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vector-toc-level-3"> <a class="vector-toc-link" href="#Genetic_operators"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.3</span> <span>Genetic operators</span> </div> </a> <ul id="toc-Genetic_operators-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heuristics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Heuristics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.4</span> <span>Heuristics</span> </div> </a> <ul id="toc-Heuristics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Termination" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Termination"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.5</span> <span>Termination</span> </div> </a> <ul id="toc-Termination-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-The_building_block_hypothesis" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#The_building_block_hypothesis"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>The building block hypothesis</span> </div> </a> <ul id="toc-The_building_block_hypothesis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Limitations" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Limitations"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Limitations</span> </div> </a> <ul id="toc-Limitations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Variants" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Variants"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Variants</span> </div> </a> <button aria-controls="toc-Variants-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Variants subsection</span> </button> <ul id="toc-Variants-sublist" class="vector-toc-list"> <li id="toc-Chromosome_representation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Chromosome_representation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Chromosome representation</span> </div> </a> <ul id="toc-Chromosome_representation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elitism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elitism"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Elitism</span> </div> </a> <ul id="toc-Elitism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Parallel_implementations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Parallel_implementations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Parallel implementations</span> </div> </a> <ul id="toc-Parallel_implementations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Adaptive_GAs" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Adaptive_GAs"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Adaptive GAs</span> </div> </a> <ul id="toc-Adaptive_GAs-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Problem_domains" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Problem_domains"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Problem domains</span> </div> </a> <ul id="toc-Problem_domains-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>History</span> </div> </a> <button aria-controls="toc-History-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle History subsection</span> </button> <ul id="toc-History-sublist" class="vector-toc-list"> <li id="toc-Commercial_products" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Commercial_products"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Commercial products</span> </div> </a> <ul id="toc-Commercial_products-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Related_techniques" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Related_techniques"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Related techniques</span> </div> </a> <button aria-controls="toc-Related_techniques-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Related techniques subsection</span> </button> <ul id="toc-Related_techniques-sublist" class="vector-toc-list"> <li id="toc-Parent_fields" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Parent_fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Parent fields</span> </div> </a> <ul id="toc-Parent_fields-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Related_fields" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Related_fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Related fields</span> </div> </a> <ul id="toc-Related_fields-sublist" class="vector-toc-list"> <li id="toc-Evolutionary_algorithms" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Evolutionary_algorithms"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.1</span> <span>Evolutionary algorithms</span> </div> </a> <ul id="toc-Evolutionary_algorithms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Swarm_intelligence" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Swarm_intelligence"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.2</span> <span>Swarm intelligence</span> </div> </a> <ul id="toc-Swarm_intelligence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_evolutionary_computing_algorithms" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Other_evolutionary_computing_algorithms"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.3</span> <span>Other evolutionary computing algorithms</span> </div> </a> <ul id="toc-Other_evolutionary_computing_algorithms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_metaheuristic_methods" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Other_metaheuristic_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.4</span> <span>Other metaheuristic methods</span> </div> </a> <ul id="toc-Other_metaheuristic_methods-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_stochastic_optimisation_methods" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Other_stochastic_optimisation_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.5</span> <span>Other stochastic optimisation methods</span> </div> </a> <ul id="toc-Other_stochastic_optimisation_methods-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <button aria-controls="toc-External_links-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle External links subsection</span> </button> <ul id="toc-External_links-sublist" class="vector-toc-list"> <li id="toc-Resources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Resources"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.1</span> <span>Resources</span> </div> </a> <ul id="toc-Resources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tutorials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tutorials"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.2</span> <span>Tutorials</span> </div> </a> <ul id="toc-Tutorials-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Genetic algorithm</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 50 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-50" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">50 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Genetiese_algoritme" title="Genetiese algoritme – Afrikaans" lang="af" hreflang="af" data-title="Genetiese algoritme" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AE%D9%88%D8%A7%D8%B1%D8%B2%D9%85%D9%8A%D8%A7%D8%AA_%D9%88%D8%B1%D8%A7%D8%AB%D9%8A%D8%A9" title="خوارزميات وراثية – Arabic" lang="ar" hreflang="ar" data-title="خوارزميات وراثية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Genetik_alqoritml%C9%99r" title="Genetik alqoritmlər – Azerbaijani" lang="az" hreflang="az" data-title="Genetik alqoritmlər" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%82%E0%A6%B6%E0%A6%BE%E0%A6%A3%E0%A7%81%E0%A6%AD%E0%A6%BF%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%85%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B2%E0%A6%97%E0%A6%B0%E0%A6%BF%E0%A6%A6%E0%A6%AE" title="বংশাণুভিত্তিক অ্যালগরিদম – Bangla" lang="bn" hreflang="bn" data-title="বংশাণুভিত্তিক অ্যালগরিদম" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%93%D0%B5%D0%BD%D0%B5%D1%82%D0%B8%D1%87%D0%B5%D0%BD_%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D1%8A%D0%BC" title="Генетичен алгоритъм – Bulgarian" lang="bg" hreflang="bg" data-title="Генетичен алгоритъм" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Algorisme_gen%C3%A8tic" title="Algorisme genètic – Catalan" lang="ca" hreflang="ca" data-title="Algorisme genètic" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Genetick%C3%BD_algoritmus" title="Genetický algoritmus – Czech" lang="cs" hreflang="cs" data-title="Genetický algoritmus" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Genetisk_algoritme" title="Genetisk algoritme – Danish" lang="da" hreflang="da" data-title="Genetisk algoritme" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Genetischer_Algorithmus" title="Genetischer Algorithmus – German" lang="de" hreflang="de" data-title="Genetischer Algorithmus" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Geneetiline_algoritm" title="Geneetiline algoritm – Estonian" lang="et" hreflang="et" data-title="Geneetiline algoritm" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CE%BD%CE%B5%CF%84%CE%B9%CE%BA%CE%BF%CE%AF_%CE%91%CE%BB%CE%B3%CF%8C%CF%81%CE%B9%CE%B8%CE%BC%CE%BF%CE%B9" title="Γενετικοί Αλγόριθμοι – Greek" lang="el" hreflang="el" data-title="Γενετικοί Αλγόριθμοι" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Algoritmo_gen%C3%A9tico" title="Algoritmo genético – Spanish" lang="es" hreflang="es" data-title="Algoritmo genético" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Algoritmo_genetiko" title="Algoritmo genetiko – Basque" lang="eu" hreflang="eu" data-title="Algoritmo genetiko" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%84%DA%AF%D9%88%D8%B1%DB%8C%D8%AA%D9%85_%DA%98%D9%86%D8%AA%DB%8C%DA%A9" title="الگوریتم ژنتیک – Persian" lang="fa" hreflang="fa" data-title="الگوریتم ژنتیک" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Algorithme_g%C3%A9n%C3%A9tique" title="Algorithme génétique – French" lang="fr" hreflang="fr" data-title="Algorithme génétique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Algoritmo_xen%C3%A9tico" title="Algoritmo xenético – Galician" lang="gl" hreflang="gl" data-title="Algoritmo xenético" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9C%A0%EC%A0%84_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98" title="유전 알고리즘 – Korean" lang="ko" hreflang="ko" data-title="유전 알고리즘" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%9C%E0%A5%87%E0%A4%A8%E0%A5%87%E0%A4%9F%E0%A4%BF%E0%A4%95_%E0%A4%8F%E0%A4%B2%E0%A5%8D%E0%A4%97%E0%A5%8B%E0%A4%B0%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AE" title="जेनेटिक एल्गोरिद्म – Hindi" lang="hi" hreflang="hi" data-title="जेनेटिक एल्गोरिद्म" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Geneti%C4%8Dki_algoritmi" title="Genetički algoritmi – Croatian" lang="hr" hreflang="hr" data-title="Genetički algoritmi" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Algoritma_genetik" title="Algoritma genetik – Indonesian" lang="id" hreflang="id" data-title="Algoritma genetik" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Algoritmo_genetico" title="Algoritmo genetico – Italian" lang="it" hreflang="it" data-title="Algoritmo genetico" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9C%D7%92%D7%95%D7%A8%D7%99%D7%AA%D7%9D_%D7%92%D7%A0%D7%98%D7%99" title="אלגוריתם גנטי – Hebrew" lang="he" hreflang="he" data-title="אלגוריתם גנטי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%A8%E0%B3%81%E0%B2%B5%E0%B2%82%E0%B2%B6%E0%B2%BF%E0%B2%95_%E0%B2%95%E0%B3%8D%E0%B2%B0%E0%B2%AE%E0%B2%BE%E0%B2%B5%E0%B2%B3%E0%B2%BF" title="ಅನುವಂಶಿಕ ಕ್ರಮಾವಳಿ – Kannada" lang="kn" hreflang="kn" data-title="ಅನುವಂಶಿಕ ಕ್ರಮಾವಳಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Algorithmus_geneticus" title="Algorithmus geneticus – Latin" lang="la" hreflang="la" data-title="Algorithmus geneticus" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C4%A2en%C4%93tiskais_algoritms" title="Ģenētiskais algoritms – Latvian" lang="lv" hreflang="lv" data-title="Ģenētiskais algoritms" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Genetinis_algoritmas" title="Genetinis algoritmas – Lithuanian" lang="lt" hreflang="lt" data-title="Genetinis algoritmas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Genetikus_algoritmus" title="Genetikus algoritmus – Hungarian" lang="hu" hreflang="hu" data-title="Genetikus algoritmus" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%9C%E0%B4%A8%E0%B4%BF%E0%B4%A4%E0%B4%95_%E0%B4%85%E0%B5%BD%E0%B4%97%E0%B5%8B%E0%B4%B0%E0%B4%BF%E0%B4%A4%E0%B4%82" title="ജനിതക അൽഗോരിതം – Malayalam" lang="ml" hreflang="ml" data-title="ജനിതക അൽഗോരിതം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Genetisch_algoritme" title="Genetisch algoritme – Dutch" lang="nl" hreflang="nl" data-title="Genetisch algoritme" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%81%BA%E4%BC%9D%E7%9A%84%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0" title="遺伝的アルゴリズム – Japanese" lang="ja" hreflang="ja" data-title="遺伝的アルゴリズム" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Genetisk_algoritme" title="Genetisk algoritme – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Genetisk algoritme" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF_%D8%AC%D9%86%D8%AA%DB%8C%DA%A9_%D8%A7%D9%84%DA%AB%D9%88%D8%B1%DB%90%D8%AA%D9%85" title="د جنتیک الګورېتم – Pashto" lang="ps" hreflang="ps" data-title="د جنتیک الګورېتم" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Algorytm_genetyczny" title="Algorytm genetyczny – Polish" lang="pl" hreflang="pl" data-title="Algorytm genetyczny" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Algoritmo_gen%C3%A9tico" title="Algoritmo genético – Portuguese" lang="pt" hreflang="pt" data-title="Algoritmo genético" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Algoritm_genetic" title="Algoritm genetic – Romanian" lang="ro" hreflang="ro" data-title="Algoritm genetic" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D0%B5%D0%BD%D0%B5%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC" title="Генетический алгоритм – Russian" lang="ru" hreflang="ru" data-title="Генетический алгоритм" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Genetic_algorithm" title="Genetic algorithm – Simple English" lang="en-simple" hreflang="en-simple" data-title="Genetic algorithm" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Genetick%C3%BD_algoritmus" title="Genetický algoritmus – Slovak" lang="sk" hreflang="sk" data-title="Genetický algoritmus" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%DB%95%D9%84%DA%AF%DB%86%D8%B1%DB%8C%D8%AA%D9%85%DB%8C_%D8%AC%DB%8C%D9%86%DB%95%D8%AA%DB%8C%DA%A9%DB%8C" title="ئەلگۆریتمی جینەتیکی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ئەلگۆریتمی جینەتیکی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Genetski_algoritam" title="Genetski algoritam – Serbian" lang="sr" hreflang="sr" data-title="Genetski algoritam" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Geneettinen_algoritmi" title="Geneettinen algoritmi – Finnish" lang="fi" hreflang="fi" data-title="Geneettinen algoritmi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Genetisk_programmering#Genetisk_algoritm" title="Genetisk programmering – Swedish" lang="sv" hreflang="sv" data-title="Genetisk programmering" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AE%B0%E0%AE%AA%E0%AF%81%E0%AE%9A%E0%AE%BE%E0%AE%B0%E0%AF%8D_%E0%AE%AA%E0%AE%9F%E0%AE%BF%E0%AE%AE%E0%AF%81%E0%AE%B1%E0%AF%88%E0%AE%A4%E0%AF%8D_%E0%AE%A4%E0%AF%80%E0%AE%B0%E0%AF%8D%E0%AE%B5%E0%AF%81" title="மரபுசார் படிமுறைத் தீர்வு – Tamil" lang="ta" hreflang="ta" data-title="மரபுசார் படிமுறைத் தீர்வு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%82%E0%B8%B1%E0%B9%89%E0%B8%99%E0%B8%95%E0%B8%AD%E0%B8%99%E0%B8%A7%E0%B8%B4%E0%B8%98%E0%B8%B5%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B8%9E%E0%B8%B1%E0%B8%99%E0%B8%98%E0%B8%B8%E0%B8%81%E0%B8%A3%E0%B8%A3%E0%B8%A1" title="ขั้นตอนวิธีเชิงพันธุกรรม – Thai" lang="th" hreflang="th" data-title="ขั้นตอนวิธีเชิงพันธุกรรม" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Genetik_algoritma" title="Genetik algoritma – Turkish" lang="tr" hreflang="tr" data-title="Genetik algoritma" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BD%D0%B5%D1%82%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC" title="Генетичний алгоритм – Ukrainian" lang="uk" hreflang="uk" data-title="Генетичний алгоритм" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Gi%E1%BA%A3i_thu%E1%BA%ADt_di_truy%E1%BB%81n" title="Giải thuật di truyền – Vietnamese" lang="vi" hreflang="vi" data-title="Giải thuật di truyền" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vo mw-list-item"><a href="https://vo.wikipedia.org/wiki/Lalgorit_Geredik" title="Lalgorit Geredik – Volapük" lang="vo" hreflang="vo" data-title="Lalgorit Geredik" data-language-autonym="Volapük" data-language-local-name="Volapük" class="interlanguage-link-target"><span>Volapük</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%81%BA%E5%82%B3%E6%BC%94%E7%AE%97%E6%B3%95" title="遺傳演算法 – Cantonese" lang="yue" hreflang="yue" data-title="遺傳演算法" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a 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evolutionary algorithm</a></li> <li><a href="/wiki/Cultural_algorithm" title="Cultural algorithm">Cultural algorithm</a></li> <li><a href="/wiki/Differential_evolution" title="Differential evolution">Differential evolution</a></li> <li><a href="/wiki/Effective_fitness" title="Effective fitness">Effective fitness</a></li> <li><a href="/wiki/Evolutionary_computation" title="Evolutionary computation">Evolutionary computation</a></li> <li><a href="/wiki/Evolution_strategy" title="Evolution strategy">Evolution strategy</a></li> <li><a href="/wiki/Gaussian_adaptation" title="Gaussian adaptation">Gaussian adaptation</a></li> <li><a href="/wiki/Grammar_induction#Grammatical_inference_by_genetic_algorithms" title="Grammar induction">Grammar induction</a></li> <li><a href="/wiki/Evolutionary_multimodal_optimization" title="Evolutionary multimodal optimization">Evolutionary multimodal optimization</a></li> <li><a href="/wiki/Particle_swarm_optimization" title="Particle swarm optimization">Particle swarm optimization</a></li> <li><a href="/wiki/Memetic_algorithm" title="Memetic algorithm">Memetic algorithm</a></li> <li><a href="/wiki/Natural_evolution_strategy" title="Natural evolution strategy">Natural evolution strategy</a></li> <li><a href="/wiki/Neuroevolution" title="Neuroevolution">Neuroevolution</a></li> <li><a href="/wiki/Promoter_based_genetic_algorithm" title="Promoter based genetic algorithm">Promoter based genetic algorithm</a></li> <li><a href="/wiki/Spiral_optimization_algorithm" title="Spiral optimization algorithm">Spiral optimization algorithm</a></li> <li><a href="/wiki/Self-modifying_code" title="Self-modifying code">Self-modifying code</a></li> <li><a href="/wiki/Polymorphic_code" title="Polymorphic code">Polymorphic code</a></li></ul></td> </tr><tr><th class="sidebar-heading"> <a class="mw-selflink selflink">Genetic algorithm</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Chromosome_(genetic_algorithm)" title="Chromosome (genetic algorithm)">Chromosome</a></li> <li><a href="/wiki/Clonal_selection_algorithm" title="Clonal selection algorithm">Clonal selection algorithm</a></li> <li><a href="/wiki/Crossover_(genetic_algorithm)" title="Crossover (genetic algorithm)">Crossover</a></li> <li><a href="/wiki/Mutation_(genetic_algorithm)" title="Mutation (genetic algorithm)">Mutation</a></li> <li><a href="/wiki/Genetic_memory_(computer_science)" title="Genetic memory (computer science)">Genetic memory</a></li> <li><a href="/wiki/Genetic_fuzzy_systems" title="Genetic fuzzy systems">Genetic fuzzy systems</a></li> <li><a href="/wiki/Selection_(genetic_algorithm)" title="Selection (genetic algorithm)">Selection</a></li> <li><a href="/wiki/Fly_algorithm" title="Fly algorithm">Fly algorithm</a></li></ul></td> </tr><tr><th class="sidebar-heading"> <a href="/wiki/Genetic_programming" title="Genetic programming">Genetic programming</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Cartesian_genetic_programming" title="Cartesian genetic programming">Cartesian genetic programming</a></li> <li><a href="/wiki/Linear_genetic_programming" title="Linear genetic programming">Linear genetic programming</a></li> <li><a href="/wiki/Grammatical_evolution" title="Grammatical evolution">Grammatical evolution</a></li> <li><a href="/wiki/Multi_expression_programming" title="Multi expression programming">Multi expression programming</a></li> <li><a href="/wiki/Genetic_improvement_(computer_science)" title="Genetic improvement (computer science)">Genetic Improvement</a></li> <li><a href="/wiki/Schema_(genetic_algorithms)" title="Schema (genetic algorithms)">Schema</a></li> <li><a href="/wiki/Eurisko" title="Eurisko">Eurisko</a></li> <li><a href="/wiki/Parity_benchmark" title="Parity benchmark">Parity benchmark</a></li></ul></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style 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class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/St_5-xband-antenna.jpg/220px-St_5-xband-antenna.jpg" decoding="async" width="220" height="282" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/St_5-xband-antenna.jpg/330px-St_5-xband-antenna.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/f/ff/St_5-xband-antenna.jpg 2x" data-file-width="435" data-file-height="558" /></a><figcaption>The 2006 NASA <a href="/wiki/Space_Technology_5" title="Space Technology 5">ST5</a> spacecraft antenna. This complicated shape was found by an evolutionary computer design program to create the best radiation pattern. It is known as an <a href="/wiki/Evolved_antenna" title="Evolved antenna">evolved antenna</a>.</figcaption></figure> <p>In <a href="/wiki/Computer_science" title="Computer science">computer science</a> and <a href="/wiki/Operations_research" title="Operations research">operations research</a>, a <b>genetic algorithm (GA)</b> is a <a href="/wiki/Metaheuristic" title="Metaheuristic">metaheuristic</a> inspired by the process of <a href="/wiki/Natural_selection" title="Natural selection">natural selection</a> that belongs to the larger class of <a href="/wiki/Evolutionary_algorithm" title="Evolutionary algorithm">evolutionary algorithms</a> (EA).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Genetic algorithms are commonly used to generate high-quality solutions to <a href="/wiki/Optimization_(mathematics)" class="mw-redirect" title="Optimization (mathematics)">optimization</a> and <a href="/wiki/Search_algorithm" title="Search algorithm">search problems</a> via biologically inspired operators such as <a href="/wiki/Selection_(genetic_algorithm)" title="Selection (genetic algorithm)">selection</a>, <a href="/wiki/Crossover_(genetic_algorithm)" title="Crossover (genetic algorithm)">crossover</a>, and <a href="/wiki/Mutation_(genetic_algorithm)" title="Mutation (genetic algorithm)">mutation</a>.<sup id="cite_ref-FOOTNOTEMitchell19962_2-0" class="reference"><a href="#cite_note-FOOTNOTEMitchell19962-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Some examples of GA applications include optimizing <a href="/wiki/Decision_tree_learning" title="Decision tree learning">decision trees</a> for better performance, solving <a href="/wiki/Sudoku_solving_algorithms" title="Sudoku solving algorithms">sudoku puzzles</a>,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Hyperparameter_optimization" title="Hyperparameter optimization">hyperparameter optimization</a>, and <a href="/wiki/Causal_inference" title="Causal inference">causal inference</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Methodology">Methodology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=1" title="Edit section: Methodology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Optimization_problems">Optimization problems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=2" title="Edit section: Optimization problems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a genetic algorithm, a <a href="/wiki/Population" title="Population">population</a> of <a href="/wiki/Candidate_solution" class="mw-redirect" title="Candidate solution">candidate solutions</a> (called individuals, creatures, organisms, or <a href="/wiki/Phenotype" title="Phenotype">phenotypes</a>) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its <a href="/wiki/Chromosome" title="Chromosome">chromosomes</a> or <a href="/wiki/Genotype" title="Genotype">genotype</a>) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible.<sup id="cite_ref-FOOTNOTEWhitley199466_5-0" class="reference"><a href="#cite_note-FOOTNOTEWhitley199466-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>The evolution usually starts from a population of randomly generated individuals, and is an <a href="/wiki/Iteration" title="Iteration">iterative process</a>, with the population in each iteration called a <i>generation</i>. In each generation, the <a href="/wiki/Fitness_(biology)" title="Fitness (biology)">fitness</a> of every individual in the population is evaluated; the fitness is usually the value of the <a href="/wiki/Objective_function" class="mw-redirect" title="Objective function">objective function</a> in the optimization problem being solved. The more fit individuals are <a href="/wiki/Stochastics" class="mw-redirect" title="Stochastics">stochastically</a> selected from the current population, and each individual's genome is modified (<a href="/wiki/Crossover_(genetic_algorithm)" title="Crossover (genetic algorithm)">recombined</a> and possibly randomly mutated) to form a new generation. The new generation of candidate solutions is then used in the next iteration of the <a href="/wiki/Algorithm" title="Algorithm">algorithm</a>. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population. </p><p>A typical genetic algorithm requires: </p> <ol><li>a <a href="/wiki/Genetic_representation" title="Genetic representation">genetic representation</a> of the solution domain,</li> <li>a <a href="/wiki/Fitness_function" title="Fitness function">fitness function</a> to evaluate the solution domain.</li></ol> <p>A standard representation of each candidate solution is as an <a href="/wiki/Bit_array" title="Bit array">array of bits</a> (also called <i>bit set</i> or <i>bit string</i>).<sup id="cite_ref-FOOTNOTEWhitley199466_5-1" class="reference"><a href="#cite_note-FOOTNOTEWhitley199466-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Arrays of other types and structures can be used in essentially the same way. The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size, which facilitates simple <a href="/wiki/Crossover_(genetic_algorithm)" title="Crossover (genetic algorithm)">crossover</a> operations. Variable length representations may also be used, but crossover implementation is more complex in this case. Tree-like representations are explored in <a href="/wiki/Genetic_programming" title="Genetic programming">genetic programming</a> and graph-form representations are explored in <a href="/wiki/Evolutionary_programming" title="Evolutionary programming">evolutionary programming</a>; a mix of both linear chromosomes and trees is explored in <a href="/wiki/Gene_expression_programming" title="Gene expression programming">gene expression programming</a>. </p><p>Once the genetic representation and the fitness function are defined, a GA proceeds to initialize a population of solutions and then to improve it through repetitive application of the mutation, crossover, inversion and selection operators. </p> <div class="mw-heading mw-heading4"><h4 id="Initialization">Initialization</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=3" title="Edit section: Initialization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The population size depends on the nature of the problem, but typically contains hundreds or thousands of possible solutions. Often, the initial population is generated randomly, allowing the entire range of possible solutions (the <a href="/wiki/Feasible_region" title="Feasible region">search space</a>). Occasionally, the solutions may be "seeded" in areas where optimal solutions are likely to be found or the distribution of the sampling probability tuned to focus in those areas of greater interest.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Selection">Selection</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=4" title="Edit section: Selection"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Selection_(genetic_algorithm)" title="Selection (genetic algorithm)">Selection (genetic algorithm)</a></div> <p>During each successive generation, a portion of the existing population is <a href="/wiki/Selection_(genetic_algorithm)" title="Selection (genetic algorithm)">selected</a> to reproduce for a new generation. Individual solutions are selected through a <i>fitness-based</i> process, where <a href="/wiki/Fitness_(biology)" title="Fitness (biology)">fitter</a> solutions (as measured by a <a href="/wiki/Fitness_function" title="Fitness function">fitness function</a>) are typically more likely to be selected. Certain selection methods rate the fitness of each solution and preferentially select the best solutions. Other methods rate only a random sample of the population, as the former process may be very time-consuming. </p><p>The fitness function is defined over the genetic representation and measures the <i>quality</i> of the represented solution. The fitness function is always problem-dependent. For instance, in the <a href="/wiki/Knapsack_problem" title="Knapsack problem">knapsack problem</a> one wants to maximize the total value of objects that can be put in a knapsack of some fixed capacity. A representation of a solution might be an array of bits, where each bit represents a different object, and the value of the bit (0 or 1) represents whether or not the object is in the knapsack. Not every such representation is valid, as the size of objects may exceed the capacity of the knapsack. The <i>fitness</i> of the solution is the sum of values of all objects in the knapsack if the representation is valid, or 0 otherwise. </p><p>In some problems, it is hard or even impossible to define the fitness expression; in these cases, a <a href="/wiki/Computer_simulation" title="Computer simulation">simulation</a> may be used to determine the fitness function value of a <a href="/wiki/Phenotype" title="Phenotype">phenotype</a> (e.g. <a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">computational fluid dynamics</a> is used to determine the air resistance of a vehicle whose shape is encoded as the phenotype), or even <a href="/wiki/Interactive_evolutionary_computation" title="Interactive evolutionary computation">interactive genetic algorithms</a> are used. </p> <div class="mw-heading mw-heading4"><h4 id="Genetic_operators">Genetic operators</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=5" title="Edit section: Genetic operators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Crossover_(genetic_algorithm)" title="Crossover (genetic algorithm)">Crossover (genetic algorithm)</a> and <a href="/wiki/Mutation_(genetic_algorithm)" title="Mutation (genetic algorithm)">Mutation (genetic algorithm)</a></div> <p>The next step is to generate a second generation population of solutions from those selected, through a combination of <a href="/wiki/Genetic_operator" title="Genetic operator">genetic operators</a>: <a href="/wiki/Crossover_(genetic_algorithm)" title="Crossover (genetic algorithm)">crossover</a> (also called recombination), and <a href="/wiki/Mutation_(genetic_algorithm)" title="Mutation (genetic algorithm)">mutation</a>. </p><p>For each new solution to be produced, a pair of "parent" solutions is selected for breeding from the pool selected previously. By producing a "child" solution using the above methods of crossover and mutation, a new solution is created which typically shares many of the characteristics of its "parents". New parents are selected for each new child, and the process continues until a new population of solutions of appropriate size is generated. Although reproduction methods that are based on the use of two parents are more "biology inspired", some research<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> suggests that more than two "parents" generate higher quality chromosomes. </p><p>These processes ultimately result in the next generation population of chromosomes that is different from the initial generation. Generally, the average fitness will have increased by this procedure for the population, since only the best organisms from the first generation are selected for breeding, along with a small proportion of less fit solutions. These less fit solutions ensure genetic diversity within the genetic pool of the parents and therefore ensure the genetic diversity of the subsequent generation of children. </p><p>Opinion is divided over the importance of crossover versus mutation. There are many references in <a href="/wiki/David_B._Fogel" title="David B. Fogel">Fogel</a> (2006) that support the importance of mutation-based search. </p><p>Although crossover and mutation are known as the main genetic operators, it is possible to use other operators such as regrouping, colonization-extinction, or migration in genetic algorithms.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2019)">citation needed</span></a></i>]</sup> </p><p>It is worth tuning parameters such as the <a href="/wiki/Mutation_(genetic_algorithm)" title="Mutation (genetic algorithm)">mutation</a> probability, <a href="/wiki/Crossover_(genetic_algorithm)" title="Crossover (genetic algorithm)">crossover</a> probability and population size to find reasonable settings for the problem class being worked on. A very small mutation rate may lead to <a href="/wiki/Genetic_drift" title="Genetic drift">genetic drift</a> (which is non-<a href="/wiki/Ergodicity" title="Ergodicity">ergodic</a> in nature). A recombination rate that is too high may lead to premature convergence of the genetic algorithm. A mutation rate that is too high may lead to loss of good solutions, unless <a href="#Elitism">elitist selection</a> is employed. An adequate population size ensures sufficient genetic diversity for the problem at hand, but can lead to a waste of computational resources if set to a value larger than required. </p> <div class="mw-heading mw-heading4"><h4 id="Heuristics">Heuristics</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=6" title="Edit section: Heuristics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In addition to the main operators above, other <a href="/wiki/Heuristic" title="Heuristic">heuristics</a> may be employed to make the calculation faster or more robust. The <i>speciation</i> heuristic penalizes crossover between candidate solutions that are too similar; this encourages population diversity and helps prevent premature convergence to a less optimal solution.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Termination">Termination</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=7" title="Edit section: Termination"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This generational process is repeated until a termination condition has been reached. Common terminating conditions are: </p> <ul><li>A solution is found that satisfies minimum criteria</li> <li>Fixed number of generations reached</li> <li>Allocated budget (computation time/money) reached</li> <li>The highest ranking solution's fitness is reaching or has reached a plateau such that successive iterations no longer produce better results</li> <li>Manual inspection</li> <li>Combinations of the above</li></ul> <div class="mw-heading mw-heading2"><h2 id="The_building_block_hypothesis">The building block hypothesis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=8" title="Edit section: The building block hypothesis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Genetic algorithms are simple to implement, but their behavior is difficult to understand. In particular, it is difficult to understand why these algorithms frequently succeed at generating solutions of high fitness when applied to practical problems. The building block hypothesis (BBH) consists of: </p> <ol><li>A description of a heuristic that performs adaptation by identifying and recombining "building blocks", i.e. low order, low defining-length <a href="/wiki/Schema_(genetic_algorithms)" title="Schema (genetic algorithms)">schemata</a> with above average fitness.</li> <li>A hypothesis that a genetic algorithm performs adaptation by implicitly and efficiently implementing this heuristic.</li></ol> <p>Goldberg describes the heuristic as follows: </p> <dl><dd>"Short, low order, and highly fit schemata are sampled, <a href="/wiki/Crossover_(genetic_algorithm)" title="Crossover (genetic algorithm)">recombined</a> [crossed over], and resampled to form strings of potentially higher fitness. In a way, by working with these particular schemata [the building blocks], we have reduced the complexity of our problem; instead of building high-performance strings by trying every conceivable combination, we construct better and better strings from the best partial solutions of past samplings.</dd></dl> <dl><dd>"Because highly fit schemata of low defining length and low order play such an important role in the action of genetic algorithms, we have already given them a special name: building blocks. Just as a child creates magnificent fortresses through the arrangement of simple blocks of wood, so does a genetic algorithm seek near optimal performance through the juxtaposition of short, low-order, high-performance schemata, or building blocks."<sup id="cite_ref-FOOTNOTEGoldberg198941_11-0" class="reference"><a href="#cite_note-FOOTNOTEGoldberg198941-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Despite the lack of consensus regarding the validity of the building-block hypothesis, it has been consistently evaluated and used as reference throughout the years. Many <a href="/wiki/Estimation_of_distribution_algorithm" title="Estimation of distribution algorithm">estimation of distribution algorithms</a>, for example, have been proposed in an attempt to provide an environment in which the hypothesis would hold.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Although good results have been reported for some classes of problems, skepticism concerning the generality and/or practicality of the building-block hypothesis as an explanation for GAs' efficiency still remains. Indeed, there is a reasonable amount of work that attempts to understand its limitations from the perspective of estimation of distribution algorithms.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Limitations">Limitations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=9" title="Edit section: Limitations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Genetic_algorithm" title="Special:EditPage/Genetic algorithm">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">March 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>The practical use of a genetic algorithm has limitations, especially as compared to alternative optimization algorithms: </p> <ul><li>Repeated <a href="/wiki/Fitness_function" title="Fitness function">fitness function</a> evaluation for complex problems is often the most prohibitive and limiting segment of artificial evolutionary algorithms. Finding the optimal solution to complex high-dimensional, multimodal problems often requires very expensive <a href="/wiki/Fitness_function" title="Fitness function">fitness function</a> evaluations. In real world problems such as structural optimization problems, a single function evaluation may require several hours to several days of complete simulation. Typical optimization methods cannot deal with such types of problem. In this case, it may be necessary to forgo an exact evaluation and use an <a href="/wiki/Fitness_approximation" title="Fitness approximation">approximated fitness</a> that is computationally efficient. It is apparent that amalgamation of <a href="/wiki/Fitness_approximation" title="Fitness approximation">approximate models</a> may be one of the most promising approaches to convincingly use GA to solve complex real life problems.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup></li> <li>Genetic algorithms do not scale well with complexity. That is, where the number of elements which are exposed to mutation is large there is often an exponential increase in search space size. This makes it extremely difficult to use the technique on problems such as designing an engine, a house or a plane <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2020)">citation needed</span></a></i>]</sup>. In order to make such problems tractable to evolutionary search, they must be broken down into the simplest representation possible. Hence we typically see evolutionary algorithms encoding designs for fan blades instead of engines, building shapes instead of detailed construction plans, and airfoils instead of whole aircraft designs. The second problem of complexity is the issue of how to protect parts that have evolved to represent good solutions from further destructive mutation, particularly when their fitness assessment requires them to combine well with other parts.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup></li> <li>The "better" solution is only in comparison to other solutions. As a result, the stopping criterion is not clear in every problem.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup></li> <li>In many problems, GAs have a tendency to converge towards <a href="/wiki/Local_optimum" class="mw-redirect" title="Local optimum">local optima</a> or even arbitrary points rather than the <a href="/wiki/Global_optimum" class="mw-redirect" title="Global optimum">global optimum</a> of the problem. This means that it does not "know how" to sacrifice short-term fitness to gain longer-term fitness. The likelihood of this occurring depends on the shape of the <a href="/wiki/Fitness_landscape" title="Fitness landscape">fitness landscape</a>: certain problems may provide an easy ascent towards a global optimum, others may make it easier for the function to find the local optima. This problem may be alleviated by using a different fitness function, increasing the rate of mutation, or by using selection techniques that maintain a diverse population of solutions,<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> although the <a href="/wiki/No_free_lunch_in_search_and_optimization" title="No free lunch in search and optimization">No Free Lunch theorem</a><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> proves that there is no general solution to this problem. A common technique to maintain diversity is to impose a "niche penalty", wherein, any group of individuals of sufficient similarity (niche radius) have a penalty added, which will reduce the representation of that group in subsequent generations, permitting other (less similar) individuals to be maintained in the population. This trick, however, may not be effective, depending on the landscape of the problem. Another possible technique would be to simply replace part of the population with randomly generated individuals, when most of the population is too similar to each other. Diversity is important in genetic algorithms (and <a href="/wiki/Genetic_programming" title="Genetic programming">genetic programming</a>) because crossing over a homogeneous population does not yield new solutions. In <a href="/wiki/Evolution_strategy" title="Evolution strategy">evolution strategies</a> and <a href="/wiki/Evolutionary_programming" title="Evolutionary programming">evolutionary programming</a>, diversity is not essential because of a greater reliance on mutation.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup></li> <li>Operating on dynamic data sets is difficult, as genomes begin to converge early on towards solutions which may no longer be valid for later data. Several methods have been proposed to remedy this by increasing genetic diversity somehow and preventing early convergence, either by increasing the probability of mutation when the solution quality drops (called <i>triggered hypermutation</i>), or by occasionally introducing entirely new, randomly generated elements into the gene pool (called <i>random immigrants</i>). Again, <a href="/wiki/Evolution_strategy" title="Evolution strategy">evolution strategies</a> and <a href="/wiki/Evolutionary_programming" title="Evolutionary programming">evolutionary programming</a> can be implemented with a so-called "comma strategy" in which parents are not maintained and new parents are selected only from offspring. This can be more effective on dynamic problems.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup></li> <li>GAs cannot effectively solve problems in which the only fitness measure is a binary pass/fail outcome (like <a href="/wiki/Decision_problem" title="Decision problem">decision problems</a>), as there is no way to converge on the solution (no hill to climb). In these cases, a random search may find a solution as quickly as a GA. However, if the situation allows the success/failure trial to be repeated giving (possibly) different results, then the ratio of successes to failures provides a suitable fitness measure.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup></li> <li>For specific optimization problems and problem instances, other optimization algorithms may be more efficient than genetic algorithms in terms of speed of convergence. Alternative and complementary algorithms include <a href="/wiki/Evolution_strategy" title="Evolution strategy">evolution strategies</a>, <a href="/wiki/Evolutionary_programming" title="Evolutionary programming">evolutionary programming</a>, <a href="/wiki/Simulated_annealing" title="Simulated annealing">simulated annealing</a>, <a href="/wiki/Gaussian_adaptation" title="Gaussian adaptation">Gaussian adaptation</a>, <a href="/wiki/Hill_climbing" title="Hill climbing">hill climbing</a>, and <a href="/wiki/Swarm_intelligence" title="Swarm intelligence">swarm intelligence</a> (e.g.: <a href="/wiki/Ant_colony_optimization" class="mw-redirect" title="Ant colony optimization">ant colony optimization</a>, <a href="/wiki/Particle_swarm_optimization" title="Particle swarm optimization">particle swarm optimization</a>) and methods based on <a href="/wiki/Integer_linear_programming" class="mw-redirect" title="Integer linear programming">integer linear programming</a>. The suitability of genetic algorithms is dependent on the amount of knowledge of the problem; well known problems often have better, more specialized approaches.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Variants">Variants</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=10" title="Edit section: Variants"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Chromosome_representation">Chromosome representation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=11" title="Edit section: Chromosome representation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Genetic_representation" title="Genetic representation">genetic representation</a></div> <p>The simplest algorithm represents each chromosome as a <a href="/wiki/Bit_array" title="Bit array">bit string</a>. Typically, numeric parameters can be represented by <a href="/wiki/Integer" title="Integer">integers</a>, though it is possible to use <a href="/wiki/Floating_point" class="mw-redirect" title="Floating point">floating point</a> representations. The floating point representation is natural to <a href="/wiki/Evolution_strategy" title="Evolution strategy">evolution strategies</a> and <a href="/wiki/Evolutionary_programming" title="Evolutionary programming">evolutionary programming</a>. The notion of real-valued genetic algorithms has been offered but is really a misnomer because it does not really represent the building block theory that was proposed by <a href="/wiki/John_Henry_Holland" title="John Henry Holland">John Henry Holland</a> in the 1970s. This theory is not without support though, based on theoretical and experimental results (see below). The basic algorithm performs crossover and mutation at the bit level. Other variants treat the chromosome as a list of numbers which are indexes into an instruction table, nodes in a <a href="/wiki/Linked_list" title="Linked list">linked list</a>, <a href="/wiki/Associative_array" title="Associative array">hashes</a>, <a href="/wiki/Object_(computer_science)" title="Object (computer science)">objects</a>, or any other imaginable <a href="/wiki/Data_structure" title="Data structure">data structure</a>. Crossover and mutation are performed so as to respect data element boundaries. For most data types, specific variation operators can be designed. Different chromosomal data types seem to work better or worse for different specific problem domains. </p><p>When bit-string representations of integers are used, <a href="/wiki/Gray_coding" class="mw-redirect" title="Gray coding">Gray coding</a> is often employed. In this way, small changes in the integer can be readily affected through mutations or crossovers. This has been found to help prevent premature convergence at so-called <i>Hamming walls</i>, in which too many simultaneous mutations (or crossover events) must occur in order to change the chromosome to a better solution. </p><p>Other approaches involve using arrays of real-valued numbers instead of bit strings to represent chromosomes. Results from the theory of schemata suggest that in general the smaller the alphabet, the better the performance, but it was initially surprising to researchers that good results were obtained from using real-valued chromosomes. This was explained as the set of real values in a finite population of chromosomes as forming a <i>virtual alphabet</i> (when selection and recombination are dominant) with a much lower cardinality than would be expected from a floating point representation.<sup id="cite_ref-Goldberg1991_19-0" class="reference"><a href="#cite_note-Goldberg1991-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Janikow1991_20-0" class="reference"><a href="#cite_note-Janikow1991-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>An expansion of the Genetic Algorithm accessible problem domain can be obtained through more complex encoding of the solution pools by concatenating several types of heterogenously encoded genes into one chromosome.<sup id="cite_ref-Patrascu2014_21-0" class="reference"><a href="#cite_note-Patrascu2014-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> This particular approach allows for solving optimization problems that require vastly disparate definition domains for the problem parameters. For instance, in problems of cascaded controller tuning, the internal loop controller structure can belong to a conventional regulator of three parameters, whereas the external loop could implement a linguistic controller (such as a fuzzy system) which has an inherently different description. This particular form of encoding requires a specialized crossover mechanism that recombines the chromosome by section, and it is a useful tool for the modelling and simulation of complex adaptive systems, especially evolution processes. </p> <div class="mw-heading mw-heading3"><h3 id="Elitism">Elitism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=12" title="Edit section: Elitism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A practical variant of the general process of constructing a new population is to allow the best organism(s) from the current generation to carry over to the next, unaltered. This strategy is known as <i>elitist selection</i> and guarantees that the solution quality obtained by the GA will not decrease from one generation to the next.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Parallel_implementations">Parallel implementations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=13" title="Edit section: Parallel implementations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Parallel_algorithm" title="Parallel algorithm">Parallel</a> implementations of genetic algorithms come in two flavors. Coarse-grained parallel genetic algorithms assume a population on each of the computer nodes and migration of individuals among the nodes. Fine-grained parallel genetic algorithms assume an individual on each processor node which acts with neighboring individuals for selection and reproduction. Other variants, like genetic algorithms for <a href="/wiki/Online_optimization" title="Online optimization">online optimization</a> problems, introduce time-dependence or noise in the fitness function. </p> <div class="mw-heading mw-heading3"><h3 id="Adaptive_GAs">Adaptive GAs</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=14" title="Edit section: Adaptive GAs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Genetic algorithms with adaptive parameters (adaptive genetic algorithms, AGAs) is another significant and promising variant of genetic algorithms. The probabilities of crossover (pc) and mutation (pm) greatly determine the degree of solution accuracy and the convergence speed that genetic algorithms can obtain. Researchers have analyzed GA convergence analytically.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>Instead of using fixed values of <i>pc</i> and <i>pm</i>, AGAs utilize the population information in each generation and adaptively adjust the <i>pc</i> and <i>pm</i> in order to maintain the population diversity as well as to sustain the convergence capacity. In AGA (adaptive genetic algorithm),<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> the adjustment of <i>pc</i> and <i>pm</i> depends on the fitness values of the solutions. There are more examples of AGA variants: Successive zooming method is an early example of improving convergence.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> In <i>CAGA</i> (clustering-based adaptive genetic algorithm),<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> through the use of clustering analysis to judge the optimization states of the population, the adjustment of <i>pc</i> and <i>pm</i> depends on these optimization states. Recent approaches use more abstract variables for deciding <i>pc</i> and <i>pm</i>. Examples are dominance & co-dominance principles<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> and LIGA (levelized interpolative genetic algorithm), which combines a flexible GA with modified A* search to tackle search space anisotropicity.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p><p>It can be quite effective to combine GA with other optimization methods. A GA tends to be quite good at finding generally good global solutions, but quite inefficient at finding the last few mutations to find the absolute optimum. Other techniques (such as <a href="/wiki/Hill_climbing" title="Hill climbing">simple hill climbing</a>) are quite efficient at finding absolute optimum in a limited region. Alternating GA and hill climbing can improve the efficiency of GA <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2016)">citation needed</span></a></i>]</sup> while overcoming the lack of robustness of hill climbing. </p><p>This means that the rules of genetic variation may have a different meaning in the natural case. For instance – provided that steps are stored in consecutive order – crossing over may sum a number of steps from maternal DNA adding a number of steps from paternal DNA and so on. This is like adding vectors that more probably may follow a ridge in the phenotypic landscape. Thus, the efficiency of the process may be increased by many orders of magnitude. Moreover, the <a href="/wiki/Chromosomal_inversion" title="Chromosomal inversion">inversion operator</a> has the opportunity to place steps in consecutive order or any other suitable order in favour of survival or efficiency.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>A variation, where the population as a whole is evolved rather than its individual members, is known as gene pool recombination. </p><p>A number of variations have been developed to attempt to improve performance of GAs on problems with a high degree of fitness epistasis, i.e. where the fitness of a solution consists of interacting subsets of its variables. Such algorithms aim to learn (before exploiting) these beneficial phenotypic interactions. As such, they are aligned with the Building Block Hypothesis in adaptively reducing disruptive recombination. Prominent examples of this approach include the mGA,<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> GEMGA<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> and LLGA.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Problem_domains">Problem domains</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=15" title="Edit section: Problem domains"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Problems which appear to be particularly appropriate for solution by genetic algorithms include <a href="/wiki/Genetic_algorithm_scheduling" title="Genetic algorithm scheduling">timetabling and scheduling problems</a>, and many scheduling software packages are based on GAs<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2011)">citation needed</span></a></i>]</sup>. GAs have also been applied to <a href="/wiki/Engineering" title="Engineering">engineering</a>.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> Genetic algorithms are often applied as an approach to solve <a href="/wiki/Global_optimization" title="Global optimization">global optimization</a> problems. </p><p>As a general rule of thumb genetic algorithms might be useful in problem domains that have a complex <a href="/wiki/Fitness_landscape" title="Fitness landscape">fitness landscape</a> as mixing, i.e., <a href="/wiki/Mutation_(genetic_algorithm)" title="Mutation (genetic algorithm)">mutation</a> in combination with <a href="/wiki/Crossover_(genetic_algorithm)" title="Crossover (genetic algorithm)">crossover</a>, is designed to move the population away from <a href="/wiki/Local_optima" class="mw-redirect" title="Local optima">local optima</a> that a traditional <a href="/wiki/Hill_climbing" title="Hill climbing">hill climbing</a> algorithm might get stuck in. Observe that commonly used crossover operators cannot change any uniform population. Mutation alone can provide <a href="/wiki/Ergodicity" title="Ergodicity">ergodicity</a> of the overall genetic algorithm process (seen as a <a href="/wiki/Markov_chain" title="Markov chain">Markov chain</a>). </p><p>Examples of problems solved by genetic algorithms include: mirrors designed to funnel sunlight to a solar collector,<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> antennae designed to pick up radio signals in space,<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> walking methods for computer figures,<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> optimal design of aerodynamic bodies in complex flowfields<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>In his <i>Algorithm Design Manual</i>, <a href="/wiki/Steven_Skiena" title="Steven Skiena">Skiena</a> advises against genetic algorithms for any task: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>[I]t is quite unnatural to model applications in terms of genetic operators like mutation and crossover on bit strings. The pseudobiology adds another level of complexity between you and your problem. Second, genetic algorithms take a very long time on nontrivial problems. [...] [T]he analogy with evolution—where significant progress require [sic] millions of years—can be quite appropriate. </p><p>[...] </p><p> I have never encountered any problem where genetic algorithms seemed to me the right way to attack it. Further, I have never seen any computational results reported using genetic algorithms that have favorably impressed me. Stick to <a href="/wiki/Simulated_annealing" title="Simulated annealing">simulated annealing</a> for your heuristic search voodoo needs.</p><div class="templatequotecite">— <cite>Steven Skiena<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 267">: 267 </span></sup></cite></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=16" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1950, <a href="/wiki/Alan_Turing" title="Alan Turing">Alan Turing</a> proposed a "learning machine" which would parallel the principles of evolution.<sup id="cite_ref-mind.oxfordjournals.org_40-0" class="reference"><a href="#cite_note-mind.oxfordjournals.org-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> Computer simulation of evolution started as early as in 1954 with the work of <a href="/wiki/Nils_Aall_Barricelli" title="Nils Aall Barricelli">Nils Aall Barricelli</a>, who was using the computer at the <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> in <a href="/wiki/Princeton,_New_Jersey" title="Princeton, New Jersey">Princeton, New Jersey</a>.<sup id="cite_ref-Barricelli_1954_45–68_41-0" class="reference"><a href="#cite_note-Barricelli_1954_45–68-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Barricelli_1957_143–182_42-0" class="reference"><a href="#cite_note-Barricelli_1957_143–182-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> His 1954 publication was not widely noticed. Starting in 1957,<sup id="cite_ref-Fraser_1957_484–491_43-0" class="reference"><a href="#cite_note-Fraser_1957_484–491-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> the Australian quantitative geneticist <a href="/wiki/Alex_Fraser_(scientist)" title="Alex Fraser (scientist)">Alex Fraser</a> published a series of papers on simulation of <a href="/wiki/Artificial_selection" class="mw-redirect" title="Artificial selection">artificial selection</a> of organisms with multiple loci controlling a measurable trait. From these beginnings, computer simulation of evolution by biologists became more common in the early 1960s, and the methods were described in books by Fraser and Burnell (1970)<sup id="cite_ref-Fraser_1970_44-0" class="reference"><a href="#cite_note-Fraser_1970-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> and Crosby (1973).<sup id="cite_ref-Crosby_1973_45-0" class="reference"><a href="#cite_note-Crosby_1973-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Fraser's simulations included all of the essential elements of modern genetic algorithms. In addition, <a href="/wiki/Hans-Joachim_Bremermann" title="Hans-Joachim Bremermann">Hans-Joachim Bremermann</a> published a series of papers in the 1960s that also adopted a population of solution to optimization problems, undergoing recombination, mutation, and selection. Bremermann's research also included the elements of modern genetic algorithms.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> Other noteworthy early pioneers include Richard Friedberg, George Friedman, and Michael Conrad. Many early papers are reprinted by <a href="/wiki/David_B._Fogel" title="David B. Fogel">Fogel</a> (1998).<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>Although Barricelli, in work he reported in 1963, had simulated the evolution of ability to play a simple game,<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Artificial_evolution" class="mw-redirect" title="Artificial evolution">artificial evolution</a> only became a widely recognized optimization method as a result of the work of <a href="/wiki/Ingo_Rechenberg" title="Ingo Rechenberg">Ingo Rechenberg</a> and <a href="/wiki/Hans-Paul_Schwefel" title="Hans-Paul Schwefel">Hans-Paul Schwefel</a> in the 1960s and early 1970s – Rechenberg's group was able to solve complex engineering problems through <a href="/wiki/Evolution_strategy" title="Evolution strategy">evolution strategies</a>.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> Another approach was the evolutionary programming technique of <a href="/wiki/Lawrence_J._Fogel" title="Lawrence J. Fogel">Lawrence J. Fogel</a>, which was proposed for generating artificial intelligence. <a href="/wiki/Evolutionary_programming" title="Evolutionary programming">Evolutionary programming</a> originally used finite state machines for predicting environments, and used variation and selection to optimize the predictive logics. Genetic algorithms in particular became popular through the work of <a href="/wiki/John_Henry_Holland" title="John Henry Holland">John Holland</a> in the early 1970s, and particularly his book <i>Adaptation in Natural and Artificial Systems</i> (1975). His work originated with studies of <a href="/wiki/Cellular_automata" class="mw-redirect" title="Cellular automata">cellular automata</a>, conducted by <a href="/wiki/John_Henry_Holland" title="John Henry Holland">Holland</a> and his students at the <a href="/wiki/University_of_Michigan" title="University of Michigan">University of Michigan</a>. Holland introduced a formalized framework for predicting the quality of the next generation, known as <a href="/wiki/Holland%27s_Schema_Theorem" class="mw-redirect" title="Holland's Schema Theorem">Holland's Schema Theorem</a>. Research in GAs remained largely theoretical until the mid-1980s, when The First International Conference on Genetic Algorithms was held in <a href="/wiki/Pittsburgh,_Pennsylvania" class="mw-redirect" title="Pittsburgh, Pennsylvania">Pittsburgh, Pennsylvania</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Commercial_products">Commercial products</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=17" title="Edit section: Commercial products"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the late 1980s, General Electric started selling the world's first genetic algorithm product, a mainframe-based toolkit designed for industrial processes.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability#Wikipedia_and_sources_that_mirror_or_use_it" title="Wikipedia:Verifiability"><span title="This claim cites another Wikipedia article. Articles need references to reliable third-party sources. (January 2021)">circular reference</span></a></i>]</sup> In 1989, Axcelis, Inc. released <a href="/wiki/Evolver_(software)" title="Evolver (software)">Evolver</a>, the world's first commercial GA product for desktop computers. <a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a> technology writer <a href="/wiki/John_Markoff" title="John Markoff">John Markoff</a> wrote<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> about Evolver in 1990, and it remained the only interactive commercial genetic algorithm until 1995.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> Evolver was sold to Palisade in 1997, translated into several languages, and is currently in its 6th version.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> Since the 1990s, <a href="/wiki/MATLAB" title="MATLAB">MATLAB</a> has built in three <a href="/wiki/Derivative-free_optimization" title="Derivative-free optimization">derivative-free optimization</a> heuristic algorithms (simulated annealing, particle swarm optimization, genetic algorithm) and two direct search algorithms (simplex search, pattern search).<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Related_techniques">Related techniques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=18" title="Edit section: Related techniques"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/List_of_genetic_algorithm_applications" title="List of genetic algorithm applications">List of genetic algorithm applications</a></div> <div class="mw-heading mw-heading3"><h3 id="Parent_fields">Parent fields</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=19" title="Edit section: Parent fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Genetic algorithms are a sub-field: </p> <ul><li><a href="/wiki/Evolutionary_algorithms" class="mw-redirect" title="Evolutionary algorithms">Evolutionary algorithms</a></li> <li><a href="/wiki/Evolutionary_computing" class="mw-redirect" title="Evolutionary computing">Evolutionary computing</a></li> <li><a href="/wiki/Metaheuristic" title="Metaheuristic">Metaheuristics</a></li> <li><a href="/wiki/Stochastic_optimization" title="Stochastic optimization">Stochastic optimization</a></li> <li><a href="/wiki/Optimization_(mathematics)" class="mw-redirect" title="Optimization (mathematics)">Optimization</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Related_fields">Related fields</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=20" title="Edit section: Related fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Evolutionary_algorithms">Evolutionary algorithms</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=21" title="Edit section: Evolutionary algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Genetic_algorithm" title="Special:EditPage/Genetic algorithm">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">May 2011</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Evolutionary_algorithm" title="Evolutionary algorithm">Evolutionary algorithm</a></div> <p>Evolutionary algorithms is a sub-field of <a href="/wiki/Evolutionary_Computation" class="mw-redirect" title="Evolutionary Computation">evolutionary computing</a>. </p> <ul><li><a href="/wiki/Evolution_strategy" title="Evolution strategy">Evolution strategies</a> (ES, see Rechenberg, 1994) evolve individuals by means of mutation and intermediate or discrete recombination. ES algorithms are designed particularly to solve problems in the real-value domain.<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> They use self-adaptation to adjust control parameters of the search. De-randomization of self-adaptation has led to the contemporary Covariance Matrix Adaptation Evolution Strategy (<a href="/wiki/CMA-ES" title="CMA-ES">CMA-ES</a>).</li> <li><a href="/wiki/Evolutionary_programming" title="Evolutionary programming">Evolutionary programming</a> (EP) involves populations of solutions with primarily mutation and selection and arbitrary representations. They use self-adaptation to adjust parameters, and can include other variation operations such as combining information from multiple parents.</li> <li><a href="/wiki/Estimation_of_Distribution_Algorithm" class="mw-redirect" title="Estimation of Distribution Algorithm">Estimation of Distribution Algorithm</a> (EDA) substitutes traditional reproduction operators by model-guided operators. Such models are learned from the population by employing machine learning techniques and represented as Probabilistic Graphical Models, from which new solutions can be sampled<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> or generated from guided-crossover.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Genetic_programming" title="Genetic programming">Genetic programming</a> (GP) is a related technique popularized by <a href="/wiki/John_Koza" title="John Koza">John Koza</a> in which computer programs, rather than function parameters, are optimized. Genetic programming often uses <a href="/wiki/Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">tree-based</a> internal <a href="/wiki/Data_structure" title="Data structure">data structures</a> to represent the computer programs for adaptation instead of the <a href="/wiki/List_(computing)" class="mw-redirect" title="List (computing)">list</a> structures typical of genetic algorithms. There are many variants of Genetic Programming, including <a href="/wiki/Cartesian_genetic_programming" title="Cartesian genetic programming">Cartesian genetic programming</a>, <a href="/wiki/Gene_expression_programming" title="Gene expression programming">Gene expression programming</a>,<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Grammatical_evolution" title="Grammatical evolution">grammatical evolution</a>, <a href="/wiki/Linear_genetic_programming" title="Linear genetic programming">Linear genetic programming</a>, <a href="/wiki/Multi_expression_programming" title="Multi expression programming">Multi expression programming</a> etc.</li> <li><a href="/w/index.php?title=Grouping_genetic_algorithm&action=edit&redlink=1" class="new" title="Grouping genetic algorithm (page does not exist)">Grouping genetic algorithm</a> (GGA) is an evolution of the GA where the focus is shifted from individual items, like in classical GAs, to groups or subset of items.<sup id="cite_ref-Falkenauer_63-0" class="reference"><a href="#cite_note-Falkenauer-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> The idea behind this GA evolution proposed by <a href="/w/index.php?title=Emanuel_Falkenauer&action=edit&redlink=1" class="new" title="Emanuel Falkenauer (page does not exist)">Emanuel Falkenauer</a> is that solving some complex problems, a.k.a. <i>clustering</i> or <i>partitioning</i> problems where a set of items must be split into disjoint group of items in an optimal way, would better be achieved by making characteristics of the groups of items equivalent to genes. These kind of problems include <a href="/wiki/Bin_packing_problem" title="Bin packing problem">bin packing</a>, line balancing, <a href="/wiki/Cluster_analysis" title="Cluster analysis">clustering</a> with respect to a distance measure, equal piles, etc., on which classic GAs proved to perform poorly. Making genes equivalent to groups implies chromosomes that are in general of variable length, and special genetic operators that manipulate whole groups of items. For bin packing in particular, a GGA hybridized with the Dominance Criterion of Martello and Toth, is arguably the best technique to date.</li> <li><a href="/wiki/Interactive_evolutionary_algorithm" class="mw-redirect" title="Interactive evolutionary algorithm">Interactive evolutionary algorithms</a> are evolutionary algorithms that use human evaluation. They are usually applied to domains where it is hard to design a computational fitness function, for example, evolving images, music, artistic designs and forms to fit users' aesthetic preference.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Swarm_intelligence">Swarm intelligence</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=22" title="Edit section: Swarm intelligence"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Swarm_intelligence" title="Swarm intelligence">Swarm intelligence</a></div> <p>Swarm intelligence is a sub-field of <a href="/wiki/Evolutionary_Computation" class="mw-redirect" title="Evolutionary Computation">evolutionary computing</a>. </p> <ul><li><a href="/wiki/Ant_colony_optimization" class="mw-redirect" title="Ant colony optimization">Ant colony optimization</a> (<b>ACO</b>) uses many ants (or agents) equipped with a pheromone model to traverse the solution space and find locally productive areas.</li> <li>Although considered an <a href="/wiki/Estimation_of_distribution_algorithm" title="Estimation of distribution algorithm">Estimation of distribution algorithm</a>,<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Particle_swarm_optimization" title="Particle swarm optimization">Particle swarm optimization</a> (PSO) is a computational method for multi-parameter optimization which also uses population-based approach. A population (swarm) of candidate solutions (particles) moves in the search space, and the movement of the particles is influenced both by their own best known position and swarm's global best known position. Like genetic algorithms, the PSO method depends on information sharing among population members. In some problems the PSO is often more computationally efficient than the GAs, especially in unconstrained problems with continuous variables.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading4"><h4 id="Other_evolutionary_computing_algorithms">Other evolutionary computing algorithms</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=23" title="Edit section: Other evolutionary computing algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Evolutionary computation is a sub-field of the <a href="/wiki/Metaheuristic" title="Metaheuristic">metaheuristic</a> methods. </p> <ul><li><a href="/wiki/Memetic_algorithm" title="Memetic algorithm">Memetic algorithm</a> (MA), often called <i>hybrid genetic algorithm</i> among others, is a population-based method in which solutions are also subject to local improvement phases. The idea of memetic algorithms comes from <a href="/wiki/Meme" title="Meme">memes</a>, which unlike genes, can adapt themselves. In some problem areas they are shown to be more efficient than traditional evolutionary algorithms.</li> <li><a href="/w/index.php?title=Bacteriologic_algorithm&action=edit&redlink=1" class="new" title="Bacteriologic algorithm (page does not exist)">Bacteriologic algorithms</a> (BA) inspired by <a href="/wiki/Evolutionary_ecology" title="Evolutionary ecology">evolutionary ecology</a> and, more particularly, bacteriologic adaptation. Evolutionary ecology is the study of living organisms in the context of their environment, with the aim of discovering how they adapt. Its basic concept is that in a heterogeneous environment, there is not one individual that fits the whole environment. So, one needs to reason at the population level. It is also believed BAs could be successfully applied to complex positioning problems (antennas for cell phones, urban planning, and so on) or data mining.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Cultural_algorithm" title="Cultural algorithm">Cultural algorithm</a> (CA) consists of the population component almost identical to that of the genetic algorithm and, in addition, a knowledge component called the belief space.</li> <li><a href="/wiki/Differential_evolution" title="Differential evolution">Differential evolution</a> (DE) inspired by migration of superorganisms.<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Gaussian_adaptation" title="Gaussian adaptation">Gaussian adaptation</a> (normal or natural adaptation, abbreviated NA to avoid confusion with GA) is intended for the maximisation of manufacturing yield of signal processing systems. It may also be used for ordinary parametric optimisation. It relies on a certain theorem valid for all regions of acceptability and all Gaussian distributions. The efficiency of NA relies on information theory and a certain theorem of efficiency. Its efficiency is defined as information divided by the work needed to get the information.<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> Because NA maximises mean fitness rather than the fitness of the individual, the landscape is smoothed such that valleys between peaks may disappear. Therefore it has a certain "ambition" to avoid local peaks in the fitness landscape. NA is also good at climbing sharp crests by adaptation of the moment matrix, because NA may maximise the disorder (<a href="/wiki/Average_information" class="mw-redirect" title="Average information">average information</a>) of the Gaussian simultaneously keeping the <a href="/wiki/Mean_fitness" class="mw-redirect" title="Mean fitness">mean fitness</a> constant.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Other_metaheuristic_methods">Other metaheuristic methods</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=24" title="Edit section: Other metaheuristic methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Metaheuristic methods broadly fall within <a href="/wiki/Stochastic_optimization" title="Stochastic optimization">stochastic</a> optimisation methods. </p> <ul><li><a href="/wiki/Simulated_annealing" title="Simulated annealing">Simulated annealing</a> (SA) is a related global optimization technique that traverses the search space by testing random mutations on an individual solution. A mutation that increases fitness is always accepted. A mutation that lowers fitness is accepted probabilistically based on the difference in fitness and a decreasing temperature parameter. In SA parlance, one speaks of seeking the lowest energy instead of the maximum fitness. SA can also be used within a standard GA algorithm by starting with a relatively high rate of mutation and decreasing it over time along a given schedule.</li> <li><a href="/wiki/Tabu_search" title="Tabu search">Tabu search</a> (TS) is similar to simulated annealing in that both traverse the solution space by testing mutations of an individual solution. While simulated annealing generates only one mutated solution, tabu search generates many mutated solutions and moves to the solution with the lowest energy of those generated. In order to prevent cycling and encourage greater movement through the solution space, a tabu list is maintained of partial or complete solutions. It is forbidden to move to a solution that contains elements of the tabu list, which is updated as the solution traverses the solution space.</li> <li><a href="/wiki/Extremal_optimization" title="Extremal optimization">Extremal optimization</a> (EO) Unlike GAs, which work with a population of candidate solutions, EO evolves a single solution and makes <a href="/wiki/Local_search_(optimization)" title="Local search (optimization)">local</a> modifications to the worst components. This requires that a suitable representation be selected which permits individual solution components to be assigned a quality measure ("fitness"). The governing principle behind this algorithm is that of <i>emergent</i> improvement through selectively removing low-quality components and replacing them with a randomly selected component. This is decidedly at odds with a GA that selects good solutions in an attempt to make better solutions.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Other_stochastic_optimisation_methods">Other stochastic optimisation methods</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=25" title="Edit section: Other stochastic optimisation methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>The <a href="/wiki/Cross-entropy_method" title="Cross-entropy method">cross-entropy (CE) method</a> generates candidate solutions via a parameterized probability distribution. The parameters are updated via cross-entropy minimization, so as to generate better samples in the next iteration.</li> <li>Reactive search optimization (RSO) advocates the integration of sub-symbolic machine learning techniques into search heuristics for solving complex optimization problems. The word reactive hints at a ready response to events during the search through an internal online feedback loop for the self-tuning of critical parameters. Methodologies of interest for Reactive Search include machine learning and statistics, in particular <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">reinforcement learning</a>, <a href="/wiki/Active_learning_(machine_learning)" title="Active learning (machine learning)">active or query learning</a>, <a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">neural networks</a>, and <a href="/wiki/Metaheuristics" class="mw-redirect" title="Metaheuristics">metaheuristics</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=26" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Genetic_programming" title="Genetic programming">Genetic programming</a></li> <li><a href="/wiki/List_of_genetic_algorithm_applications" title="List of genetic algorithm applications">List of genetic algorithm applications</a></li> <li><a href="/wiki/Particle_filter" title="Particle filter">Genetic algorithms in signal processing (a.k.a. particle filters)</a></li> <li><a href="/wiki/Propagation_of_schema" class="mw-redirect" title="Propagation of schema">Propagation of schema</a></li> <li><a href="/wiki/Universal_Darwinism" title="Universal Darwinism">Universal Darwinism</a></li> <li><a href="/wiki/Metaheuristics" class="mw-redirect" title="Metaheuristics">Metaheuristics</a></li> <li><a href="/wiki/Learning_classifier_system" title="Learning classifier system">Learning classifier system</a></li> <li><a href="/wiki/Rule-based_machine_learning" title="Rule-based machine learning">Rule-based machine learning</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=27" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFPétrowskiBen-Hamida2017" class="citation book cs1">Pétrowski, Alain; Ben-Hamida, Sana (2017). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=GlGpDgAAQBAJ&dq=genetic+algorithm+evolutionary+algorithms&pg=PP2"><i>Evolutionary algorithms</i></a>. John Wiley & Sons. p. 30. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-119-13638-5" title="Special:BookSources/978-1-119-13638-5"><bdi>978-1-119-13638-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Evolutionary+algorithms&rft.pages=30&rft.pub=John+Wiley+%26+Sons&rft.date=2017&rft.isbn=978-1-119-13638-5&rft.aulast=P%C3%A9trowski&rft.aufirst=Alain&rft.au=Ben-Hamida%2C+Sana&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DGlGpDgAAQBAJ%26dq%3Dgenetic%2Balgorithm%2Bevolutionary%2Balgorithms%26pg%3DPP2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEMitchell19962-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMitchell19962_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMitchell1996">Mitchell 1996</a>, p. 2.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGergesZoueinAzar2018" class="citation book cs1">Gerges, Firas; Zouein, Germain; Azar, Danielle (12 March 2018). <a rel="nofollow" class="external text" href="https://doi.org/10.1145/3194452.3194463">"Genetic Algorithms with Local Optima Handling to Solve Sudoku Puzzles"</a>. <i>Proceedings of the 2018 International Conference on Computing and Artificial Intelligence</i>. ICCAI 2018. 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London: John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-18880-3" title="Special:BookSources/978-0-471-18880-3"><bdi>978-0-471-18880-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computer+Simulation+in+Genetics&rft.place=London&rft.pub=John+Wiley+%26+Sons&rft.date=1973&rft.isbn=978-0-471-18880-3&rft.aulast=Crosby&rft.aufirst=Jack+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://berkeley.edu/news/media/releases/96legacy/releases.96/14319.html">02.27.96 - UC Berkeley's Hans Bremermann, professor emeritus and pioneer in mathematical biology, has died at 69</a></span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFogel1998" class="citation book cs1">Fogel, David B., ed. (1998). <i>Evolutionary Computation: The Fossil Record</i>. New York: IEEE Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7803-3481-6" title="Special:BookSources/978-0-7803-3481-6"><bdi>978-0-7803-3481-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Evolutionary+Computation%3A+The+Fossil+Record&rft.place=New+York&rft.pub=IEEE+Press&rft.date=1998&rft.isbn=978-0-7803-3481-6&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarricelli1963" class="citation journal cs1">Barricelli, Nils Aall (1963). "Numerical testing of evolution theories. Part II. Preliminary tests of performance, symbiogenesis and terrestrial life". <i>Acta Biotheoretica</i>. <b>16</b> (3–4): 99–126. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01556602">10.1007/BF01556602</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:86717105">86717105</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Biotheoretica&rft.atitle=Numerical+testing+of+evolution+theories.+Part+II.+Preliminary+tests+of+performance%2C+symbiogenesis+and+terrestrial+life&rft.volume=16&rft.issue=3%E2%80%934&rft.pages=99-126&rft.date=1963&rft_id=info%3Adoi%2F10.1007%2FBF01556602&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A86717105%23id-name%3DS2CID&rft.aulast=Barricelli&rft.aufirst=Nils+Aall&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRechenberg1973" class="citation book cs1">Rechenberg, Ingo (1973). <i>Evolutionsstrategie</i>. Stuttgart: Holzmann-Froboog. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-7728-0373-4" title="Special:BookSources/978-3-7728-0373-4"><bdi>978-3-7728-0373-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Evolutionsstrategie&rft.place=Stuttgart&rft.pub=Holzmann-Froboog&rft.date=1973&rft.isbn=978-3-7728-0373-4&rft.aulast=Rechenberg&rft.aufirst=Ingo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwefel1974" class="citation book cs1">Schwefel, Hans-Paul (1974). <i>Numerische Optimierung von Computer-Modellen (PhD thesis)</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numerische+Optimierung+von+Computer-Modellen+%28PhD+thesis%29&rft.date=1974&rft.aulast=Schwefel&rft.aufirst=Hans-Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwefel1977" class="citation book cs1">Schwefel, Hans-Paul (1977). <i>Numerische Optimierung von Computor-Modellen mittels der Evolutionsstrategie : mit einer vergleichenden Einführung in die Hill-Climbing- und Zufallsstrategie</i>. Basel; Stuttgart: Birkhäuser. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-7643-0876-6" title="Special:BookSources/978-3-7643-0876-6"><bdi>978-3-7643-0876-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numerische+Optimierung+von+Computor-Modellen+mittels+der+Evolutionsstrategie+%3A+mit+einer+vergleichenden+Einf%C3%BChrung+in+die+Hill-Climbing-+und+Zufallsstrategie&rft.place=Basel%3B+Stuttgart&rft.pub=Birkh%C3%A4user&rft.date=1977&rft.isbn=978-3-7643-0876-6&rft.aulast=Schwefel&rft.aufirst=Hans-Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwefel1981" class="citation book cs1">Schwefel, Hans-Paul (1981). <i>Numerical optimization of computer models (Translation of 1977 Numerische Optimierung von Computor-Modellen mittels der Evolutionsstrategie</i>. Chichester; New York: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-09988-8" title="Special:BookSources/978-0-471-09988-8"><bdi>978-0-471-09988-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numerical+optimization+of+computer+models+%28Translation+of+1977+Numerische+Optimierung+von+Computor-Modellen+mittels+der+Evolutionsstrategie&rft.place=Chichester%3B+New+York&rft.pub=Wiley&rft.date=1981&rft.isbn=978-0-471-09988-8&rft.aulast=Schwefel&rft.aufirst=Hans-Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAldawoodi2008" class="citation book cs1">Aldawoodi, Namir (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-MszVdu_PAMC&q=general+electric+genetic+algorithm+mainframe"><i>An Approach to Designing an Unmanned Helicopter Autopilot Using Genetic Algorithms and Simulated Annealing</i></a>. p. 99. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0549773498" title="Special:BookSources/978-0549773498"><bdi>978-0549773498</bdi></a> – via Google Books.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Approach+to+Designing+an+Unmanned+Helicopter+Autopilot+Using+Genetic+Algorithms+and+Simulated+Annealing&rft.pages=99&rft.date=2008&rft.isbn=978-0549773498&rft.aulast=Aldawoodi&rft.aufirst=Namir&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-MszVdu_PAMC%26q%3Dgeneral%2Belectric%2Bgenetic%2Balgorithm%2Bmainframe&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarkoff1990" class="citation news cs1">Markoff, John (29 August 1990). <a rel="nofollow" class="external text" href="https://www.nytimes.com/1990/08/29/business/business-technology-what-s-the-best-answer-it-s-survival-of-the-fittest.html">"What's the Best Answer? It's Survival of the Fittest"</a>. <i>New York Times</i><span class="reference-accessdate">. Retrieved <span class="nowrap">13 July</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=New+York+Times&rft.atitle=What%27s+the+Best+Answer%3F+It%27s+Survival+of+the+Fittest&rft.date=1990-08-29&rft.aulast=Markoff&rft.aufirst=John&rft_id=https%3A%2F%2Fwww.nytimes.com%2F1990%2F08%2F29%2Fbusiness%2Fbusiness-technology-what-s-the-best-answer-it-s-survival-of-the-fittest.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text">Ruggiero, Murray A.. (1 August 2009) <a rel="nofollow" class="external text" href="http://www.futuresmag.com/2009/08/01/fifteen-years-and-counting?t=technology&page=2">Fifteen years and counting</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160130054823/http://www.futuresmag.com/2009/08/01/fifteen-years-and-counting?t=technology&page=2">Archived</a> 30 January 2016 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. Futuresmag.com. Retrieved on 2013-08-07.</span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.palisade.com/evolver/">Evolver: Sophisticated Optimization for Spreadsheets</a>. Palisade. Retrieved on 2013-08-07.</span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiSaldivarBaiChen2019" class="citation journal cs1">Li, Lin; Saldivar, Alfredo Alan Flores; Bai, Yun; Chen, Yi; Liu, Qunfeng; Li, Yun (2019). <a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FACCESS.2019.2923092">"Benchmarks for Evaluating Optimization Algorithms and Benchmarking MATLAB Derivative-Free Optimizers for Practitioners' Rapid Access"</a>. <i>IEEE Access</i>. <b>7</b>: 79657–79670. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2019IEEEA...779657L">2019IEEEA...779657L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FACCESS.2019.2923092">10.1109/ACCESS.2019.2923092</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:195774435">195774435</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Access&rft.atitle=Benchmarks+for+Evaluating+Optimization+Algorithms+and+Benchmarking+MATLAB+Derivative-Free+Optimizers+for+Practitioners%27+Rapid+Access&rft.volume=7&rft.pages=79657-79670&rft.date=2019&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A195774435%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FACCESS.2019.2923092&rft_id=info%3Abibcode%2F2019IEEEA...779657L&rft.aulast=Li&rft.aufirst=Lin&rft.au=Saldivar%2C+Alfredo+Alan+Flores&rft.au=Bai%2C+Yun&rft.au=Chen%2C+Yi&rft.au=Liu%2C+Qunfeng&rft.au=Li%2C+Yun&rft_id=https%3A%2F%2Fdoi.org%2F10.1109%252FACCESS.2019.2923092&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohoon2002" class="citation book cs1">Cohoon, J; et al. (2002). <a rel="nofollow" class="external text" href="https://www.ifte.de/mitarbeiter/lienig/cohoon.pdf"><i>Evolutionary algorithms for the physical design of VLSI circuits</i></a> <span class="cs1-format">(PDF)</span>. Springer, pp. 683-712, 2003. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-43330-9" title="Special:BookSources/978-3-540-43330-9"><bdi>978-3-540-43330-9</bdi></a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/https://www.ifte.de/mitarbeiter/lienig/cohoon.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 9 October 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Evolutionary+algorithms+for+the+physical+design+of+VLSI+circuits&rft.pub=Springer%2C+pp.+683-712%2C+2003&rft.date=2002&rft.isbn=978-3-540-43330-9&rft.aulast=Cohoon&rft.aufirst=J&rft_id=https%3A%2F%2Fwww.ifte.de%2Fmitarbeiter%2Flienig%2Fcohoon.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPelikanGoldbergCantú-Paz1999" class="citation book cs1">Pelikan, Martin; Goldberg, David E.; Cantú-Paz, Erick (1 January 1999). <a rel="nofollow" class="external text" href="http://dl.acm.org/citation.cfm?id=2933973"><i>BOA: The Bayesian Optimization Algorithm</i></a>. Gecco'99. pp. 525–532. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781558606111" title="Special:BookSources/9781558606111"><bdi>9781558606111</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=BOA%3A+The+Bayesian+Optimization+Algorithm&rft.series=Gecco%2799&rft.pages=525-532&rft.date=1999-01-01&rft.isbn=9781558606111&rft.aulast=Pelikan&rft.aufirst=Martin&rft.au=Goldberg%2C+David+E.&rft.au=Cant%C3%BA-Paz%2C+Erick&rft_id=http%3A%2F%2Fdl.acm.org%2Fcitation.cfm%3Fid%3D2933973&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPelikan2005" class="citation book cs1">Pelikan, Martin (2005). <i>Hierarchical Bayesian optimization algorithm : toward a new generation of evolutionary algorithms</i> (1st ed.). Berlin [u.a.]: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-23774-7" title="Special:BookSources/978-3-540-23774-7"><bdi>978-3-540-23774-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hierarchical+Bayesian+optimization+algorithm+%3A+toward+a+new+generation+of+evolutionary+algorithms&rft.place=Berlin+%5Bu.a.%5D&rft.edition=1st&rft.pub=Springer&rft.date=2005&rft.isbn=978-3-540-23774-7&rft.aulast=Pelikan&rft.aufirst=Martin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThierens2010" class="citation book cs1">Thierens, Dirk (11 September 2010). "The Linkage Tree Genetic Algorithm". <i>Parallel Problem Solving from Nature, PPSN XI</i>. pp. 264–273. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-15844-5_27">10.1007/978-3-642-15844-5_27</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-15843-8" title="Special:BookSources/978-3-642-15843-8"><bdi>978-3-642-15843-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Linkage+Tree+Genetic+Algorithm&rft.btitle=Parallel+Problem+Solving+from+Nature%2C+PPSN+XI&rft.pages=264-273&rft.date=2010-09-11&rft_id=info%3Adoi%2F10.1007%2F978-3-642-15844-5_27&rft.isbn=978-3-642-15843-8&rft.aulast=Thierens&rft.aufirst=Dirk&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFerreira2001" class="citation journal cs1">Ferreira, C (2001). <a rel="nofollow" class="external text" href="http://www.gene-expression-programming.com/webpapers/GEP.pdf">"Gene Expression Programming: A New Adaptive Algorithm for Solving Problems"</a> <span class="cs1-format">(PDF)</span>. <i>Complex Systems</i>. <b>13</b> (2): 87–129. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/cs/0102027">cs/0102027</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001cs........2027F">2001cs........2027F</a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://www.gene-expression-programming.com/webpapers/GEP.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 9 October 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Complex+Systems&rft.atitle=Gene+Expression+Programming%3A+A+New+Adaptive+Algorithm+for+Solving+Problems&rft.volume=13&rft.issue=2&rft.pages=87-129&rft.date=2001&rft_id=info%3Aarxiv%2Fcs%2F0102027&rft_id=info%3Abibcode%2F2001cs........2027F&rft.aulast=Ferreira&rft.aufirst=C&rft_id=http%3A%2F%2Fwww.gene-expression-programming.com%2Fwebpapers%2FGEP.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-Falkenauer-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-Falkenauer_63-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFalkenauer1997" class="citation book cs1"><a href="/w/index.php?title=Emanuel_Falkenauer&action=edit&redlink=1" class="new" title="Emanuel Falkenauer (page does not exist)">Falkenauer, Emanuel</a> (1997). <i>Genetic Algorithms and Grouping Problems</i>. Chichester, England: John Wiley & Sons Ltd. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-97150-4" title="Special:BookSources/978-0-471-97150-4"><bdi>978-0-471-97150-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Genetic+Algorithms+and+Grouping+Problems&rft.place=Chichester%2C+England&rft.pub=John+Wiley+%26+Sons+Ltd&rft.date=1997&rft.isbn=978-0-471-97150-4&rft.aulast=Falkenauer&rft.aufirst=Emanuel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZlochinBirattariMeuleauDorigo2004" class="citation journal cs1">Zlochin, Mark; Birattari, Mauro; Meuleau, Nicolas; Dorigo, Marco (1 October 2004). "Model-Based Search for Combinatorial Optimization: A Critical Survey". <i>Annals of Operations Research</i>. <b>131</b> (1–4): 373–395. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.427">10.1.1.3.427</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1023%2FB%3AANOR.0000039526.52305.af">10.1023/B:ANOR.0000039526.52305.af</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0254-5330">0254-5330</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:63137">63137</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Operations+Research&rft.atitle=Model-Based+Search+for+Combinatorial+Optimization%3A+A+Critical+Survey&rft.volume=131&rft.issue=1%E2%80%934&rft.pages=373-395&rft.date=2004-10-01&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.3.427%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A63137%23id-name%3DS2CID&rft.issn=0254-5330&rft_id=info%3Adoi%2F10.1023%2FB%3AANOR.0000039526.52305.af&rft.aulast=Zlochin&rft.aufirst=Mark&rft.au=Birattari%2C+Mauro&rft.au=Meuleau%2C+Nicolas&rft.au=Dorigo%2C+Marco&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text">Rania Hassan, Babak Cohanim, Olivier de Weck, Gerhard Vente r (2005) <a rel="nofollow" class="external text" href="https://www.mit.edu/~deweck/PDF_archive/3%20Refereed%20Conference/3_50_AIAA-2005-1897.pdf">A comparison of particle swarm optimization and the genetic algorithm</a></span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaudryFranck_FleureyJean-Marc_JézéquelYves_Le_Traon2005" class="citation journal cs1">Baudry, Benoit; Franck Fleurey; <a href="/wiki/Jean-Marc_J%C3%A9z%C3%A9quel" title="Jean-Marc Jézéquel">Jean-Marc Jézéquel</a>; Yves Le Traon (March–April 2005). <a rel="nofollow" class="external text" href="http://www.irisa.fr/triskell/publis/2005/Baudry05d.pdf">"Automatic Test Case Optimization: A Bacteriologic Algorithm"</a> <span class="cs1-format">(PDF)</span>. <i>IEEE Software</i>. <b>22</b> (2): 76–82. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FMS.2005.30">10.1109/MS.2005.30</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3559602">3559602</a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://www.irisa.fr/triskell/publis/2005/Baudry05d.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 9 October 2022<span class="reference-accessdate">. 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(December 1991). "On the Efficiency of Gaussian Adaptation". <i>Journal of Optimization Theory and Applications</i>. <b>71</b> (3): 589–597. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00941405">10.1007/BF00941405</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:116847975">116847975</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Optimization+Theory+and+Applications&rft.atitle=On+the+Efficiency+of+Gaussian+Adaptation&rft.volume=71&rft.issue=3&rft.pages=589-597&rft.date=1991-12&rft_id=info%3Adoi%2F10.1007%2FBF00941405&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A116847975%23id-name%3DS2CID&rft.aulast=Kjellstr%C3%B6m&rft.aufirst=G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=28" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBanzhafNordinKellerFrancone1998" class="citation book cs1">Banzhaf, Wolfgang; Nordin, Peter; Keller, Robert; Francone, Frank (1998). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/geneticprogrammi00wolf"><i>Genetic Programming – An Introduction</i></a></span>. San Francisco, CA: Morgan Kaufmann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1558605107" title="Special:BookSources/978-1558605107"><bdi>978-1558605107</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Genetic+Programming+%26ndash%3B+An+Introduction&rft.place=San+Francisco%2C+CA&rft.pub=Morgan+Kaufmann&rft.date=1998&rft.isbn=978-1558605107&rft.aulast=Banzhaf&rft.aufirst=Wolfgang&rft.au=Nordin%2C+Peter&rft.au=Keller%2C+Robert&rft.au=Francone%2C+Frank&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgeneticprogrammi00wolf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBiesMuldoonPollockManuck2006" class="citation journal cs1">Bies, Robert R.; Muldoon, Matthew F.; Pollock, Bruce G.; Manuck, Steven; Smith, Gwenn; Sale, Mark E. 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(2009). "A Genetic Algorithm for Constructing Compact Binary Decision Trees". <i>Journal of Pattern Recognition Research</i>. <b>4</b> (1): 1–13. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.8314">10.1.1.154.8314</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.13176%2F11.44">10.13176/11.44</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Pattern+Recognition+Research&rft.atitle=A+Genetic+Algorithm+for+Constructing+Compact+Binary+Decision+Trees&rft.volume=4&rft.issue=1&rft.pages=1-13&rft.date=2009&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.154.8314%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.13176%2F11.44&rft.aulast=Cha&rft.aufirst=Sung-Hyuk&rft.au=Tappert%2C+Charles+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEibenSmith2003" class="citation book cs1">Eiben, Agoston; Smith, James (2003). <i>Introduction to Evolutionary Computing</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3540401841" title="Special:BookSources/978-3540401841"><bdi>978-3540401841</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Evolutionary+Computing&rft.pub=Springer&rft.date=2003&rft.isbn=978-3540401841&rft.aulast=Eiben&rft.aufirst=Agoston&rft.au=Smith%2C+James&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFraser1957" class="citation journal cs1">Fraser, Alex S. (1957). <a rel="nofollow" class="external text" href="https://doi.org/10.1071%2FBI9570484">"Simulation of Genetic Systems by Automatic Digital Computers. I. Introduction"</a>. <i>Australian Journal of Biological Sciences</i>. <b>10</b> (4): 484–491. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1071%2FBI9570484">10.1071/BI9570484</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Australian+Journal+of+Biological+Sciences&rft.atitle=Simulation+of+Genetic+Systems+by+Automatic+Digital+Computers.+I.+Introduction&rft.volume=10&rft.issue=4&rft.pages=484-491&rft.date=1957&rft_id=info%3Adoi%2F10.1071%2FBI9570484&rft.aulast=Fraser&rft.aufirst=Alex+S.&rft_id=https%3A%2F%2Fdoi.org%2F10.1071%252FBI9570484&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoldberg1989" class="citation book cs1">Goldberg, David (1989). <i>Genetic Algorithms in Search, Optimization and Machine Learning</i>. Reading, MA: Addison-Wesley Professional. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0201157673" title="Special:BookSources/978-0201157673"><bdi>978-0201157673</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Genetic+Algorithms+in+Search%2C+Optimization+and+Machine+Learning&rft.place=Reading%2C+MA&rft.pub=Addison-Wesley+Professional&rft.date=1989&rft.isbn=978-0201157673&rft.aulast=Goldberg&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoldberg2002" class="citation book cs1">Goldberg, David (2002). <i>The Design of Innovation: Lessons from and for Competent Genetic Algorithms</i>. Norwell, MA: Kluwer Academic Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1402070983" title="Special:BookSources/978-1402070983"><bdi>978-1402070983</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Design+of+Innovation%3A+Lessons+from+and+for+Competent+Genetic+Algorithms&rft.place=Norwell%2C+MA&rft.pub=Kluwer+Academic+Publishers&rft.date=2002&rft.isbn=978-1402070983&rft.aulast=Goldberg&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFogel2006" class="citation book cs1">Fogel, David (2006). <i>Evolutionary Computation: Toward a New Philosophy of Machine Intelligence</i> (3rd ed.). Piscataway, NJ: IEEE Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0471669517" title="Special:BookSources/978-0471669517"><bdi>978-0471669517</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Evolutionary+Computation%3A+Toward+a+New+Philosophy+of+Machine+Intelligence&rft.place=Piscataway%2C+NJ&rft.edition=3rd&rft.pub=IEEE+Press&rft.date=2006&rft.isbn=978-0471669517&rft.aulast=Fogel&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHingstonBaroneMichalewicz2008" class="citation book cs1">Hingston, Philip; Barone, Luigi; Michalewicz, Zbigniew (2008). <i>Design by Evolution: Advances in Evolutionary Design</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3540741091" title="Special:BookSources/978-3540741091"><bdi>978-3540741091</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Design+by+Evolution%3A+Advances+in+Evolutionary+Design&rft.pub=Springer&rft.date=2008&rft.isbn=978-3540741091&rft.aulast=Hingston&rft.aufirst=Philip&rft.au=Barone%2C+Luigi&rft.au=Michalewicz%2C+Zbigniew&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHolland1992" class="citation book cs1">Holland, John (1992). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/adaptationinnatu00holl"><i>Adaptation in Natural and Artificial Systems</i></a></span>. Cambridge, MA: MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0262581110" title="Special:BookSources/978-0262581110"><bdi>978-0262581110</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Adaptation+in+Natural+and+Artificial+Systems&rft.place=Cambridge%2C+MA&rft.pub=MIT+Press&rft.date=1992&rft.isbn=978-0262581110&rft.aulast=Holland&rft.aufirst=John&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fadaptationinnatu00holl&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKoza1992" class="citation book cs1">Koza, John (1992). <i>Genetic Programming: On the Programming of Computers by Means of Natural Selection</i>. Cambridge, MA: MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0262111706" title="Special:BookSources/978-0262111706"><bdi>978-0262111706</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Genetic+Programming%3A+On+the+Programming+of+Computers+by+Means+of+Natural+Selection&rft.place=Cambridge%2C+MA&rft.pub=MIT+Press&rft.date=1992&rft.isbn=978-0262111706&rft.aulast=Koza&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMichalewicz1996" class="citation book cs1">Michalewicz, Zbigniew (1996). <i>Genetic Algorithms + Data Structures = Evolution Programs</i>. Springer-Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3540606765" title="Special:BookSources/978-3540606765"><bdi>978-3540606765</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Genetic+Algorithms+%2B+Data+Structures+%3D+Evolution+Programs&rft.pub=Springer-Verlag&rft.date=1996&rft.isbn=978-3540606765&rft.aulast=Michalewicz&rft.aufirst=Zbigniew&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMitchell1996" class="citation book cs1">Mitchell, Melanie (1996). <i>An Introduction to Genetic Algorithms</i>. Cambridge, MA: MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780585030944" title="Special:BookSources/9780585030944"><bdi>9780585030944</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Genetic+Algorithms&rft.place=Cambridge%2C+MA&rft.pub=MIT+Press&rft.date=1996&rft.isbn=9780585030944&rft.aulast=Mitchell&rft.aufirst=Melanie&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoliLangdonMcPhee2008" class="citation book cs1">Poli, R.; Langdon, W. B.; McPhee, N. F. (2008). <i>A Field Guide to Genetic Programming</i>. Lulu.com, freely available from the internet. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4092-0073-4" title="Special:BookSources/978-1-4092-0073-4"><bdi>978-1-4092-0073-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Field+Guide+to+Genetic+Programming&rft.pub=Lulu.com%2C+freely+available+from+the+internet&rft.date=2008&rft.isbn=978-1-4092-0073-4&rft.aulast=Poli&rft.aufirst=R.&rft.au=Langdon%2C+W.+B.&rft.au=McPhee%2C+N.+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability#Self-published_sources" title="Wikipedia:Verifiability"><span title="The material near this tag may rely on a self-published source. (February 2020)">self-published source?</span></a></i>]</sup></li> <li>Rechenberg, Ingo (1994): Evolutionsstrategie '94, Stuttgart: Fromman-Holzboog.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmittNehanivFujii1998" class="citation journal cs1">Schmitt, Lothar M.; Nehaniv, Chrystopher L.; Fujii, Robert H. (1998). <a rel="nofollow" class="external text" href="https://www.sciencedirect.com/science/article/pii/S0304397598000048/pdf?md5=28a658a4dc5aef635bbf3c8560129925&pid=1-s2.0-S0304397598000048-main.pdf&_valck=1">"Linear analysis of genetic algorithms"</a>. <i>Theoretical Computer Science</i>. <b>208</b>: 111–148.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Theoretical+Computer+Science&rft.atitle=Linear+analysis+of+genetic+algorithms&rft.volume=208&rft.pages=111-148&rft.date=1998&rft.aulast=Schmitt&rft.aufirst=Lothar+M.&rft.au=Nehaniv%2C+Chrystopher+L.&rft.au=Fujii%2C+Robert+H.&rft_id=https%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0304397598000048%2Fpdf%3Fmd5%3D28a658a4dc5aef635bbf3c8560129925%26pid%3D1-s2.0-S0304397598000048-main.pdf%26_valck%3D1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmitt2001" class="citation journal cs1">Schmitt, Lothar M. (2001). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0304-3975%2800%2900406-0">"Theory of Genetic Algorithms"</a>. <i>Theoretical Computer Science</i>. <b>259</b> (1–2): 1–61. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0304-3975%2800%2900406-0">10.1016/S0304-3975(00)00406-0</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Theoretical+Computer+Science&rft.atitle=Theory+of+Genetic+Algorithms&rft.volume=259&rft.issue=1%E2%80%932&rft.pages=1-61&rft.date=2001&rft_id=info%3Adoi%2F10.1016%2FS0304-3975%2800%2900406-0&rft.aulast=Schmitt&rft.aufirst=Lothar+M.&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252FS0304-3975%252800%252900406-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmitt2004" class="citation journal cs1">Schmitt, Lothar M. (2004). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0304-3975%2803%2900393-1">"Theory of Genetic Algorithms II: models for genetic operators over the string-tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling"</a>. <i>Theoretical Computer Science</i>. <b>310</b> (1–3): 181–231. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0304-3975%2803%2900393-1">10.1016/S0304-3975(03)00393-1</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Theoretical+Computer+Science&rft.atitle=Theory+of+Genetic+Algorithms+II%3A+models+for+genetic+operators+over+the+string-tensor+representation+of+populations+and+convergence+to+global+optima+for+arbitrary+fitness+function+under+scaling&rft.volume=310&rft.issue=1%E2%80%933&rft.pages=181-231&rft.date=2004&rft_id=info%3Adoi%2F10.1016%2FS0304-3975%2803%2900393-1&rft.aulast=Schmitt&rft.aufirst=Lothar+M.&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252FS0304-3975%252803%252900393-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li>Schwefel, Hans-Paul (1974): Numerische Optimierung von Computer-Modellen (PhD thesis). Reprinted by Birkhäuser (1977).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVose1999" class="citation book cs1">Vose, Michael (1999). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/TheSimpleG_00_Vose"><i>The Simple Genetic Algorithm: Foundations and Theory</i></a></span>. Cambridge, MA: MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0262220583" title="Special:BookSources/978-0262220583"><bdi>978-0262220583</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Simple+Genetic+Algorithm%3A+Foundations+and+Theory&rft.place=Cambridge%2C+MA&rft.pub=MIT+Press&rft.date=1999&rft.isbn=978-0262220583&rft.aulast=Vose&rft.aufirst=Michael&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2FTheSimpleG_00_Vose&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhitley1994" class="citation journal cs1">Whitley, Darrell (1994). <a rel="nofollow" class="external text" href="http://cobweb.cs.uga.edu/~potter/CompIntell/ga_tutorial.pdf">"A genetic algorithm tutorial"</a> <span class="cs1-format">(PDF)</span>. <i>Statistics and Computing</i>. <b>4</b> (2): 65–85. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.184.3999">10.1.1.184.3999</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00175354">10.1007/BF00175354</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3447126">3447126</a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://cobweb.cs.uga.edu/~potter/CompIntell/ga_tutorial.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 9 October 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Statistics+and+Computing&rft.atitle=A+genetic+algorithm+tutorial&rft.volume=4&rft.issue=2&rft.pages=65-85&rft.date=1994&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.184.3999%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3447126%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF00175354&rft.aulast=Whitley&rft.aufirst=Darrell&rft_id=http%3A%2F%2Fcobweb.cs.uga.edu%2F~potter%2FCompIntell%2Fga_tutorial.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGenetic+algorithm" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=29" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Resources">Resources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=30" title="Edit section: Resources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external autonumber" href="https://web.archive.org/web/20160303215222/http://www.geneticprogramming.com/ga/index.htm">[1]</a> Provides a list of resources in the genetic algorithms field</li> <li><a rel="nofollow" class="external text" href="https://www.staracle.com/general/evolutionaryAlgorithms.php">An Overview of the History and Flavors of Evolutionary Algorithms</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Tutorials">Tutorials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Genetic_algorithm&action=edit&section=31" title="Edit section: Tutorials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www2.econ.iastate.edu/tesfatsi/holland.gaintro.htm">Genetic Algorithms - Computer programs that "evolve" in ways that resemble natural selection can solve complex problems even their creators do not fully understand</a> An excellent introduction to GA by John Holland and with an application to the Prisoner's Dilemma</li> <li><a rel="nofollow" class="external text" href="http://www.i4ai.org/EA-demo/">An online interactive Genetic Algorithm tutorial for a reader to practise or learn how a GA works</a>: Learn step by step or watch global convergence in batch, change the population size, crossover rates/bounds, mutation rates/bounds and selection mechanisms, and add constraints.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130615042000/http://samizdat.mines.edu/ga_tutorial/ga_tutorial.ps">A Genetic Algorithm Tutorial by Darrell Whitley Computer Science Department Colorado State University</a> An excellent tutorial with much theory</li> <li><a rel="nofollow" class="external text" href="http://cs.gmu.edu/~sean/book/metaheuristics/">"Essentials of Metaheuristics"</a>, 2009 (225 p). Free open text by Sean Luke.</li> <li><a rel="nofollow" class="external text" href="http://www.it-weise.de/projects/book.pdf">Global Optimization Algorithms – Theory and Application</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080911075107/http://www.it-weise.de/projects/book.pdf">Archived</a> 11 September 2008 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://mpatacchiola.github.io/blog/2017/03/14/dissecting-reinforcement-learning-5.html">Genetic Algorithms in Python</a> Tutorial with the intuition behind GAs and Python implementation.</li> <li><a rel="nofollow" class="external text" href="http://www-personal.umich.edu/~axe/research/Evolving.pdf">Genetic Algorithms evolves to solve the prisoner's dilemma.</a> Written by Robert Axelrod.</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title 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optimization">Evolutionary multimodal optimization</a></li> <li><a href="/wiki/Human-based_evolutionary_computation" title="Human-based evolutionary computation">Human-based evolutionary computation</a></li> <li><a href="/wiki/Interactive_evolutionary_computation" title="Interactive evolutionary computation">Interactive evolutionary computation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Algorithm" title="Algorithm">Algorithms</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cellular_evolutionary_algorithm" title="Cellular evolutionary algorithm">Cellular evolutionary algorithm</a></li> <li><a href="/wiki/CMA-ES" title="CMA-ES">Covariance Matrix Adaptation Evolution Strategy (CMA-ES)</a></li> <li><a href="/wiki/Cultural_algorithm" title="Cultural algorithm">Cultural algorithm</a></li> <li><a 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techniques</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Swarm_intelligence" title="Swarm intelligence">Swarm intelligence</a></li> <li><a href="/wiki/Ant_colony_optimization" class="mw-redirect" title="Ant colony optimization">Ant colony optimization</a></li> <li><a href="/wiki/Bees_algorithm" title="Bees algorithm">Bees algorithm</a></li> <li><a href="/wiki/Cuckoo_search" title="Cuckoo search">Cuckoo search</a></li> <li><a href="/wiki/Particle_swarm_optimization" title="Particle swarm optimization">Particle swarm optimization</a></li> <li><a href="/wiki/Bacterial_Colony_Optimization" class="mw-redirect" title="Bacterial Colony Optimization">Bacterial Colony Optimization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Metaheuristic" title="Metaheuristic">Metaheuristic methods</a></th><td class="navbox-list-with-group 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