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<!DOCTYPE html> <html > <head> <meta charset="utf-8"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <meta content="width=device-width, initial-scale=1" name="viewport"> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs"> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="6CEpZiZDNwMZK10gy2/g6AgaX81TcuQSoUeY0EHOB1eygScttnhkRIVJ7oGNXhvEsz7oY1YLzSPZw2Le+/+Jzw==" /> <meta name="citation_title" content="An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions" /> <meta name="citation_publication_date" content="2005/01/01" /> <meta name="citation_journal_title" content="Journal of Mechanical Design" /> <meta name="citation_author" content="Gary Wang" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:url" content="https://www.academia.edu/66455908/An_Efficient_Pareto_Set_Identification_Approach_for_Multiobjective_Optimization_on_Black_Box_Functions" /> <meta name="twitter:title" content="An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions" /> <meta name="twitter:description" content="Both multiple objectives and computation-intensive black-box functions often exist simultaneously in engineering design problems. 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In this" /> <title>(PDF) An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions | Gary Wang - Academia.edu</title> <link rel="canonical" href="https://www.academia.edu/66455908/An_Efficient_Pareto_Set_Identification_Approach_for_Multiobjective_Optimization_on_Black_Box_Functions" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '49879c2402910372f4abc62630a427bbe033d190'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1732389578000); window.Aedu.timeDifference = new Date().getTime() - 1732389578000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"Both multiple objectives and computation-intensive black-box functions often exist simultaneously in engineering design problems. Few of existing multiobjective optimization approaches addresses problems with expensive black-box functions. In this paper, a new method called the Pareto set pursuing (PSP) method is developed. By developing sampling guidance functions based on approximation models, this approach progressively provides a designer with a rich and evenly distributed set of Pareto optimal points. This work describes PSP procedures in detail. From testing and design application, PSP demonstrates considerable promises in efficiency, accuracy, and robustness. Properties of PSP and differences between PSP and other approximation-based methods are also discussed. 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"https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F66455908%2FAn_Efficient_Pareto_Set_Identification_Approach_for_Multiobjective_Optimization_on_Black_Box_Functions%3Fauto%3Ddownload"; window.loswp.translateUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F66455908%2FAn_Efficient_Pareto_Set_Identification_Approach_for_Multiobjective_Optimization_on_Black_Box_Functions%3Fshow_translation%3Dtrue"; window.loswp.previewableAttachments = [{"id":77640126,"identifier":"Attachment_77640126","shouldShowBulkDownload":false}]; window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":66455908,"created_at":"2021-12-29T16:27:12.354-08:00","from_world_paper_id":189715906,"updated_at":"2021-12-29T17:08:28.281-08:00","_data":{"abstract":"Both multiple objectives and computation-intensive black-box functions often exist simultaneously in engineering design problems. Few of existing multiobjective optimization approaches addresses problems with expensive black-box functions. In this paper, a new method called the Pareto set pursuing (PSP) method is developed. By developing sampling guidance functions based on approximation models, this approach progressively provides a designer with a rich and evenly distributed set of Pareto optimal points. This work describes PSP procedures in detail. From testing and design application, PSP demonstrates considerable promises in efficiency, accuracy, and robustness. Properties of PSP and differences between PSP and other approximation-based methods are also discussed. It is believed that PSP has a great potential to be a practical tool for multiobjective optimization problems.","publisher":"ASME International","publication_date":"2005,,","publication_name":"Journal of Mechanical Design"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [11579]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":77640126,"attachmentType":"pdf"}"><img alt="First page of “An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/77640126/mini_magick20211229-17867-1qx6xk.png?1640826407" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="11579" href="https://sfu.academia.edu/GaryWang"><img alt="Profile image of Gary Wang" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Gary Wang</a></div><p class="ds-work-card--detail ds2-5-body-sm">2005, Journal of Mechanical Design</p><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">Both multiple objectives and computation-intensive black-box functions often exist simultaneously in engineering design problems. Few of existing multiobjective optimization approaches addresses problems with expensive black-box functions. In this paper, a new method called the Pareto set pursuing (PSP) method is developed. By developing sampling guidance functions based on approximation models, this approach progressively provides a designer with a rich and evenly distributed set of Pareto optimal points. This work describes PSP procedures in detail. From testing and design application, PSP demonstrates considerable promises in efficiency, accuracy, and robustness. Properties of PSP and differences between PSP and other approximation-based methods are also discussed. It is believed that PSP has a great potential to be a practical tool for multiobjective optimization problems.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":77640126,"attachmentType":"pdf","workUrl":"https://www.academia.edu/66455908/An_Efficient_Pareto_Set_Identification_Approach_for_Multiobjective_Optimization_on_Black_Box_Functions"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":77640126,"attachmentType":"pdf","workUrl":"https://www.academia.edu/66455908/An_Efficient_Pareto_Set_Identification_Approach_for_Multiobjective_Optimization_on_Black_Box_Functions"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="77640126" data-landing_url="https://www.academia.edu/66455908/An_Efficient_Pareto_Set_Identification_Approach_for_Multiobjective_Optimization_on_Black_Box_Functions" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="73949557" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/73949557/Optimization_and_Engineering_manuscript_No_will_be_inserted_by_the_editor_Multiobjective_Optimization_of_Expensive_Black_Box_Functions_via_Expected_Maximin_Improvement">Optimization and Engineering manuscript No. (will be inserted by the editor) Multiobjective Optimization of Expensive Black-Box Functions via Expected Maximin Improvement</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37978259" href="https://independent.academia.edu/ThomasSantner">Thomas Santner</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2014</p><p class="ds-related-work--abstract ds2-5-body-sm">Many engineering design optimization problems contain multiple objective functions all of which it is desired to minimize, say. 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First, it proposes an improvement function based on the mo...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Optimization and Engineering manuscript No. (will be inserted by the editor) Multiobjective Optimization of Expensive Black-Box Functions via Expected Maximin Improvement","attachmentId":82281281,"attachmentType":"pdf","work_url":"https://www.academia.edu/73949557/Optimization_and_Engineering_manuscript_No_will_be_inserted_by_the_editor_Multiobjective_Optimization_of_Expensive_Black_Box_Functions_via_Expected_Maximin_Improvement","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" 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href="https://umich.academia.edu/PanosPapalambros">Panos Papalambros</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Structural and Multidisciplinary Optimization, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Pareto set analysis: local measures of objective coupling in multiobjective design optimization","attachmentId":87143370,"attachmentType":"pdf","work_url":"https://www.academia.edu/80923453/Pareto_set_analysis_local_measures_of_objective_coupling_in_multiobjective_design_optimization","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" 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class="ds-related-work--metadata ds2-5-body-xs">Journal of Computational and Applied Mathematics, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization","attachmentId":91380795,"attachmentType":"pdf","work_url":"https://www.academia.edu/87064295/A_method_for_generating_a_well_distributed_Pareto_set_in_nonlinear_multiobjective_optimization","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/87064295/A_method_for_generating_a_well_distributed_Pareto_set_in_nonlinear_multiobjective_optimization"><span 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href="https://www.academia.edu/523777/A_pareto_compliant_surrogate_approach_for_multiobjective_optimization"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="87064213" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/87064213/Numerical_method_for_generating_the_entire_Pareto_frontier_in_multiobjective_optimization">Numerical method for generating the entire Pareto frontier in multiobjective optimization</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="8765724" href="https://manchester.academia.edu/SergeiUtyuzhnikov">Sergei Utyuzhnikov</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2005</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Numerical method for generating the entire Pareto frontier in multiobjective optimization","attachmentId":91380736,"attachmentType":"pdf","work_url":"https://www.academia.edu/87064213/Numerical_method_for_generating_the_entire_Pareto_frontier_in_multiobjective_optimization","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/87064213/Numerical_method_for_generating_the_entire_Pareto_frontier_in_multiobjective_optimization"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="54805846" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/54805846/Finding_Innovative_Design_Principles_for_Multiobjective_Optimization_Problems">Finding Innovative Design Principles for Multiobjective Optimization Problems</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="3619100" href="https://independent.academia.edu/ashutoshtiwari1">ashutosh tiwari</a></div><p class="ds-related-work--metadata ds2-5-body-xs">IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 2000</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Finding Innovative Design Principles for Multiobjective Optimization Problems","attachmentId":70991346,"attachmentType":"pdf","work_url":"https://www.academia.edu/54805846/Finding_Innovative_Design_Principles_for_Multiobjective_Optimization_Problems","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/54805846/Finding_Innovative_Design_Principles_for_Multiobjective_Optimization_Problems"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="77582359" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/77582359/Approximating_Multiobjective_Optimization_Problems_with_Complex_Pareto_Fronts">Approximating Multiobjective Optimization Problems with Complex Pareto Fronts</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46060617" href="https://independent.academia.edu/IqbalRai">Iqbal Rai</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2015</p><p class="ds-related-work--abstract ds2-5-body-sm">The main goal of multiobjective optimization is to achieve a set of well-converged and evenly-distributed Pareto optimal points. While evolutionary algorithms have been reported to converge well, their distribution performance might not be as uniform as we expected, especially when the problems to be optimized involve complex Pareto fronts. In this paper, with the aid of a set of uniformly-distributed reference points, multiobjective optimization problems (MOPs) can be handled by minimizing least reference distances (LRD), which measure the proximity of solutions to their nearest reference points. This way, the uniformity of approximated solutions is implicitly controlled by the reference point set, and convergence is in the charge of LRD. The proposed LRD algorithm (LRDA) is tested and compared with several popular algorithms on a number of old and newly-developed MOPs that have complex Pareto fronts, showing that this method is very promising to obtain evenlydistributed Pareto opt...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Approximating Multiobjective Optimization Problems with Complex Pareto Fronts","attachmentId":84861397,"attachmentType":"pdf","work_url":"https://www.academia.edu/77582359/Approximating_Multiobjective_Optimization_Problems_with_Complex_Pareto_Fronts","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/77582359/Approximating_Multiobjective_Optimization_Problems_with_Complex_Pareto_Fronts"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="73949410" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/73949410/Multiobjective_Optimization_of_Expensive_Black_Box_Functions_via_Expected_Maximin_Improvement">Multiobjective Optimization of Expensive Black-Box Functions via Expected Maximin Improvement</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37978259" href="https://independent.academia.edu/ThomasSantner">Thomas Santner</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2011</p><p class="ds-related-work--abstract ds2-5-body-sm">Many engineering design optimization problems contain multiple objective functions all of which it is desired to minimize, say. One approach to solving this problem is to identify those inputs to the objective functions that produce an output (vector) on the Pareto Front; the inputs that produce outputs on the Pareto Front form the Pareto Set. This paper proposes a method for identifying the Pareto Front and the Pareto Set when the objective functions are expensive to compute. The method replaces the objective function evaluations by a rapidly computable approximator based on an interpolating Gaussian process (GP) model. It sequentially selects new input sites guided by an improvement function; the next input to evaluate each output is that vector which maximizes the conditional expected value of this improvement function given the current data. The method introduced in this paper provides two advances within this framework. First, it proposes an improvement function based on the mo...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multiobjective Optimization of Expensive Black-Box Functions via Expected Maximin Improvement","attachmentId":82281253,"attachmentType":"pdf","work_url":"https://www.academia.edu/73949410/Multiobjective_Optimization_of_Expensive_Black_Box_Functions_via_Expected_Maximin_Improvement","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/73949410/Multiobjective_Optimization_of_Expensive_Black_Box_Functions_via_Expected_Maximin_Improvement"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="31487023" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/31487023/A_method_for_selecting_Pareto_optimal_solutions_in_multiobjective_optimization">A method for selecting Pareto optimal solutions in multiobjective optimization</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="60240190" href="https://uus.academia.edu/BassemJarboui">Bassem Jarboui</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A method for selecting Pareto optimal solutions in multiobjective optimization","attachmentId":51837266,"attachmentType":"pdf","work_url":"https://www.academia.edu/31487023/A_method_for_selecting_Pareto_optimal_solutions_in_multiobjective_optimization","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/31487023/A_method_for_selecting_Pareto_optimal_solutions_in_multiobjective_optimization"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":77640126,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":77640126,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_77640126" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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