{"id":1196,"date":"2021-11-20T19:30:47","date_gmt":"2021-11-20T10:30:47","guid":{"rendered":"https:\/\/nic.lab.uec.ac.jp\/?page_id=1196"},"modified":"2021-11-20T21:59:08","modified_gmt":"2021-11-20T12:59:08","slug":"mecs","status":"publish","type":"page","link":"https:\/\/nic.lab.uec.ac.jp\/index.php\/mecs\/","title":{"rendered":"\u3044\u308d\u3044\u308d\u306a\u591a\u76ee\u7684\u9032\u5316\u8a08\u7b97"},"content":{"rendered":"\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u306f\u3058\u3081\u306b\">\u306f\u3058\u3081\u306b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u3067\u5b9a\u7fa9\u3055\u308c\u308b3\u76ee\u7684\u306eDTLZ2\u95a2\u6570\u3092\u6700\u9069\u5316\u3059\u308b\u89e3\u306e\u9032\u5316\u306e\u904e\u7a0b\u3092\u793a\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\text{Minimize } f_1(\\boldsymbol{x}) = \\cos(x_1\\pi\/2)\\cos(x_2\\pi\/2)(1+g(\\boldsymbol{x}))$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\text{Minimize } f_2(\\boldsymbol{x}) = \\cos(x_1\\pi\/2)\\sin(x_2\\pi\/2)(1+g(\\boldsymbol{x}))$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\text{Minimize } f_2(\\boldsymbol{x}) = \\sin(x_1\\pi\/2)(1+g(\\boldsymbol{x}))$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$g(\\boldsymbol{x}) = \\sum_{k=3}^{K}{(x_k-0.5)^2}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\boldsymbol{x}=(x_1,x_2,\\dotsc,x_K)\\in[0,1]^K, K=12$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f\u984c\uff0c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff0c\u8868\u793a\u306f\uff0cPlatEMO\u306e\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u5229\u7528\u3057\u3066\u3044\u307e\u3059\uff0ePlatEMO\u306e\u958b\u767a\u306b\u643a\u308f\u3063\u3066\u3044\u308b\u7814\u7a76\u8005\u306b\u656c\u610f\u3092\u793a\u3059\u3068\u3068\u3082\u306b\uff0c\u7d20\u6674\u3089\u3057\u3044\u30bd\u30d5\u30c8\u3092\u5229\u7528\u3067\u304d\u308b\u3053\u3068\u306b\u611f\u8b1d\u7533\u3057\u4e0a\u3052\u307e\u3059\uff0e<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Ye Tian, Ran Cheng, Xingyi Zhang, and Yaochu Jin, PlatEMO: A MATLAB platform for evolutionary multi-objective optimization [educational forum], IEEE Computational Intelligence Magazine, 2017, 12(4): 73-87.<\/li><li>https:\/\/github.com\/BIMK\/PlatEMO<\/li><\/ul>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u591a\u76ee\u7684\u9032\u5316\u8a08\u7b97\">\u591a\u76ee\u7684\u9032\u5316\u8a08\u7b97<\/h2>\n\n\n\n<div class=\"wp-block-columns alignfull is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"nsga-ii\">SPEA2 [Zitzler+, &#8217;01]<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default\"><a href=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_SPEA2.gif\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"656\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_SPEA2.gif\" alt=\"\" class=\"wp-image-1205\"\/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"moea-d\">NSGA-II [Deb+, &#8217;02]<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-style-rounded\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"656\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_NSGA-II.gif\" alt=\"\" class=\"wp-image-1202\"\/><\/figure>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"nsga-ii\">MOPSO [Coello+, &#8217;02]<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default\"><a href=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_MOPSO.gif\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"656\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_MOPSO.gif\" alt=\"\" class=\"wp-image-1201\"\/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"moea-d\">IBEA [Zitzler+, &#8217;04]<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-style-rounded\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"656\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_IBEA.gif\" alt=\"\" class=\"wp-image-1199\"\/><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns alignfull is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"smsemoa-emmerich-06\">SMSEMOA [Emmerich+, &#8217;06] <\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default\"><a href=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_SMSEMOA.gif\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"656\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_SMSEMOA.gif\" alt=\"\" class=\"wp-image-1204\"\/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"moea-d-zhang-07\">MOEA\/D [Zhang+, &#8217;07]<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-style-rounded\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"656\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_MOEA-D.gif\" alt=\"\" class=\"wp-image-1200\"\/><\/figure>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"nsga-ii\">GrEA [Yang+, &#8217;13]<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default\"><a href=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_GrEA.gif\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"656\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_GrEA.gif\" alt=\"\" class=\"wp-image-1198\"\/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"moea-d\">NSGA-III [Deb+, &#8217;14]<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-style-rounded\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"656\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/11\/DTLZ2_NSGA-III.gif\" alt=\"\" class=\"wp-image-1203\"\/><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u306f\u3058\u3081\u306b \u4ee5\u4e0b\u3067\u5b9a\u7fa9\u3055\u308c\u308b3\u76ee\u7684\u306eDTLZ2\u95a2\u6570\u3092\u6700\u9069\u5316\u3059\u308b\u89e3\u306e\u9032\u5316\u306e\u904e\u7a0b\u3092\u793a\u3057\u307e\u3059\uff0e $$\\text{Minimize } f_1(\\boldsymbol{x}) = \\cos(x_1\\pi\/2)\\cos(x_2\\pi&hellip;&nbsp;<a href=\"https:\/\/nic.lab.uec.ac.jp\/index.php\/mecs\/\" rel=\"bookmark\">\u7d9a\u304d\u3092\u8aad\u3080 &raquo;<span class=\"screen-reader-text\">\u3044\u308d\u3044\u308d\u306a\u591a\u76ee\u7684\u9032\u5316\u8a08\u7b97<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_crdt_document":"","neve_meta_sidebar":"full-width","neve_meta_container":"","neve_meta_enable_content_width":"on","neve_meta_content_width":100,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","footnotes":""},"class_list":["post-1196","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/pages\/1196","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/comments?post=1196"}],"version-history":[{"count":12,"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/pages\/1196\/revisions"}],"predecessor-version":[{"id":1223,"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/pages\/1196\/revisions\/1223"}],"wp:attachment":[{"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/media?parent=1196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}