Speeding up Smartphone-Based Dew Computing: In Vivo Experiments Setup Via an Evolutionary 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?1732286508"> <meta name="title" content="Speeding up Smartphone-Based Dew Computing: In Vivo Experiments Setup Via an Evolutionary Algorithm"> <meta name="description" content="Dew computing aims to minimize the dependency on remote clouds by exploiting nearby nodes for solving non-trivial computational tasks, e.g., AI inferences. Nowadays, smartphones are good candidates for computing nodes; hence, smartphone clusters have been proposed to accomplish this task and load balancing is frequently a subject of research. Using the same real—i.e., in vivo—testbeds to evaluate different load balancing strategies based on energy utilization is challenging and time consuming. In principle, test repetition requires a platform to control battery charging periods between repetitions. Our Motrol hard-soft device has such a capability; however, it lacks a mechanism to assure and reduce the time in which all smartphone batteries reach the level required by the next test. We propose an evolutionary algorithm to execute smartphone battery (dis)charging plans to minimize test preparation time. Charging plans proposed by the algorithm include charging at different speeds, which is achieved by charging at maximum speed while exercising energy hungry components (the CPU and screen). To evaluate the algorithm, we use various charging/discharging battery traces of real smartphones and we compare the time-taken for our method to collectively prepare a set of smartphones versus that of individually (dis)charging all smartphones at maximum speed." > <link rel="image_src" href="https://pub.mdpi-res.com/img/journals/sensors-logo.png?8600e93ff98dbf14" > <meta name="dc.title" content="Speeding up Smartphone-Based Dew Computing: In Vivo Experiments Setup Via an Evolutionary Algorithm"> <meta name="dc.creator" content="Virginia Yannibelli"> <meta name="dc.creator" content="Matías Hirsch"> <meta name="dc.creator" content="Juan Toloza"> <meta name="dc.creator" content="Tim A. Majchrzak"> <meta name="dc.creator" content="Alejandro Zunino"> <meta name="dc.creator" content="Cristian Mateos"> <meta name="dc.type" content="Article"> <meta name="dc.source" content="Sensors 2023, Vol. 23, Page 1388"> <meta name="dc.date" content="2023-01-26"> <meta name ="dc.identifier" content="10.3390/s23031388"> <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="Dew computing aims to minimize the dependency on remote clouds by exploiting nearby nodes for solving non-trivial computational tasks, e.g., AI inferences. Nowadays, smartphones are good candidates for computing nodes; hence, smartphone clusters have been proposed to accomplish this task and load balancing is frequently a subject of research. Using the same real—i.e., in vivo—testbeds to evaluate different load balancing strategies based on energy utilization is challenging and time consuming. In principle, test repetition requires a platform to control battery charging periods between repetitions. Our Motrol hard-soft device has such a capability; however, it lacks a mechanism to assure and reduce the time in which all smartphone batteries reach the level required by the next test. We propose an evolutionary algorithm to execute smartphone battery (dis)charging plans to minimize test preparation time. Charging plans proposed by the algorithm include charging at different speeds, which is achieved by charging at maximum speed while exercising energy hungry components (the CPU and screen). To evaluate the algorithm, we use various charging/discharging battery traces of real smartphones and we compare the time-taken for our method to collectively prepare a set of smartphones versus that of individually (dis)charging all smartphones at maximum speed." > <meta name="dc.subject" content="dew computing" > <meta name="dc.subject" content="smartphones" > <meta name="dc.subject" content="profiling" > <meta name="dc.subject" content="benchmarking" > <meta name="dc.subject" content="Motrol" > <meta name="dc.subject" content="evolutionary computing" > <meta name ="prism.issn" content="1424-8220"> <meta name ="prism.publicationName" content="Sensors"> <meta name ="prism.publicationDate" content="2023-01-26"> <meta name ="prism.volume" content="23"> <meta name ="prism.number" content="3"> <meta name ="prism.section" content="Article" > <meta name ="prism.startingPage" content="1388" > <meta name="citation_issn" content="1424-8220"> <meta name="citation_journal_title" content="Sensors"> <meta name="citation_publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="citation_title" content="Speeding up Smartphone-Based Dew Computing: In Vivo Experiments Setup Via an Evolutionary Algorithm"> <meta name="citation_publication_date" content="2023/1"> <meta name="citation_online_date" content="2023/01/26"> <meta name="citation_volume" content="23"> <meta name="citation_issue" content="3"> <meta name="citation_firstpage" content="1388"> <meta name="citation_author" content="Yannibelli, Virginia"> <meta name="citation_author" content="Hirsch, Matías"> <meta name="citation_author" content="Toloza, Juan"> <meta name="citation_author" content="Majchrzak, Tim A."> <meta name="citation_author" content="Zunino, Alejandro"> <meta name="citation_author" content="Mateos, Cristian"> <meta name="citation_doi" content="10.3390/s23031388"> <meta name="citation_id" content="mdpi-s23031388"> <meta name="citation_abstract_html_url" content="https://www.mdpi.com/1424-8220/23/3/1388"> <meta name="citation_pdf_url" content="https://www.mdpi.com/1424-8220/23/3/1388/pdf?version=1674743766"> <link rel="alternate" type="application/pdf" title="PDF Full-Text" href="https://www.mdpi.com/1424-8220/23/3/1388/pdf?version=1674743766"> <meta name="fulltext_pdf" content="https://www.mdpi.com/1424-8220/23/3/1388/pdf?version=1674743766"> <meta name="citation_fulltext_html_url" content="https://www.mdpi.com/1424-8220/23/3/1388/htm"> <link rel="alternate" type="text/html" title="HTML Full-Text" href="https://www.mdpi.com/1424-8220/23/3/1388/htm"> <meta name="fulltext_html" content="https://www.mdpi.com/1424-8220/23/3/1388/htm"> <link rel="alternate" type="text/xml" title="XML Full-Text" href="https://www.mdpi.com/1424-8220/23/3/1388/xml"> <meta name="fulltext_xml" content="https://www.mdpi.com/1424-8220/23/3/1388/xml"> <meta name="citation_xml_url" content="https://www.mdpi.com/1424-8220/23/3/1388/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/sensors-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/1424-8220/23/3/1388" /> <meta property="og:title" content="Speeding up Smartphone-Based Dew Computing: In Vivo Experiments Setup Via an Evolutionary Algorithm" /> <meta property="og:description" content="Dew computing aims to minimize the dependency on remote clouds by exploiting nearby nodes for solving non-trivial computational tasks, e.g., AI inferences. Nowadays, smartphones are good candidates for computing nodes; hence, smartphone clusters have been proposed to accomplish this task and load balancing is frequently a subject of research. Using the same real—i.e., in vivo—testbeds to evaluate different load balancing strategies based on energy utilization is challenging and time consuming. In principle, test repetition requires a platform to control battery charging periods between repetitions. Our Motrol hard-soft device has such a capability; however, it lacks a mechanism to assure and reduce the time in which all smartphone batteries reach the level required by the next test. We propose an evolutionary algorithm to execute smartphone battery (dis)charging plans to minimize test preparation time. Charging plans proposed by the algorithm include charging at different speeds, which is achieved by charging at maximum speed while exercising energy hungry components (the CPU and screen). To evaluate the algorithm, we use various charging/discharging battery traces of real smartphones and we compare the time-taken for our method to collectively prepare a set of smartphones versus that of individually (dis)charging all smartphones at maximum speed." /> <meta property="og:image" content="https://pub.mdpi-res.com/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g001-550.jpg?1674743854" /> <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="Cookiebot" data-cfasync="false" src="https://consent.cookiebot.com/uc.js" data-cbid="51491ddd-fe7a-4425-ab39-69c78c55829f" type="text/javascript" async></script>  <script type="text/plain" data-cookieconsent="statistics"> (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); 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hypothesis_container"> by <span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop10159351' data-options='is_hover:true, hover_timeout:5000'> Virginia Yannibelli</div><div id="profile-card-drop10159351" 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="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Virginia Yannibelli</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a href="https://sciprofiles.com/profile/author/RkxpVEZiMldSY3piWk10RmJRd2d4Smxyb0U4eENNVnRVTVdOYm9oZWx4eUR3VVJNNXk0blI4ZkRoYzVlYVo3TQ==?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name" class="button 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target="_blank" rel="noopener noreferrer"><img src="https://pub.mdpi-res.com/img/design/orcid.png?0465bc3812adeb52?1732286508" title="ORCID" style="position: relative; width: 13px; margin-left: 3px; max-width: 13px !important; height: auto; top: -5px;"></a>, </span><span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop10159353' data-options='is_hover:true, hover_timeout:5000'> Juan Toloza</div><div id="profile-card-drop10159353" 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="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Juan Toloza</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a 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width: 13px; margin-left: 3px; max-width: 13px !important; height: auto; top: -5px;"></a> and </span><span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop10159356' data-options='is_hover:true, hover_timeout:5000'> Cristian Mateos</div><div id="profile-card-drop10159356" 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="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Cristian Mateos</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a href="https://sciprofiles.com/profile/239441?utm_source=mdpi.com&utm_medium=website&utm_campaign=avatar_name" class="button button--color-inversed" target="_blank"> SciProfiles </a><a href="https://scilit.net/scholars?q=Cristian%20Mateos" class="button button--color-inversed" target="_blank"> Scilit </a><a href="https://www.preprints.org/search?search1=Cristian%20Mateos&field1=authors" class="button button--color-inversed" target="_blank"> Preprints.org </a><a href="https://scholar.google.com/scholar?q=Cristian%20Mateos" class="button button--color-inversed" target="_blank" rels="noopener noreferrer"> Google Scholar </a></div></div><sup> 1</sup><a href="https://orcid.org/0000-0001-5761-1898" target="_blank" rel="noopener noreferrer"><img src="https://pub.mdpi-res.com/img/design/orcid.png?0465bc3812adeb52?1732286508" title="ORCID" style="position: relative; width: 13px; 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 ">ISISTAN (UNICEN-CONICET), Tandil 7000, Argentina</div> </div> <div class="affiliation "> <div class="affiliation-item"><sup>2</sup></div> <div class="affiliation-name ">Department of Information Systems, University of Agder (UiA), 4604 Kristiansand, Norway</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>Sensors</em> <b>2023</b>, <em>23</em>(3), 1388; <a href="https://doi.org/10.3390/s23031388">https://doi.org/10.3390/s23031388</a> </div> <div class="pubhistory" style="font-weight: bold; padding-bottom: 10px;"> <span style="display: inline-block">Submission received: 5 December 2022</span> / <span style="display: inline-block">Revised: 18 January 2023</span> / <span style="display: inline-block">Accepted: 19 January 2023</span> / <span style="display: inline-block">Published: 26 January 2023</span> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/sensors/sections/Intelligent_Sensors">Intelligent Sensors</a>)<br/> </div> <div class="highlight-box1"> <div class="download"> <a class="button button--color-inversed button--drop-down" data-dropdown="drop-download-1047543" aria-controls="drop-supplementary-1047543" aria-expanded="false"> Download <i class="material-icons">keyboard_arrow_down</i> </a> <div id="drop-download-1047543" class="f-dropdown label__btn__dropdown label__btn__dropdown--button" data-dropdown-content aria-hidden="true" tabindex="-1"> <a class="UD_ArticlePDF" href="/1424-8220/23/3/1388/pdf?version=1674743766" data-name="Speeding up Smartphone-Based Dew Computing: In Vivo Experiments Setup Via an Evolutionary Algorithm" data-journal="sensors">Download PDF</a> <br/> <a id="js-pdf-with-cover-access-captcha" href="#" data-target="/1424-8220/23/3/1388/pdf-with-cover" class="accessCaptcha">Download PDF with Cover</a> <br/> <a id="js-xml-access-captcha" href="#" data-target="/1424-8220/23/3/1388/xml" class="accessCaptcha">Download XML</a> <br/> <a href="/1424-8220/23/3/1388/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/1424-8220/23/3/1388/browse" >Browse Figures</a> </div> <div id="article-popup" class="popupgallery" style="display: inline; line-height: 200%"> <a href="https://pub.mdpi-res.com/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g001.png?1674743853" title=" <strong>Figure 1</strong><br/> <p>Synchronized test specification examples.</p> "> </a> <a href="https://pub.mdpi-res.com/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g002.png?1674743850" title=" <strong>Figure 2</strong><br/> <p>Overview of Motrol synchronized test plan execution workflow.</p> "> </a> <a href="https://pub.mdpi-res.com/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g003.png?1674743841" title=" <strong>Figure 3</strong><br/> <p>Charging traces for smartphones considered in the experiments.</p> "> </a> <a href="https://pub.mdpi-res.com/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g004.png?1674743847" title=" <strong>Figure 4</strong><br/> <p>Discharging traces for smartphones considered in the experiments.</p> "> </a> <a href="https://pub.mdpi-res.com/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g005.png?1674743843" title=" <strong>Figure 5</strong><br/> <p>Encoded solution for an example case.</p> "> </a> <a href="https://pub.mdpi-res.com/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g006.png?1674743844" title=" <strong>Figure 6</strong><br/> <p>MAPE values and times <span class="html-italic">t</span>(<span class="html-italic">s<sub>i</sub></span>) of two feasible solutions for an example case (Y axis is in milliseconds).</p> "> </a> <a href="https://pub.mdpi-res.com/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g007.png?1674743839" title=" <strong>Figure 7</strong><br/> <p>Example of the crossover process.</p> "> </a> <a href="https://pub.mdpi-res.com/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g008.png?1674743842" title=" <strong>Figure 8</strong><br/> <p>Mutation process example.</p> "> </a> </div> <a class="button button--color-inversed" href="/1424-8220/23/3/1388/review_report">Review Reports</a> <a class="button button--color-inversed" href="/1424-8220/23/3/1388/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">Dew computing aims to minimize the dependency on remote clouds by exploiting nearby nodes for solving non-trivial computational tasks, e.g., AI inferences. Nowadays, smartphones are good candidates for computing nodes; hence, smartphone clusters have been proposed to accomplish this task and load balancing is frequently a subject of research. Using the same real—i.e., in vivo—testbeds to evaluate different load balancing strategies based on energy utilization is challenging and time consuming. In principle, test repetition requires a platform to control battery charging periods between repetitions. Our Motrol hard-soft device has such a capability; however, it lacks a mechanism to assure and reduce the time in which all smartphone batteries reach the level required by the next test. We propose an evolutionary algorithm to execute smartphone battery (dis)charging plans to minimize test preparation time. Charging plans proposed by the algorithm include charging at different speeds, which is achieved by charging at maximum speed while exercising energy hungry components (the CPU and screen). To evaluate the algorithm, we use various charging/discharging battery traces of real smartphones and we compare the time-taken for our method to collectively prepare a set of smartphones versus that of individually (dis)charging all smartphones at maximum speed.</div> </section> <div id="html-keywords"> <div class="html-gwd-group"><div id="html-keywords-title">Keywords: </div><a href="/search?q=dew+computing">dew computing</a>; <a href="/search?q=smartphones">smartphones</a>; <a href="/search?q=profiling">profiling</a>; <a href="/search?q=benchmarking">benchmarking</a>; <a href="/search?q=Motrol">Motrol</a>; <a href="/search?q=evolutionary+computing">evolutionary computing</a></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-sensors-23-01388' type='intro'><h2 data-nested='1'> 1. Introduction</h2><div class='html-p'>Dew computing is an emerging paradigm that promotes the utilization of on-premise edge computing resources to execute different kinds of user applications, with the aim of reducing the dependency on remote computing resources provided by the cloud [<a href="#B13-sensors-23-01388" class="html-bibr">13</a>] and fog environments [<a href="#B14-sensors-23-01388" class="html-bibr">14</a>], and thus improving user experience due to reduced network latency [<a href="#B1-sensors-23-01388" class="html-bibr">1</a>]. </div><div class='html-p'>In Dew environments, smartphones are considered as valuable on-premise computing resources [<a href="#B2-sensors-23-01388" class="html-bibr">2</a>]. This is mainly because of the capabilities of the newest smartphone models in the market in terms of computing power, battery capacity, and energy management. However, to build knowledge on the collective capabilities of these nodes in such environments, a platform that facilitates the execution and reproduction of battery-driven live tests, which are focused on studying the impact on battery usage of scavenging user’s smartphone resources is essential.</div><div class='html-p'>In this respect, one of the most recently proposed platforms to study smartphone capabilities in Dew environments is Motrol [<a href="#B3-sensors-23-01388" class="html-bibr">3</a>,<a href="#B7-sensors-23-01388" class="html-bibr">7</a>]. This platform offers the possibility to execute benchmarks and battery profiling tests on a set of attached smartphones, whose energy supply is controlled via a REST API. The platform is supported on Android smartphones due to the popularity of this mobile OS [<a href="#B15-sensors-23-01388" class="html-bibr">15</a>], with over 70% of the market share as of August 2022; nevertheless, the concepts presented in this paper and the broader research line are mobile OS agnostic.</div><div class='html-p'>Benchmarks aim to measure individual capabilities of smartphones when performing certain tasks, such as determining MFLOPs through the Linpack benchmark. Battery profiling records timestamped battery level changes registered in the context of using a combination of certain components, for example, maintaining CPU usage at 100% while the screen is on. Battery level change events can be read through the API exposed by Android [<a href="#B10-sensors-23-01388" class="html-bibr">10</a>] or iOS [<a href="#B11-sensors-23-01388" class="html-bibr">11</a>]. Collecting battery profiles of the same smartphone by varying components combined usage while combining portions of these profiles in a unique timeline allow researchers to model battery behavior based on real world data [<a href="#B8-sensors-23-01388" class="html-bibr">8</a>].</div><div class='html-p'>There is another type of test, called a synchronized test, which aims to study collective capabilities of smartphones in executing a compute-intensive scenario, for example, a set of distributable workloads from a specialized AI application such as object recognition from images using neural networks [<a href="#B9-sensors-23-01388" class="html-bibr">9</a>]. With this type of test, it is relevant to study different load balancing algorithms to distribute such workloads, with a common base of comparison given by measuring energy utilization disparity among smartphones performed by each algorithm. In this kind of test, the experimentation steps are as follows:</div><div class='html-p'><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>Define a workload;</div></dd><dt id=''>(2)</dt><dd><div class='html-p'>Define the initial conditions for the testbed;</div></dd><dt id=''>(3)</dt><dd><div class='html-p'>For each load balancing algorithm within the set of load balancing algorithms under evaluation: </div><div class='html-p'><dl class='html-alpha-lower'><dt id=''>(a)</dt><dd><div class='html-p'>Assure initial conditions for the testbed;</div></dd><dt id=''>(b)</dt><dd><div class='html-p'>Run the workload on the testbed using the current load balancing algorithm;</div></dd><dt id=''>(c)</dt><dd><div class='html-p'>Collect results for further analysis.</div></dd></dl></div></dd></dl></div><div class='html-p'>Since real–i.e., in vivo–testbeds with battery-driven devices are involved, recreating experimental conditions, i.e., performing step 3a, is challenging. In order to make workload assignment comparisons as fair as possible, device battery levels should be restored from test to test to the value configured for the experimental scenario. The latter might require that Device A has x%, Device B has y% and Device C has z% battery levels when workload assignment of a particular load balancing algorithm starts. Thus, assuring these battery levels upon starting the evaluation of each load balancing algorithm is necessary for the sake of fair comparison.</div><div class='html-p'>The contributions of this work regarding the state-of-the-art methodologies to run battery-driven tests on smartphone cluster testbeds are the following:</div><div class='html-p'><dl class='html-bullet'><dt id=''>–</dt><dd><div class='html-p'>Inclusion of a multi-device battery preparation stage as an optimization problem that uses time-related battery (dis)charging events as input;</div></dd><dt id=''>–</dt><dd><div class='html-p'>Proposal of an evolutionary algorithm to automate and minimize the battery preparation time, evaluated using real smartphone battery traces and several combinations of smartphone cluster sizes and target battery levels;</div></dd><dt id=''>–</dt><dd><div class='html-p'>Publicly available evolutionary algorithm and simulation engine code, experiment configuration and battery traces for reuse and modification. </div></dd></dl></div><div class='html-p'>The remainder of the paper is organized as follows. In <a href="#sec2-sensors-23-01388" class="html-sec">Section 2</a>, we present an overview of the Motrol platform, designed to study smartphone capabilities in Dew environments. In <a href="#sec3-sensors-23-01388" class="html-sec">Section 3</a>, we present our novel software component for Motrol, which aims to prepare smartphones for synchronized tests using evolutionary computing. In <a href="#sec4-sensors-23-01388" class="html-sec">Section 4</a>, we present the experiments carried out to evaluate this novel component. <a href="#sec5-sensors-23-01388" class="html-sec">Section 5</a> presents related work. Finally, in <a href="#sec6-sensors-23-01388" class="html-sec">Section 6</a>, we present the conclusions of this work and future works.</div></section><section id='sec2-sensors-23-01388' type=''><h2 data-nested='1'> 2. The Motrol Platform: Background on the Architecture and Basic Concepts</h2><div class='html-p'>The Motrol platform is aimed to evaluate individual and collective capabilities of smartphones. To achieve this, this platform utilizes a backend server and an Android application named Normapp [<a href="#B24-sensors-23-01388" class="html-bibr">24</a>]. The platform allows users to attach up to four smartphones and dynamically control their energy supply via custom hardware [<a href="#B7-sensors-23-01388" class="html-bibr">7</a>] considering three energy states (no energy supply, AC power, and USB charging). We describe below the characteristics of the backend server and Normapp, and the collaboration between them to reach the aim of this platform. Moreover, we describe where on this platform the new software component proposed in this paper is located, and how the component interacts with the existing ones.</div><div class='html-p'>Motrol is an in-lab experimental platform that follows the client-server architectural style. In this sense, a backend server that runs on an Ri4 [<a href="#B12-sensors-23-01388" class="html-bibr">12</a>] receives jobs to be executed on the attached smartphones. The clients are the smartphones that, while rendering service to the platform, listen for jobs to be executed and send results back to the server. Currently, the platform supports two kinds of jobs: benchmarks/profiling and synchronized tests.</div><div class='html-p'>The main purpose of benchmarking/profiling jobs is to individually characterize smartphone capabilities [<a href="#B4-sensors-23-01388" class="html-bibr">4</a>]. Feeding the platform with a set of benchmarking/profiling jobs means that all the attached smartphones process the entire set in parallel. An example of a benchmark job is the Linpack benchmark which measures the floating-point operations a device can achieve per second. </div><div class='html-p'>A profiling job, specifically a (dis)charging battery profile, captures the battery behavior of a device under certain resource usage conditions. For example, a profile might provide time-related information of battery discharging events under a configured CPU usage, e.g., 100%, and screen state, e.g., screen on, during the time the battery level starts at 100% until it reaches 1%. The output of such a profiling job is a battery trace which can then be used to model battery behavior for simulation purposes [<a href="#B8-sensors-23-01388" class="html-bibr">8</a>].</div><div class='html-p'>Synchronized tests, in contrast, aim to evaluate the aggregated computational capabilities of smartphone groups; hence, they are useful for evaluating load balancing algorithms [<a href="#B5-sensors-23-01388" class="html-bibr">5</a>]. This in turn is relevant, for instance, to study how different algorithms impact the smartphone’s battery usage while processing the input workload. To run this kind of test, it is required to first define a <span class='html-italic'>scenario</span>, which consists of selecting a starting battery level (not necessarily the same) for all smartphones participating in the test and a workload. <a href="#sensors-23-01388-f001" class="html-fig">Figure 1</a> shows three scenario descriptor files (associated with synchronized tests) in JSON format, which have been simplified to highlight relevant parts. These parts are the participating smartphones with the desired start battery levels—which along with the configured workload, remain the same in our example for the three files—and load balancing algorithms, which vary from test to test.</div><div class='html-p'><a href="#sensors-23-01388-f002" class="html-fig">Figure 2</a> depicts an overview of all stages involved in the execution of synchronized tests. As said, the first stage requires human intervention and involves writing at least one synchronized test specification to indicate the platform relevant runtime entities, including participating devices (smartphones models)—each of them configured with a start battery level—, a workload represented by a series of items (images) that a Java module implemented as part of Normapp processes to produce a result (e.g., object recognition associated with an specific application), and a specific load balancing algorithm to distribute the workload among participant devices. Since this stage mainly involves writing test specifications in the JSON format, there are no steps in the figure that are associated with this stage.</div><div class='html-p'>The second stage is semi-automatic because it requires user intervention to attach and register devices to Motrol sockets. This stage is where platform setup is performed. For a detailed explanation of this stage, please refer to [<a href="#B7-sensors-23-01388" class="html-bibr">7</a>], where the involved steps are illustrated in a video.</div><div class='html-p'>The last step is synchronized test plan execution, which aims to be a smart, automatic stage with the proposed evolutionary algorithm introduced in this work. A detailed look into this stage reveals three steps that are performed upon the initiation of a new synchronized test. The first step is the one targeted by the proposed solution and comprises device battery preparation. This is facilitated by a software/hardware platform [<a href="#B4-sensors-23-01388" class="html-bibr">4</a>]. However, doing this automatically while reducing preparation time so as to complete a set of synchronized tests as early as possible is not addressed by the platform. This preparation time might account for a considerable time per test, considering that while some smartphones might quickly reach the target level, others might be slower in doing so, which in turn jeopardizes the preparation of the former. It is worth mentioning that battery level preparation does not necessarily mean that all devices participating in a test should reach the same battery level. Instead, within a real Dew computing scenario, devices might collaborate with task computation while joining the group with a different battery level. The goal of this step is then to assure reproducibility of certain battery level configurations for all devices when the same scenario is exercised for different load balancing algorithms; thus, a common ground for comparison is established.</div><div class='html-p'>The test execution and results post processing steps are shown to complete the description of the synchronized test plan execution stage. These steps do not affect the main functioning of the proposed evolutionary algorithm.</div><section id='TheBatteryPreparationProblemforRunningSynchronizedTests' type=''><h4 class='html-italic' data-nested='2'> The Battery Preparation Problem for Running Synchronized Tests</h4><div class='html-p'>Motrol provides a basic functionality to individually charge or discharge, i.e., <span class='html-italic'>prepare</span>, a device battery to run a synchronized test. However, preparing devices for running a synchronized test requires a component with a global view of the preparation progress of the whole set of devices. Once a device reaches its configured battery level, e.g., x%, the platform marks it as ready for start the synchronized test, and only when all devices participating in a test are marked as ready does the test effectively start. However, by following this device preparation logic, it is not hard to fall into situations where a device (marked as ready) waits for other devices to reach their configured battery level, causing its own battery level to deviate from the required one, forcing another wait for a preparation state, the complexity of which varies with the number of devices participating in a test.</div><div class='html-p'>A way of avoiding this situation is by applying sequences of charge/discharge actions on the devices in the set so that all of them reach the configured battery levels at similar points in time. However, determining these sequences of actions, while keeping the time-taken for this to a minimum for the set of devices, leads to a complex combinatorial optimization problem. In this paper, we present a novel software component for Motrol that tackles this problem, which automatically prepares a set of devices to start a synchronized test. This component uses a specially designed evolutionary algorithm that has a global view of the smartphone preparation progress.</div></section></section><section id='sec3-sensors-23-01388' type=''><h2 data-nested='1'> 3. Evolutionary-based Preparation of Smartphones for Synchronized Test Plans</h2><div class='html-p'>We developed a novel software component for Motrol, which is aimed to automatically prepare a given set of smartphones for executing a synchronized test. This component considers a usual pre-condition of synchronized test plans. This pre-condition imposes pre-defined start battery levels for the smartphones in the set. Then, the component utilizes a specially designed evolutionary algorithm that produces a sequence of charging/discharging actions to prepare the whole set of smartphones so that this pre-condition is satisfied. Specifically, the algorithm is aimed at reaching the configured start battery levels in the minimum possible amount of time for the set of smartphones. We detail below the input to this component. Then, we describe in detail the general behavior in terms of evolutionary computing used by this component.</div><section id='sec3dot1-sensors-23-01388' type=''><h4 class='html-italic' data-nested='2'> 3.1. Input Data of the Component and Pre-Condition Considered</h4><div class='html-p'>The component receives as input data a given set of <span class='html-italic'>m</span> smartphones attached to Motrol. Each one of the smartphones in the set has a known initial current battery level, where this level is represented as an integer in the range [0,100]%. In addition, each smartphone has associated timestamped battery charge/discharge profiles. Battery profiles represent realistic time-related information of a smartphones charging/discharging behavior, i.e., they allow the evolutionary algorithm to know the time (in milliseconds) required to charge/discharge the battery of the smartphone from a given level to another given level.</div><div class='html-p'>We firstly collected discharging and charging profiles in a laboratory context by following the procedure documented in [<a href="#B8-sensors-23-01388" class="html-bibr">8</a>]. Capturing battery profiles is a time-consuming task, especially when considering the energy consumption impact of all hardware components and its different operational modes, e.g., DVFS (dynamic voltage frequency scaling), for CPUs. Then, for practical reasons but without losing generality, we obtained profiles targeting certain combinations of discrete CPU usages <0, 30, 50, 75, 100> (in %) and screen states (on/off), resulting in different energy consumption rates. <a href="#sensors-23-01388-f003" class="html-fig">Figure 3</a> and <a href="#sensors-23-01388-f004" class="html-fig">Figure 4</a> show a timeline representation of all charging and discharging battery profiles for the smartphones considered in the experiment. Combinations of CPU usage and screen state were not deliberately selected but aim to represent the common mobile usage patterns. For instance, a profile with 0% CPU usage and an off screen represents an idle smartphone; a profile with 30% CPU usage and an on screen represents a low demand interactive task, e.g., video playback; and so on.</div><div class='html-p'>This component also considers a pre-condition given by the start battery levels (not necessarily the same) for the <span class='html-italic'>m</span> smartphones in the set. Thus, the component also receives the given start battery level for each smartphone in the set as input data, where this level is represented as an integer in the range [0,100]%.</div></section><section id='sec3dot2-sensors-23-01388' type=''><h4 class='html-italic' data-nested='2'> 3.2. The Designed Evolutionary Algorithm</h4><div class='html-p'>Once the component receives all the input data detailed in <a href="#sec3dot1-sensors-23-01388" class="html-sec">Section 3.1</a>, it applies our designed evolutionary algorithm. This algorithm explores different sequences of charge/discharge actions that, at experimentation time, could be applied on the smartphones in the set to reach the given start battery levels, with the aim of finding the sequences of actions that reach these levels at the minimal possible time for the set of smartphones. In other words, this implies minimizing the preparation time for these smartphones under the given pre-conditions.</div><div class='html-p'>This evolutionary algorithm begins by creating an initial population with <span class='html-italic'>s</span> feasible encoded solutions. Each solution encodes and represents sequences of charge/discharge actions that could be applied on the <span class='html-italic'>m</span> smartphones to achieve the given start battery levels based on the current battery levels of the smartphones. Then, each solution in this population is evaluated by a fitness evaluation process, according to the considered objective: reaching the given start battery levels in the minimum possible amount of time for the set of smartphones. Then, the algorithm develops an iterative behavior until reaching the stop condition.</div><div class='html-p'>In each iteration, a parent selection process is applied to the current population to determine which solutions of this population will compose the mating pool, and therefore will be utilized to generate new encoded solutions. In this respect, the well-known tournament selection process [<a href="#B6-sensors-23-01388" class="html-bibr">6</a>] is applied with a tournament size <span class='html-italic'>k</span>, to promote the selection of diverse high-fitness solutions regarding the sequences of actions indicated for the <span class='html-italic'>m</span> smartphones. Then, the solutions in the mating pool are paired, and a crossover process is applied on each pair of solutions with a probability <span class='html-italic'>P<sub>c</sub></span> to generate a pool of new solutions. In this sense, we designed a crossover process feasible for the used encoding of solutions, which generates new solutions by interchanging the sequences of actions indicated for the <span class='html-italic'>m</span> smartphones in the parent solutions. Then, a mutation process is applied on each new solution with a probability <span class='html-italic'>P<sub>m</sub></span> to incorporate diversity in the pool of new solutions. In this respect, we designed a mutation process feasible for the used encoding of solutions, which generates changes in the sequences of actions indicated for the <span class='html-italic'>m</span> smartphones. After that, each new solution is evaluated by the fitness evaluation process. Then, a survival selection process is applied on the current population and the pool of new solutions to decide which solutions will compose the new population for the next iteration. In this respect, the well-known steady-state selection process is applied [<a href="#B6-sensors-23-01388" class="html-bibr">6</a>], with a replacement percentage <span class='html-italic'>r</span>, in order to preserve the best solutions obtained by the algorithm so far.</div><div class='html-p'>Once the algorithm reaches the stop condition (i.e., after a given number of iterations, the algorithm outputs the best solution in the last population as result). This solution is used by the component to automatically prepare the whole set of <span class='html-italic'>m</span> smartphones.</div><section id='sec3dot2dot1-sensors-23-01388' type=''><h4 class='' data-nested='3'> 3.2.1. Encoding of Solutions</h4><div class='html-p'>Each solution in the population of the algorithm is represented as an <span class='html-italic'>m</span>-tuple <<span class='html-italic'>s</span><sub>1</sub>, <span class='html-italic'>s</span><sub>2</sub>, …, <span class='html-italic'>s<sub>m</sub></span>>, where <span class='html-italic'>m</span> is the number of smartphones considered, i.e., attached to the platform at the time the synchronized test starts. Then, the term <span class='html-italic'>s<sub>i</sub></span> (<span class='html-italic'>i</span> = 1,…, <span class='html-italic'>m</span>) represents a feasible sequence of charge/discharge actions (<span class='html-italic'>a<sub>i</sub></span><sub>1</sub>, <span class='html-italic'>a<sub>i</sub></span><sub>2</sub>, …, <span class='html-italic'>a<sub>in(i)</sub></span>) for smartphone <span class='html-italic'>i</span>, which allows to reach <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) (the start battery level corresponding to <span class='html-italic'>i</span>) from <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) (the current battery level of <span class='html-italic'>i</span>). When <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) is lower than <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) must be increased; thus, sequence <span class='html-italic'>s<sub>i</sub></span> only includes battery charge actions. Otherwise, when <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) is higher than <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) must be decreased; thus, sequence <span class='html-italic'>s<sub>i</sub></span> only includes discharge actions. In both cases, the number, <span class='html-italic'>n(i)</span>, of actions of the sequence <span class='html-italic'>s<sub>i</sub></span> is calculated as detailed in Equations (1) and (2). <div class='html-disp-formula-info' id='FD1-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>n</mi> <mfenced> <mi>i</mi> </mfenced> <mo>=</mo> <mi>a</mi> <mi>c</mi> <mi>t</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mfenced> <mi>i</mi> </mfenced> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(1)</label> </div> </div><div class='html-disp-formula-info' id='FD2-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>a</mi> <mi>c</mi> <mi>t</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mfenced> <mi>i</mi> </mfenced> <mo>=</mo> <mfenced close="|" open="|"> <mrow> <mo> </mo> <mi>c</mi> <mi>b</mi> <mi>l</mi> <mfenced> <mi>i</mi> </mfenced> <mo>−</mo> <mi>s</mi> <mi>b</mi> <mi>l</mi> <mfenced> <mi>i</mi> </mfenced> </mrow> </mfenced> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(2)</label> </div> </div></div><div class='html-p'>Each action <span class='html-italic'>a<sub>ij</sub></span> (<span class='html-italic'>j</span> = 1,…,<span class='html-italic'>n(i)</span>) is represented as a tuple with five elements: <<span class='html-italic'>k_action</span>, <span class='html-italic'>initial_level</span>, <span class='html-italic'>finish_level</span>, <span class='html-italic'>CPU_load</span>, <span class='html-italic'>screen_state</span>>, where <span class='html-italic'>k_action</span> refers to the kind of battery-related action (i.e., charge/discharge), <span class='html-italic'>initial_level</span> indicates the initial battery level for the action, and <span class='html-italic'>finish_level</span> indicates the end battery level for the action. The element <span class='html-italic'>CPU_load</span> refers to the CPU load under which the action increases/decreases from/to <span class='html-italic'>initial_level</span>. As mentioned in <a href="#sec3dot1-sensors-23-01388" class="html-sec">Section 3.1</a>, CPU load belongs to the set {0, 30, 50, 75, 100}%. Finally, the element <span class='html-italic'>screen_state</span> refers to the screen state (i.e., on/off) under which the action increases/decreases from/to <span class='html-italic'>initial_level</span>.</div><div class='html-p'>Thus, the length of an encoded solution <<span class='html-italic'>s</span><sub>1</sub>, <span class='html-italic'>s</span><sub>2</sub>, …, <span class='html-italic'>s<sub>m</sub></span>> is calculated as detailed in Equation (3). <div class='html-disp-formula-info' id='FD3-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>l</mi> <mi>e</mi> <mi>n</mi> <mi>g</mi> <mi>t</mi> <mi>h</mi> <mfenced> <mrow> <mfenced close="⟩" open="⟨"> <mrow> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>s</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>s</mi> <mi>m</mi> </msub> </mrow> </mfenced> </mrow> </mfenced> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <mi>n</mi> <mfenced> <mi>i</mi> </mfenced> <mo>∗</mo> <mn>5</mn> </mrow> </mstyle> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(3)</label> </div> </div></div><div class='html-p'><a href="#sensors-23-01388-f005" class="html-fig">Figure 5</a> shows a sample encoded solution where two smartphones are considered, and a test plan requiring these smartphones to start with 23% and 71% of battery, respectively. In relation to smartphone 1, it has a current battery level of 20%. Thus, the solution proposes a sequence of three charge actions for this smartphone. In this sequence, the first action increases the battery level from 20% to 21% under a CPU load of 30% with the screen on. Then, the second action increases the battery level from 21% to 22% under a CPU load of 75% with the screen off. Finally, the third action increases the battery level from 22% to 23% under a CPU load of 100% with the screen on. Thus, this sequence starts from the battery level 20% and reaches the required battery level of 23%. Regarding smartphone 2, it has a current battery level of 75%. Here, the solution proposes a sequence of four discharge actions for this smartphone. This sequence starts from the battery level 75% and reaches the required battery level of 71%.</div></section><section id='sec3dot2dot2-sensors-23-01388' type=''><h4 class='' data-nested='3'> 3.2.2. Fitness Evaluation Process</h4><div class='html-p'>This process is applied to evaluate each encoded solution of the population according to the objective considered. Recall that the objective is to reach the pre-defined start battery levels for the <span class='html-italic'>m</span> smartphones in the minimum amount of time for the set of smartphones. Considering that, as detailed below, the minimal possible time to prepare the set of <span class='html-italic'>m</span> smartphones can be estimated as per the existence of (dis)charge profiles, then the mentioned objective means minimizing the difference (i.e., the error) between the time required by each smartphone to achieve the corresponding start battery level and the minimal possible time to prepare the set of <span class='html-italic'>m</span> smartphones. In order to evaluate each encoded solution regarding this objective, the process follows the steps described below.</div><div class='html-p'>Given an encoded solution <<span class='html-italic'>s</span><sub>1</sub>, <span class='html-italic'>s</span><sub>2</sub>, …, <span class='html-italic'>s<sub>m</sub></span>>, where <span class='html-italic'>s<sub>i</sub></span> represents a feasible sequence of charge/discharge actions to prepare the smartphone <span class='html-italic'>i</span>, the process calculates the average difference (i.e., average error) between the time of each sequence <span class='html-italic'>s<sub>i</sub></span> and the minimum amount of time to prepare the <span class='html-italic'>m</span> smartphones. This average difference is determined by a well-known metric named mean absolute percentage error (MAPE). This metric is calculated as detailed in Equation (4), where <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>) refers to the time (milliseconds) of <span class='html-italic'>s<sub>i</sub></span> and <span class='html-italic'>T</span> is the minimal possible time (milliseconds) to prepare the <span class='html-italic'>m</span> smartphones. The term <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>) is calculated by Equation (5), where <span class='html-italic'>t</span>(<span class='html-italic'>a<sub>ij</sub></span>) represents the time (milliseconds) required to develop the action <span class='html-italic'>a<sub>ij</sub></span>. In this respect, the times of actions <span class='html-italic'>a<sub>ij</sub></span> are provided by the charge/discharge profiles of smartphone <span class='html-italic'>i</span>.</div><div class='html-p'>The term <span class='html-italic'>T</span> is calculated by Equation (6), where <span class='html-italic'>min</span>(<span class='html-italic'>i</span>) refers to the minimum amount of time in milliseconds (i.e., optimal time) for preparing smartphone <span class='html-italic'>i</span>. Then, the maximum of these minimum preparation times defines the minimal possible time to prepare the whole set of <span class='html-italic'>m</span> smartphones so they all reach the next battery level as specified in the test plan being exercised. Regarding min(<span class='html-italic'>i</span>), this time is provided by the existing charge/discharge profiles of <span class='html-italic'>i</span>. Specifically, when the current battery level of <span class='html-italic'>i</span> must be charged to reach the start battery level pre-defined for <span class='html-italic'>i</span>, the minimal possible time is achieved by charging the battery under a CPU load of 0% with the screen off. Thus, the minimal possible time to prepare <span class='html-italic'>i</span> is provided by the charge profile inherent to a CPU load of 0% with the screen off. This is the case when the current test specifies a higher battery level than the current battery level of smartphone <span class='html-italic'>i</span>; thus, a CPU load of 0% with the screen off means <span class='html-italic'>charging</span> at a high rate. On the other hand, when the current battery level of <span class='html-italic'>i</span> must be discharged to reach the start battery level pre-defined for <span class='html-italic'>i</span>, the minimal possible time is achieved by discharging the battery under a CPU load of 100% with the screen on. Therefore, the minimal possible time to prepare <span class='html-italic'>i</span> is provided by the discharge profile inherent to a CPU load of 100% with the screen on. This is the case when the current test specifies a lower battery level than the current battery level of smartphone <span class='html-italic'>i</span>; thus, a CPU load of 100% with the screen on means <span class='html-italic'>discharging</span> at a high rate.</div><div class='html-p'>By applying Equation (4), an MAPE value higher than or equal to 0% is assigned as the fitness value of each encoded solution. Better MAPE values (i.e., lower MAPE values) are assigned to those solutions in which the times, <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>), of the sequences <span class='html-italic'>s<sub>i</sub></span> detailed for preparing the <span class='html-italic'>m</span> smartphones are closest to <span class='html-italic'>T</span>. In these solutions, the times, <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>), of the sequences <span class='html-italic'>s<sub>i</sub></span> are also closer to each other. Therefore, these solutions minimize the discharge of the <span class='html-italic'>m</span> smartphones once these are prepared according to the sequences <span class='html-italic'>s<sub>i</sub></span> (i.e., once the start battery levels, <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), are reached).</div><div class='html-p'><a href="#sensors-23-01388-f006" class="html-fig">Figure 6</a> shows the MAPE values and the times <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>) of the sequences <span class='html-italic'>s<sub>i</sub></span> of two feasible solutions A and B for an example case where a set of four smartphones have to be prepared. These solutions differ considerably regarding their MAPE value. In this sense, the MAPE value of solution A (0.01%) is much better (i.e., much lower) than that of solution B (52.37%). This is because the times, <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>), of solution A (i.e., <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>1</sub>) = 16,575,027, <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>2</sub>) = 16,575,096, <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>3</sub>) = 16,584,583, and <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>4</sub>) = 16,575,097) are closer to <span class='html-italic'>T</span> than those of solution B (i.e., <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>1</sub>) = 5,819,963, <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>2</sub>) = 16,575,096, <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>3</sub>) = 1,623,840, and <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>4</sub>) = 7,560,004). As a result, the times, <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>), of solution A are closer to each other. Specifically, the times, <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>), of solution A have very low differences among them (i.e., differences are in the range of [1,9556] ms), whereas the times, <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>), of solution B have very significant differences among them (i.e., the differences are in the range of [9,015,092, 14,951,256] ms).</div><div class='html-p'>This means than these solutions differ with respect to the discharge of the smartphones once the start battery levels, <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), are reached. In this sense, in solution A, the time <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>3</sub></span>) is the maximum of the times <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>). Therefore, smartphone 1 will reach <span class='html-italic'>sbl</span>(1) at <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>1</sub>), and so it will be prepared before smartphone 3 reaches <span class='html-italic'>sbl</span>(3). Then, given that the time between <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>1</sub>) and <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>3</sub>) (i.e., 9556 ms) is not enough to decrease <span class='html-italic'>sbl</span>(1), smartphone 1 will maintain <span class='html-italic'>sbl</span>(1) until smartphone 3 reaches <span class='html-italic'>sbl</span>(3). In a similar way, smartphone 2 will maintain <span class='html-italic'>sbl</span>(2) and smartphone 4 will maintain <span class='html-italic'>sbl</span>(4) until smartphone 3 reaches <span class='html-italic'>sbl</span>(3). Thus, solution A prevents the discharge of the start battery levels <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) reached by the smartphones. Unlike solution A, in solution B, the time <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>2</sub>) is the maximum of the times <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>). Thus, smartphone 4 will reach <span class='html-italic'>sbl</span>(4) at <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>4</sub>), and it will be prepared before smartphone 2 reaches <span class='html-italic'>sbl</span>(2). Then, since the time between <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>4</sub>) and <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>2</sub>) (i.e., 9,015,092 ms) is long enough to decrease <span class='html-italic'>sbl</span>(4), smartphone 4 will not be able to maintain <span class='html-italic'>sbl</span>(4) until smartphone 2 reaches <span class='html-italic'>sbl</span>(2). Likewise, smartphone 1 will not be able to maintain <span class='html-italic'>sbl</span>(1) and smartphone 3 will not be able to maintain <span class='html-italic'>sbl</span>(3) until smartphone 2 reaches <span class='html-italic'>sbl</span>(2). Note that the decrease in the levels of <span class='html-italic'>sbl</span>(4)/<span class='html-italic'>sbl</span>(1)/<span class='html-italic'>sbl</span>(3) (in battery units) depends on the time between <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>4</sub>)/<span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>1</sub>)/<span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>3</sub>) and <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>2</sub>). The longer the time between <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>4</sub>)/<span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>1</sub>)/<span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>3</sub>) and <span class='html-italic'>t</span>(<span class='html-italic'>s</span><sub>2</sub>), the higher the decrease in <span class='html-italic'>sbl</span>(4)/<span class='html-italic'>sbl</span>(1)/<span class='html-italic'>sbl</span>(3). Therefore, solution B enables the discharge of the start battery levels <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) reached by the smartphones. All in all, solution A outperforms solution B in terms of minimizing the discharge of the smartphones once the start battery levels <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) are reached. <div class='html-disp-formula-info' id='FD4-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <mi>E</mi> <mfenced> <mrow> <mfenced close="⟩" open="⟨"> <mrow> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>s</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>s</mi> <mi>m</mi> </msub> </mrow> </mfenced> </mrow> </mfenced> <mo>=</mo> <mfrac> <mrow> <mn>100</mn> </mrow> <mi>m</mi> </mfrac> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <mfrac> <mrow> <mfenced close="|" open="|"> <mrow> <mi>T</mi> <mo>−</mo> <mi>t</mi> <mfenced> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> </mrow> </mfenced> </mrow> </mfenced> </mrow> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(4)</label> </div> </div><div class='html-disp-formula-info' id='FD5-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>t</mi> <mfenced> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> </mrow> </mfenced> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>i</mi> <mo stretchy="false">)</mo> </mrow> </munderover> <mrow> <mi>t</mi> <mfenced> <mrow> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </mfenced> </mrow> </mstyle> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(5)</label> </div> </div><div class='html-disp-formula-info' id='FD6-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>T</mi> <mo>=</mo> <msubsup> <mrow> <mi>max</mi> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </msubsup> <mo> </mo> <mfenced> <mrow> <mi>min</mi> <mfenced> <mi>i</mi> </mfenced> </mrow> </mfenced> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(6)</label> </div> </div></div></section><section id='sec3dot2dot3-sensors-23-01388' type=''><h4 class='' data-nested='3'> 3.2.3. Crossover Process</h4><div class='html-p'>A crossover process is applied to generate new encoded solutions from the solutions in the mating pool. In this respect, the evolutionary algorithm decides which solutions from the current population will compose the mating pool by applying the well-known tournament selection process [<a href="#B6-sensors-23-01388" class="html-bibr">6</a>]. Then, the solutions in the mating pool are organized in pairs, and the crossover process is applied on each pair of solutions with a probability <span class='html-italic'>P<sub>c</sub></span> to generate new encoded solutions. We designed a crossover process feasible for the encoding of solutions presented in <a href="#sec3dot2dot1-sensors-23-01388" class="html-sec">Section 3.2.1</a>. The details of this process is described below.</div><div class='html-p'>Given two encoded solutions, <span class='html-italic'>p</span>1 and <span class='html-italic'>p</span>2, the crossover process generates two new encoded solutions, <span class='html-italic'>o</span>1 and <span class='html-italic'>o</span>2, by following the next iterative behavior. For each one of the smartphones <span class='html-italic'>i</span>, this process considers the sequences of actions <span class='html-italic'>s<sub>i</sub></span> detailed in <span class='html-italic'>p</span>1 and <span class='html-italic'>p</span>2 for <span class='html-italic'>i</span>, and after that analyzes one by one the actions, <span class='html-italic'>a<sub>ij</sub></span>, of each sequence. For each action, <span class='html-italic'>a<sub>ij</sub></span>, of the sequence <span class='html-italic'>s<sub>i</sub></span> detailed in <span class='html-italic'>p</span>1(<span class='html-italic'>p</span>2), the process considers the five elements which compose the action and then copies the values detailed in <span class='html-italic'>p</span>1(<span class='html-italic'>p</span>2) for <span class='html-italic'>k_action</span>, <span class='html-italic'>initial_level</span>, and <span class='html-italic'>finish_level</span> to the new solution <span class='html-italic'>o</span>1(<span class='html-italic'>o</span>2), in the same positions for these values in <span class='html-italic'>p</span>1(<span class='html-italic'>p</span>2). Regarding the values detailed in <span class='html-italic'>p</span>1(<span class='html-italic'>p</span>2) for the elements <span class='html-italic'>CPU_load</span> and <span class='html-italic'>screen_state</span>, each of these values is copied to the new solution, <span class='html-italic'>o</span>1(<span class='html-italic'>o</span>2), according to a given probability, <span class='html-italic'>u</span>. Specifically, for each of the mentioned elements, the process generates a random number in the range of [0,1]. If this number is lower than <span class='html-italic'>u</span>, the process copies the value detailed in <span class='html-italic'>p</span>1(<span class='html-italic'>p</span>2) for the element to <span class='html-italic'>o</span>1(<span class='html-italic'>o</span>2), in the same position for this value in <span class='html-italic'>p</span>1(<span class='html-italic'>p</span>2). Otherwise, if this number is higher than or equal to <span class='html-italic'>u</span>, the process copies the value detailed in <span class='html-italic'>p</span>1(<span class='html-italic'>p</span>2) for the element to <span class='html-italic'>o</span>2(<span class='html-italic'>o</span>1), in the same position for this value in <span class='html-italic'>p</span>1(<span class='html-italic'>p</span>2). Therefore, this crossover process allows the generation of two new encoded solutions by interspersing the values detailed in <span class='html-italic'>p</span>1 and <span class='html-italic'>p</span>2 for the elements of the actions of each sequence.</div><div class='html-p'><a href="#sensors-23-01388-f007" class="html-fig">Figure 7</a> shows an example of the crossover process. In this example, the process is applied on the encoded solutions <span class='html-italic'>p</span>1 and <span class='html-italic'>p</span>2 and generates the encoded solutions <span class='html-italic'>o</span>1 and <span class='html-italic'>o</span>2. Bold values in <span class='html-italic'>o</span>1 and <span class='html-italic'>o</span>2 indicate values interchanged between <span class='html-italic'>p</span>1 and <span class='html-italic'>p</span>2.</div></section><section id='sec3dot2dot4-sensors-23-01388' type=''><h4 class='' data-nested='3'> 3.2.4. Mutation Process</h4><div class='html-p'>A mutation process is applied to each solution obtained by the crossover process with a probability <span class='html-italic'>P<sub>m</sub></span>, so as to incorporate diversity into the pool of new encoded solutions, and thus to preserve the diversity of the population throughout the generations of the algorithm. We designed a mutation process feasible for the encoding of solutions presented in <a href="#sec3dot2dot1-sensors-23-01388" class="html-sec">Section 3.2.1</a>. The behavior of this process is described below.</div><div class='html-p'>Considering an encoded solution <span class='html-italic'>p</span>1, our mutation process generates a new encoded solution <span class='html-italic'>o</span>1, by following the next iterative behavior. For each of the smartphones <span class='html-italic'>i</span>, this process considers the sequence of actions, <span class='html-italic'>s<sub>i</sub></span><sub>,</sub> detailed in <span class='html-italic'>p</span>1 for <span class='html-italic'>i</span>, and then analyzes one by one the actions, <span class='html-italic'>a<sub>ij</sub></span>, of this sequence. For each action, <span class='html-italic'>a<sub>ij</sub></span>, the process considers the five elements that compose the action. Then, the process copies the values detailed in <span class='html-italic'>p</span>1 for <span class='html-italic'>k_action</span>, <span class='html-italic'>initial_level</span>, and <span class='html-italic'>finish_level</span> to the new solution <span class='html-italic'>o</span>1, in the same positions for these values in <span class='html-italic'>p</span>1. In relation to the values detailed in <span class='html-italic'>p</span>1 for the elements <span class='html-italic'>CPU_load</span> and <span class='html-italic'>screen_state</span>, each one of these values is copied to the new solution <span class='html-italic'>o</span>1 according to the mutation probability, <span class='html-italic'>P<sub>m</sub></span>. In particular, for each one of the two mentioned elements, the process generates a random number in the range of [0,1]. When this number is higher than <span class='html-italic'>P<sub>m</sub></span>, the process copies the value detailed in <span class='html-italic'>p</span>1 for the element to <span class='html-italic'>o</span>1 to the same position for this value in <span class='html-italic'>p</span>1. On the other hand, when this number is lower than or equal to <span class='html-italic'>P<sub>m</sub></span>, the process does not copy the value detailed in <span class='html-italic'>p</span>1 for the element to <span class='html-italic'>o</span>1. In this case, the process randomly chooses other possible value for the element, and then copies this value to <span class='html-italic'>o</span>1 to the same position for the value detailed in <span class='html-italic'>p</span>1. Thus, this mutation process allows the generation of a new encoded solution by changing the values detailed in <span class='html-italic'>p</span>1 for the elements of the actions of each sequence according to <span class='html-italic'>P<sub>m</sub></span>.</div><div class='html-p'><a href="#sensors-23-01388-f008" class="html-fig">Figure 8</a> shows an example of the mutation process. In this example, the process is applied on the encoded solution <span class='html-italic'>p</span>1, and generates the encoded solution <span class='html-italic'>o</span>1. Bold values in <span class='html-italic'>o</span>1 indicate new values compared to those in <span class='html-italic'>p</span>1.</div></section></section></section><section id='sec4-sensors-23-01388' type=''><h2 data-nested='1'> 4. Computational Experiments</h2><div class='html-p'>As described in <a href="#sec3-sensors-23-01388" class="html-sec">Section 3</a>, the new software component proposed for Motrol uses the described evolutionary algorithm to automatically prepare a given set of smartphones. Thus, we developed computational experiments to evaluate the performance of this evolutionary algorithm on different instances of the addressed problem. The preparation time was simulated using battery profiles as described in <a href="#sec3dot1-sensors-23-01388" class="html-sec">Section 3.1</a>. By interleaving excerpts of different profiles of the same smartphone it is possible to realistically evaluate the effect of solutions proposed by the evolutionary algorithm.</div><div class='html-p'>In <a href="#sec4dot1-sensors-23-01388" class="html-sec">Section 4.1</a>, we present the example sets utilized to develop these experiments. In <a href="#sec4dot2-sensors-23-01388" class="html-sec">Section 4.2</a>, we detail the experimental settings defined for these experiments. Finally, in <a href="#sec4dot3-sensors-23-01388" class="html-sec">Section 4.3</a>, we present and analyze the obtained results.</div><section id='sec4dot1-sensors-23-01388' type=''><h4 class='html-italic' data-nested='2'> 4.1. Instance Sets</h4><div class='html-p'>As explained in <a href="#sec3-sensors-23-01388" class="html-sec">Section 3</a>, given a set of <span class='html-italic'>m</span> smartphones where each smartphone <span class='html-italic'>i</span> must (dis)charge from its current battery level, <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>), to a target (also called start) battery level, <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), the problem consists of finding the sequences of charge/discharge actions to be applied on the <span class='html-italic'>m</span> smartphones, in order to reach the target <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) levels at the same point in time and in the minimum possible amount of time.</div><div class='html-p'>To evaluate the performance of the evolutionary algorithm on diverse realistic experimental scenarios, we defined 27 sets of instances of the addressed problem. Each of these instance sets contains 10 different instances. Each instance of these sets contains a number of smartphones to be prepared. The 27 defined instance sets correspond to diverse realistic preparation scenarios in terms of the number of smartphones to be prepared (aspect S) and battery level actions (aspect A and aspect V) required to prepare the smartphones. In this sense, the category of an instance is defined in relation to these three aspects that are described below.</div><div class='html-p'><b><span class='html-italic'>Aspect S</span></b>. This aspect refers to the number of smartphones <span class='html-italic'>m</span> considered in the instance. Here, this number belongs to the following set: {4, 8, 16}. Considering that the local facet of Dew computing comprises on-premise devices within the boundaries of a wireless local area network, aspect S corresponds to potential on-premise devices in a Dew computing setting, for which we selected 16 as an upper limit representing the number of devices a domestic router can handle without compromising the delivered QoS. Thus, three different categories were considered in relation to the number of smartphones, namely S4, S8, and S16.</div><div class='html-p'><b><span class='html-italic'>Aspect A</span></b>. This aspect refers to the total number of charge/discharge actions (1 percent battery level changes) to be applied by the <span class='html-italic'>m</span> smartphones considered in the set to reach the desired start battery levels (i.e., the sum of current-to-target battery level differences of all smartphones considered in the instance). This number is named <span class='html-italic'>A</span>, and is calculated as detailed in Equation (7), where <span class='html-italic'>actions</span>(<span class='html-italic'>i</span>) refers to the number of actions to be applied by smartphone <span class='html-italic'>i</span>. Note that <span class='html-italic'>actions</span>(<span class='html-italic'>i</span>) is calculated as detailed in Equation (2) (<a href="#sec3dot2dot1-sensors-23-01388" class="html-sec">Section 3.2.1</a>). Thus, <span class='html-italic'>A</span> belongs to the value range [1*<span class='html-italic'>m</span>, 100*<span class='html-italic'>m</span>]. In this value range, the value 1*<span class='html-italic'>m</span> corresponds to the instances where each smartphone <span class='html-italic'>i</span> must apply only one action to reach the desired start battery level from the current battery level, and the value 100*<span class='html-italic'>m</span> corresponds to the instances where each smartphone <span class='html-italic'>i</span> must apply 100 actions to reach the start battery level from the current battery level. This value range has been divided into three distinct subranges in order to consider three different categories in relation to <span class='html-italic'>A</span>. Specifically, this range has been divided into the following subranges: [1*<span class='html-italic'>m</span>, 40*<span class='html-italic'>m</span>], [41*<span class='html-italic'>m</span>, 70*<span class='html-italic'>m</span>], and [71*<span class='html-italic'>m</span>, 100*<span class='html-italic'>m</span>], in order to define the categories Low A (LA), Medium A (MA), and High A (HA) with similar subrange width, respectively. <div class='html-disp-formula-info' id='FD7-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>A</mi> <mo>=</mo> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <mi>a</mi> <mi>c</mi> <mi>t</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mfenced> <mi>i</mi> </mfenced> </mrow> </mstyle> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(7)</label> </div> </div></div><div class='html-p'><b><span class='html-italic'>Aspect V</span></b>. This aspect refers to the variation in the number of charge/discharge actions among the <span class='html-italic'>m</span> smartphones considered in the set. In other words, it is a way to differentiate problem instances based on how the total number of actions (Aspect A) is distributed among participating smartphones. That is, a smartphone set where a few smartphones have to perform the majority of the total number of actions presents a quite different challenge regarding all of them performing the same percentage of the total number of actions. This variation is measured by a well-known metric named coefficient of variation (CV). This metric is calculated as detailed in Equation (8), where <span class='html-italic'>M</span> refers to the average number of actions to be applied by the <span class='html-italic'>m</span> smartphones (Equation (10)) and <span class='html-italic'>SD</span> refers to the standard deviation of the number of actions to be carried out by the <span class='html-italic'>m</span> smartphones (Equation (9)). Thus, this metric provides a real value in the range of [0,100]%. In this range, the value 0% corresponds to the instances where the <span class='html-italic'>m</span> smartphones must develop the same number of actions to reach <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) from <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) (i.e., there is no variation regarding the number of actions among the <span class='html-italic'>m</span> smartphones). This range also has been divided into three distinct subranges in order to consider three different categories in relation to V. In particular, this range has been divided into the following subranges: [0,10]%, [10,50]%, and [50,100]%, which determines the categories Low V (LV), Medium V (MV), and High V (HV), respectively. <div class='html-disp-formula-info' id='FD8-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>C</mi> <mi>V</mi> <mo>=</mo> <mfrac> <mrow> <mi>S</mi> <mi>D</mi> </mrow> <mi>M</mi> </mfrac> <mo> </mo> <mo>∗</mo> <mo> </mo> <mn>100</mn> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(8)</label> </div> </div><div class='html-disp-formula-info' id='FD9-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>S</mi> <mi>D</mi> <mo>=</mo> <msqrt> <mrow> <mfrac> <mrow> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <msup> <mrow> <mfenced> <mrow> <mi>a</mi> <mi>c</mi> <mi>t</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mfenced> <mi>i</mi> </mfenced> <mo>−</mo> <mi>M</mi> </mrow> </mfenced> </mrow> <mn>2</mn> </msup> </mrow> </mstyle> </mrow> <mi>m</mi> </mfrac> </mrow> </msqrt> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(9)</label> </div> </div><div class='html-disp-formula-info' id='FD10-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>M</mi> <mo>=</mo> <mfrac> <mrow> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <mi>a</mi> <mi>c</mi> <mi>t</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mfenced> <mi>i</mi> </mfenced> </mrow> </mstyle> </mrow> <mi>m</mi> </mfrac> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(10)</label> </div> </div></div><div class='html-p'><a href="#sensors-23-01388-t001" class="html-table">Table 1</a> details the characteristics of the 27 defined instance sets regarding the three aspects previously mentioned. Column 1 indicates the name of each set. Column 2 details the value of the instances of each set in relation to aspect S. Columns 3 and 4 detail the value range of the instances of each set in relation to the aspects A and V, respectively. Finally, Column 5 indicates the number of instances of each set.</div></section><section id='sec4dot2-sensors-23-01388' type=''><h4 class='html-italic' data-nested='2'> 4.2. Experimental Setting</h4><div class='html-p'>We ran the evolutionary algorithm on each one of the 10 instances of each instance set presented in <a href="#sensors-23-01388-t002" class="html-table">Table 2</a>. Considering that evolutionary algorithms are non-deterministic by nature, we ran this evolutionary algorithm several times (i.e., 30 runs) for each instance to obtain reliable statistical results. For each run, we recorded the solution provided by the algorithm for the instance under evaluation, the MAPE value of this solution, and the computing time taken by the algorithm to obtain this solution.</div><div class='html-p'>To run the evolutionary algorithm, we used the parameter settings detailed in <a href="#sensors-23-01388-t002" class="html-table">Table 2</a>. These parameter settings were defined based on preliminary experiments. In these experiments, we considered different parameter settings, which are usually suggested in the technical literature on evolutionary algorithms [<a href="#B6-sensors-23-01388" class="html-bibr">6</a>]. <a href="#sensors-23-01388-t003" class="html-table">Table 3</a> details the parameter settings considered. Then, for each of these parameter settings, we ran the evolutionary algorithm several times (i.e., 30 runs) for each instance and we calculated the average MAPE value of the 30 solutions obtained for each instance. These experiments showed that the parameter setting detailed in <a href="#sensors-23-01388-t002" class="html-table">Table 2</a> yielded the best average MAPE values for the evaluated instances.</div><div class='html-p'>In relation to the parameter <span class='html-italic'>P<sub>m</sub></span>, note that one of the considered settings is 1/L. The term L refers to the number of elements on which the mutation is applied, with <span class='html-italic'>P<sub>m</sub></span>, in an encoded solution. In this case, as detailed in <a href="#sec3dot2dot4-sensors-23-01388" class="html-sec">Section 3.2.4</a>, given an encoded solution, the mutation is applied, with <span class='html-italic'>P<sub>m</sub></span>, on two elements of each action of each one of the <span class='html-italic'>m</span> smartphones considered in the solution. Thus, L is equal to 2*(<span class='html-italic'>n</span>(1) + <span class='html-italic'>n</span>(2) + … + <span class='html-italic'>n</span>(<span class='html-italic'>m</span>)), where <span class='html-italic'>n</span>(<span class='html-italic'>i</span>) is the number of actions corresponding to the smartphone <span class='html-italic'>i</span> in the encoded solution, as described in <a href="#sec3dot2dot1-sensors-23-01388" class="html-sec">Section 3.2.1</a>.</div></section><section id='sec4dot3-sensors-23-01388' type=''><h4 class='html-italic' data-nested='2'> 4.3. Current Method to Prepare Smartphones in the Context of Motrol</h4><div class='html-p'>To contextualize the performance of the evolutionary algorithm, we considered the method currently used by Motrol to determine the preparation of a given set of <span class='html-italic'>m</span> smartphones for synchronized test plans. For simplicity, we will refer to this method as the Motrol method.</div><div class='html-p'>Given a set of <span class='html-italic'>m</span> smartphones, this method defines a feasible solution to prepare the <span class='html-italic'>m</span> smartphones, considering the current battery level, <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>), of each smartphone <span class='html-italic'>i</span> in the set and the start battery level, <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), to be reached by each smartphone <span class='html-italic'>i</span> in the set. Specifically, for each smartphone <span class='html-italic'>i</span>, this method defines one charge/discharge action, <span class='html-italic'>a<sub>i</sub></span>, which allows the battery to reach the level <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) from <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) in the minimal possible amount of time for the smartphone <span class='html-italic'>i</span>. When <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) is lower than <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) must be increased to reach <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>). Thus, the method defines a charge action, <span class='html-italic'>a<sub>i</sub></span>, which must be developed from the level <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) and must continue until <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) is reached. In addition, <span class='html-italic'>a<sub>i</sub></span> must be developed under a CPU load of 0% with the screen off to achieve <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) in the minimum possible time for <span class='html-italic'>i</span>. Otherwise, when <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) is higher than <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) must be decreased to reach <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>). Therefore, the method defines a discharge action, <span class='html-italic'>a<sub>i</sub></span>, which must be carried out from <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) and must continue until <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) is reached. Moreover, <span class='html-italic'>a<sub>i</sub></span> must be carried out under a CPU load of 100% with the screen on in order to achieve <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) in the minimum possible amount of time for <span class='html-italic'>i</span>. Finally, this method provides a solution, which is composed of the <span class='html-italic'>m</span> actions <span class='html-italic'>a<sub>i</sub></span> defined to prepare the <span class='html-italic'>m</span> smartphones.</div><div class='html-p'>We applied this method on each one of the ten instances of each instance set. For each instance, we recorded the solution obtained by this method and we calculated the MAPE value of this solution in order to compare this value with those of the 30 solutions obtained by the evolutionary algorithm for each instance.</div><div class='html-p'>It is worth mentioning that this method differs from the proposed evolutionary algorithm in two main aspects. First, the method defines one action, <span class='html-italic'>a<sub>i</sub></span>, for each smartphone <span class='html-italic'>i</span>, which allows Motrol to reach <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) from <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) in the minimum possible amount of time for the smartphone <span class='html-italic'>i</span>. Thus, the action, <span class='html-italic'>a<sub>i</sub></span>, of each smartphone <span class='html-italic'>i</span> is defined independently of the actions of the other smartphones in the set. Unlike this, the evolutionary algorithm explores many different sequences, <span class='html-italic'>s<sub>i</sub></span>, of actions for each smartphone <span class='html-italic'>i</span>, with the aim of finding a sequence, <span class='html-italic'>s<sub>i</sub></span>, to collectively reach <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) from <span class='html-italic'>cbl</span>(<span class='html-italic'>i</span>) at time <span class='html-italic'>T</span>. As described in <a href="#sec3dot2dot2-sensors-23-01388" class="html-sec">Section 3.2.2</a>, <span class='html-italic'>T</span> is the minimum possible time-taken to prepare the set of <span class='html-italic'>m</span> smartphones. Second, this method does not consider the difference among the times of the actions, <span class='html-italic'>a<sub>i</sub></span>, defined for the <span class='html-italic'>m</span> smartphones. In contrast to this, the evolutionary algorithm considers the difference between the time of the sequence <span class='html-italic'>s<sub>i</sub></span> determined for each of the <span class='html-italic'>m</span> smartphones and the time <span class='html-italic'>T</span>, and consequently considers the difference among the times of the sequences <span class='html-italic'>s<sub>i</sub></span>, which is important to minimize the discharge of the <span class='html-italic'>m</span> smartphones once these are prepared according to the sequences <span class='html-italic'>s<sub>i</sub></span> (i.e., once the start battery levels <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) are reached).</div></section><section id='sec4dot4-sensors-23-01388' type=''><h4 class='html-italic' data-nested='2'> 4.4. Experimental Results</h4><div class='html-p'>In <a href="#sensors-23-01388-t004" class="html-table">Table 4</a>, we present the main results obtained from the conducted computational experiments. Column 1 indicates the name of each instance set used in the experiments. columns 2 and 3 detail the average MAPE value of the solutions obtained by the evolutionary algorithm and the Motrol method for the instances of each set, respectively. Then, columns 4 and 5 detail the maximum MAPE value obtained by the evolutionary algorithm and the Motrol method for each instance set, respectively. Finally, columns 6 and 7 detail the minimum MAPE value obtained by the evolutionary algorithm and the Motrol method for each instance set, respectively.</div><div class='html-p'>From <a href="#sensors-23-01388-t004" class="html-table">Table 4</a>, it can be seen that the average MAPE value of the solutions obtained by the evolutionary algorithm for each instance set is much lower than that of the solutions obtained by the Motrol method. For each of the instance sets S4_*A_*V, the difference between the average MAPE values achieved by the evolutionary algorithm and the Motrol method is in the range of [25.84, 35.88] %. Similarly, for each of the instance sets S8_*A_*V and S16_*A_*V, the measured difference is in the range of [27.9, 42.13] % and [29.02, 39.97] %, respectively. These results regarding the average MAPE value are mainly due to the following reasons. For most instance sets (i.e., 22 of the 27 sets), the maximum MAPE value achieved by the evolutionary algorithm is lower than the minimum MAPE value obtained by the Motrol method. In addition, for each of the 270 instances used, the MAPE values of the 30 solutions obtained by the runs of the evolutionary algorithm are significantly lower than the MAPE value of the solution provided by the Motrol method. The statistical significance of these results was ascertained by the Mann–Whitney U test, with a confidence level of α = 0.001.</div><div class='html-p'>Based on these results, the solutions achieved by the evolutionary algorithm decrease the MAPE value for the instances considered. This means that, according to the MAPE definition given in <a href="#sec3dot2dot2-sensors-23-01388" class="html-sec">Section 3.2.2</a>, these solutions reduce the difference between the preparation time of each of the <span class='html-italic'>m</span> smartphones and the time <span class='html-italic'>T</span>, and as a consequence, reduce the difference among the preparation times of the <span class='html-italic'>m</span> smartphones. Therefore, as described in <a href="#sec3dot2dot2-sensors-23-01388" class="html-sec">Section 3.2.2</a>, these solutions will reduce the discharge of the <span class='html-italic'>m</span> smartphones once these are prepared (i.e., once the start battery levels, <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), are reached). The smaller the difference among the preparation times of the <span class='html-italic'>m</span> smartphones, the lower the amount of unnecessary (dis)charge actions of the <span class='html-italic'>m</span> smartphones once these are prepared.</div><div class='html-p'>Considering the above, in <a href="#sensors-23-01388-t005" class="html-table">Table 5</a>, we present the average, maximum, and minimum RPD (relative percentage difference) of the solutions achieved by the evolutionary algorithm, regarding the solutions provided by the Motrol method and in terms of the estimated discharge of the <span class='html-italic'>m</span> smartphones once these are prepared. The metric RPD computes the average percentage difference of the estimated discharge of the <span class='html-italic'>m</span> smartphones once these are prepared according to <span class='html-italic'>s<sub>EA</sub></span> (i.e., the solution given by the evolutionary algorithm), regarding the estimated discharge of the <span class='html-italic'>m</span> smartphones once these are prepared according to <span class='html-italic'>s<sub>M</sub></span> (i.e., the solution given by the Motrol method). This metric is calculated according to Equation (11), where <span class='html-italic'>bud</span>(<span class='html-italic'>s<sub>M</sub></span>, <span class='html-italic'>i</span>) and <span class='html-italic'>bud</span>(<span class='html-italic'>s<sub>EA</sub></span>, <span class='html-italic'>i</span>) refer to the estimated discharge (in battery units) of smartphone <span class='html-italic'>i</span> once it is prepared according to the solutions of <span class='html-italic'>s<sub>M</sub></span> and <span class='html-italic'>s<sub>EA</sub></span>, respectively. When the RPD value is positive, this means that <span class='html-italic'>s<sub>EA</sub></span> has achieved a saving when compared to <span class='html-italic'>s<sub>M</sub></span> in terms of the estimated discharge (in battery units) of the <span class='html-italic'>m</span> smartphones once these are prepared.</div><div class='html-p'>The value of <span class='html-italic'>bud</span>(<span class='html-italic'>s</span>, <span class='html-italic'>i</span>) is estimated as follows. Given a solution, <span class='html-italic'>s</span>, represented as the <span class='html-italic'>m</span>-tuple <<span class='html-italic'>s</span><sub>1</sub>, <span class='html-italic'>s</span><sub>2</sub>, …, <span class='html-italic'>s<sub>m</sub></span>> described in <a href="#sec3dot2dot1-sensors-23-01388" class="html-sec">Section 3.2.1</a>, we first calculated the preparation time <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>) of smartphone <span class='html-italic'>i</span>, by applying Equation (5) detailed in <a href="#sec3dot2dot1-sensors-23-01388" class="html-sec">Section 3.2.1</a>. After that, we calculated the maximal preparation time, <span class='html-italic'>MPT</span>(<span class='html-italic'>s</span>), of the <span class='html-italic'>m</span> smartphones with Equation (12), which determines the preparation time of the set of <span class='html-italic'>m</span> smartphones. As described in <a href="#sec3dot2dot2-sensors-23-01388" class="html-sec">Section 3.2.2</a>, when <span class='html-italic'>MPT</span>(<span class='html-italic'>s</span>) is higher than <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>), smartphone <span class='html-italic'>i</span> will be prepared (i.e., smartphone <span class='html-italic'>i</span> will reach its start battery level <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>)) before the smartphones that require a preparation time of <span class='html-italic'>MPT</span>(<span class='html-italic'>s</span>). Thus, smartphone <span class='html-italic'>i</span> will discharge its battery level, <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>), during the time between <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>) and <span class='html-italic'>MPT</span>(<span class='html-italic'>s</span>). This discharge of <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) (in battery units) depends on the time between <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>) and <span class='html-italic'>MPT</span>(<span class='html-italic'>s</span>). The longer this time, the higher the discharge of <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>). Therefore, we calculated this time <span class='html-italic'>td</span>(<span class='html-italic'>s</span>, <span class='html-italic'>i</span>), as detailed in Equation (13). Once <span class='html-italic'>td</span>(<span class='html-italic'>s</span>, <span class='html-italic'>i</span>) is calculated, the estimated discharge (in battery units), <span class='html-italic'>bud</span>(<span class='html-italic'>s</span>, <span class='html-italic'>i</span>), of <span class='html-italic'>sbl</span>(<span class='html-italic'>i</span>) during <span class='html-italic'>td</span>(<span class='html-italic'>s</span>, <span class='html-italic'>i</span>) can be determined from the battery discharge profile of smartphone <span class='html-italic'>i</span> (i.e., battery discharge profile inherent to a CPU load of 0% with the screen off). <div class='html-disp-formula-info' id='FD11-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>R</mi> <mi>P</mi> <mi>D</mi> <mo>=</mo> <mfrac> <mrow> <mn>100</mn> </mrow> <mi>m</mi> </mfrac> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <mfrac> <mrow> <mi>b</mi> <mi>u</mi> <mi>d</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mi>M</mi> </msub> <mo>,</mo> <mo> </mo> <mi>i</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>b</mi> <mi>u</mi> <mi>d</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mrow> <mi>E</mi> <mi>A</mi> </mrow> </msub> <mo>,</mo> <mo> </mo> <mi>i</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>b</mi> <mi>u</mi> <mi>d</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mi>M</mi> </msub> <mo>,</mo> <mo> </mo> <mi>i</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(11)</label> </div> </div><div class='html-disp-formula-info' id='FD12-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>M</mi> <mi>P</mi> <mi>T</mi> <mo> </mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo> </mo> <munderover> <mi mathvariant="italic">max</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mfenced> <mrow> <mi>t</mi> <mfenced> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> </mrow> </mfenced> </mrow> </mfenced> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(12)</label> </div> </div><div class='html-disp-formula-info' id='FD13-sensors-23-01388'> <div class='f'> <math display='block'><semantics> <mrow> <mrow> <mi>t</mi> <mi>d</mi> <mfenced> <mrow> <mi>s</mi> <mo>,</mo> <mo> </mo> <mi>i</mi> </mrow> </mfenced> <mo>=</mo> <mi>M</mi> <mi>P</mi> <mi>T</mi> <mfenced> <mi>s</mi> </mfenced> <mo>−</mo> <mi>t</mi> <mfenced> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> </mrow> </mfenced> </mrow> </mrow> </semantics></math> </div> <div class='l'> <label >(13)</label> </div> </div></div><div class='html-p'>From the results in <a href="#sensors-23-01388-t005" class="html-table">Table 5</a>, it follows that the solutions obtained by the evolutionary algorithm for each instance set provide a considerable average saving (average RPD) in terms of the discharge (in battery units) of the <span class='html-italic'>m</span> smartphones once these are prepared. For the instance sets S4_*A_*V and S8_*A_*V, the average saving is in the range of [32.81, 56.25] % and [31.40, 61.98] %, respectively. For most of the instance sets S16_*A_*V (i.e., eight out of the nine sets), the average saving is in the range of [44.69, 61.05] %. In addition, the solutions obtained by the evolutionary algorithm for each instance set also provide very good minimal and maximal savings (minimal and maximal RPD). For the instance sets S4_*A_*V and S8_*A_*V, the minimal saving is in the range of [18.75, 35.42] % and [12.50, 50.00] %, respectively. For the instance sets S16_*A_*V, the minimal saving is in the range of [12.50, 50.00] %. These results regarding the minimal saving show that for each one of the 270 instances used, the 30 solutions obtained by the runs of the evolutionary algorithm provide a saving in terms of the discharge (in battery units) of the <span class='html-italic'>m</span> smartphones once these are prepared.</div><div class='html-p'>In addition to the results presented in <a href="#sensors-23-01388-t004" class="html-table">Table 4</a> and <a href="#sensors-23-01388-t005" class="html-table">Table 5</a>, in <a href="#sensors-23-01388-t006" class="html-table">Table 6</a>, we present the average, maximum, and minimum computing time (in seconds) required by the evolutionary algorithm for each of the instance sets. In this sense, all the computational experiments were executed on a PC equipped with an Intel core i7-3610QM 2.3GHz CPU, a 6.00 GB memory, a 1 TB HD, and a 64-bit Windows 10 operating system. In addition, the evolutionary algorithm was implemented in Java 1.8.</div><div class='html-p'>As shown in <a href="#sensors-23-01388-t006" class="html-table">Table 6</a>, the higher the total number of actions to be applied by the <span class='html-italic'>m</span> smartphones considered in the instance (see values of A in <a href="#sensors-23-01388-t001" class="html-table">Table 1</a>), the higher the computing time (in seconds) required by the evolutionary algorithm. This is mainly because of the following reason. As described in <a href="#sec3dot2-sensors-23-01388" class="html-sec">Section 3.2</a>, the main processes of the evolutionary algorithm (i.e., fitness evaluation, crossover, and mutation processes) are applied in solutions encoded as an <span class='html-italic'>m</span>-tuple <<span class='html-italic'>s</span><sub>1</sub>, <span class='html-italic'>s</span><sub>2</sub>, …, <span class='html-italic'>s<sub>m</sub></span>>, where <span class='html-italic'>s<sub>i</sub></span> represents a feasible sequence of actions for smartphone <span class='html-italic'>i</span>. Therefore, the computing time of these processes, and consequently the computing time of the algorithm, depend on the length of the encoded solutions. As detailed in <a href="#sec3dot2dot1-sensors-23-01388" class="html-sec">Section 3.2.1</a>, the length of the encoded solutions is proportional to the total number of actions to be applied by the <span class='html-italic'>m</span> smartphones in the set. Thus, the higher the total number of actions, the higher the length of the encoded solutions; therefore, the higher the computing time of the evolutionary algorithm.</div></section></section><section id='sec5-sensors-23-01388' type=''><h2 data-nested='1'> 5. Related Work</h2><div class='html-p'>Consumer electronic devices such as smartphones play a vital role as computing resource providers in Dew computing. Testbeds and experimentation platforms especially designed for Dew computing research are scarce. For instance, testbeds—also known as device farms—such as Firebase Test Lab, Samsung Remote Test Lab, AWS Device Farms, Sauce Labs, and Xamarin Test Cloud have been designed for developers to test mobile applications on a diverse fleet of devices. The main objective was to help developers to code their applications to support device heterogeneity. Device heterogeneity is a key aspect present in Dew computing but not the only one to be considered [<a href="#B17-sensors-23-01388" class="html-bibr">17</a>]. Other crucial aspects, particularly related to service provisioning and load balancing using clusters of consumer electronic devices, are mobility, energy management of battery and non-battery driven devices, local node collaboration, and coordination with nodes located in the fog and cloud layers. Due to the complexity of including all these aspects in a testbed, simulation is widely accepted and practiced as a performance evaluation methodology [<a href="#B16-sensors-23-01388" class="html-bibr">16</a>,<a href="#B17-sensors-23-01388" class="html-bibr">17</a>,<a href="#B18-sensors-23-01388" class="html-bibr">18</a>,<a href="#B19-sensors-23-01388" class="html-bibr">19</a>]. Simulation allows researchers to model complex interactions among entities that could be hard to realize, not to mention reproduce, with real testbeds. Particularly, Markus et al. [<a href="#B17-sensors-23-01388" class="html-bibr">17</a>] analyzed several simulation toolkits including iFogSim, MobFogSim, IoTSim-Edge, EdgeCloudSim, DewSim, and DISSECT-CF-Fog and classified them based on the abstractions and functionalities offered in relation to relevant Dew computing aspects.</div><div class='html-p'>Although testbeds for Dew computing are difficult to set up, these are necessary to validate simulation results. At the time of writing this paper, platforms for automating Dew computing experiments using testbeds are in the very early development stage. However, advances in other related research fields can be applied towards building a platform that holistically provides the means for experimenting and validating results in Dew computing research. One of these advances is in the line of achieving reproducibility of device mobility, a problem originally tackled in MANETs research field via the application of mobile robot technology [<a href="#B20-sensors-23-01388" class="html-bibr">20</a>]. Others refer to interfacing nodes communicating using different wireless protocols through web services to facilitate the evaluation of local collaboration among sensor and computing nodes, and the efficiency of message dissemination protocols. Concerns such as these are relevant for wireless sensor networks and IoT research; CaBIUs [<a href="#B21-sensors-23-01388" class="html-bibr">21</a>] and Indriya2 [<a href="#B22-sensors-23-01388" class="html-bibr">22</a>] are examples of recent testbeds providing such facilities.</div><div class='html-p'>With regard to achieving reproducibility of battery-driven Dew experiments, we have initiated efforts with a software–hardware toolkit [<a href="#B7-sensors-23-01388" class="html-bibr">7</a>] that provides researchers with basic support to (dis)charge smartphones based on a configured battery level. Such functionality has been vital to automate battery profiling whose resulting traces are used as elementary input for Dew simulations. After exploratory research using simulations, results validation becomes a necessary step to advance state-of-the-art load balancing strategies for executing tasks in clusters of smartphones and to measure the impact on energy utilization of individual smartphones. However, to make a test reproducible and the effect of load balancing strategies comparable, a feature to reset all smartphones battery-related states to the values configured in the testing scenario is required. Such a reset feature hinders the necessary (dis)charging speed synchronization between all smartphones, which is currently achieved with human intervention. To advance the automation of this necessary feature, we proposed an evolutionary algorithm that prepares smartphone battery states to run live Dew computing scenarios on real testbeds.</div></section><section id='sec6-sensors-23-01388' type='conclusions'><h2 data-nested='1'> 6. Conclusions and Future Work</h2><div class='html-p'>With the aim of covering a gap in the area of Dew computing associated with reproducing battery-driven tests on real testbeds, we proposed an evolutionary algorithm to tackle the problem of preparing batteries of smartphone clusters. This state-of-the-art method using Motrol allows researchers to (dis)charge smartphones to a configured battery level. However, applying such a method to a cluster of smartphones requires a fine coordination of smartphone (dis)charging speeds, which is currently executed with human intervention. This makes the process of running battery-driven tests error prone and difficult to scale and reproduce. We designed an algorithm to perform such a preparation, consequently allowing Dew researchers not only to automate the execution of a series of battery-driven tests, e.g., the evaluation of several load balancing strategies, but also to simultaneously reduce the time taken to start each test.</div><div class='html-p'>The performance of the proposed algorithm was evaluated by simulating battery behavior using real smartphone traces and covering 270 combinations of different battery levels and smartphone cluster sizes. The average MAPE obtained with the evolutionary algorithm was 12.84%, indicating that (dis)charging plans differ on average by around 12% of the time the slowest smartphone takes to reach the start battery level. This represents a considerable improvement over the MAPE value obtained with the default approach to prepare smartphones, called the Motrol method, which was 46.05% on average. Moreover, when comparing the amount of battery units that smartphones vary by from the time each one reaches the start battery level until all in the set are prepared, the evolutionary algorithm reports between 12 and 61% savings on average w.r.t the Motrol method, meaning that the evolutionary algorithm prepares a test with less battery variations.</div><div class='html-p'>In future work, we plan to design an approach with a global view of both the preparation and test execution, assuming several preparation scenarios along with test execution estimations as input. The resulting sequence might involve different scenarios, i.e., scenarios that do not necessarily share the same battery conditions. It is interesting to study to what extent an approach such as this saves time and battery changes compared to plans with a local view of scenario preparation as those derived from the proposed evolutionary algorithm. Moreover, in the experiments, the computational time of solutions provided by the evolutionary algorithm increases with the number of smartphones and the total amount of battery changes involved in the preparation scenario, reaching nearly fifty seconds for the most complex tested scenario. Therefore, an extension we are planning for this research is improving the execution time of the algorithm by parallelizing the exploration of the solution space [<a href="#B23-sensors-23-01388" class="html-bibr">23</a>].</div></section> </div> <div class="html-back"> <section class='html-notes'><h2 >Author Contributions</h2><div class='html-p'>Conceptualization, V.Y., M.H., J.T., and C.M.; methodology, V.Y.; software, V.Y., M.H., J.T., and C.M; validation, V.Y.; formal analysis, V.Y.; investigation, V.Y, M.H., T.A.M., A.Z., and C.M.; resources, A.Z. and C.M.; data curation, V.Y.; writing—original draft preparation, V.Y., M.H., and T.A.M.; visualization, V.Y. and M.H.; supervision, M.H. and C.M.; project administration, C.M. 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 >Institutional Review Board Statement</h2><div class='html-p'>Not applicable.</div></section><section class='html-notes'><h2 >Informed Consent Statement</h2><div class='html-p'>Not applicable.</div></section><section class='html-notes'><h2 >Data Availability Statement</h2><div class='html-p'>The software and data (i.e., problem instances) used to test the proposed solution and the implemented evolutionary algorithm can be found at <a href='https://github.com/matieber/mobilebattprep' target='_blank' rel="noopener noreferrer">https://github.com/matieber/mobilebattprep</a>, accessed on 1 October 2022.</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-references_list'><h2>References</h2><ol class='html-xx'><li id='B1-sensors-23-01388' class='html-x' data-content='1.'>Ray, P.P. 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class="html-fig-wrap" id="sensors-23-01388-f001"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f001"> <img alt="Sensors 23 01388 g001 550" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g001.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g001.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g001-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f001"></a> </div> </div> <div class="html-fig_description"> <b>Figure 1.</b> Synchronized test specification examples.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sensors-23-01388-f001" > <div class="html-caption" > <b>Figure 1.</b> Synchronized test specification examples.</div> <div class="html-img"><img alt="Sensors 23 01388 g001" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g001.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g001.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g001.png" /></div> </div><div class="html-fig-wrap" id="sensors-23-01388-f002"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f002"> <img alt="Sensors 23 01388 g002 550" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g002.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g002.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g002-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f002"></a> </div> </div> <div class="html-fig_description"> <b>Figure 2.</b> Overview of Motrol synchronized test plan execution workflow.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sensors-23-01388-f002" > <div class="html-caption" > <b>Figure 2.</b> Overview of Motrol synchronized test plan execution workflow.</div> <div class="html-img"><img alt="Sensors 23 01388 g002" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g002.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g002.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g002.png" /></div> </div><div class="html-fig-wrap" id="sensors-23-01388-f003"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f003"> <img alt="Sensors 23 01388 g003 550" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g003.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g003.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g003-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f003"></a> </div> </div> <div class="html-fig_description"> <b>Figure 3.</b> Charging traces for smartphones considered in the experiments.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sensors-23-01388-f003" > <div class="html-caption" > <b>Figure 3.</b> Charging traces for smartphones considered in the experiments.</div> <div class="html-img"><img alt="Sensors 23 01388 g003" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g003.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g003.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g003.png" /></div> </div><div class="html-fig-wrap" id="sensors-23-01388-f004"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f004"> <img alt="Sensors 23 01388 g004 550" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g004.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g004.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g004-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f004"></a> </div> </div> <div class="html-fig_description"> <b>Figure 4.</b> Discharging traces for smartphones considered in the experiments.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sensors-23-01388-f004" > <div class="html-caption" > <b>Figure 4.</b> Discharging traces for smartphones considered in the experiments.</div> <div class="html-img"><img alt="Sensors 23 01388 g004" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g004.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g004.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g004.png" /></div> </div><div class="html-fig-wrap" id="sensors-23-01388-f005"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f005"> <img alt="Sensors 23 01388 g005 550" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g005.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g005.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g005-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f005"></a> </div> </div> <div class="html-fig_description"> <b>Figure 5.</b> Encoded solution for an example case.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sensors-23-01388-f005" > <div class="html-caption" > <b>Figure 5.</b> Encoded solution for an example case.</div> <div class="html-img"><img alt="Sensors 23 01388 g005" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g005.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g005.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g005.png" /></div> </div><div class="html-fig-wrap" id="sensors-23-01388-f006"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f006"> <img alt="Sensors 23 01388 g006 550" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g006.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g006.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g006-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f006"></a> </div> </div> <div class="html-fig_description"> <b>Figure 6.</b> MAPE values and times <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>) of two feasible solutions for an example case (Y axis is in milliseconds).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sensors-23-01388-f006" > <div class="html-caption" > <b>Figure 6.</b> MAPE values and times <span class='html-italic'>t</span>(<span class='html-italic'>s<sub>i</sub></span>) of two feasible solutions for an example case (Y axis is in milliseconds).</div> <div class="html-img"><img alt="Sensors 23 01388 g006" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g006.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g006.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g006.png" /></div> </div><div class="html-fig-wrap" id="sensors-23-01388-f007"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f007"> <img alt="Sensors 23 01388 g007 550" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g007.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g007.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g007-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f007"></a> </div> </div> <div class="html-fig_description"> <b>Figure 7.</b> Example of the crossover process.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sensors-23-01388-f007" > <div class="html-caption" > <b>Figure 7.</b> Example of the crossover process.</div> <div class="html-img"><img alt="Sensors 23 01388 g007" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g007.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g007.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g007.png" /></div> </div><div class="html-fig-wrap" id="sensors-23-01388-f008"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f008"> <img alt="Sensors 23 01388 g008 550" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g008.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g008.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g008-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href="#fig_body_display_sensors-23-01388-f008"></a> </div> </div> <div class="html-fig_description"> <b>Figure 8.</b> Mutation process example.  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sensors-23-01388-f008" > <div class="html-caption" > <b>Figure 8.</b> Mutation process example.</div> <div class="html-img"><img alt="Sensors 23 01388 g008" data-large="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g008.png" data-original="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g008.png" data-lsrc="/sensors/sensors-23-01388/article_deploy/html/images/sensors-23-01388-g008.png" /></div> </div><div class="html-table-wrap" id="sensors-23-01388-t001"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href='#table_body_display_sensors-23-01388-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/1424-8220/23/3/1388/display" href="#table_body_display_sensors-23-01388-t001"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 1.</b> Characteristics of the defined instance sets. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_sensors-23-01388-t001" > <div class="html-caption" ><b>Table 1.</b> Characteristics of the defined instance sets.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Instance Set</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >S</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >A</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >V (%)</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Nr. of Instances</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_LV</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >[4, 160]</td><td align='center' valign='middle' class='html-align-center' >[0, 10]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_MV</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >[4, 160]</td><td align='center' valign='middle' class='html-align-center' >(10, 50]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_HV</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >[4, 160]</td><td align='center' valign='middle' class='html-align-center' >(50, 100]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_LV</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >[164, 280]</td><td align='center' valign='middle' class='html-align-center' >[0, 10]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_MV</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >[164, 280]</td><td align='center' valign='middle' class='html-align-center' >(10, 50]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_HV</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >[164, 280]</td><td align='center' valign='middle' class='html-align-center' >(50, 100]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_LV</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >[284, 400]</td><td align='center' valign='middle' class='html-align-center' >[0, 10]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_MV</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >[284, 400]</td><td align='center' valign='middle' class='html-align-center' >(10, 50]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_HV</td><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >[284, 400]</td><td align='center' valign='middle' class='html-align-center' >(50, 100]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_LV</td><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >[8, 320]</td><td align='center' valign='middle' class='html-align-center' >[0, 10]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_MV</td><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >[8, 320]</td><td align='center' valign='middle' class='html-align-center' >(10, 50]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_HV</td><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >[8, 320]</td><td align='center' valign='middle' class='html-align-center' >(50, 100]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_LV</td><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >[328, 560]</td><td align='center' valign='middle' class='html-align-center' >[0, 10]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_MV</td><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >[328, 560]</td><td align='center' valign='middle' class='html-align-center' >(10, 50]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_HV</td><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >[328, 560]</td><td align='center' valign='middle' class='html-align-center' >(50, 100]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_LV</td><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >[568, 800]</td><td align='center' valign='middle' class='html-align-center' >[0, 10]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_MV</td><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >[568, 800]</td><td align='center' valign='middle' class='html-align-center' >(10, 50]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_HV</td><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >[568, 800]</td><td align='center' valign='middle' class='html-align-center' >(50, 100]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_LV</td><td align='center' valign='middle' class='html-align-center' >16</td><td align='center' valign='middle' class='html-align-center' >[16, 640]</td><td align='center' valign='middle' class='html-align-center' >[0, 10]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_MV</td><td align='center' valign='middle' class='html-align-center' >16</td><td align='center' valign='middle' class='html-align-center' >[16, 640]</td><td align='center' valign='middle' class='html-align-center' >(10, 50]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_HV</td><td align='center' valign='middle' class='html-align-center' >16</td><td align='center' valign='middle' class='html-align-center' >[16, 640]</td><td align='center' valign='middle' class='html-align-center' >(50, 100]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_LV</td><td align='center' valign='middle' class='html-align-center' >16</td><td align='center' valign='middle' class='html-align-center' >[656, 1120]</td><td align='center' valign='middle' class='html-align-center' >[0, 10]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_MV</td><td align='center' valign='middle' class='html-align-center' >16</td><td align='center' valign='middle' class='html-align-center' >[656, 1120]</td><td align='center' valign='middle' class='html-align-center' >(10, 50]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_HV</td><td align='center' valign='middle' class='html-align-center' >16</td><td align='center' valign='middle' class='html-align-center' >[656, 1120]</td><td align='center' valign='middle' class='html-align-center' >(50, 100]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_HA_LV</td><td align='center' valign='middle' class='html-align-center' >16</td><td align='center' valign='middle' class='html-align-center' >[1136, 1600]</td><td align='center' valign='middle' class='html-align-center' >[0, 10]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_HA_MV</td><td align='center' valign='middle' class='html-align-center' >16</td><td align='center' valign='middle' class='html-align-center' >[1136, 1600]</td><td align='center' valign='middle' class='html-align-center' >(10, 50]</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >S16_HA_HV</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >16</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >[1136, 1600]</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >(50, 100]</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10</td></tr></tbody> </table> </div><div class="html-table-wrap" id="sensors-23-01388-t002"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href='#table_body_display_sensors-23-01388-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/1424-8220/23/3/1388/display" href="#table_body_display_sensors-23-01388-t002"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 2.</b> Parameter settings of the evolutionary algorithm. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_sensors-23-01388-t002" > <div class="html-caption" ><b>Table 2.</b> Parameter settings of the evolutionary algorithm.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Parameter</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Value</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>Population size</span></td><td align='center' valign='middle' class='html-align-center' >100</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>k</span> (<span class='html-italic'>tournament selection</span>)</td><td align='center' valign='middle' class='html-align-center' >10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>P<sub>c</sub></span> (<span class='html-italic'>crossover</span>)</td><td align='center' valign='middle' class='html-align-center' >1.0</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>P<sub>m</sub></span> (<span class='html-italic'>mutation</span>)</td><td align='center' valign='middle' class='html-align-center' >1/L</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>r</span> (<span class='html-italic'>steady-state selection</span>)</td><td align='center' valign='middle' class='html-align-center' >50%</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>Number of generations or iterations</span></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2000</td></tr></tbody> </table> </div><div class="html-table-wrap" id="sensors-23-01388-t003"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href='#table_body_display_sensors-23-01388-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/1424-8220/23/3/1388/display" href="#table_body_display_sensors-23-01388-t003"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 3.</b> Parameter settings considered in the preliminary experiments. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_sensors-23-01388-t003" > <div class="html-caption" ><b>Table 3.</b> Parameter settings considered in the preliminary experiments.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Parameter</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Values Considered</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>Population size</span></td><td align='center' valign='middle' class='html-align-center' >{100, 200}</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>k</span> (<span class='html-italic'>tournament selection</span>)</td><td align='center' valign='middle' class='html-align-center' >{2, 5, 10}</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>P<sub>c</sub></span> (<span class='html-italic'>crossover</span>)</td><td align='center' valign='middle' class='html-align-center' >{0.7, 0.8, 0.9, 1.0}</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>P<sub>m</sub></span> (<span class='html-italic'>mutation</span>)</td><td align='center' valign='middle' class='html-align-center' >{1/L} U {0.1, 0.2, 0.3}</td></tr><tr ><td align='center' valign='middle' class='html-align-center' ><span class='html-italic'>r</span> (<span class='html-italic'>steady-state selection</span>)</td><td align='center' valign='middle' class='html-align-center' >{25%, 50%}</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><span class='html-italic'>Number of generations or iterations</span></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >{1000, 2000, 3000, 4000, 5000}</td></tr></tbody> </table> </div><div class="html-table-wrap" id="sensors-23-01388-t004"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href='#table_body_display_sensors-23-01388-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/1424-8220/23/3/1388/display" href="#table_body_display_sensors-23-01388-t004"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 4.</b> Average, maximum, and minimum MAPE (%) value obtained by the evolutionary algorithm (EA) and the Motrol method (M) for each instance set. Bold values indicate better average MAPE (%) values. The symbol * indicates that the maximum MAPE (%) value reached by EA is lower than the minimum MAPE (%) value reached by M. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_sensors-23-01388-t004" > <div class="html-caption" ><b>Table 4.</b> Average, maximum, and minimum MAPE (%) value obtained by the evolutionary algorithm (EA) and the Motrol method (M) for each instance set. Bold values indicate better average MAPE (%) values. The symbol * indicates that the maximum MAPE (%) value reached by EA is lower than the minimum MAPE (%) value reached by M.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin' class='html-align-center' > </th><th colspan='6' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >MAPE (%)</th></tr><tr ><th align='center' valign='middle' class='html-align-center' >Instance Set</th><th colspan='2' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average</th><th colspan='2' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Maximum</th><th colspan='2' align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Minimum</th></tr><tr ><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >EA</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >M</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >EA</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >M</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >EA</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >M</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_LV</td><td align='center' valign='middle' class='html-align-center' ><b>17.09</b></td><td align='center' valign='middle' class='html-align-center' >46.66</td><td align='center' valign='middle' class='html-align-center' >64.11</td><td align='center' valign='middle' class='html-align-center' >70.56</td><td align='center' valign='middle' class='html-align-center' >3,E-04</td><td align='center' valign='middle' class='html-align-center' >22.31</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_MV</td><td align='center' valign='middle' class='html-align-center' ><b>12.19</b></td><td align='center' valign='middle' class='html-align-center' >48.07</td><td align='center' valign='middle' class='html-align-center' >* 33.26</td><td align='center' valign='middle' class='html-align-center' >66.73</td><td align='center' valign='middle' class='html-align-center' >0.01</td><td align='center' valign='middle' class='html-align-center' >34.58</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_HV</td><td align='center' valign='middle' class='html-align-center' ><b>26.30</b></td><td align='center' valign='middle' class='html-align-center' >52.14</td><td align='center' valign='middle' class='html-align-center' >53.49</td><td align='center' valign='middle' class='html-align-center' >68.72</td><td align='center' valign='middle' class='html-align-center' >4.63</td><td align='center' valign='middle' class='html-align-center' >26.70</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_LV</td><td align='center' valign='middle' class='html-align-center' ><b>5.05</b></td><td align='center' valign='middle' class='html-align-center' >33.53</td><td align='center' valign='middle' class='html-align-center' >* 12.51</td><td align='center' valign='middle' class='html-align-center' >43.64</td><td align='center' valign='middle' class='html-align-center' >2,E-05</td><td align='center' valign='middle' class='html-align-center' >19.13</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_MV</td><td align='center' valign='middle' class='html-align-center' ><b>8.26</b></td><td align='center' valign='middle' class='html-align-center' >37.48</td><td align='center' valign='middle' class='html-align-center' >25.96</td><td align='center' valign='middle' class='html-align-center' >47.53</td><td align='center' valign='middle' class='html-align-center' >1,E-04</td><td align='center' valign='middle' class='html-align-center' >21.26</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_HV</td><td align='center' valign='middle' class='html-align-center' ><b>17.99</b></td><td align='center' valign='middle' class='html-align-center' >50.37</td><td align='center' valign='middle' class='html-align-center' >36.87</td><td align='center' valign='middle' class='html-align-center' >65.05</td><td align='center' valign='middle' class='html-align-center' >1,E-03</td><td align='center' valign='middle' class='html-align-center' >34.56</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_LV</td><td align='center' valign='middle' class='html-align-center' ><b>3.80</b></td><td align='center' valign='middle' class='html-align-center' >31.43</td><td align='center' valign='middle' class='html-align-center' >* 10.22</td><td align='center' valign='middle' class='html-align-center' >45.21</td><td align='center' valign='middle' class='html-align-center' >2,E-05</td><td align='center' valign='middle' class='html-align-center' >13.45</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_MV</td><td align='center' valign='middle' class='html-align-center' ><b>5.14</b></td><td align='center' valign='middle' class='html-align-center' >35.93</td><td align='center' valign='middle' class='html-align-center' >* 19.95</td><td align='center' valign='middle' class='html-align-center' >48.84</td><td align='center' valign='middle' class='html-align-center' >1,E-04</td><td align='center' valign='middle' class='html-align-center' >22.49</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_HV</td><td align='center' valign='middle' class='html-align-center' ><b>10.74</b></td><td align='center' valign='middle' class='html-align-center' >45.25</td><td align='center' valign='middle' class='html-align-center' >* 23.86</td><td align='center' valign='middle' class='html-align-center' >52.37</td><td align='center' valign='middle' class='html-align-center' >0.01</td><td align='center' valign='middle' class='html-align-center' >36.29</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_LV</td><td align='center' valign='middle' class='html-align-center' ><b>20.07</b></td><td align='center' valign='middle' class='html-align-center' >50.23</td><td align='center' valign='middle' class='html-align-center' >53.35</td><td align='center' valign='middle' class='html-align-center' >73.70</td><td align='center' valign='middle' class='html-align-center' >4.19</td><td align='center' valign='middle' class='html-align-center' >28.71</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_MV</td><td align='center' valign='middle' class='html-align-center' ><b>11.62</b></td><td align='center' valign='middle' class='html-align-center' >52.40</td><td align='center' valign='middle' class='html-align-center' >* 27.99</td><td align='center' valign='middle' class='html-align-center' >62.00</td><td align='center' valign='middle' class='html-align-center' >2.32</td><td align='center' valign='middle' class='html-align-center' >38.80</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_HV</td><td align='center' valign='middle' class='html-align-center' ><b>15.75</b></td><td align='center' valign='middle' class='html-align-center' >57.88</td><td align='center' valign='middle' class='html-align-center' >* 24.92</td><td align='center' valign='middle' class='html-align-center' >71.31</td><td align='center' valign='middle' class='html-align-center' >4.15</td><td align='center' valign='middle' class='html-align-center' >41.10</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_LV</td><td align='center' valign='middle' class='html-align-center' ><b>5.76</b></td><td align='center' valign='middle' class='html-align-center' >33.66</td><td align='center' valign='middle' class='html-align-center' >* 11.30</td><td align='center' valign='middle' class='html-align-center' >45.77</td><td align='center' valign='middle' class='html-align-center' >3,E-04</td><td align='center' valign='middle' class='html-align-center' >19.21</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_MV</td><td align='center' valign='middle' class='html-align-center' ><b>16.15</b></td><td align='center' valign='middle' class='html-align-center' >49.84</td><td align='center' valign='middle' class='html-align-center' >* 30.59</td><td align='center' valign='middle' class='html-align-center' >58.13</td><td align='center' valign='middle' class='html-align-center' >1.47</td><td align='center' valign='middle' class='html-align-center' >36.37</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_HV</td><td align='center' valign='middle' class='html-align-center' ><b>13.81</b></td><td align='center' valign='middle' class='html-align-center' >48.21</td><td align='center' valign='middle' class='html-align-center' >* 27.63</td><td align='center' valign='middle' class='html-align-center' >55.87</td><td align='center' valign='middle' class='html-align-center' >0.01</td><td align='center' valign='middle' class='html-align-center' >36.78</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_LV</td><td align='center' valign='middle' class='html-align-center' ><b>5.72</b></td><td align='center' valign='middle' class='html-align-center' >40.60</td><td align='center' valign='middle' class='html-align-center' >* 15.69</td><td align='center' valign='middle' class='html-align-center' >52.64</td><td align='center' valign='middle' class='html-align-center' >7,E-05</td><td align='center' valign='middle' class='html-align-center' >32.41</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_MV</td><td align='center' valign='middle' class='html-align-center' ><b>6.39</b></td><td align='center' valign='middle' class='html-align-center' >40.93</td><td align='center' valign='middle' class='html-align-center' >* 19.22</td><td align='center' valign='middle' class='html-align-center' >57.58</td><td align='center' valign='middle' class='html-align-center' >0.01</td><td align='center' valign='middle' class='html-align-center' >29.26</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_HV</td><td align='center' valign='middle' class='html-align-center' ><b>16.51</b></td><td align='center' valign='middle' class='html-align-center' >49.29</td><td align='center' valign='middle' class='html-align-center' >* 30.29</td><td align='center' valign='middle' class='html-align-center' >57.37</td><td align='center' valign='middle' class='html-align-center' >2.34</td><td align='center' valign='middle' class='html-align-center' >37.24</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_LV</td><td align='center' valign='middle' class='html-align-center' ><b>6.22</b></td><td align='center' valign='middle' class='html-align-center' >35.24</td><td align='center' valign='middle' class='html-align-center' >*8.59</td><td align='center' valign='middle' class='html-align-center' >43.22</td><td align='center' valign='middle' class='html-align-center' >2.50</td><td align='center' valign='middle' class='html-align-center' >24.87</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_MV</td><td align='center' valign='middle' class='html-align-center' ><b>18.83</b></td><td align='center' valign='middle' class='html-align-center' >58.69</td><td align='center' valign='middle' class='html-align-center' >* 25.76</td><td align='center' valign='middle' class='html-align-center' >65.45</td><td align='center' valign='middle' class='html-align-center' >9.37</td><td align='center' valign='middle' class='html-align-center' >54.63</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_HV</td><td align='center' valign='middle' class='html-align-center' ><b>25.45</b></td><td align='center' valign='middle' class='html-align-center' >61.99</td><td align='center' valign='middle' class='html-align-center' >* 46.31</td><td align='center' valign='middle' class='html-align-center' >75.78</td><td align='center' valign='middle' class='html-align-center' >14.60</td><td align='center' valign='middle' class='html-align-center' >51.59</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_LV</td><td align='center' valign='middle' class='html-align-center' ><b>4.42</b></td><td align='center' valign='middle' class='html-align-center' >34.97</td><td align='center' valign='middle' class='html-align-center' >* 10.38</td><td align='center' valign='middle' class='html-align-center' >50.27</td><td align='center' valign='middle' class='html-align-center' >2,E-03</td><td align='center' valign='middle' class='html-align-center' >24.70</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_MV</td><td align='center' valign='middle' class='html-align-center' ><b>15.42</b></td><td align='center' valign='middle' class='html-align-center' >55.39</td><td align='center' valign='middle' class='html-align-center' >* 23.81</td><td align='center' valign='middle' class='html-align-center' >64.78</td><td align='center' valign='middle' class='html-align-center' >7.56</td><td align='center' valign='middle' class='html-align-center' >48.38</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_HV</td><td align='center' valign='middle' class='html-align-center' ><b>23.41</b></td><td align='center' valign='middle' class='html-align-center' >61.45</td><td align='center' valign='middle' class='html-align-center' >* 36.31</td><td align='center' valign='middle' class='html-align-center' >67.81</td><td align='center' valign='middle' class='html-align-center' >14.75</td><td align='center' valign='middle' class='html-align-center' >53.77</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_HA_LV</td><td align='center' valign='middle' class='html-align-center' ><b>4.87</b></td><td align='center' valign='middle' class='html-align-center' >35.31</td><td align='center' valign='middle' class='html-align-center' >* 7.75</td><td align='center' valign='middle' class='html-align-center' >42.60</td><td align='center' valign='middle' class='html-align-center' >0.14</td><td align='center' valign='middle' class='html-align-center' >28.25</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_HA_MV</td><td align='center' valign='middle' class='html-align-center' ><b>12.70</b></td><td align='center' valign='middle' class='html-align-center' >46.82</td><td align='center' valign='middle' class='html-align-center' >* 22.34</td><td align='center' valign='middle' class='html-align-center' >52.11</td><td align='center' valign='middle' class='html-align-center' >7.57</td><td align='center' valign='middle' class='html-align-center' >37.75</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >S16_HA_HV</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>16.99</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >49.82</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >* 24.05</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >57.52</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' >38.72</td></tr></tbody> </table> </div><div class="html-table-wrap" id="sensors-23-01388-t005"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href='#table_body_display_sensors-23-01388-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/1424-8220/23/3/1388/display" href="#table_body_display_sensors-23-01388-t005"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 5.</b> Average, maximum, and minimum RPD (%) values obtained by the evolutionary algorithm for each instance set. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_sensors-23-01388-t005" > <div class="html-caption" ><b>Table 5.</b> Average, maximum, and minimum RPD (%) values obtained by the evolutionary algorithm for each instance set.</div> <table > <thead ><tr ><th rowspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Instance Set</th><th colspan='3' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >RPD (%)</th></tr><tr ><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Maximum</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Minimum</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_LV</td><td align='center' valign='middle' class='html-align-center' >32.81</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_MV</td><td align='center' valign='middle' class='html-align-center' >45.00</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_HV</td><td align='center' valign='middle' class='html-align-center' >33.10</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_LV</td><td align='center' valign='middle' class='html-align-center' >50.00</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_MV</td><td align='center' valign='middle' class='html-align-center' >49.54</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >18.75</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_HV</td><td align='center' valign='middle' class='html-align-center' >50.83</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >35.42</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_LV</td><td align='center' valign='middle' class='html-align-center' >56.25</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_MV</td><td align='center' valign='middle' class='html-align-center' >52.50</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_HV</td><td align='center' valign='middle' class='html-align-center' >50.21</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_LV</td><td align='center' valign='middle' class='html-align-center' >31.40</td><td align='center' valign='middle' class='html-align-center' >62.50</td><td align='center' valign='middle' class='html-align-center' >12.50</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_MV</td><td align='center' valign='middle' class='html-align-center' >51.98</td><td align='center' valign='middle' class='html-align-center' >87.50</td><td align='center' valign='middle' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_HV</td><td align='center' valign='middle' class='html-align-center' >50.17</td><td align='center' valign='middle' class='html-align-center' >77.08</td><td align='center' valign='middle' class='html-align-center' >12.50</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_LV</td><td align='center' valign='middle' class='html-align-center' >41.25</td><td align='center' valign='middle' class='html-align-center' >56.25</td><td align='center' valign='middle' class='html-align-center' >29.17</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_MV</td><td align='center' valign='middle' class='html-align-center' >50.73</td><td align='center' valign='middle' class='html-align-center' >68.75</td><td align='center' valign='middle' class='html-align-center' >19.79</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_HV</td><td align='center' valign='middle' class='html-align-center' >41.87</td><td align='center' valign='middle' class='html-align-center' >62.50</td><td align='center' valign='middle' class='html-align-center' >18.75</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_LV</td><td align='center' valign='middle' class='html-align-center' >61.98</td><td align='center' valign='middle' class='html-align-center' >81.25</td><td align='center' valign='middle' class='html-align-center' >50.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_MV</td><td align='center' valign='middle' class='html-align-center' >58.44</td><td align='center' valign='middle' class='html-align-center' >75.00</td><td align='center' valign='middle' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_HV</td><td align='center' valign='middle' class='html-align-center' >52.50</td><td align='center' valign='middle' class='html-align-center' >71.88</td><td align='center' valign='middle' class='html-align-center' >37.50</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_LV</td><td align='center' valign='middle' class='html-align-center' >12.95</td><td align='center' valign='middle' class='html-align-center' >15.63</td><td align='center' valign='middle' class='html-align-center' >12.50</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_MV</td><td align='center' valign='middle' class='html-align-center' >53.93</td><td align='center' valign='middle' class='html-align-center' >68.75</td><td align='center' valign='middle' class='html-align-center' >29.69</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_HV</td><td align='center' valign='middle' class='html-align-center' >53.58</td><td align='center' valign='middle' class='html-align-center' >68.75</td><td align='center' valign='middle' class='html-align-center' >33.33</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_LV</td><td align='center' valign='middle' class='html-align-center' >44.69</td><td align='center' valign='middle' class='html-align-center' >65.63</td><td align='center' valign='middle' class='html-align-center' >31.25</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_MV</td><td align='center' valign='middle' class='html-align-center' >61.05</td><td align='center' valign='middle' class='html-align-center' >83.33</td><td align='center' valign='middle' class='html-align-center' >49.48</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_HV</td><td align='center' valign='middle' class='html-align-center' >53.31</td><td align='center' valign='middle' class='html-align-center' >71.46</td><td align='center' valign='middle' class='html-align-center' >25.63</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_HA_LV</td><td align='center' valign='middle' class='html-align-center' >53.39</td><td align='center' valign='middle' class='html-align-center' >65.63</td><td align='center' valign='middle' class='html-align-center' >31.25</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_HA_MV</td><td align='center' valign='middle' class='html-align-center' >58.88</td><td align='center' valign='middle' class='html-align-center' >67.19</td><td align='center' valign='middle' class='html-align-center' >50.00</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >S16_HA_HV</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >54.36</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >69.27</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >41.07</td></tr></tbody> </table> </div><div class="html-table-wrap" id="sensors-23-01388-t006"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/1424-8220/23/3/1388/display" href='#table_body_display_sensors-23-01388-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/1424-8220/23/3/1388/display" href="#table_body_display_sensors-23-01388-t006"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 6.</b> Average, maximum, and minimum computing time (in seconds) required by the evolutionary algorithm for each instance set. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_sensors-23-01388-t006" > <div class="html-caption" ><b>Table 6.</b> Average, maximum, and minimum computing time (in seconds) required by the evolutionary algorithm for each instance set.</div> <table > <thead ><tr ><th rowspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Instance Set</th><th colspan='3' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Computing Time (in Seconds)</th></tr><tr ><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Maximum</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Minimum</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_LV</td><td align='center' valign='middle' class='html-align-center' >5.00</td><td align='center' valign='middle' class='html-align-center' >7.20</td><td align='center' valign='middle' class='html-align-center' >2.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_MV</td><td align='center' valign='middle' class='html-align-center' >5.96</td><td align='center' valign='middle' class='html-align-center' >7.60</td><td align='center' valign='middle' class='html-align-center' >3.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_LA_HV</td><td align='center' valign='middle' class='html-align-center' >5.64</td><td align='center' valign='middle' class='html-align-center' >7.60</td><td align='center' valign='middle' class='html-align-center' >3.20</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_LV</td><td align='center' valign='middle' class='html-align-center' >9.92</td><td align='center' valign='middle' class='html-align-center' >13.20</td><td align='center' valign='middle' class='html-align-center' >5.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_MV</td><td align='center' valign='middle' class='html-align-center' >9.64</td><td align='center' valign='middle' class='html-align-center' >13.20</td><td align='center' valign='middle' class='html-align-center' >6.80</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_MA_HV</td><td align='center' valign='middle' class='html-align-center' >7.88</td><td align='center' valign='middle' class='html-align-center' >10.00</td><td align='center' valign='middle' class='html-align-center' >6.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_LV</td><td align='center' valign='middle' class='html-align-center' >13.16</td><td align='center' valign='middle' class='html-align-center' >16.40</td><td align='center' valign='middle' class='html-align-center' >10.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_MV</td><td align='center' valign='middle' class='html-align-center' >11.96</td><td align='center' valign='middle' class='html-align-center' >14.80</td><td align='center' valign='middle' class='html-align-center' >9.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S4_HA_HV</td><td align='center' valign='middle' class='html-align-center' >11.60</td><td align='center' valign='middle' class='html-align-center' >13.60</td><td align='center' valign='middle' class='html-align-center' >9.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_LV</td><td align='center' valign='middle' class='html-align-center' >10.32</td><td align='center' valign='middle' class='html-align-center' >14.80</td><td align='center' valign='middle' class='html-align-center' >3.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_MV</td><td align='center' valign='middle' class='html-align-center' >11.84</td><td align='center' valign='middle' class='html-align-center' >14.80</td><td align='center' valign='middle' class='html-align-center' >8.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_LA_HV</td><td align='center' valign='middle' class='html-align-center' >11.48</td><td align='center' valign='middle' class='html-align-center' >14.80</td><td align='center' valign='middle' class='html-align-center' >8.80</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_LV</td><td align='center' valign='middle' class='html-align-center' >19.80</td><td align='center' valign='middle' class='html-align-center' >25.60</td><td align='center' valign='middle' class='html-align-center' >13.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_MV</td><td align='center' valign='middle' class='html-align-center' >18.12</td><td align='center' valign='middle' class='html-align-center' >24.40</td><td align='center' valign='middle' class='html-align-center' >10.80</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_MA_HV</td><td align='center' valign='middle' class='html-align-center' >15.24</td><td align='center' valign='middle' class='html-align-center' >21.60</td><td align='center' valign='middle' class='html-align-center' >10.80</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_LV</td><td align='center' valign='middle' class='html-align-center' >26.88</td><td align='center' valign='middle' class='html-align-center' >35.20</td><td align='center' valign='middle' class='html-align-center' >19.20</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_MV</td><td align='center' valign='middle' class='html-align-center' >23.92</td><td align='center' valign='middle' class='html-align-center' >30.00</td><td align='center' valign='middle' class='html-align-center' >18.80</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S8_HA_HV</td><td align='center' valign='middle' class='html-align-center' >22.64</td><td align='center' valign='middle' class='html-align-center' >26.80</td><td align='center' valign='middle' class='html-align-center' >18.80</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_LV</td><td align='center' valign='middle' class='html-align-center' >20.58</td><td align='center' valign='middle' class='html-align-center' >22.60</td><td align='center' valign='middle' class='html-align-center' >18.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_MV</td><td align='center' valign='middle' class='html-align-center' >20.80</td><td align='center' valign='middle' class='html-align-center' >22.40</td><td align='center' valign='middle' class='html-align-center' >19.20</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_LA_HV</td><td align='center' valign='middle' class='html-align-center' >20.36</td><td align='center' valign='middle' class='html-align-center' >22.80</td><td align='center' valign='middle' class='html-align-center' >18.00</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_LV</td><td align='center' valign='middle' class='html-align-center' >29.88</td><td align='center' valign='middle' class='html-align-center' >40.00</td><td align='center' valign='middle' class='html-align-center' >23.20</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_MV</td><td align='center' valign='middle' class='html-align-center' >33.64</td><td align='center' valign='middle' class='html-align-center' >36.80</td><td align='center' valign='middle' class='html-align-center' >29.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_MA_HV</td><td align='center' valign='middle' class='html-align-center' >28.92</td><td align='center' valign='middle' class='html-align-center' >34.80</td><td align='center' valign='middle' class='html-align-center' >23.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_HA_LV</td><td align='center' valign='middle' class='html-align-center' >49.04</td><td align='center' valign='middle' class='html-align-center' >59.60</td><td align='center' valign='middle' class='html-align-center' >41.60</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >S16_HA_MV</td><td align='center' valign='middle' class='html-align-center' >42.32</td><td align='center' valign='middle' class='html-align-center' >45.20</td><td align='center' valign='middle' class='html-align-center' >41.20</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >S16_HA_HV</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >41.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >42.80</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >40.40</td></tr></tbody> </table> </div></section><section class='html-fn_group'><table><tr id=''><td></td><td><div class='html-p'><b>Disclaimer/Publisher’s Note:</b> The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). 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