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The idea of using a population of search agents that collectively approximate the Pareto front resonates well with processes in natural evolution, immune systems, and swarm intelligence. Methods such as NSGA-II, SPEA2, SMS-EMOA, MOPSO, and MOEA/D became standard solvers when it comes to solving multiobjective optimization problems. This tutorial will review some of the most important fundamentals in multiobjective optimization and then introduce representative algorithms, illustrate their working principles, and discuss their application scope. In addition, the tutorial will discuss statistical performance assessment. Finally, it highlights recent important trends and closely related research fields. The tutorial is intended for readers, who want to acquire basic knowledge on the mathematical foundations of multiobjective optimization and state-of-the-art methods in evolutionary multiobjective optimization. The aim is to provide a starting point for researching in this active area, and it should also help the advanced reader to identify open research topics.","publication_date":"2018,,","publication_name":"Natural Computing","grobid_abstract_attachment_id":"101722868"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"A tutorial on multiobjective optimization: fundamentals and evolutionary methods","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [249601801]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; 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":101722868,"attachmentType":"pdf"}"><img alt="First page of “A tutorial on multiobjective optimization: fundamentals and evolutionary methods”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/101722868/mini_magick20230502-1-bej22o.png?1683000964" /><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">A tutorial on multiobjective optimization: fundamentals and evolutionary methods</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="249601801" href="https://independent.academia.edu/MichaelEmmerich3"><img alt="Profile image of Michael Emmerich" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/249601801/103397250/92572862/s65_michael.emmerich.png" />Michael Emmerich</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2018, Natural Computing</p></div><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":101722868,"attachmentType":"pdf","workUrl":"https://www.academia.edu/101086217/A_tutorial_on_multiobjective_optimization_fundamentals_and_evolutionary_methods"}">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":101722868,"attachmentType":"pdf","workUrl":"https://www.academia.edu/101086217/A_tutorial_on_multiobjective_optimization_fundamentals_and_evolutionary_methods"}"><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="101722868" data-landing_url="https://www.academia.edu/101086217/A_tutorial_on_multiobjective_optimization_fundamentals_and_evolutionary_methods" 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="2723803" 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/2723803/J_Evolutionary_Multiobjective_Optimization">J. 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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":"A Simple Approach to Evolutionary Multiobjective Optimization","attachmentId":68068782,"attachmentType":"pdf","work_url":"https://www.academia.edu/49871799/A_Simple_Approach_to_Evolutionary_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/49871799/A_Simple_Approach_to_Evolutionary_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="4" data-entity-id="82274583" 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/82274583/EVOLUTIONARY_ALGORITHMS_FOR_MULTIOBJECTIVE_OPTIMIZATION">EVOLUTIONARY ALGORITHMS FOR 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="219058816" href="https://independent.academia.edu/ademusmeal">adem usmeal</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":"EVOLUTIONARY ALGORITHMS FOR MULTIOBJECTIVE 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href="https://www.academia.edu/74133370/A_Review_towards_Evolutionary_Multiobjective_optimization_Algorithms">A Review towards Evolutionary Multiobjective optimization Algorithms</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="148870971" href="https://independent.academia.edu/sunnysharma186">sunny sharma</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2014</p><p class="ds-related-work--abstract ds2-5-body-sm">Multi objective optimization is a promising field which is increasingly being encountered in many areas worldwide. Various metaheuristic techniques such as differential evolution (DE), genetic algorithm (GA), gravitational search algorithm (GSA), and particle swarm optimization (PSO) have been used to solve Multi objective problems. Various multiobjective evolutionary algorithms have been developed. Their principal reason for development is their ability to find multiple Pareto optimal solution in single run. Their Basic motive of evolutionary multiobjective optimization in contrast to singleobjective optimization was optimality, decision making algorithm design (fitness, diversity, and elitism), constraints, and preference. The goal of this paper is to trace the genealogy & review the state of the art of evolutionary multiobjective optimization algorithms.</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 Review towards Evolutionary Multiobjective optimization Algorithms","attachmentId":82394377,"attachmentType":"pdf","work_url":"https://www.academia.edu/74133370/A_Review_towards_Evolutionary_Multiobjective_optimization_Algorithms","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/74133370/A_Review_towards_Evolutionary_Multiobjective_optimization_Algorithms"><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="103740730" 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/103740730/Evolutionary_multiobjective_optimization_open_research_areas_and_some_challenges_lying_ahead">Evolutionary multiobjective optimization: open research areas and some challenges lying ahead</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="13867137" href="https://azc-uam.academia.edu/SilviaBeatrizGonz%C3%A1lezBrambila">Silvia B González Brambila</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Complex &amp; Intelligent Systems, 2019</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":"Evolutionary multiobjective optimization: open research areas and some challenges lying ahead","attachmentId":103665153,"attachmentType":"pdf","work_url":"https://www.academia.edu/103740730/Evolutionary_multiobjective_optimization_open_research_areas_and_some_challenges_lying_ahead","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/103740730/Evolutionary_multiobjective_optimization_open_research_areas_and_some_challenges_lying_ahead"><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="57472964" 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/57472964/Survey_of_evolutionary_algorithms_used_in_multiobjective_optimization">Survey of evolutionary algorithms used 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="47469692" href="https://independent.academia.edu/VassilGuliashki">Vassil Guliashki</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Problems of Engineering …, 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":"Survey of evolutionary algorithms used in multiobjective optimization","attachmentId":72359850,"attachmentType":"pdf","work_url":"https://www.academia.edu/57472964/Survey_of_evolutionary_algorithms_used_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/57472964/Survey_of_evolutionary_algorithms_used_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="8" data-entity-id="88688762" 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/88688762/Comparison_of_Multiobjective_Evolutionary_Algorithms_Empirical_Results">Comparison of Multiobjective Evolutionary Algorithms: Empirical Results</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="139258406" href="https://independent.academia.edu/GERMANHERNANDEZ118">GERMAN HERNANDEZ</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Evolutionary Computation, 2000</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.</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":"Comparison of Multiobjective Evolutionary Algorithms: Empirical Results","attachmentId":92616610,"attachmentType":"pdf","work_url":"https://www.academia.edu/88688762/Comparison_of_Multiobjective_Evolutionary_Algorithms_Empirical_Results","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/88688762/Comparison_of_Multiobjective_Evolutionary_Algorithms_Empirical_Results"><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="63817188" 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/63817188/An_Evolution_Strategy_for_the_Multiobjective_Optimization">An Evolution Strategy for the 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="199495055" href="https://independent.academia.edu/ThanhB%C3%ACnh192">Thanh Bình</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1996</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper presents an evolution strategy for the multiobjective optimization with any constraints.The main advantage of the evolution strategy is to allow to handle simultaneously multipleobjectives and constraints, and to achieve the good approximation of the complete paretooptimalset. However, it is essentially a global search method for the scalar optimization. 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