middle' class='html-align-center' >0.23</td><td align='center' valign='middle' class='html-align-center' >0.46</td><td align='center' valign='middle' class='html-align-center' >0.19</td><td align='center' valign='middle' class='html-align-center' >0.31</td><td align='center' valign='middle' class='html-align-center' >0.04</td><td align='center' valign='middle' class='html-align-center' >0.95</td><td align='center' valign='middle' class='html-align-center' >27.14</td><td align='center' valign='middle' class='html-align-center' >0.12</td><td align='center' valign='middle' class='html-align-center' >0.10</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F28</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>800.50</b></td><td align='center' valign='middle' class='html-align-center' >821.33</td><td align='center' valign='middle' class='html-align-center' >821.40</td><td align='center' valign='middle' class='html-align-center' >821.03</td><td align='center' valign='middle' class='html-align-center' >844.05</td><td align='center' valign='middle' class='html-align-center' >823.18</td><td align='center' valign='middle' class='html-align-center' >813.43</td><td align='center' valign='middle' class='html-align-center' >807.33</td><td align='center' valign='middle' class='html-align-center' >812.15</td><td align='center' valign='middle' class='html-align-center' >876.28</td><td align='center' valign='middle' class='html-align-center' >801.79</td><td align='center' valign='middle' class='html-align-center' >800.66</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>6.27 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' >1.11 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >9.72 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >7.53 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.58 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.02 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >5.44 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >4.71 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >5.70</td><td align='center' valign='middle' class='html-align-center' >8.27</td><td align='center' valign='middle' class='html-align-center' >1.15</td><td align='center' valign='middle' class='html-align-center' >1.05</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F29</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>907.18</b></td><td align='center' valign='middle' class='html-align-center' >920.93</td><td align='center' valign='middle' class='html-align-center' >925.22</td><td align='center' valign='middle' class='html-align-center' >937.34</td><td align='center' valign='middle' class='html-align-center' >950.57</td><td align='center' valign='middle' class='html-align-center' >931.37</td><td align='center' valign='middle' class='html-align-center' >931.48</td><td align='center' valign='middle' class='html-align-center' >914.54</td><td align='center' valign='middle' class='html-align-center' >914.91</td><td align='center' valign='middle' class='html-align-center' >960.42</td><td align='center' valign='middle' class='html-align-center' >915.39</td><td align='center' valign='middle' class='html-align-center' >914.65</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>2.58</b></td><td align='center' valign='middle' class='html-align-center' >9.25</td><td align='center' valign='middle' class='html-align-center' >8.72</td><td align='center' valign='middle' class='html-align-center' >5.75</td><td align='center' valign='middle' class='html-align-center' >19.54</td><td align='center' valign='middle' class='html-align-center' >10.36</td><td align='center' valign='middle' class='html-align-center' >9.98</td><td align='center' valign='middle' class='html-align-center' >5.91</td><td align='center' valign='middle' class='html-align-center' >6.21</td><td align='center' valign='middle' class='html-align-center' >5.63</td><td align='center' valign='middle' class='html-align-center' >5.69</td><td align='center' valign='middle' class='html-align-center' >3.48</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F30</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1010.54</b></td><td align='center' valign='middle' class='html-align-center' >1571.44</td><td align='center' valign='middle' class='html-align-center' >1457.97</td><td align='center' valign='middle' class='html-align-center' >1186.07</td><td align='center' valign='middle' class='html-align-center' >1610.08</td><td align='center' valign='middle' class='html-align-center' >1580.21</td><td align='center' valign='middle' class='html-align-center' >1104.67</td><td align='center' valign='middle' class='html-align-center' >1169.31</td><td align='center' valign='middle' class='html-align-center' >1370.39</td><td align='center' valign='middle' class='html-align-center' >2107.30</td><td align='center' valign='middle' class='html-align-center' >1145.39</td><td align='center' valign='middle' class='html-align-center' >1068.08</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>30.00</b></td><td align='center' valign='middle' class='html-align-center' >257.58</td><td align='center' valign='middle' class='html-align-center' >238.56</td><td align='center' valign='middle' class='html-align-center' >120.79</td><td align='center' valign='middle' class='html-align-center' >352.70</td><td align='center' valign='middle' class='html-align-center' >273.00</td><td align='center' valign='middle' class='html-align-center' >76.89</td><td align='center' valign='middle' class='html-align-center' >146.30</td><td align='center' valign='middle' class='html-align-center' >141.26</td><td align='center' valign='middle' class='html-align-center' >167.86</td><td align='center' valign='middle' class='html-align-center' >110.93</td><td align='center' valign='middle' class='html-align-center' >53.37</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F31</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >1888.08</td><td align='center' valign='middle' class='html-align-center' >2.37 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.98 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' ><b>1.69 × 10<sup>3</sup></b></td><td align='center' valign='middle' class='html-align-center' >2.99 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.99 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.87 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.71 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1823.92</td><td align='center' valign='middle' class='html-align-center' >2501.55</td><td align='center' valign='middle' class='html-align-center' >1950.17</td><td align='center' valign='middle' class='html-align-center' >2447.27</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >202.29</td><td align='center' valign='middle' class='html-align-center' >3.49 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >3.28 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' ><b>2.35 × 10<sup>2</sup></b></td><td align='center' valign='middle' class='html-align-center' >5.38 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >3.30 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >3.50 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >3.17 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >405.02</td><td align='center' valign='middle' class='html-align-center' >203.72</td><td align='center' valign='middle' class='html-align-center' >258.79</td><td align='center' valign='middle' class='html-align-center' >193.51</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F32</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1200.12</b></td><td align='center' valign='middle' class='html-align-center' >1200.24</td><td align='center' valign='middle' class='html-align-center' >1200.29</td><td align='center' valign='middle' class='html-align-center' >1200.26</td><td align='center' valign='middle' class='html-align-center' >1200.77</td><td align='center' valign='middle' class='html-align-center' >1200.39</td><td align='center' valign='middle' class='html-align-center' >1200.35</td><td align='center' valign='middle' class='html-align-center' >1200.32</td><td align='center' valign='middle' class='html-align-center' >1200.75</td><td align='center' valign='middle' class='html-align-center' >1201.28</td><td align='center' valign='middle' class='html-align-center' >1200.14</td><td align='center' valign='middle' class='html-align-center' >1200.64</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.04</b></td><td align='center' valign='middle' class='html-align-center' >0.19</td><td align='center' valign='middle' class='html-align-center' >0.18</td><td align='center' valign='middle' class='html-align-center' >0.16</td><td align='center' valign='middle' class='html-align-center' >0.29</td><td align='center' valign='middle' class='html-align-center' >0.30</td><td align='center' valign='middle' class='html-align-center' >0.20</td><td align='center' valign='middle' class='html-align-center' >0.17</td><td align='center' valign='middle' class='html-align-center' >0.65</td><td align='center' valign='middle' class='html-align-center' >0.30</td><td align='center' valign='middle' class='html-align-center' >0.08</td><td align='center' valign='middle' class='html-align-center' >0.11</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F33</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >1300.16</td><td align='center' valign='middle' class='html-align-center' >1300.25</td><td align='center' valign='middle' class='html-align-center' >1300.28</td><td align='center' valign='middle' class='html-align-center' >1300.46</td><td align='center' valign='middle' class='html-align-center' >1300.44</td><td align='center' valign='middle' class='html-align-center' >1300.36</td><td align='center' valign='middle' class='html-align-center' >1300.46</td><td align='center' valign='middle' class='html-align-center' ><b>1300.08</b></td><td align='center' valign='middle' class='html-align-center' >1300.19</td><td align='center' valign='middle' class='html-align-center' >1303.57</td><td align='center' valign='middle' class='html-align-center' >1300.29</td><td align='center' valign='middle' class='html-align-center' >1300.16</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.04</b></td><td align='center' valign='middle' class='html-align-center' >0.11</td><td align='center' valign='middle' class='html-align-center' >0.14</td><td align='center' valign='middle' class='html-align-center' >0.18</td><td align='center' valign='middle' class='html-align-center' >0.17</td><td align='center' valign='middle' class='html-align-center' >0.18</td><td align='center' valign='middle' class='html-align-center' >0.21</td><td align='center' valign='middle' class='html-align-center' ><b>0.04</b></td><td align='center' valign='middle' class='html-align-center' >0.05</td><td align='center' valign='middle' class='html-align-center' >0.74</td><td align='center' valign='middle' class='html-align-center' >0.09</td><td align='center' valign='middle' class='html-align-center' ><b>0.04</b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F34</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1400.19</b></td><td align='center' valign='middle' class='html-align-center' >1400.23</td><td align='center' valign='middle' class='html-align-center' >1400.29</td><td align='center' valign='middle' class='html-align-center' >1400.42</td><td align='center' valign='middle' class='html-align-center' >1400.32</td><td align='center' valign='middle' class='html-align-center' >1400.29</td><td align='center' valign='middle' class='html-align-center' >1400.40</td><td align='center' valign='middle' class='html-align-center' >1400.20</td><td align='center' valign='middle' class='html-align-center' >1400.29</td><td align='center' valign='middle' class='html-align-center' >1414.11</td><td align='center' valign='middle' class='html-align-center' >1400.21</td><td align='center' valign='middle' class='html-align-center' ><b>1400.19</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.06</b></td><td align='center' valign='middle' class='html-align-center' >0.12</td><td align='center' valign='middle' class='html-align-center' >0.11</td><td align='center' valign='middle' class='html-align-center' >0.22</td><td align='center' valign='middle' class='html-align-center' >0.23</td><td align='center' valign='middle' class='html-align-center' >0.17</td><td align='center' valign='middle' class='html-align-center' >0.23</td><td align='center' valign='middle' class='html-align-center' >0.09</td><td align='center' valign='middle' class='html-align-center' >0.19</td><td align='center' valign='middle' class='html-align-center' >6.76</td><td align='center' valign='middle' class='html-align-center' >0.10</td><td align='center' valign='middle' class='html-align-center' ><b>0.06</b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F35</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1500.82</b></td><td align='center' valign='middle' class='html-align-center' >1501.59</td><td align='center' valign='middle' class='html-align-center' >1501.76</td><td align='center' valign='middle' class='html-align-center' >1503.14</td><td align='center' valign='middle' class='html-align-center' >1506.37</td><td align='center' valign='middle' class='html-align-center' >1503.11</td><td align='center' valign='middle' class='html-align-center' >1503.73</td><td align='center' valign='middle' class='html-align-center' >1501.13</td><td align='center' valign='middle' class='html-align-center' >1501.90</td><td align='center' valign='middle' class='html-align-center' >6731.90</td><td align='center' valign='middle' class='html-align-center' >1501.09</td><td align='center' valign='middle' class='html-align-center' >1501.76</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.22</b></td><td align='center' valign='middle' class='html-align-center' >0.64</td><td align='center' valign='middle' class='html-align-center' >0.88</td><td align='center' valign='middle' class='html-align-center' >2.12</td><td align='center' valign='middle' class='html-align-center' >2.84</td><td align='center' valign='middle' class='html-align-center' >2.23</td><td align='center' valign='middle' class='html-align-center' >2.13</td><td align='center' valign='middle' class='html-align-center' >0.40</td><td align='center' valign='middle' class='html-align-center' >0.89</td><td align='center' valign='middle' class='html-align-center' >5786.78</td><td align='center' valign='middle' class='html-align-center' >0.41</td><td align='center' valign='middle' class='html-align-center' >0.29</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F36</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1602.35</b></td><td align='center' valign='middle' class='html-align-center' >1602.70</td><td align='center' valign='middle' class='html-align-center' >1603.03</td><td align='center' valign='middle' class='html-align-center' >1602.85</td><td align='center' valign='middle' class='html-align-center' >1603.36</td><td align='center' valign='middle' class='html-align-center' >1603.06</td><td align='center' valign='middle' class='html-align-center' >1602.98</td><td align='center' valign='middle' class='html-align-center' ><b>1602.35</b></td><td align='center' valign='middle' class='html-align-center' >1602.64</td><td align='center' valign='middle' class='html-align-center' >1603.75</td><td align='center' valign='middle' class='html-align-center' >1602.76</td><td align='center' valign='middle' class='html-align-center' >1602.61</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.38</b></td><td align='center' valign='middle' class='html-align-center' >0.59</td><td align='center' valign='middle' class='html-align-center' >0.42</td><td align='center' valign='middle' class='html-align-center' >0.41</td><td align='center' valign='middle' class='html-align-center' >0.35</td><td align='center' valign='middle' class='html-align-center' >0.30</td><td align='center' valign='middle' class='html-align-center' >0.42</td><td align='center' valign='middle' class='html-align-center' >0.52</td><td align='center' valign='middle' class='html-align-center' >0.50</td><td align='center' valign='middle' class='html-align-center' >0.13</td><td align='center' valign='middle' class='html-align-center' >0.32</td><td align='center' valign='middle' class='html-align-center' >0.30</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F37</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1717.64</b></td><td align='center' valign='middle' class='html-align-center' >5.92 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >2.27 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >7.35 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.62 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >2.58 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.07 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >5.48 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >63,042.13</td><td align='center' valign='middle' class='html-align-center' >477,784.19</td><td align='center' valign='middle' class='html-align-center' >7797.80</td><td align='center' valign='middle' class='html-align-center' >1873.12</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>22.39</b></td><td align='center' valign='middle' class='html-align-center' >3.38 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >3.96 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >3.66 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >2.13 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.25 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >8.26 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >3.86 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >129,932.00</td><td align='center' valign='middle' class='html-align-center' >109,260.79</td><td align='center' valign='middle' class='html-align-center' >5659.29</td><td align='center' valign='middle' class='html-align-center' >434.71</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F38</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1800.85</b></td><td align='center' valign='middle' class='html-align-center' >14,446.41</td><td align='center' valign='middle' class='html-align-center' >2319.86</td><td align='center' valign='middle' class='html-align-center' >9682.72</td><td align='center' valign='middle' class='html-align-center' >9696.15</td><td align='center' valign='middle' class='html-align-center' >1885.23</td><td align='center' valign='middle' class='html-align-center' >10,609.80</td><td align='center' valign='middle' class='html-align-center' >9356.68</td><td align='center' valign='middle' class='html-align-center' >10,610.02</td><td align='center' valign='middle' class='html-align-center' >40,067.12</td><td align='center' valign='middle' class='html-align-center' >11,422.57</td><td align='center' valign='middle' class='html-align-center' >1803.87</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.59</b></td><td align='center' valign='middle' class='html-align-center' >10,403.74</td><td align='center' valign='middle' class='html-align-center' >1076.15</td><td align='center' valign='middle' class='html-align-center' >3555.45</td><td align='center' valign='middle' class='html-align-center' >10,255.49</td><td align='center' valign='middle' class='html-align-center' >46.85</td><td align='center' valign='middle' class='html-align-center' >8071.84</td><td align='center' valign='middle' class='html-align-center' >5017.19</td><td align='center' valign='middle' class='html-align-center' >5783.75</td><td align='center' valign='middle' class='html-align-center' >46,220.31</td><td align='center' valign='middle' class='html-align-center' >10,865.40</td><td align='center' valign='middle' class='html-align-center' >10.84</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F39</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1900.46</b></td><td align='center' valign='middle' class='html-align-center' >1903.04</td><td align='center' valign='middle' class='html-align-center' >1902.59</td><td align='center' valign='middle' class='html-align-center' >1903.04</td><td align='center' valign='middle' class='html-align-center' >1906.12</td><td align='center' valign='middle' class='html-align-center' >1902.60</td><td align='center' valign='middle' class='html-align-center' >1903.54</td><td align='center' valign='middle' class='html-align-center' >1901.84</td><td align='center' valign='middle' class='html-align-center' >1902.94</td><td align='center' valign='middle' class='html-align-center' >1921.26</td><td align='center' valign='middle' class='html-align-center' >1901.82</td><td align='center' valign='middle' class='html-align-center' >1900.90</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.27</b></td><td align='center' valign='middle' class='html-align-center' >0.98</td><td align='center' valign='middle' class='html-align-center' >1.41</td><td align='center' valign='middle' class='html-align-center' >0.87</td><td align='center' valign='middle' class='html-align-center' >1.40</td><td align='center' valign='middle' class='html-align-center' >1.26</td><td align='center' valign='middle' class='html-align-center' >1.28</td><td align='center' valign='middle' class='html-align-center' >0.96</td><td align='center' valign='middle' class='html-align-center' >0.92</td><td align='center' valign='middle' class='html-align-center' >16.06</td><td align='center' valign='middle' class='html-align-center' >0.65</td><td align='center' valign='middle' class='html-align-center' >0.69</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F40</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >2000.58</td><td align='center' valign='middle' class='html-align-center' >3418.70</td><td align='center' valign='middle' class='html-align-center' >2108.10</td><td align='center' valign='middle' class='html-align-center' >5264.04</td><td align='center' valign='middle' class='html-align-center' >8152.17</td><td align='center' valign='middle' class='html-align-center' >2056.55</td><td align='center' valign='middle' class='html-align-center' >8010.60</td><td align='center' valign='middle' class='html-align-center' >2121.66</td><td align='center' valign='middle' class='html-align-center' >5439.36</td><td align='center' valign='middle' class='html-align-center' >12,224.03</td><td align='center' valign='middle' class='html-align-center' >7640.34</td><td align='center' valign='middle' class='html-align-center' ><b>2000.40</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >0.47</td><td align='center' valign='middle' class='html-align-center' >1781.61</td><td align='center' valign='middle' class='html-align-center' >82.85</td><td align='center' valign='middle' class='html-align-center' >2176.01</td><td align='center' valign='middle' class='html-align-center' >4028.66</td><td align='center' valign='middle' class='html-align-center' >41.84</td><td align='center' valign='middle' class='html-align-center' >4783.81</td><td align='center' valign='middle' class='html-align-center' >74.55</td><td align='center' valign='middle' class='html-align-center' >3862.97</td><td align='center' valign='middle' class='html-align-center' >6303.34</td><td align='center' valign='middle' class='html-align-center' >6685.14</td><td align='center' valign='middle' class='html-align-center' ><b>0.44</b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F41</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2100.53</b></td><td align='center' valign='middle' class='html-align-center' >5295.60</td><td align='center' valign='middle' class='html-align-center' >2406.77</td><td align='center' valign='middle' class='html-align-center' >4838.31</td><td align='center' valign='middle' class='html-align-center' >90,227.96</td><td align='center' valign='middle' class='html-align-center' >2505.53</td><td align='center' valign='middle' class='html-align-center' >9494.63</td><td align='center' valign='middle' class='html-align-center' >2388.96</td><td align='center' valign='middle' class='html-align-center' >14,867.98</td><td align='center' valign='middle' class='html-align-center' >1.27 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >4290.40</td><td align='center' valign='middle' class='html-align-center' >2117.89</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>2.91 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' >4294.39</td><td align='center' valign='middle' class='html-align-center' >239.42</td><td align='center' valign='middle' class='html-align-center' >3095.47</td><td align='center' valign='middle' class='html-align-center' >202,328.35</td><td align='center' valign='middle' class='html-align-center' >261.30</td><td align='center' valign='middle' class='html-align-center' >6275.18</td><td align='center' valign='middle' class='html-align-center' >209.28</td><td align='center' valign='middle' class='html-align-center' >35,581.10</td><td align='center' valign='middle' class='html-align-center' >2.94 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >3157.23</td><td align='center' valign='middle' class='html-align-center' >44.31</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F42</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2200.81</b></td><td align='center' valign='middle' class='html-align-center' >2252.82</td><td align='center' valign='middle' class='html-align-center' >2272.19</td><td align='center' valign='middle' class='html-align-center' >2307.98</td><td align='center' valign='middle' class='html-align-center' >2309.89</td><td align='center' valign='middle' class='html-align-center' >2238.24</td><td align='center' valign='middle' class='html-align-center' >2271.60</td><td align='center' valign='middle' class='html-align-center' >2250.98</td><td align='center' valign='middle' class='html-align-center' >2285.78</td><td align='center' valign='middle' class='html-align-center' >2409.37</td><td align='center' valign='middle' class='html-align-center' >2228.42</td><td align='center' valign='middle' class='html-align-center' >2213.01</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>3.02</b></td><td align='center' valign='middle' class='html-align-center' >47.42</td><td align='center' valign='middle' class='html-align-center' >64.65</td><td align='center' valign='middle' class='html-align-center' >57.30</td><td align='center' valign='middle' class='html-align-center' >71.55</td><td align='center' valign='middle' class='html-align-center' >33.97</td><td align='center' valign='middle' class='html-align-center' >60.97</td><td align='center' valign='middle' class='html-align-center' >53.87</td><td align='center' valign='middle' class='html-align-center' >60.31</td><td align='center' valign='middle' class='html-align-center' >81.86</td><td align='center' valign='middle' class='html-align-center' >34.60</td><td align='center' valign='middle' class='html-align-center' >25.09</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F43</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >2581.99</td><td align='center' valign='middle' class='html-align-center' >2629.46</td><td align='center' valign='middle' class='html-align-center' ><b>2500.00</b></td><td align='center' valign='middle' class='html-align-center' >2500.00</td><td align='center' valign='middle' class='html-align-center' >2616.13</td><td align='center' valign='middle' class='html-align-center' >2500.00</td><td align='center' valign='middle' class='html-align-center' >2500.00</td><td align='center' valign='middle' class='html-align-center' >2629.46</td><td align='center' valign='middle' class='html-align-center' >2634.66</td><td align='center' valign='middle' class='html-align-center' >2500.00</td><td align='center' valign='middle' class='html-align-center' >2500.00</td><td align='center' valign='middle' class='html-align-center' >2629.46</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >63.45</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >46.43</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >4.52</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >0.00</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F44</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2515.12</b></td><td align='center' valign='middle' class='html-align-center' >2552.08</td><td align='center' valign='middle' class='html-align-center' >2532.18</td><td align='center' valign='middle' class='html-align-center' >2547.45</td><td align='center' valign='middle' class='html-align-center' >2574.63</td><td align='center' valign='middle' class='html-align-center' >2582.52</td><td align='center' valign='middle' class='html-align-center' >2582.07</td><td align='center' valign='middle' class='html-align-center' >2580.26</td><td align='center' valign='middle' class='html-align-center' >2543.12</td><td align='center' valign='middle' class='html-align-center' >2538.92</td><td align='center' valign='middle' class='html-align-center' >2599.43</td><td align='center' valign='middle' class='html-align-center' >2536.95</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>3.96</b></td><td align='center' valign='middle' class='html-align-center' >8.58</td><td align='center' valign='middle' class='html-align-center' >9.38</td><td align='center' valign='middle' class='html-align-center' >25.72</td><td align='center' valign='middle' class='html-align-center' >30.06</td><td align='center' valign='middle' class='html-align-center' >23.13</td><td align='center' valign='middle' class='html-align-center' >28.47</td><td align='center' valign='middle' class='html-align-center' >27.82</td><td align='center' valign='middle' class='html-align-center' >36.12</td><td align='center' valign='middle' class='html-align-center' >29.87</td><td align='center' valign='middle' class='html-align-center' >1.78</td><td align='center' valign='middle' class='html-align-center' >29.67</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F45</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2633.50</b></td><td align='center' valign='middle' class='html-align-center' >2696.49</td><td align='center' valign='middle' class='html-align-center' >2678.16</td><td align='center' valign='middle' class='html-align-center' >2682.90</td><td align='center' valign='middle' class='html-align-center' >2696.47</td><td align='center' valign='middle' class='html-align-center' >2694.01</td><td align='center' valign='middle' class='html-align-center' >2696.55</td><td align='center' valign='middle' class='html-align-center' >2696.56</td><td align='center' valign='middle' class='html-align-center' >2690.04</td><td align='center' valign='middle' class='html-align-center' >2693.41</td><td align='center' valign='middle' class='html-align-center' >2699.88</td><td align='center' valign='middle' class='html-align-center' >2694.51</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>10.38</b></td><td align='center' valign='middle' class='html-align-center' >1.17 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >3.10 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >2.32 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.05 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.29 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.36 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >8.76 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >21.16</td><td align='center' valign='middle' class='html-align-center' >18.89</td><td align='center' valign='middle' class='html-align-center' >0.65</td><td align='center' valign='middle' class='html-align-center' >17.36</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F46</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2700.14</b></td><td align='center' valign='middle' class='html-align-center' >2700.65</td><td align='center' valign='middle' class='html-align-center' >2700.18</td><td align='center' valign='middle' class='html-align-center' >2700.28</td><td align='center' valign='middle' class='html-align-center' >2700.17</td><td align='center' valign='middle' class='html-align-center' >2700.34</td><td align='center' valign='middle' class='html-align-center' >2700.24</td><td align='center' valign='middle' class='html-align-center' >2700.30</td><td align='center' valign='middle' class='html-align-center' >2703.40</td><td align='center' valign='middle' class='html-align-center' >2703.48</td><td align='center' valign='middle' class='html-align-center' >2709.86</td><td align='center' valign='middle' class='html-align-center' >2700.22</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.04</b></td><td align='center' valign='middle' class='html-align-center' >0.12</td><td align='center' valign='middle' class='html-align-center' >0.08</td><td align='center' valign='middle' class='html-align-center' >0.17</td><td align='center' valign='middle' class='html-align-center' >0.08</td><td align='center' valign='middle' class='html-align-center' >0.17</td><td align='center' valign='middle' class='html-align-center' >0.12</td><td align='center' valign='middle' class='html-align-center' >0.15</td><td align='center' valign='middle' class='html-align-center' >18.25</td><td align='center' valign='middle' class='html-align-center' >18.23</td><td align='center' valign='middle' class='html-align-center' >19.72</td><td align='center' valign='middle' class='html-align-center' >0.08</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F47</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2823.87</b></td><td align='center' valign='middle' class='html-align-center' >3002.57</td><td align='center' valign='middle' class='html-align-center' >3010.43</td><td align='center' valign='middle' class='html-align-center' >2842.06</td><td align='center' valign='middle' class='html-align-center' >2874.38</td><td align='center' valign='middle' class='html-align-center' >3084.23</td><td align='center' valign='middle' class='html-align-center' >2854.69</td><td align='center' valign='middle' class='html-align-center' >2893.57</td><td align='center' valign='middle' class='html-align-center' >3027.04</td><td align='center' valign='middle' class='html-align-center' >3032.32</td><td align='center' valign='middle' class='html-align-center' >2900.00</td><td align='center' valign='middle' class='html-align-center' >2893.39</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>154.31</b></td><td align='center' valign='middle' class='html-align-center' >171.71</td><td align='center' valign='middle' class='html-align-center' >158.02</td><td align='center' valign='middle' class='html-align-center' >90.03</td><td align='center' valign='middle' class='html-align-center' >66.44</td><td align='center' valign='middle' class='html-align-center' >135.58</td><td align='center' valign='middle' class='html-align-center' >83.53</td><td align='center' valign='middle' class='html-align-center' >35.20</td><td align='center' valign='middle' class='html-align-center' >116.70</td><td align='center' valign='middle' class='html-align-center' >98.70</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >36.19</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F48</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >3155.87</td><td align='center' valign='middle' class='html-align-center' >3278.03</td><td align='center' valign='middle' class='html-align-center' >3209.81</td><td align='center' valign='middle' class='html-align-center' >3000.00</td><td align='center' valign='middle' class='html-align-center' >3000.00</td><td align='center' valign='middle' class='html-align-center' >3349.79</td><td align='center' valign='middle' class='html-align-center' >3000.00</td><td align='center' valign='middle' class='html-align-center' >3000.00</td><td align='center' valign='middle' class='html-align-center' >3255.21</td><td align='center' valign='middle' class='html-align-center' >3248.91</td><td align='center' valign='middle' class='html-align-center' >3000.00</td><td align='center' valign='middle' class='html-align-center' >3000.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >67.80</td><td align='center' valign='middle' class='html-align-center' >53.44</td><td align='center' valign='middle' class='html-align-center' >58.10</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >159.11</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >79.92</td><td align='center' valign='middle' class='html-align-center' >78.45</td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >0.00</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F49</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>3076.80</b></td><td align='center' valign='middle' class='html-align-center' >9000.02</td><td align='center' valign='middle' class='html-align-center' >61,591.92</td><td align='center' valign='middle' class='html-align-center' >183,714.47</td><td align='center' valign='middle' class='html-align-center' >3824.55</td><td align='center' valign='middle' class='html-align-center' >244,952.31</td><td align='center' valign='middle' class='html-align-center' >74,649.01</td><td align='center' valign='middle' class='html-align-center' >3643.30</td><td align='center' valign='middle' class='html-align-center' >413,389.22</td><td align='center' valign='middle' class='html-align-center' >545,401.12</td><td align='center' valign='middle' class='html-align-center' >3100.00</td><td align='center' valign='middle' class='html-align-center' >36,135.91</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>48.99</b></td><td align='center' valign='middle' class='html-align-center' >6617.79</td><td align='center' valign='middle' class='html-align-center' >314,631.79</td><td align='center' valign='middle' class='html-align-center' >551,709.97</td><td align='center' valign='middle' class='html-align-center' >588.88</td><td align='center' valign='middle' class='html-align-center' >625,545.37</td><td align='center' valign='middle' class='html-align-center' >390,869.63</td><td align='center' valign='middle' class='html-align-center' >622.98</td><td align='center' valign='middle' class='html-align-center' >836,534.22</td><td align='center' valign='middle' class='html-align-center' >1.02 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >0.00</td><td align='center' valign='middle' class='html-align-center' >179,113.96</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' > </td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' >3523.72</td><td align='center' valign='middle' class='html-align-center' >4608.66</td><td align='center' valign='middle' class='html-align-center' >4241.32</td><td align='center' valign='middle' class='html-align-center' >3990.04</td><td align='center' valign='middle' class='html-align-center' >4470.61</td><td align='center' valign='middle' class='html-align-center' >5031.79</td><td align='center' valign='middle' class='html-align-center' >3991.63</td><td align='center' valign='middle' class='html-align-center' >4425.03</td><td align='center' valign='middle' class='html-align-center' >3810.93</td><td align='center' valign='middle' class='html-align-center' >4322.67</td><td align='center' valign='middle' class='html-align-center' ><b><span class='underline'>3200.00</span></b></td><td align='center' valign='middle' class='html-align-center' >3608.58</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F50</td><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' >52.44</td><td align='center' valign='middle' class='html-align-center' >608.68</td><td align='center' valign='middle' class='html-align-center' >508.03</td><td align='center' valign='middle' class='html-align-center' >545.97</td><td align='center' valign='middle' class='html-align-center' >451.97</td><td align='center' valign='middle' class='html-align-center' >982.39</td><td align='center' valign='middle' class='html-align-center' >332.96</td><td align='center' valign='middle' class='html-align-center' >523.84</td><td align='center' valign='middle' class='html-align-center' >304.68</td><td align='center' valign='middle' class='html-align-center' >692.91</td><td align='center' valign='middle' class='html-align-center' ><b><span class='underline'>0.00</span></b></td><td align='center' valign='middle' class='html-align-center' >307.80</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b><span class='underline'>1.00</span></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t009"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t009'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t009"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 9.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC-2014 test suite (F21–F50). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t009" > <div class="html-caption" ><b>Table 9.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC-2014 test suite (F21–F50).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Fun</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F21</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F22</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.85 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F23</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.16 × 10<sup>−2</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Multimodal</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F24</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.49 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.41 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.52 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.42 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.93 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.86 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−8</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F25</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.57 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.79 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.29 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.85 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.13 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.77 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.48 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.43 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F26</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.07 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.69 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.19 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.90 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F27</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.78 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.08 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.84 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F28</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.55 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.54 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.55 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.55 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.54 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.54 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.78 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.55 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.55 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.68 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.08 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.06 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.96 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.73 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.25 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.29 × 10<sup>−9</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F30</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.35 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.45 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.43 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.45 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.42 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.78 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.65 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.35 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.42 × 10<sup>−9</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F31</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.52 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.12 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.08 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.52 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.52 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.15 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.50 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.92 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.71 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.92 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F32</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.44 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.61 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.01 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.48 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.07 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.25 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.65 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F33</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.77 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.07 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.55 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.36 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.01 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.47 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.02 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.87 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F34</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.60 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.83 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.29 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.03 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.83 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.17 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.38 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.53 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F35</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.04 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.61 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.98 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.89 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.44 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.10 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.07 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F36</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.69 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.09 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.16 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.26 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.78 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.71 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.19 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.32 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.24 × 10<sup>−2</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F37</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.37 × 10<sup>−5</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F38</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.20 × 10<sup>−5</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F39</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.07 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.92 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.68 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F41</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.32 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F42</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.49 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.92 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.15 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.51 × 10<sup>−2</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.45 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.45 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.51 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.45 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.45 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.43 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.45 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.45 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.39 × 10<sup>−4</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F44</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.86 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.09 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.79 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.16 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.38 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.16 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.16 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.78 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.23 × 10<sup>−9</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.77 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.93 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.93 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.44 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.60 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.34 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.53 × 10<sup>−8</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F46</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.97 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.60 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.67 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.07 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.29 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.53 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.49 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.01 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.29 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.13 × 10<sup>−5</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F47</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.25 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.68 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.76 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.15 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.50 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.91 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.80 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.60 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.32 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.77 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.35 × 10<sup>−4</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F48</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.56 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.76 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.82 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.69 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.51 × 10<sup>−9</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F49</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.17 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.52 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.58 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.89 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.83 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F50</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.20 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.47 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.82 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.97 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.60 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.56 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.50 × 10<sup>−2</sup></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t010"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t010'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t010"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 10.</b> Avr and SD of CEC2017 for 25 independent runs (The bolded value is the best overall). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t010" > <div class="html-caption" ><b>Table 10.</b> Avr and SD of CEC2017 for 25 independent runs (The bolded value is the best overall).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >F</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Index</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >LSO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F51</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1.00 × 10<sup>2</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.02 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.75 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >3.41 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >4.66 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >3.13 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >4.12 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.79 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >4.87 × 10<sup>7</sup></td><td align='center' valign='middle' class='html-align-center' >1.14 × 10<sup>10</sup></td><td align='center' valign='middle' class='html-align-center' >7.46 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >4.60 × 10<sup>2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>3.56 × 10<sup>−14</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.59 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.71 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.77 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >6.92 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >3.24 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >4.04 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.93 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.26 × 10<sup>8</sup></td><td align='center' valign='middle' class='html-align-center' >3.64 × 10<sup>9</sup></td><td align='center' valign='middle' class='html-align-center' >4.48 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.19 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F52</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>300.00</b></td><td align='center' valign='middle' class='html-align-center' >300.00</td><td align='center' valign='middle' class='html-align-center' >300.00</td><td align='center' valign='middle' class='html-align-center' >300.00</td><td align='center' valign='middle' class='html-align-center' >1617.08</td><td align='center' valign='middle' class='html-align-center' >300.00</td><td align='center' valign='middle' class='html-align-center' >300.00</td><td align='center' valign='middle' class='html-align-center' >300.00</td><td align='center' valign='middle' class='html-align-center' >2542.88</td><td align='center' valign='middle' class='html-align-center' >10,392.16</td><td align='center' valign='middle' class='html-align-center' >300.00</td><td align='center' valign='middle' class='html-align-center' >300.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' >7.30 × 10<sup>−10</sup></td><td align='center' valign='middle' class='html-align-center' >4.88 × 10<sup>−13</sup></td><td align='center' valign='middle' class='html-align-center' >1.17 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >1.73 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >4.70 × 10<sup>−10</sup></td><td align='center' valign='middle' class='html-align-center' >2.93 × 10<sup>−9</sup></td><td align='center' valign='middle' class='html-align-center' >4.92 × 10<sup>−10</sup></td><td align='center' valign='middle' class='html-align-center' >2.02 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >3.07 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.62 × 10<sup>−3</sup></td><td align='center' valign='middle' class='html-align-center' >1.06 × 10<sup>−14</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Multimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F53</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>400.00</b></td><td align='center' valign='middle' class='html-align-center' >405.28</td><td align='center' valign='middle' class='html-align-center' >401.36</td><td align='center' valign='middle' class='html-align-center' >403.35</td><td align='center' valign='middle' class='html-align-center' >428.61</td><td align='center' valign='middle' class='html-align-center' >402.75</td><td align='center' valign='middle' class='html-align-center' >408.82</td><td align='center' valign='middle' class='html-align-center' >403.49</td><td align='center' valign='middle' class='html-align-center' >418.77</td><td align='center' valign='middle' class='html-align-center' >1226.25</td><td align='center' valign='middle' class='html-align-center' >408.54</td><td align='center' valign='middle' class='html-align-center' >406.25</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>6.83 × 10<sup>−7</sup></b></td><td align='center' valign='middle' class='html-align-center' >10.06</td><td align='center' valign='middle' class='html-align-center' >0.49</td><td align='center' valign='middle' class='html-align-center' >2.18</td><td align='center' valign='middle' class='html-align-center' >36.66</td><td align='center' valign='middle' class='html-align-center' >1.38</td><td align='center' valign='middle' class='html-align-center' >17.51</td><td align='center' valign='middle' class='html-align-center' >1.28</td><td align='center' valign='middle' class='html-align-center' >20.57</td><td align='center' valign='middle' class='html-align-center' >579.17</td><td align='center' valign='middle' class='html-align-center' >13.53</td><td align='center' valign='middle' class='html-align-center' >1.24</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F54</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>506.00</b></td><td align='center' valign='middle' class='html-align-center' >519.80</td><td align='center' valign='middle' class='html-align-center' >526.09</td><td align='center' valign='middle' class='html-align-center' >533.13</td><td align='center' valign='middle' class='html-align-center' >555.93</td><td align='center' valign='middle' class='html-align-center' >526.93</td><td align='center' valign='middle' class='html-align-center' >537.46</td><td align='center' valign='middle' class='html-align-center' >516.16</td><td align='center' valign='middle' class='html-align-center' >519.42</td><td align='center' valign='middle' class='html-align-center' >584.87</td><td align='center' valign='middle' class='html-align-center' >514.30</td><td align='center' valign='middle' class='html-align-center' >514.54</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>2.22</b></td><td align='center' valign='middle' class='html-align-center' >9.38</td><td align='center' valign='middle' class='html-align-center' >12.38</td><td align='center' valign='middle' class='html-align-center' >8.51</td><td align='center' valign='middle' class='html-align-center' >26.06</td><td align='center' valign='middle' class='html-align-center' >12.75</td><td align='center' valign='middle' class='html-align-center' >14.36</td><td align='center' valign='middle' class='html-align-center' >5.66</td><td align='center' valign='middle' class='html-align-center' >8.78</td><td align='center' valign='middle' class='html-align-center' >15.78</td><td align='center' valign='middle' class='html-align-center' >6.18</td><td align='center' valign='middle' class='html-align-center' >3.31</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F55</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>600.00</b></td><td align='center' valign='middle' class='html-align-center' >609.86</td><td align='center' valign='middle' class='html-align-center' >601.84</td><td align='center' valign='middle' class='html-align-center' >618.91</td><td align='center' valign='middle' class='html-align-center' >638.19</td><td align='center' valign='middle' class='html-align-center' >609.14</td><td align='center' valign='middle' class='html-align-center' >610.07</td><td align='center' valign='middle' class='html-align-center' >600.06</td><td align='center' valign='middle' class='html-align-center' >601.57</td><td align='center' valign='middle' class='html-align-center' >645.54</td><td align='center' valign='middle' class='html-align-center' >600.15</td><td align='center' valign='middle' class='html-align-center' >600.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' class='html-align-center' >7.52 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >3.06 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >8.59 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.37 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >7.16 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >6.92 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >3.17 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >2.14 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >6.58 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >4.35 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >2.08 × 10<sup>−6</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F56</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>717.07</b></td><td align='center' valign='middle' class='html-align-center' >732.33</td><td align='center' valign='middle' class='html-align-center' >737.11</td><td align='center' valign='middle' class='html-align-center' >762.79</td><td align='center' valign='middle' class='html-align-center' >775.78</td><td align='center' valign='middle' class='html-align-center' >756.31</td><td align='center' valign='middle' class='html-align-center' >765.61</td><td align='center' valign='middle' class='html-align-center' >723.21</td><td align='center' valign='middle' class='html-align-center' >732.39</td><td align='center' valign='middle' class='html-align-center' >806.57</td><td align='center' valign='middle' class='html-align-center' >726.05</td><td align='center' valign='middle' class='html-align-center' >726.99</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>2.58</b></td><td align='center' valign='middle' class='html-align-center' >9.87</td><td align='center' valign='middle' class='html-align-center' >11.64</td><td align='center' valign='middle' class='html-align-center' >12.14</td><td align='center' valign='middle' class='html-align-center' >23.43</td><td align='center' valign='middle' class='html-align-center' >17.12</td><td align='center' valign='middle' class='html-align-center' >20.50</td><td align='center' valign='middle' class='html-align-center' >5.84</td><td align='center' valign='middle' class='html-align-center' >8.53</td><td align='center' valign='middle' class='html-align-center' >12.89</td><td align='center' valign='middle' class='html-align-center' >7.54</td><td align='center' valign='middle' class='html-align-center' >3.86</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F57</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>806.62</b></td><td align='center' valign='middle' class='html-align-center' >821.03</td><td align='center' valign='middle' class='html-align-center' >822.97</td><td align='center' valign='middle' class='html-align-center' >827.43</td><td align='center' valign='middle' class='html-align-center' >840.82</td><td align='center' valign='middle' class='html-align-center' >824.91</td><td align='center' valign='middle' class='html-align-center' >828.43</td><td align='center' valign='middle' class='html-align-center' >813.33</td><td align='center' valign='middle' class='html-align-center' >815.53</td><td align='center' valign='middle' class='html-align-center' >854.98</td><td align='center' valign='middle' class='html-align-center' >816.32</td><td align='center' valign='middle' class='html-align-center' >814.53</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>3.42</b></td><td align='center' valign='middle' class='html-align-center' >10.61</td><td align='center' valign='middle' class='html-align-center' >8.06</td><td align='center' valign='middle' class='html-align-center' >6.00</td><td align='center' valign='middle' class='html-align-center' >16.83</td><td align='center' valign='middle' class='html-align-center' >9.14</td><td align='center' valign='middle' class='html-align-center' >10.25</td><td align='center' valign='middle' class='html-align-center' >4.85</td><td align='center' valign='middle' class='html-align-center' >5.62</td><td align='center' valign='middle' class='html-align-center' >7.67</td><td align='center' valign='middle' class='html-align-center' >7.52</td><td align='center' valign='middle' class='html-align-center' >3.69</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F58</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>900.00</b></td><td align='center' valign='middle' class='html-align-center' >903.92</td><td align='center' valign='middle' class='html-align-center' >924.99</td><td align='center' valign='middle' class='html-align-center' >1056.95</td><td align='center' valign='middle' class='html-align-center' >1498.95</td><td align='center' valign='middle' class='html-align-center' >993.42</td><td align='center' valign='middle' class='html-align-center' >1090.74</td><td align='center' valign='middle' class='html-align-center' >900.20</td><td align='center' valign='middle' class='html-align-center' >927.36</td><td align='center' valign='middle' class='html-align-center' >1542.77</td><td align='center' valign='middle' class='html-align-center' >900.00</td><td align='center' valign='middle' class='html-align-center' ><b><span class='underline'>900.00</span></b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' class='html-align-center' >7.74 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >4.43 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.01 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >4.48 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >8.62 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.80 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5.29 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >5.44 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.67 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >1.64 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' ><b><span class='underline'>0.00</span></b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b><span class='underline'>1.00</span></b></td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F59</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1350.60</b></td><td align='center' valign='middle' class='html-align-center' >1772.60</td><td align='center' valign='middle' class='html-align-center' >1835.55</td><td align='center' valign='middle' class='html-align-center' >1582.06</td><td align='center' valign='middle' class='html-align-center' >2158.15</td><td align='center' valign='middle' class='html-align-center' >2000.11</td><td align='center' valign='middle' class='html-align-center' >1852.32</td><td align='center' valign='middle' class='html-align-center' >1541.39</td><td align='center' valign='middle' class='html-align-center' >1639.92</td><td align='center' valign='middle' class='html-align-center' >2623.40</td><td align='center' valign='middle' class='html-align-center' >1601.13</td><td align='center' valign='middle' class='html-align-center' >1449.25</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>143.76</b></td><td align='center' valign='middle' class='html-align-center' >259.50</td><td align='center' valign='middle' class='html-align-center' >342.45</td><td align='center' valign='middle' class='html-align-center' >241.56</td><td align='center' valign='middle' class='html-align-center' >392.70</td><td align='center' valign='middle' class='html-align-center' >311.11</td><td align='center' valign='middle' class='html-align-center' >312.11</td><td align='center' valign='middle' class='html-align-center' >222.43</td><td align='center' valign='middle' class='html-align-center' >314.70</td><td align='center' valign='middle' class='html-align-center' >171.28</td><td align='center' valign='middle' class='html-align-center' >224.02</td><td align='center' valign='middle' class='html-align-center' >262.92</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F60</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1101.17</b></td><td align='center' valign='middle' class='html-align-center' >2158.63</td><td align='center' valign='middle' class='html-align-center' >1120.62</td><td align='center' valign='middle' class='html-align-center' >1126.24</td><td align='center' valign='middle' class='html-align-center' >1378.55</td><td align='center' valign='middle' class='html-align-center' >1126.78</td><td align='center' valign='middle' class='html-align-center' >1138.46</td><td align='center' valign='middle' class='html-align-center' >1108.96</td><td align='center' valign='middle' class='html-align-center' >1141.03</td><td align='center' valign='middle' class='html-align-center' >19,833.64</td><td align='center' valign='middle' class='html-align-center' >1116.24</td><td align='center' valign='middle' class='html-align-center' >1102.18</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>1.16</b></td><td align='center' valign='middle' class='html-align-center' >464.08</td><td align='center' valign='middle' class='html-align-center' >27.18</td><td align='center' valign='middle' class='html-align-center' >7.71</td><td align='center' valign='middle' class='html-align-center' >443.63</td><td align='center' valign='middle' class='html-align-center' >17.50</td><td align='center' valign='middle' class='html-align-center' >39.91</td><td align='center' valign='middle' class='html-align-center' >8.28</td><td align='center' valign='middle' class='html-align-center' >36.04</td><td align='center' valign='middle' class='html-align-center' >48,865.27</td><td align='center' valign='middle' class='html-align-center' >7.73</td><td align='center' valign='middle' class='html-align-center' >2.31</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F61</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1233.50</b></td><td align='center' valign='middle' class='html-align-center' >1.20 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >1.06 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >2.18 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >4.62 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >1.40 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >3.87 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.01 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >6.84 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >2.75 × 10<sup>8</sup></td><td align='center' valign='middle' class='html-align-center' >4.51 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >3.83 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>52.56</b></td><td align='center' valign='middle' class='html-align-center' >9.97 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.25 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >1.87 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >5.01 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >1.22 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >4.73 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >6.61 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >8.47 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.59 × 10<sup>8</sup></td><td align='center' valign='middle' class='html-align-center' >2.89 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >6.45 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F62</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1303.75</b></td><td align='center' valign='middle' class='html-align-center' >16,604.03</td><td align='center' valign='middle' class='html-align-center' >1815.02</td><td align='center' valign='middle' class='html-align-center' >10,568.95</td><td align='center' valign='middle' class='html-align-center' >16,564.10</td><td align='center' valign='middle' class='html-align-center' >1466.29</td><td align='center' valign='middle' class='html-align-center' >10,902.04</td><td align='center' valign='middle' class='html-align-center' >7359.12</td><td align='center' valign='middle' class='html-align-center' >11,669.47</td><td align='center' valign='middle' class='html-align-center' >49,487,747.88</td><td align='center' valign='middle' class='html-align-center' >15,922.68</td><td align='center' valign='middle' class='html-align-center' >1309.37</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>2.55</b></td><td align='center' valign='middle' class='html-align-center' >11,742.29</td><td align='center' valign='middle' class='html-align-center' >304.94</td><td align='center' valign='middle' class='html-align-center' >5329.62</td><td align='center' valign='middle' class='html-align-center' >13,327.54</td><td align='center' valign='middle' class='html-align-center' >149.89</td><td align='center' valign='middle' class='html-align-center' >8235.90</td><td align='center' valign='middle' class='html-align-center' >6429.88</td><td align='center' valign='middle' class='html-align-center' >6780.52</td><td align='center' valign='middle' class='html-align-center' >77,696,384.86</td><td align='center' valign='middle' class='html-align-center' >13,216.90</td><td align='center' valign='middle' class='html-align-center' >7.75</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F63</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1400.60</b></td><td align='center' valign='middle' class='html-align-center' >1498.92</td><td align='center' valign='middle' class='html-align-center' >1480.73</td><td align='center' valign='middle' class='html-align-center' >2086.66</td><td align='center' valign='middle' class='html-align-center' >1803.91</td><td align='center' valign='middle' class='html-align-center' >1457.81</td><td align='center' valign='middle' class='html-align-center' >1790.54</td><td align='center' valign='middle' class='html-align-center' >1455.40</td><td align='center' valign='middle' class='html-align-center' >2955.58</td><td align='center' valign='middle' class='html-align-center' >10,856.69</td><td align='center' valign='middle' class='html-align-center' >1581.31</td><td align='center' valign='middle' class='html-align-center' >1402.50</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.62</b></td><td align='center' valign='middle' class='html-align-center' >40.21</td><td align='center' valign='middle' class='html-align-center' >38.32</td><td align='center' valign='middle' class='html-align-center' >589.06</td><td align='center' valign='middle' class='html-align-center' >728.21</td><td align='center' valign='middle' class='html-align-center' >24.43</td><td align='center' valign='middle' class='html-align-center' >554.19</td><td align='center' valign='middle' class='html-align-center' >27.24</td><td align='center' valign='middle' class='html-align-center' >1781.83</td><td align='center' valign='middle' class='html-align-center' >18,963.95</td><td align='center' valign='middle' class='html-align-center' >642.53</td><td align='center' valign='middle' class='html-align-center' >5.99</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F64</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1500.29</b></td><td align='center' valign='middle' class='html-align-center' >2251.04</td><td align='center' valign='middle' class='html-align-center' >1593.26</td><td align='center' valign='middle' class='html-align-center' >2267.56</td><td align='center' valign='middle' class='html-align-center' >6197.31</td><td align='center' valign='middle' class='html-align-center' >1559.16</td><td align='center' valign='middle' class='html-align-center' >3328.43</td><td align='center' valign='middle' class='html-align-center' >1600.40</td><td align='center' valign='middle' class='html-align-center' >4020.66</td><td align='center' valign='middle' class='html-align-center' >11,243.41</td><td align='center' valign='middle' class='html-align-center' >2344.58</td><td align='center' valign='middle' class='html-align-center' >1500.66</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.34</b></td><td align='center' valign='middle' class='html-align-center' >883.94</td><td align='center' valign='middle' class='html-align-center' >74.16</td><td align='center' valign='middle' class='html-align-center' >783.57</td><td align='center' valign='middle' class='html-align-center' >4167.90</td><td align='center' valign='middle' class='html-align-center' >52.61</td><td align='center' valign='middle' class='html-align-center' >1537.34</td><td align='center' valign='middle' class='html-align-center' >76.54</td><td align='center' valign='middle' class='html-align-center' >3824.80</td><td align='center' valign='middle' class='html-align-center' >5685.89</td><td align='center' valign='middle' class='html-align-center' >1528.88</td><td align='center' valign='middle' class='html-align-center' >0.61</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F65</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1600.46</b></td><td align='center' valign='middle' class='html-align-center' >1709.98</td><td align='center' valign='middle' class='html-align-center' >1740.23</td><td align='center' valign='middle' class='html-align-center' >1783.44</td><td align='center' valign='middle' class='html-align-center' >1899.10</td><td align='center' valign='middle' class='html-align-center' >1701.90</td><td align='center' valign='middle' class='html-align-center' >1797.66</td><td align='center' valign='middle' class='html-align-center' >1664.51</td><td align='center' valign='middle' class='html-align-center' >1725.36</td><td align='center' valign='middle' class='html-align-center' >2127.09</td><td align='center' valign='middle' class='html-align-center' >1691.78</td><td align='center' valign='middle' class='html-align-center' >1611.95</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.26</b></td><td align='center' valign='middle' class='html-align-center' >117.63</td><td align='center' valign='middle' class='html-align-center' >107.09</td><td align='center' valign='middle' class='html-align-center' >108.96</td><td align='center' valign='middle' class='html-align-center' >116.03</td><td align='center' valign='middle' class='html-align-center' >85.88</td><td align='center' valign='middle' class='html-align-center' >123.84</td><td align='center' valign='middle' class='html-align-center' >66.64</td><td align='center' valign='middle' class='html-align-center' >107.02</td><td align='center' valign='middle' class='html-align-center' >117.70</td><td align='center' valign='middle' class='html-align-center' >78.57</td><td align='center' valign='middle' class='html-align-center' >25.13</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F66</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1702.47</b></td><td align='center' valign='middle' class='html-align-center' >1770.91</td><td align='center' valign='middle' class='html-align-center' >1761.37</td><td align='center' valign='middle' class='html-align-center' >1758.72</td><td align='center' valign='middle' class='html-align-center' >1793.83</td><td align='center' valign='middle' class='html-align-center' >1750.44</td><td align='center' valign='middle' class='html-align-center' >1780.81</td><td align='center' valign='middle' class='html-align-center' >1742.65</td><td align='center' valign='middle' class='html-align-center' >1749.74</td><td align='center' valign='middle' class='html-align-center' >1849.72</td><td align='center' valign='middle' class='html-align-center' >1756.58</td><td align='center' valign='middle' class='html-align-center' >1706.13</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>4.52</b></td><td align='center' valign='middle' class='html-align-center' >41.62</td><td align='center' valign='middle' class='html-align-center' >43.18</td><td align='center' valign='middle' class='html-align-center' >21.79</td><td align='center' valign='middle' class='html-align-center' >44.20</td><td align='center' valign='middle' class='html-align-center' >21.82</td><td align='center' valign='middle' class='html-align-center' >46.96</td><td align='center' valign='middle' class='html-align-center' >17.18</td><td align='center' valign='middle' class='html-align-center' >20.45</td><td align='center' valign='middle' class='html-align-center' >50.83</td><td align='center' valign='middle' class='html-align-center' >38.02</td><td align='center' valign='middle' class='html-align-center' >8.25</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F67</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1800.18</b></td><td align='center' valign='middle' class='html-align-center' >1.63 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >4.67 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.68 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >1.76 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >3.13 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.40 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >1.42 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >2.64 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >1.55 × 10<sup>8</sup></td><td align='center' valign='middle' class='html-align-center' >2.80 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >1.81 × 10<sup>3</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.27</b></td><td align='center' valign='middle' class='html-align-center' >1.01 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >4.95 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >9.94 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.31 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >2.79 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >9.74 × 10<sup>3</sup></td><td align='center' valign='middle' class='html-align-center' >1.08 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >1.63 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >3.78 × 10<sup>8</sup></td><td align='center' valign='middle' class='html-align-center' >1.42 × 10<sup>4</sup></td><td align='center' valign='middle' class='html-align-center' >8.76 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F68</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>1900.11</b></td><td align='center' valign='middle' class='html-align-center' >2551.75</td><td align='center' valign='middle' class='html-align-center' >1987.39</td><td align='center' valign='middle' class='html-align-center' >8849.78</td><td align='center' valign='middle' class='html-align-center' >52,403.86</td><td align='center' valign='middle' class='html-align-center' >1955.14</td><td align='center' valign='middle' class='html-align-center' >7572.26</td><td align='center' valign='middle' class='html-align-center' >1954.94</td><td align='center' valign='middle' class='html-align-center' >15,942.55</td><td align='center' valign='middle' class='html-align-center' >2,103,955.73</td><td align='center' valign='middle' class='html-align-center' >6030.92</td><td align='center' valign='middle' class='html-align-center' >1900.30</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.27</b></td><td align='center' valign='middle' class='html-align-center' >886.53</td><td align='center' valign='middle' class='html-align-center' >77.78</td><td align='center' valign='middle' class='html-align-center' >6841.59</td><td align='center' valign='middle' class='html-align-center' >85,717.24</td><td align='center' valign='middle' class='html-align-center' >49.95</td><td align='center' valign='middle' class='html-align-center' >6392.57</td><td align='center' valign='middle' class='html-align-center' >34.09</td><td align='center' valign='middle' class='html-align-center' >47,387.19</td><td align='center' valign='middle' class='html-align-center' >3,083,821.04</td><td align='center' valign='middle' class='html-align-center' >6113.48</td><td align='center' valign='middle' class='html-align-center' >0.55</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F69</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2000.23</b></td><td align='center' valign='middle' class='html-align-center' >2088.91</td><td align='center' valign='middle' class='html-align-center' >2093.27</td><td align='center' valign='middle' class='html-align-center' >2125.33</td><td align='center' valign='middle' class='html-align-center' >2205.96</td><td align='center' valign='middle' class='html-align-center' >2082.82</td><td align='center' valign='middle' class='html-align-center' >2098.95</td><td align='center' valign='middle' class='html-align-center' >2055.37</td><td align='center' valign='middle' class='html-align-center' >2081.95</td><td align='center' valign='middle' class='html-align-center' >2300.60</td><td align='center' valign='middle' class='html-align-center' >2025.85</td><td align='center' valign='middle' class='html-align-center' >2002.40</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>0.38</b></td><td align='center' valign='middle' class='html-align-center' >57.36</td><td align='center' valign='middle' class='html-align-center' >63.21</td><td align='center' valign='middle' class='html-align-center' >54.09</td><td align='center' valign='middle' class='html-align-center' >67.36</td><td align='center' valign='middle' class='html-align-center' >50.96</td><td align='center' valign='middle' class='html-align-center' >75.83</td><td align='center' valign='middle' class='html-align-center' >61.47</td><td align='center' valign='middle' class='html-align-center' >60.40</td><td align='center' valign='middle' class='html-align-center' >73.00</td><td align='center' valign='middle' class='html-align-center' >9.52</td><td align='center' valign='middle' class='html-align-center' >6.32</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F70</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2215.36</b></td><td align='center' valign='middle' class='html-align-center' >2276.54</td><td align='center' valign='middle' class='html-align-center' >2274.36</td><td align='center' valign='middle' class='html-align-center' >2233.44</td><td align='center' valign='middle' class='html-align-center' >2306.01</td><td align='center' valign='middle' class='html-align-center' >2222.91</td><td align='center' valign='middle' class='html-align-center' >2252.57</td><td align='center' valign='middle' class='html-align-center' >2312.71</td><td align='center' valign='middle' class='html-align-center' >2317.95</td><td align='center' valign='middle' class='html-align-center' >2337.09</td><td align='center' valign='middle' class='html-align-center' >2302.12</td><td align='center' valign='middle' class='html-align-center' >2308.46</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>34.45</b></td><td align='center' valign='middle' class='html-align-center' >58.28</td><td align='center' valign='middle' class='html-align-center' >60.70</td><td align='center' valign='middle' class='html-align-center' >54.68</td><td align='center' valign='middle' class='html-align-center' >64.60</td><td align='center' valign='middle' class='html-align-center' >48.29</td><td align='center' valign='middle' class='html-align-center' >67.13</td><td align='center' valign='middle' class='html-align-center' >22.59</td><td align='center' valign='middle' class='html-align-center' >5.76</td><td align='center' valign='middle' class='html-align-center' >59.07</td><td align='center' valign='middle' class='html-align-center' >45.92</td><td align='center' valign='middle' class='html-align-center' >36.96</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F71</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2291.09</b></td><td align='center' valign='middle' class='html-align-center' >2350.02</td><td align='center' valign='middle' class='html-align-center' >2300.86</td><td align='center' valign='middle' class='html-align-center' >2305.55</td><td align='center' valign='middle' class='html-align-center' >2579.66</td><td align='center' valign='middle' class='html-align-center' >2302.98</td><td align='center' valign='middle' class='html-align-center' >2337.24</td><td align='center' valign='middle' class='html-align-center' >2316.37</td><td align='center' valign='middle' class='html-align-center' >2348.58</td><td align='center' valign='middle' class='html-align-center' >3123.29</td><td align='center' valign='middle' class='html-align-center' >2387.92</td><td align='center' valign='middle' class='html-align-center' >2300.47</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>24.29</b></td><td align='center' valign='middle' class='html-align-center' >177.41</td><td align='center' valign='middle' class='html-align-center' >13.46</td><td align='center' valign='middle' class='html-align-center' >11.34</td><td align='center' valign='middle' class='html-align-center' >536.23</td><td align='center' valign='middle' class='html-align-center' >10.16</td><td align='center' valign='middle' class='html-align-center' >192.17</td><td align='center' valign='middle' class='html-align-center' >85.77</td><td align='center' valign='middle' class='html-align-center' >152.10</td><td align='center' valign='middle' class='html-align-center' >345.67</td><td align='center' valign='middle' class='html-align-center' >286.27</td><td align='center' valign='middle' class='html-align-center' >0.80</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F72</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2597.61</b></td><td align='center' valign='middle' class='html-align-center' >2620.27</td><td align='center' valign='middle' class='html-align-center' >2624.73</td><td align='center' valign='middle' class='html-align-center' >2620.77</td><td align='center' valign='middle' class='html-align-center' >2646.73</td><td align='center' valign='middle' class='html-align-center' >2631.16</td><td align='center' valign='middle' class='html-align-center' >2640.09</td><td align='center' valign='middle' class='html-align-center' >2615.40</td><td align='center' valign='middle' class='html-align-center' >2618.59</td><td align='center' valign='middle' class='html-align-center' >2701.83</td><td align='center' valign='middle' class='html-align-center' >2620.81</td><td align='center' valign='middle' class='html-align-center' >2612.69</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>56.22</b></td><td align='center' valign='middle' class='html-align-center' >8.88</td><td align='center' valign='middle' class='html-align-center' >12.93</td><td align='center' valign='middle' class='html-align-center' >6.95</td><td align='center' valign='middle' class='html-align-center' >21.63</td><td align='center' valign='middle' class='html-align-center' >17.77</td><td align='center' valign='middle' class='html-align-center' >17.08</td><td align='center' valign='middle' class='html-align-center' >5.37</td><td align='center' valign='middle' class='html-align-center' >7.67</td><td align='center' valign='middle' class='html-align-center' >22.14</td><td align='center' valign='middle' class='html-align-center' >8.01</td><td align='center' valign='middle' class='html-align-center' >4.21</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F73</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2650.08</b></td><td align='center' valign='middle' class='html-align-center' >2749.50</td><td align='center' valign='middle' class='html-align-center' >2698.60</td><td align='center' valign='middle' class='html-align-center' >2740.68</td><td align='center' valign='middle' class='html-align-center' >2765.21</td><td align='center' valign='middle' class='html-align-center' >2723.20</td><td align='center' valign='middle' class='html-align-center' >2735.38</td><td align='center' valign='middle' class='html-align-center' >2744.79</td><td align='center' valign='middle' class='html-align-center' >2748.32</td><td align='center' valign='middle' class='html-align-center' >2872.14</td><td align='center' valign='middle' class='html-align-center' >2755.56</td><td align='center' valign='middle' class='html-align-center' >2751.45</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>112.94</b></td><td align='center' valign='middle' class='html-align-center' >9.32</td><td align='center' valign='middle' class='html-align-center' >112.23</td><td align='center' valign='middle' class='html-align-center' >46.31</td><td align='center' valign='middle' class='html-align-center' >62.33</td><td align='center' valign='middle' class='html-align-center' >89.82</td><td align='center' valign='middle' class='html-align-center' >94.83</td><td align='center' valign='middle' class='html-align-center' >7.51</td><td align='center' valign='middle' class='html-align-center' >10.93</td><td align='center' valign='middle' class='html-align-center' >44.62</td><td align='center' valign='middle' class='html-align-center' >10.18</td><td align='center' valign='middle' class='html-align-center' >5.29</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F74</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2902.82</b></td><td align='center' valign='middle' class='html-align-center' >2921.26</td><td align='center' valign='middle' class='html-align-center' >2934.68</td><td align='center' valign='middle' class='html-align-center' >2935.62</td><td align='center' valign='middle' class='html-align-center' >2938.57</td><td align='center' valign='middle' class='html-align-center' >2919.17</td><td align='center' valign='middle' class='html-align-center' >2927.29</td><td align='center' valign='middle' class='html-align-center' >2930.31</td><td align='center' valign='middle' class='html-align-center' >2938.18</td><td align='center' valign='middle' class='html-align-center' >3349.41</td><td align='center' valign='middle' class='html-align-center' >2945.50</td><td align='center' valign='middle' class='html-align-center' >2929.57</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>13.79</b></td><td align='center' valign='middle' class='html-align-center' >24.61</td><td align='center' valign='middle' class='html-align-center' >29.09</td><td align='center' valign='middle' class='html-align-center' >20.38</td><td align='center' valign='middle' class='html-align-center' >63.39</td><td align='center' valign='middle' class='html-align-center' >66.92</td><td align='center' valign='middle' class='html-align-center' >24.71</td><td align='center' valign='middle' class='html-align-center' >22.34</td><td align='center' valign='middle' class='html-align-center' >28.39</td><td align='center' valign='middle' class='html-align-center' >117.10</td><td align='center' valign='middle' class='html-align-center' >33.08</td><td align='center' valign='middle' class='html-align-center' >22.53</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F75</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>2845.98</b></td><td align='center' valign='middle' class='html-align-center' >2975.91</td><td align='center' valign='middle' class='html-align-center' >2980.81</td><td align='center' valign='middle' class='html-align-center' >2993.65</td><td align='center' valign='middle' class='html-align-center' >3345.53</td><td align='center' valign='middle' class='html-align-center' >2989.79</td><td align='center' valign='middle' class='html-align-center' >3250.79</td><td align='center' valign='middle' class='html-align-center' >2973.06</td><td align='center' valign='middle' class='html-align-center' >3263.92</td><td align='center' valign='middle' class='html-align-center' >4146.59</td><td align='center' valign='middle' class='html-align-center' >3176.37</td><td align='center' valign='middle' class='html-align-center' >3001.41</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>103.36</b></td><td align='center' valign='middle' class='html-align-center' >249.95</td><td align='center' valign='middle' class='html-align-center' >114.69</td><td align='center' valign='middle' class='html-align-center' >213.33</td><td align='center' valign='middle' class='html-align-center' >446.62</td><td align='center' valign='middle' class='html-align-center' >129.74</td><td align='center' valign='middle' class='html-align-center' >529.36</td><td align='center' valign='middle' class='html-align-center' >253.79</td><td align='center' valign='middle' class='html-align-center' >442.08</td><td align='center' valign='middle' class='html-align-center' >290.19</td><td align='center' valign='middle' class='html-align-center' >427.89</td><td align='center' valign='middle' class='html-align-center' >231.12</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F76</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>3090.28</b></td><td align='center' valign='middle' class='html-align-center' >3092.86</td><td align='center' valign='middle' class='html-align-center' >3097.64</td><td align='center' valign='middle' class='html-align-center' >3094.37</td><td align='center' valign='middle' class='html-align-center' >3141.37</td><td align='center' valign='middle' class='html-align-center' >3099.69</td><td align='center' valign='middle' class='html-align-center' >3101.52</td><td align='center' valign='middle' class='html-align-center' >3095.37</td><td align='center' valign='middle' class='html-align-center' >3099.26</td><td align='center' valign='middle' class='html-align-center' >3189.41</td><td align='center' valign='middle' class='html-align-center' >3091.13</td><td align='center' valign='middle' class='html-align-center' >3092.04</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>1.78</b></td><td align='center' valign='middle' class='html-align-center' >3.08</td><td align='center' valign='middle' class='html-align-center' >4.37</td><td align='center' valign='middle' class='html-align-center' >2.27</td><td align='center' valign='middle' class='html-align-center' >37.19</td><td align='center' valign='middle' class='html-align-center' >18.88</td><td align='center' valign='middle' class='html-align-center' >8.87</td><td align='center' valign='middle' class='html-align-center' >8.41</td><td align='center' valign='middle' class='html-align-center' >12.72</td><td align='center' valign='middle' class='html-align-center' >84.08</td><td align='center' valign='middle' class='html-align-center' >1.51</td><td align='center' valign='middle' class='html-align-center' >3.12</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F77</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>3111.62</b></td><td align='center' valign='middle' class='html-align-center' >3312.50</td><td align='center' valign='middle' class='html-align-center' >3315.61</td><td align='center' valign='middle' class='html-align-center' >3340.49</td><td align='center' valign='middle' class='html-align-center' >3433.65</td><td align='center' valign='middle' class='html-align-center' >3317.49</td><td align='center' valign='middle' class='html-align-center' >3324.96</td><td align='center' valign='middle' class='html-align-center' >3342.76</td><td align='center' valign='middle' class='html-align-center' >3335.87</td><td align='center' valign='middle' class='html-align-center' >3780.91</td><td align='center' valign='middle' class='html-align-center' >3367.88</td><td align='center' valign='middle' class='html-align-center' >3334.58</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>150.21</b></td><td align='center' valign='middle' class='html-align-center' >185.24</td><td align='center' valign='middle' class='html-align-center' >138.98</td><td align='center' valign='middle' class='html-align-center' >108.50</td><td align='center' valign='middle' class='html-align-center' >181.80</td><td align='center' valign='middle' class='html-align-center' >188.84</td><td align='center' valign='middle' class='html-align-center' >128.45</td><td align='center' valign='middle' class='html-align-center' >122.45</td><td align='center' valign='middle' class='html-align-center' >112.63</td><td align='center' valign='middle' class='html-align-center' >145.33</td><td align='center' valign='middle' class='html-align-center' >164.48</td><td align='center' valign='middle' class='html-align-center' >108.44</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F78</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>3157.42</b></td><td align='center' valign='middle' class='html-align-center' >3185.14</td><td align='center' valign='middle' class='html-align-center' >3246.87</td><td align='center' valign='middle' class='html-align-center' >3206.20</td><td align='center' valign='middle' class='html-align-center' >3327.95</td><td align='center' valign='middle' class='html-align-center' >3220.80</td><td align='center' valign='middle' class='html-align-center' >3278.28</td><td align='center' valign='middle' class='html-align-center' >3192.92</td><td align='center' valign='middle' class='html-align-center' >3213.86</td><td align='center' valign='middle' class='html-align-center' >3463.17</td><td align='center' valign='middle' class='html-align-center' >3198.95</td><td align='center' valign='middle' class='html-align-center' >3170.47</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>9.57</b></td><td align='center' valign='middle' class='html-align-center' >43.95</td><td align='center' valign='middle' class='html-align-center' >73.76</td><td align='center' valign='middle' class='html-align-center' >36.66</td><td align='center' valign='middle' class='html-align-center' >74.48</td><td align='center' valign='middle' class='html-align-center' >48.13</td><td align='center' valign='middle' class='html-align-center' >79.14</td><td align='center' valign='middle' class='html-align-center' >48.33</td><td align='center' valign='middle' class='html-align-center' >48.58</td><td align='center' valign='middle' class='html-align-center' >140.12</td><td align='center' valign='middle' class='html-align-center' >67.35</td><td align='center' valign='middle' class='html-align-center' >16.12</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F79</td><td align='center' valign='middle' class='html-align-center' >Avr</td><td align='center' valign='middle' class='html-align-center' ><b>3.49 × 10<sup>3</sup></b></td><td align='center' valign='middle' class='html-align-center' >3.12 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >8.06 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.67 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >9.11 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.90 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >1.64 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >3.38 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >9.62 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >9.67 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >2.33 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.48 × 10<sup>5</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >SD</td><td align='center' valign='middle' class='html-align-center' ><b>2.20 × 10<sup>2</sup></b></td><td align='center' valign='middle' class='html-align-center' >4.94 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.16 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >2.06 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >8.87 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >2.98 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >2.50 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >4.89 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >1.74 × 10<sup>6</sup></td><td align='center' valign='middle' class='html-align-center' >1.32 × 10<sup>7</sup></td><td align='center' valign='middle' class='html-align-center' >4.27 × 10<sup>5</sup></td><td align='center' valign='middle' class='html-align-center' >3.07 × 10<sup>5</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t011"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t011'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t011"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 11.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC-2017 test suite (F51–F79). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t011" > <div class="html-caption" ><b>Table 11.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC-2017 test suite (F51–F79).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Fun</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F51</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.92 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F52</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.53 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Multimodal</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F53</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.33 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.33 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.96 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.01 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.68 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.49 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.01 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.01 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.01 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.01 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.01 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F54</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.60 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.47 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.69 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.20 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.65 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.12 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.48 × 10<sup>−9</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F55</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.48 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.02 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F56</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.92 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.28 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.69 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.19 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−10</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F57</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.25 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.96 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.62 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.97 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.17 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.19 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−9</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.26 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.63 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.09 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.15 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.10 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F59</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.19 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.19 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.66 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.96 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.15 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.52 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.03 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.78 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.51 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−1</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.92 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.69 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.31 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.08 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F61</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F62</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.60 × 10<sup>−7</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F63</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.55 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.35 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F65</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.70 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.08 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.09 × 10<sup>−8</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F66</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.08 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.69 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.49 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.69 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.43 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F68</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.76 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F69</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.22 × 10<sup>−2</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F70</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.32 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.32 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.46 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.44 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.94 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.86 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.70 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.96 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.44 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.26 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.08 × 10<sup>−8</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F71</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.55 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.82 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.82 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.17 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.31 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.77 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.98 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.07 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F72</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.67 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.49 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.07 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.48 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.96 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.74 × 10<sup>−6</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F73</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.60 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.76 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.38 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.23 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.32 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.20 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.32 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.04 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.61 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.87 × 10<sup>−10</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F74</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.57 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.53 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.61 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.86 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.66 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.44 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.44 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.30 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.91 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.51 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>−6</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F75</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.77 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.48 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.88 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.80 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.34 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.13 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.12 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.55 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.44 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.64 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.62 × 10<sup>−7</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F76</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.32 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.63 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.80 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.98 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.32 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.39 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.80 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.99 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.98 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.17 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.20 × 10<sup>−4</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F77</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.78 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.35 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.09 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.73 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.24 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.28 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.49 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.09 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.60 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.40 × 10<sup>−8</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F78</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.87 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.38 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.26 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.18 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.07 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.86 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.46 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.51 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.03 × 10<sup>−4</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F79</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.07 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.46 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.69 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.01 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.87 × 10<sup>−10</sup></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t012"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t012'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t012"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 12.</b> Avr and SD of CEC2020 for 25 independent runs (The bolded value is the best overall). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t012" > <div class="html-caption" ><b>Table 12.</b> Avr and SD of CEC2020 for 25 independent runs (The bolded value is the best overall).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >F</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Index</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >LSO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F80</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00 × 10<sup>2</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.04 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.82 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.94 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.69 × 10<sup>6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.85 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.76 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.89 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.74 × 10<sup>7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.27 × 10<sup>+10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7257.82</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >704.92</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2.64 × 10<sup>−13</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.47 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.05 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.04 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.04 × 10<sup>6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.19 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.52 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.64 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.60 × 10<sup>8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.15 × 10<sup>9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4390.97</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2059.48</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Multimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F81</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1347.02</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1766.98</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1839.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1636.20</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2059.68</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1954.49</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1902.30</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1476.48</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1682.49</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2648.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1665.28</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1604.18</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.52 × 10<sup>2</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.87 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.42 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.98 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.46 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.39 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.92 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.48 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.37 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >158.68</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >251.92</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F82</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>718.49</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >732.59</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >744.51</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >761.38</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >784.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >758.14</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >769.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >725.86</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >732.62</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >806.17</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >727.48</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >726.59</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>3.37</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.83</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >15.30</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >21.87</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >18.01</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >19.84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.09</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.31</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F83</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1900.02</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1901.35</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1900.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1900.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1900.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1900.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1900.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1900.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1900.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1900.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1900.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1901.16</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.09</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.56</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.46</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.26</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.17</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>3.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>4.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>5.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>6.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>7.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1712.49</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6902.12</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2245.58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6702.53</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >294,472.06</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2278.87</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7280.40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3432.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >39,529.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >414,990.21</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9364.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1834.94</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>7.64 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.34 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.81 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.78 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.64 × 10<sup>5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.21 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.18 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.92 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.03 × 10<sup>5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.37 × 10<sup>5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5902.78</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >239.86</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F85</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1604.58</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1713.70</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1746.69</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1756.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1824.55</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1776.96</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1788.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1671.19</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1747.52</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2137.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1722.52</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1618.83</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>21.66</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >87.85</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >97.05</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >77.33</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >115.43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >101.48</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >106.80</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >94.61</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >87.98</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >213.01</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >52.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >47.72</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F86</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2100.92</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5038.57</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2561.38</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5704.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >45,897.21</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2546.39</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8936.41</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2417.44</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9055.12</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1,045,287.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5349.38</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2115.06</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>3.01</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3364.65</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >263.40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3932.69</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >38,048.22</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >354.82</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6470.47</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >208.65</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4287.62</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1,690,081.52</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4114.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >51.19</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F87</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2291.63</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2298.76</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2299.33</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2305.76</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2401.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2305.77</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2336.93</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2294.71</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2308.68</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3188.89</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2413.02</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2300.39</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2.33 × 10<sup>1</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.93 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.74 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.09 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.60 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.59 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.82 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.32 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.43 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.97 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >308.22</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.56</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F88</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2654.71</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2748.83</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2717.24</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2740.74</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2774.76</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2707.03</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2777.68</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2742.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2745.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2860.81</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2746.39</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2749.71</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>113.82</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.28</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >99.81</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >46.31</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >57.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >105.77</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >22.49</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.95</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >48.68</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >34.68</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >47.52</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.42</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F89</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2894.33</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2922.20</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2937.04</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2929.85</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2952.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2926.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2931.74</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2932.25</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2936.16</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3372.91</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2927.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2936.00</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>57.51</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >24.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >22.48</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >23.57</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >23.42</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >24.33</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >23.04</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >22.98</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >18.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >150.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >31.06</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >19.13</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t013"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t013'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t013"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 13.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC-2020 test suite (F80–F89). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t013" > <div class="html-caption" ><b>Table 13.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC-2020 test suite (F80–F89).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >F</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F80</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.49 × 10<sup>−1</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Multimodal</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F81</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.06 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.83 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.60 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.87 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.67 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.22 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.60 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.65 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.66 × 10<sup>−5</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F82</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.67 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.15 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.15 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.53 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.34 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−9</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F83</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.44 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.12 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.46 × 10<sup>−6</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F85</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.09 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.70 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.08 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.98 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.49 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.72 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.07 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.98 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.70 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F86</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.31 × 10<sup>−3</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F87</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.52 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.35 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.82 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.18 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.89 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.07 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.52 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.19 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F88</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.48 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.28 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.53 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.11 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.98 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.60 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.92 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.37 × 10<sup>−10</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F89</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.39 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.49 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.64 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.37 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.03 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.84 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.66 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.77 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.84 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.24 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.79 × 10<sup>−8</sup></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t014"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t014'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t014"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 14.</b> Avr and SD of CEC2022 for 25 independent runs (The bolded value is the best overall). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t014" > <div class="html-caption" ><b>Table 14.</b> Avr and SD of CEC2022 for 25 independent runs (The bolded value is the best overall).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >F</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Index</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >LSO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>300.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.55 × 10<sup>4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.44 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10,731.57</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>300.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>300.00</b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.61 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.37 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.20 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.57 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.31 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.18 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.20 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3788.59</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Multimodal</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F91</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>400.96</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >410.29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >405.42</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >405.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >428.03</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >410.25</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >413.99</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >409.75</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >434.34</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1066.53</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >409.80</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >407.52</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2.13 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.96 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.66 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.56 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.74 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.22 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.71 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.63 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >814.53</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.35</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.32</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F92</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>600.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >606.09</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >601.30</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >617.36</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >632.26</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >609.38</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >611.84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >600.15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >601.21</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >645.65</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >600.08</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >600.00</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.62</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.85</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.56</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.30</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.62</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.86</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.13</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.05</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.07 × 10<sup>−6</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F93</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>810.72</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >821.06</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >821.13</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >823.32</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >836.29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >824.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >831.03</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >812.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >814.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >848.55</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >825.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >824.02</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2.96</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.98</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.21</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.31</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >16.19</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.72</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.71</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.37</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.22</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F94</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >900.02</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >908.19</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >921.08</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1021.89</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1447.74</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1019.31</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1210.33</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >900.38</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >917.15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1432.77</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >902.70</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>900.00</b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.29 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.65 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.66 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.76 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.10 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.10 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.75 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.17 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.84 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >104.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.25</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.60 × 10<sup>−6</sup></b></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F95</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1800.36</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3566.29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2258.98</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3181.78</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3989.73</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1874.01</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3629.15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3691.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5032.02</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.66 × 10<sup>8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5411.36</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1826.60</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.34</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1735.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1245.49</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1115.74</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1954.69</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >50.56</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1615.83</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1945.92</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2475.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.41 × 10<sup>8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2210.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >117.17</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F96</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2000.35</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2033.78</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2027.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2042.25</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2066.69</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2032.20</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2033.24</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2032.42</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2033.04</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2139.27</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2020.43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2002.21</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.54</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.08</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.42</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >28.19</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >16.41</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.51</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >38.20</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >15.80</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >41.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.76</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.18</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F97</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2201.57</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2223.04</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2221.27</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2224.21</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2232.31</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2221.58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2224.61</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2222.82</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2224.73</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2263.95</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2220.57</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2204.54</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>3.83 × 10<sup>0</sup></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.12 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.01 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.34 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.42 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.81 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.93 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.33 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.53 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >29.43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.76</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.49</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td></tr><tr ><td colspan='14' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F98</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2529.28</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2529.43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2534.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2529.29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2564.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2529.55</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2534.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2529.28</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2580.54</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2771.04</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2529.28</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2529.28</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.19</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >26.83</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >39.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.87</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >26.83</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >39.65</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >61.34</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.79 × 10<sup>−10</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F99</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>2500.36</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2508.72</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2516.28</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2553.99</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2616.35</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2532.77</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2558.84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2553.16</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2573.33</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2690.10</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2523.74</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2527.05</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.06</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >32.01</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >40.44</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >57.97</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >214.36</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >54.42</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >63.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >60.40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >63.44</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >195.95</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >53.37</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >49.31</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F100</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2825.01</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.82 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.78 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.70 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.92 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b><span class='underline'>2.68 × 10<sup>3</sup></span></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.78 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.85 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00 × 10<sup>3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4092.28</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2750.51</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2895.74</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >129.15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.24 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.76 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.38 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.55 × 10<sup>1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b><span class='underline'>1.27 × 10<sup>2</sup></span></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.48 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.15 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.74 × 10<sup>2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >331.37</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >175.84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >27.73</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b><span class='underline'>1.00</span></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F101</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Avr</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2862.69</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2863.95</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2865.40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2864.29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2894.24</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2864.79</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2866.37</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2863.94</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2866.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2971.50</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b><span class='underline'>2862.46</span></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2863.56</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.49</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.80</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.78</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >35.17</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.76</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.73</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.78</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >114.51</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b><span class='underline'>1.67</span></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.45</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b><span class='underline'>1.00</span></b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t015"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t015'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t015"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 15.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC-2022 test suite (F90–F101). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t015" > <div class="html-caption" ><b>Table 15.</b> <span class='html-italic'>p</span>-values of LSO with each rival optimizer on CEC-2022 test suite (F90–F101).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >F</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Unimodal</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >NaN</td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Multimodal</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F91</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.36 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.03 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.42 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.07 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.53 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.44 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.08 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.76 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.10 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.40 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.68 × 10<sup>−10</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F92</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.37 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.72 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.00 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F93</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.32 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.59 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.16 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.82 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.86 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.49 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.63 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.05 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.69 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F94</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.44 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.88 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.88 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.88 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.88 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.88 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.20 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.08 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.88 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.22 × 10<sup>−5</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Hybrid</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F95</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.99 × 10<sup>−11</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F96</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.03 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.99 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.65 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.15 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F97</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.96 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.15 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.87 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.61 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>−1</sup></td></tr><tr ><td colspan='12' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Composition</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F98</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.61 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.16 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.65 × 10<sup>−8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.15 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.21 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.34 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F99</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.08 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.15 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.62 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.97 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.62 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.69 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.46 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.02 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.64 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.95 × 10<sup>−1</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >F100</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.85 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.36 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.44 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.41 × 10<sup>−10</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.37 × 10<sup>−2</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.51 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.91 × 10<sup>−9</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.31 × 10<sup>−12</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.02 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.47 × 10<sup>−3</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >F101</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.59 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.62 × 10<sup>−6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.19 × 10<sup>−4</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.38 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.59 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.66 × 10<sup>−7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.86 × 10<sup>−3</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.80 × 10<sup>−5</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.95 × 10<sup>−11</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.29 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.41 × 10<sup>−2</sup></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t016"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t016'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t016"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 16.</b> Overall effectiveness over five investigated benchmarks (The bolded and red value is the best overall). </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t016" > <div class="html-caption" ><b>Table 16.</b> Overall effectiveness over five investigated benchmarks (The bolded and red value is the best overall).</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >F</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Index</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >LSO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GBO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RUN</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >WOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GTO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >AVOA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >EO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >GWO</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RSA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SMA</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DE</th></tr></thead><tbody ><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >CEC2005</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.10</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.70</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.60</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.50</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.50</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.55</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.75</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.60</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>0.10</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >646.25</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.63</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7101.71</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.14</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.59</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.24</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5749.12</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >O × 10 (%)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>85.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >25.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >50.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >50.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >40.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >70.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>85.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >30.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >25.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >45.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >65.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >20.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >CEC2014</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.66</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.28</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.55</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.72</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.07</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.48</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.79</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.41</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.93</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.21</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.45</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>22.57</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17,917.37</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10,668.42</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >22,738.20</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >256,429.26</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >21,129.59</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17,868.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2636.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.75 × 10<sup>6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.93 × 10<sup>7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2470.27</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6338.28</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >O × 10 (%)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>79.31</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.90</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >CEC2017</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.11</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.57</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.39</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.21</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.46</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.50</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.43</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.68</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.32</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>32.47</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >52,413.76</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >40,719.95</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >14,459.54</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >446,168.54</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >103,439.53</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >26,051.38</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17,788.92</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.44 × 10<sup>6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.47 × 10<sup>8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17,155.85</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10,876.18</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >O × 10 (%)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>100.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.45</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >CEC2020</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.78</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.44</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.44</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.78</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.33</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.22</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.22</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.44</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>38.24</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1161.15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >318.84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1012.58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >264,287.33</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >335.90</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1482.46</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >518.82</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.60 × 10<sup>7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.15 × 10<sup>8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1501.58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >267.78</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >O × 10 (%)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>90.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td></tr><tr ><td rowspan='3' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >CEC2022</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rank </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.64</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.73</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.09</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.91</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.82</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.36</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.64</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >SD</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>11.73</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >172.93</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >128.52</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >119.23</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >782.34</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >32.96</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >173.73</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >184.05</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >420.22</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.01 × 10<sup>7</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >206.53</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17.99</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >O × 10 (%)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>75.00</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.33</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >16.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >16.67</td></tr><tr ><td colspan='2' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Avg. Rank:</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>1.64</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.65</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.13</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.68</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.94</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.52</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.85</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.30</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.69</td></tr><tr ><td colspan='2' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Avg. SD:</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>21.02</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >14,462.29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10,367.27</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7666.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >194,953.84</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >24,987.62</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9115.19</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4225.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.04 × 10<sup>6</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.30 × 10<sup>8</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4266.89</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4649.87</td></tr><tr ><td colspan='2' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Avg.OE</b> (<b>%</b>)<b>:</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>85.86</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >12.69</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.38</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >15.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.38</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17.71</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.40</td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t017"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t017'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t017"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 17.</b> Comparison of the results for tension/compression spring design optimization problem. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t017" > <div class="html-caption" ><b>Table 17.</b> Comparison of the results for tension/compression spring design optimization problem.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >No.</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Algorithm</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>1</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>2</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>3</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">f</mi> <mrow> <mi mathvariant="bold-italic">m</mi> <mi mathvariant="bold-italic">i</mi> <mi mathvariant="bold-italic">n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>)</mo> </mrow> </mrow> </mstyle> </semantics> </math></th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >1</td><td align='left' valign='middle' class='html-align-left' >LSO</td><td align='center' valign='middle' class='html-align-center' ><b>5.1689 × 10<sup>−2</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.5671 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.1290 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.2665233 × 10<sup>−2</sup></b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >2</td><td align='left' valign='middle' class='html-align-left' >SSA</td><td align='center' valign='middle' class='html-align-center' >5.0000 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.1737 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.4051 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.2735631 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >3</td><td align='left' valign='middle' class='html-align-left' >GBO</td><td align='center' valign='middle' class='html-align-center' >5.3274 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.9605 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >9.3074 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.2709931 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >4</td><td align='left' valign='middle' class='html-align-left' >RUN</td><td align='center' valign='middle' class='html-align-center' >5.1960 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.6328 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.0914 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.2666568 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >5</td><td align='left' valign='middle' class='html-align-left' >WOA</td><td align='center' valign='middle' class='html-align-center' >5.2797 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.8396 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >9.8542 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.2687243 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >6</td><td align='left' valign='middle' class='html-align-left' >GTO</td><td align='center' valign='middle' class='html-align-center' >5.2437 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.7499 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.0293 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.2675330 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >7</td><td align='left' valign='middle' class='html-align-left' >AVOA</td><td align='center' valign='middle' class='html-align-center' >5.1702 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.5704 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.1270 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.2665236 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >8</td><td align='left' valign='middle' class='html-align-left' >EO</td><td align='center' valign='middle' class='html-align-center' >5.3212 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.9449 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >9.3755 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.2706550 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >9</td><td align='left' valign='middle' class='html-align-left' >GWO</td><td align='center' valign='middle' class='html-align-center' >5.2770 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.8328 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >9.8863 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.2686160 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >10</td><td align='left' valign='middle' class='html-align-left' >RSA</td><td align='center' valign='middle' class='html-align-center' >5.1387 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.4946 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.1734 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.2673204 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >11</td><td align='left' valign='middle' class='html-align-left' >SMA</td><td align='center' valign='middle' class='html-align-center' >5.0000 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.1050 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.5000 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.3196460 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >12</td><td align='left' valign='middle' class='html-align-left' >DE</td><td align='center' valign='middle' class='html-align-center' >5.2354 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.7292 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.0399 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.2673207 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >13</td><td align='left' valign='middle' class='html-align-left' >PO</td><td align='center' valign='middle' class='html-align-center' >5.1778 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.5884 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.1166 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.26665924 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >14</td><td align='left' valign='middle' class='html-align-left' >SO</td><td align='center' valign='middle' class='html-align-center' >5.1403 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.4988 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.1701 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.26667301 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >15</td><td align='left' valign='middle' class='html-align-left' >BWO</td><td align='center' valign='middle' class='html-align-center' >5.4611 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >4.2818 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >9.0696 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.41360583 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >16</td><td align='left' valign='middle' class='html-align-left' >DTBO</td><td align='center' valign='middle' class='html-align-center' >5.3059 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.8966 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >9.6233 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.27507490 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >17</td><td align='left' valign='middle' class='html-align-left' >CCAA</td><td align='center' valign='middle' class='html-align-center' >5.2012 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.6453 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.0846 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.26674032 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >18</td><td align='left' valign='middle' class='html-align-left' >RO</td><td align='center' valign='middle' class='html-align-center' >5.13700 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.49096 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.17628 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.2678800 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >19</td><td align='left' valign='middle' class='html-align-left' >ES</td><td align='center' valign='middle' class='html-align-center' >5.1989 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.6397 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.08905 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.2681 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >20</td><td align='left' valign='middle' class='html-align-left' >GSA</td><td align='center' valign='middle' class='html-align-center' >5.02760 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.2368 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.352541 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.27022 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >21</td><td align='left' valign='middle' class='html-align-left' >TS</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >1.2935 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >22</td><td align='left' valign='middle' class='html-align-left' >Swarm strategy</td><td align='center' valign='middle' class='html-align-center' >5.0417 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.2153 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.3980 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.3060 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >23</td><td align='left' valign='middle' class='html-align-left' >UPSO</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >1.31 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >24</td><td align='left' valign='middle' class='html-align-left' >CA</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >1.2867 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >25</td><td align='left' valign='middle' class='html-align-left' >TANA-3</td><td align='center' valign='middle' class='html-align-center' >5.8400 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >5.4170 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >5.2745 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >1.3400 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >26</td><td align='left' valign='middle' class='html-align-left' >PSO</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >1.2857 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >27</td><td align='left' valign='middle' class='html-align-left' >ACO</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >1.3223 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >28</td><td align='left' valign='middle' class='html-align-left' >GA</td><td align='center' valign='middle' class='html-align-center' >5.8231 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >5.2106 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >5.8845 × 10</td><td align='center' valign='middle' class='html-align-center' >1.3931 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >29</td><td align='left' valign='middle' class='html-align-left' >QEA</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >1.2928 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >30</td><td align='left' valign='middle' class='html-align-left' >PC</td><td align='center' valign='middle' class='html-align-center' >5.06 × 10<sup>−2</sup></td><td align='center' valign='middle' class='html-align-center' >3.28 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.41 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.35 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >31</td><td align='left' valign='middle' class='html-align-left' >SIGA</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >N/A</td><td align='center' valign='middle' class='html-align-center' >1.3076 × 10<sup>−2</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >32</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >PSIGA</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >N/A</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >N/A</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >N/A</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.2864 × 10<sup>−2</sup></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t018"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t018'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t018"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 18.</b> Comparison of the results for weld beam design problem. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t018" > <div class="html-caption" ><b>Table 18.</b> Comparison of the results for weld beam design problem.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >No.</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Algorithm</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>1</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>2</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>3</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>4</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">f</mi> <mrow> <mi mathvariant="bold-italic">m</mi> <mi mathvariant="bold-italic">i</mi> <mi mathvariant="bold-italic">n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>)</mo> </mrow> </mrow> </mstyle> </semantics> </math></th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >1</td><td align='left' valign='middle' class='html-align-left' >LSO</td><td align='center' valign='middle' class='html-align-center' ><b>2.0572 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.4707 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>9.0366 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0573 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.7248658</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >2</td><td align='left' valign='middle' class='html-align-left' >SSA</td><td align='center' valign='middle' class='html-align-center' >2.0548 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4757 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0369 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0573 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.7252086</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >3</td><td align='left' valign='middle' class='html-align-left' >GBO</td><td align='center' valign='middle' class='html-align-center' ><b>2.0572 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.4707 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>9.0366 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0573 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.7248658</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >4</td><td align='left' valign='middle' class='html-align-left' >RUN</td><td align='center' valign='middle' class='html-align-center' >2.0572 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4708 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0366 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0573 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.7248746</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >5</td><td align='left' valign='middle' class='html-align-left' >WOA</td><td align='center' valign='middle' class='html-align-center' >1.9721 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.6965 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0151 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0671 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.7454019</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >6</td><td align='left' valign='middle' class='html-align-left' >GTO</td><td align='center' valign='middle' class='html-align-center' ><b>2.0572 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.4707 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>9.0366 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0573 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.7248658</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >7</td><td align='left' valign='middle' class='html-align-left' >AVOA</td><td align='center' valign='middle' class='html-align-center' >2.0567 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4718 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0366 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0573 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.7249388</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >8</td><td align='left' valign='middle' class='html-align-left' >EO</td><td align='center' valign='middle' class='html-align-center' ><b>2.0572 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.4707 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>9.0366 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0573 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.7248658</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >9</td><td align='left' valign='middle' class='html-align-left' >GWO</td><td align='center' valign='middle' class='html-align-center' >2.0557 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4741 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0376 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0573 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.7253039</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >10</td><td align='left' valign='middle' class='html-align-left' >RSA</td><td align='center' valign='middle' class='html-align-center' >2.0615 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4694 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0775 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.2698 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.8945096</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >11</td><td align='left' valign='middle' class='html-align-left' >SMA</td><td align='center' valign='middle' class='html-align-center' >2.0572 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4707 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0366 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0573 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.7248689</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >12</td><td align='left' valign='middle' class='html-align-left' >DE</td><td align='center' valign='middle' class='html-align-center' ><b>2.0572 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.4707 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>9.0366 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0573 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.7248658</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >13</td><td align='left' valign='middle' class='html-align-left' >PO</td><td align='center' valign='middle' class='html-align-center' >2.0572 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4707 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0366 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0573 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.72486608</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >14</td><td align='left' valign='middle' class='html-align-left' >SO</td><td align='center' valign='middle' class='html-align-center' ><b>2.0572 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.4707 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>9.0366 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0573 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.7248658</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >15</td><td align='left' valign='middle' class='html-align-left' >BWO</td><td align='center' valign='middle' class='html-align-center' ><b>1.8639 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.9876 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>8.9766 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.1300 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.8076732</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >16</td><td align='left' valign='middle' class='html-align-left' >DTBO</td><td align='center' valign='middle' class='html-align-center' ><b>2.0571 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.4709 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>9.0368 × 10<sup>0</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0574 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>1.7249588</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >17</td><td align='left' valign='middle' class='html-align-left' >CCAA</td><td align='center' valign='middle' class='html-align-center' >2.0572 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4707 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0367 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0573 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.72487987</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >18</td><td align='left' valign='middle' class='html-align-left' >RO</td><td align='center' valign='middle' class='html-align-center' >2.03687 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.52847 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.00423 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.07241 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.735344</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >19</td><td align='left' valign='middle' class='html-align-left' >RO</td><td align='center' valign='middle' class='html-align-center' >2.03687 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.52847 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.00423 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.072410 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.735344 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >20</td><td align='left' valign='middle' class='html-align-left' >WOA</td><td align='center' valign='middle' class='html-align-center' >2.05396 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.48429 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.03743 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.06276 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.73050 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >21</td><td align='left' valign='middle' class='html-align-left' >HS</td><td align='center' valign='middle' class='html-align-center' >2.4420 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >6.2231 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >8.29150 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.4430 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >2.38070 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >22</td><td align='left' valign='middle' class='html-align-left' >CSS&PSO I </td><td align='center' valign='middle' class='html-align-center' >2.0639 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4236 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.1241 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0531 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.7314 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >23</td><td align='left' valign='middle' class='html-align-left' >CSS&PSO II</td><td align='center' valign='middle' class='html-align-center' >2.0546 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.4800 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.05401 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0578 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.72910 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >24</td><td align='left' valign='middle' class='html-align-left' >PSOStr</td><td align='center' valign='middle' class='html-align-center' >2.0150 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.5620 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0414 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0571 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.73118 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >25</td><td align='left' valign='middle' class='html-align-left' >FA</td><td align='center' valign='middle' class='html-align-center' >2.015 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.5620 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.0414 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.0570 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >1.73121 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >26</td><td align='left' valign='middle' class='html-align-left' >DE</td><td align='center' valign='middle' class='html-align-center' >2.444 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >6.2175 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >8.2915 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >2.4440 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >2.3810 × 10<sup>0</sup></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >27</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >AIS-GA</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.444 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.2183 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.2912 × 10<sup>0</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.444 × 10<sup>−1</sup></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.3812 × 10<sup>0</sup></td></tr></tbody> </table> </div><div class="html-table-wrap" id="mathematics-10-03466-t019"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href='#table_body_display_mathematics-10-03466-t019'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-7390/10/19/3466/display" href="#table_body_display_mathematics-10-03466-t019"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 19.</b> Comparison of the results for pressure vessel design optimization problem. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_mathematics-10-03466-t019" > <div class="html-caption" ><b>Table 19.</b> Comparison of the results for pressure vessel design optimization problem.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >No.</th><th align='left' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-left' >Algorithm</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>1</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>2</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>3</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">x</mi> <mn>4</mn> </msub> </mrow> </mstyle> </semantics> </math></th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mstyle mathvariant="bold"> <mrow> <msub> <mi mathvariant="bold-italic">f</mi> <mrow> <mi mathvariant="bold-italic">m</mi> <mi mathvariant="bold-italic">i</mi> <mi mathvariant="bold-italic">n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>)</mo> </mrow> </mrow> </mstyle> </semantics> </math></th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >1</td><td align='left' valign='middle' class='html-align-left' >LSO</td><td align='center' valign='middle' class='html-align-center' ><b>7.7818 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.8466 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>4.0320 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0000 × 10<sup>2</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>5885.43417456</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >2</td><td align='left' valign='middle' class='html-align-left' >SSA</td><td align='center' valign='middle' class='html-align-center' >7.8272 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.8690 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0555 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.9675 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5893.25120195</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >3</td><td align='left' valign='middle' class='html-align-left' >GBO</td><td align='center' valign='middle' class='html-align-center' >7.7818 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.8466 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0320 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >2.0000 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5885.44199882</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >4</td><td align='left' valign='middle' class='html-align-left' >RUN</td><td align='center' valign='middle' class='html-align-center' >7.7824 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.8471 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0323 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.9995 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5885.60517789</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >5</td><td align='left' valign='middle' class='html-align-left' >WOA</td><td align='center' valign='middle' class='html-align-center' >1.0863 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >5.5859 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >5.6156 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >5.5940 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >6779.76692510</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >6</td><td align='left' valign='middle' class='html-align-left' >GTO</td><td align='center' valign='middle' class='html-align-center' ><b>7.7818 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.8466 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>4.0320 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0000 × 10<sup>2</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>5885.43417456</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >7</td><td align='left' valign='middle' class='html-align-left' >AVOA</td><td align='center' valign='middle' class='html-align-center' >7.7820 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.8467 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0321 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.9998 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5885.47556956</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >8</td><td align='left' valign='middle' class='html-align-left' >EO</td><td align='center' valign='middle' class='html-align-center' >8.2691 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0875 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.2845 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.6760 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5974.05971856</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >9</td><td align='left' valign='middle' class='html-align-left' >GWO</td><td align='center' valign='middle' class='html-align-center' >7.7854 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.8509 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0332 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.9986 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5888.33742107</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >10</td><td align='left' valign='middle' class='html-align-left' >RSA</td><td align='center' valign='middle' class='html-align-center' >1.2411 × 10<sup>0</sup></td><td align='center' valign='middle' class='html-align-center' >9.5886 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.5644 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.3730 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >10,457.57367139</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >11</td><td align='left' valign='middle' class='html-align-left' >SMA</td><td align='center' valign='middle' class='html-align-center' >7.7818 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.8466 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0320 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >2.0000 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5885.43624519</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >12</td><td align='left' valign='middle' class='html-align-left' >DE</td><td align='center' valign='middle' class='html-align-center' ><b>7.7818 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>3.8466 × 10<sup>−1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>4.0320 × 10<sup>1</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>2.0000 × 10<sup>2</sup></b></td><td align='center' valign='middle' class='html-align-center' ><b>5885.43417456</b></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >13</td><td align='left' valign='middle' class='html-align-left' >PO</td><td align='center' valign='middle' class='html-align-center' >7.7818 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.8466 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0320 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >2.0000 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5885.43636261</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >14</td><td align='left' valign='middle' class='html-align-left' >SO</td><td align='center' valign='middle' class='html-align-center' >7.7818 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.8470 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0320 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >2.0000 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5885.54986448</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >15</td><td align='left' valign='middle' class='html-align-left' >BWO</td><td align='center' valign='middle' class='html-align-center' >7.9249 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.9708 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0982 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.9550 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >6036.98073005</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >16</td><td align='left' valign='middle' class='html-align-left' >DTBO</td><td align='center' valign='middle' class='html-align-center' >8.7638 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.5781 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.5407 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.3954 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >6165.77458390</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >17</td><td align='left' valign='middle' class='html-align-left' >CCAA</td><td align='center' valign='middle' class='html-align-center' >7.7837 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >3.8488 × 10<sup>−1</sup></td><td align='center' valign='middle' class='html-align-center' >4.0327 × 10<sup>1</sup></td><td align='center' valign='middle' class='html-align-center' >1.9989 × 10<sup>2</sup></td><td align='center' valign='middle' class='html-align-center' >5886.45565028</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >18</td><td align='left' valign='middle' class='html-align-left' >HHO</td><td align='center' valign='middle' class='html-align-center' >0.817583</td><td align='center' valign='middle' class='html-align-center' >0.40729</td><td align='center' valign='middle' class='html-align-center' >42.0917</td><td align='center' valign='middle' class='html-align-center' >176.7196</td><td align='center' valign='middle' class='html-align-center' >6000.46259</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >19</td><td align='left' valign='middle' class='html-align-left' >GWO</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.4345</td><td align='center' valign='middle' class='html-align-center' >42.089181</td><td align='center' valign='middle' class='html-align-center' >176.758731</td><td align='center' valign='middle' class='html-align-center' >6051.5639</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >20</td><td align='left' valign='middle' class='html-align-left' >HPSO</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.437500</td><td align='center' valign='middle' class='html-align-center' >42.0984</td><td align='center' valign='middle' class='html-align-center' >176.6366</td><td align='center' valign='middle' class='html-align-center' >6059.7143</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >21</td><td align='left' valign='middle' class='html-align-left' >G-QPSO</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.437500</td><td align='center' valign='middle' class='html-align-center' >42.0984</td><td align='center' valign='middle' class='html-align-center' >176.6372</td><td align='center' valign='middle' class='html-align-center' >6059.7208</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >22</td><td align='left' valign='middle' class='html-align-left' >WEO</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.437500</td><td align='center' valign='middle' class='html-align-center' >42.0984</td><td align='center' valign='middle' class='html-align-center' >176.6366</td><td align='center' valign='middle' class='html-align-center' >6059.71</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >23</td><td align='left' valign='middle' class='html-align-left' >BA</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.437500</td><td align='center' valign='middle' class='html-align-center' >42.098445</td><td align='center' valign='middle' class='html-align-center' >176.63659</td><td align='center' valign='middle' class='html-align-center' >6059.7143</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >24</td><td align='left' valign='middle' class='html-align-left' >MFO</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.4375</td><td align='center' valign='middle' class='html-align-center' >42.098445</td><td align='center' valign='middle' class='html-align-center' >176.636596</td><td align='center' valign='middle' class='html-align-center' >6059.7143</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >25</td><td align='left' valign='middle' class='html-align-left' >CSS</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.4375</td><td align='center' valign='middle' class='html-align-center' >42.103624</td><td align='center' valign='middle' class='html-align-center' >176.572656</td><td align='center' valign='middle' class='html-align-center' >6059.0888</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >26</td><td align='left' valign='middle' class='html-align-left' >ESs</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.4375</td><td align='center' valign='middle' class='html-align-center' >42.098087</td><td align='center' valign='middle' class='html-align-center' >176.640518</td><td align='center' valign='middle' class='html-align-center' >6059.7456</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >27</td><td align='left' valign='middle' class='html-align-left' >BIANCA</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.4375</td><td align='center' valign='middle' class='html-align-center' >42.0968</td><td align='center' valign='middle' class='html-align-center' >176.658</td><td align='center' valign='middle' class='html-align-center' >6059.9384</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >28</td><td align='left' valign='middle' class='html-align-left' >MDDE</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.4375</td><td align='center' valign='middle' class='html-align-center' >42.098446</td><td align='center' valign='middle' class='html-align-center' >176.636047</td><td align='center' valign='middle' class='html-align-center' >6059.70166</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >29</td><td align='left' valign='middle' class='html-align-left' >DELC</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.4375</td><td align='center' valign='middle' class='html-align-center' >42.0984456</td><td align='center' valign='middle' class='html-align-center' >176.6365958</td><td align='center' valign='middle' class='html-align-center' >6059.7143</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >30</td><td align='left' valign='middle' class='html-align-left' >WOA</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.4375</td><td align='center' valign='middle' class='html-align-center' >42.0982699</td><td align='center' valign='middle' class='html-align-center' >176.638998</td><td align='center' valign='middle' class='html-align-center' >6059.7410</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >31</td><td align='left' valign='middle' class='html-align-left' >NPGA</td><td align='center' valign='middle' class='html-align-center' >0.8125</td><td align='center' valign='middle' class='html-align-center' >0.4375</td><td align='center' valign='middle' class='html-align-center' >42.0974</td><td align='center' valign='middle' class='html-align-center' >176.654</td><td align='center' valign='middle' class='html-align-center' >6059.9463</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >32</td><td align='left' valign='middle' class='html-align-left' >Lagrangian multiplier</td><td align='center' valign='middle' class='html-align-center' >1.125</td><td align='center' valign='middle' class='html-align-center' >0.625</td><td align='center' valign='middle' class='html-align-center' >58.291</td><td align='center' valign='middle' class='html-align-center' >43.69</td><td align='center' valign='middle' class='html-align-center' >7198.0428</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >33</td><td align='left' valign='middle' style='border-bottom:solid thin' class='html-align-left' >Branch-bound</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.125</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.625</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >47.7</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >117.701</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8129.1036</td></tr></tbody> </table> </div></section><section class='html-fn_group'><table><tr id=''><td></td><td><div class='html-p'><b>Publisher’s Note:</b> MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.</div></td></tr></table></section> <section 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Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm. <em>Mathematics</em> <b>2022</b>, <em>10</em>, 3466. https://doi.org/10.3390/math10193466 </p> <div style="display: block"> <b>AMA Style</b><br> <p> Abdel-Basset M, Mohamed R, Sallam KM, Chakrabortty RK. Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm. <em>Mathematics</em>. 2022; 10(19):3466. https://doi.org/10.3390/math10193466 </p> <b>Chicago/Turabian Style</b><br> <p> Abdel-Basset, Mohamed, Reda Mohamed, Karam M. Sallam, and Ripon K. Chakrabortty. 2022. "Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm" <em>Mathematics</em> 10, no. 19: 3466. https://doi.org/10.3390/math10193466 </p> <b>APA Style</b><br> <p> Abdel-Basset, M., Mohamed, R., Sallam, K. M., & Chakrabortty, R. K. (2022). Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm. <em>Mathematics</em>, <em>10</em>(19), 3466. https://doi.org/10.3390/math10193466 </p> </div> </div> <div class="info-box no-margin"> Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. 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Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm. <em>Mathematics</em> <b>2022</b>, <em>10</em>, 3466. https://doi.org/10.3390/math10193466 </p> <div style="display: block"> <b>AMA Style</b><br> <p> Abdel-Basset M, Mohamed R, Sallam KM, Chakrabortty RK. Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm. <em>Mathematics</em>. 2022; 10(19):3466. https://doi.org/10.3390/math10193466 </p> <b>Chicago/Turabian Style</b><br> <p> Abdel-Basset, Mohamed, Reda Mohamed, Karam M. Sallam, and Ripon K. Chakrabortty. 2022. "Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm" <em>Mathematics</em> 10, no. 19: 3466. https://doi.org/10.3390/math10193466 </p> <b>APA Style</b><br> <p> Abdel-Basset, M., Mohamed, R., Sallam, K. M., & Chakrabortty, R. K. (2022). Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm. <em>Mathematics</em>, <em>10</em>(19), 3466. https://doi.org/10.3390/math10193466 </p> </div> </div> <div class="info-box no-margin"> Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. 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