{"id":7700,"date":"2020-03-10T11:32:36","date_gmt":"2020-03-10T10:32:36","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=7700"},"modified":"2022-12-03T23:03:45","modified_gmt":"2022-12-03T22:03:45","slug":"algorithme-evolutif-de-pareto-fort","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/algorithms-devolution-2\/strong-pareto-evolutionary-algorithm\/","title":{"rendered":"Strong evolutionary Pareto algorithm"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"7700\" class=\"elementor elementor-7700\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ae36253 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ae36253\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c54bce4\" data-id=\"c54bce4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-54af6b4 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"54af6b4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/algorithms-devolution-2\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Evolution 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class=\"elementor-button-text\">Home page<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e924e60\" data-id=\"e924e60\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-00d0449 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"00d0449\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-540-30217-9_75?error=cookies_not_supported&#038;code=bb279a8c-f073-4edf-99ed-9dc8e620ca8e\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-81ba446 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"81ba446\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1f5cacc\" data-id=\"1f5cacc\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6a578dd elementor-widget elementor-widget-progress\" data-id=\"6a578dd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"progress.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<span class=\"elementor-title\" id=\"elementor-progress-bar-6a578dd\">\n\t\t\t\tDifficulty\t\t\t<\/span>\n\t\t\n\t\t<div aria-labelledby=\"elementor-progress-bar-6a578dd\" class=\"elementor-progress-wrapper\" role=\"progressbar\" aria-valuemin=\"0\" aria-valuemax=\"100\" aria-valuenow=\"50\" aria-valuetext=\"50% (Moyen)\">\n\t\t\t<div class=\"elementor-progress-bar\" data-max=\"50\">\n\t\t\t\t<span class=\"elementor-progress-text\">Average<\/span>\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-progress-percentage\">50%<\/span>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-221b9daa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"221b9daa\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-38640850\" data-id=\"38640850\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9018f8 elementor-widget elementor-widget-text-editor\" data-id=\"9018f8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/algorithms-devolution-2\/strong-pareto-evolutionary-algorithm\/#Algorithme-evolutif-de-Pareto-fort-SPEA\" >Strong Pareto evolutionary algorithm SPEA<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Algorithme-evolutif-de-Pareto-fort-SPEA\"><\/span>Strong Pareto evolutionary algorithm SPEA<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-text-align-justify\">The goal of the strong Pareto evolutionary algorithm SPEA is to locate and maintain a front of non-dominated solutions, ideally a set of optimal Pareto solutions. This is achieved by using an evolutionary process (with surrogate procedures for genetic recombination and mutation) to explore the search space, and a selection process that uses a combination of the degree of dominance of a candidate solution (strong ) and an estimate of the density of the Pareto front as an assigned fitness.<\/p>\n<p class=\"has-text-align-justify\">An archive of the non-dominated set is kept separate from the population of candidate solutions used in the evolutionary process, providing a form of elitism.<\/p>\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-7703 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/spea2.png\" alt=\"strong Pareto evolutionary algorithm SPEA\" width=\"463\" height=\"569\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/spea2.png 463w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/03\/spea2-244x300.png 244w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/figure>\n\n<p class=\"has-text-align-justify\">Here are the functions of the strong Pareto evolutionary algorithm SPEA.<\/p>\n<p class=\"has-text-align-justify\">The CalculateRawFitness function calculates raw fitness as the sum of the strength values of the solutions that dominate a given candidate, where strength is the number of solutions that a given solution dominates. The CandidateDensity function estimates the density of an area of the Pareto front as 1 \/ (o ^ k + 2) where o ^ k is the Euclidean distance of the objective values between a given solution, the kth nearest neighbor of the solution, and k is the square root of the combined population and archive size.<\/p>\n<p class=\"has-text-align-justify\">The PopulateWithRemainingBest function iteratively populates the archive with the remaining candidate solutions in order of fitness. The RemoveMostSimilar function truncates the archive population by removing members with the smallest o ^ k values calculated against the archive.<\/p>\n<p class=\"has-text-align-justify\">The SelectParents function selects the parents of a population using a selection method of the<a href=\"https:\/\/complex-systems-ai.com\/en\/algorithms-devolution-2\/genetic-algorithms\/\">genetic algorithm<\/a> such as the selection of binary tournaments. The CrossoverAndMutation function performs the genetic algorithm crossover and mutation operators.<\/p>\n\n<p class=\"has-text-align-justify\">The strong Pareto evolutionary algorithm SPEA has been designed and adapted to instances of optimization problems with multiple combinatorial objectives and continuous function. A binary representation can be used for continuous function optimization problems in conjunction with classical genetic operators such as point crossing and point mutation. A k value of 1 can be used for efficiency while providing useful results. The size of the archives is generally smaller than the size of the population.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Evolution algorithms Home page Wiki Difficulty Medium 50% Evolutionary strong Pareto algorithm SPEA The objective of the evolutionary strong Pareto algorithm SPEA is to locate\u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":7110,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7700","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/7700","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=7700"}],"version-history":[{"count":3,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/7700\/revisions"}],"predecessor-version":[{"id":18879,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/7700\/revisions\/18879"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/7110"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=7700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}