{"id":719,"date":"2021-06-21T21:22:39","date_gmt":"2021-06-21T12:22:39","guid":{"rendered":"http:\/\/bic.lab.uec.ac.jp\/?page_id=719"},"modified":"2021-10-19T17:06:58","modified_gmt":"2021-10-19T08:06:58","slug":"emo","status":"publish","type":"page","link":"https:\/\/nic.lab.uec.ac.jp\/index.php\/emo\/","title":{"rendered":"\u9032\u5316\u8a08\u7b97\u306b\u3088\u308b\u591a\u76ee\u7684\u6700\u9069\u5316"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u306f\u3058\u3081\u306b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u751f\u7269\u306e\u907a\u4f1d\u3068\u9032\u5316\u306e\u904e\u7a0b\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3066\u69cb\u7bc9\u3055\u308c\u305f\u9032\u5316\u578b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0(Evolutionary Algorithms\uff0c\u4ee5\u4e0bEA) \u306f\uff0c\u63a2\u7d22\uff0c\u5b66\u7fd2\uff0c\u6700\u9069\u5316\uff0c\u5206\u985e\u306a\u3069\u306e\u624b\u6bb5\u3068\u3057\u3066\uff0c\u5e45\u5e83\u3044\u5206\u91ce\u3067\u6709\u7528\u6027\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\uff0eEA \u306b\u3088\u308b\u6700\u9069\u5316\u554f\u984c\u306e\u89e3\u6cd5\u3067\u306f\uff0c\u3053\u308c\u307e\u3067\uff0c\u4e3b\u306b\u5358\u4e00\u76ee\u7684\u95a2\u6570\u306e\u6700\u9069\u5316\u306e\u691c\u8a0e\u304c\u591a\u6570\u884c\u308f\u308c\u3066\u304d\u307e\u3057\u305f\uff0e\u3057\u304b\u3057\uff0c\u610f\u601d\u6c7a\u5b9a\u306a\u3069\u306e\u73fe\u5b9f\u554f\u984c\u3067\u306f\uff0c\u6700\u9069\u5316\u3059\u3079\u304d\u76ee\u7684\u95a2\u6570\u304c1\u3064\u3060\u3051\u3067\u3042\u308b\u3053\u3068\u306f\u7a00\u3067\uff0c\u8907\u6570\u306e\u76ee\u7684\u95a2\u6570\u304c\u4e92\u3044\u306b\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306e\u95a2\u4fc2\u3068\u306a\u3063\u3066\u5b58\u5728\u3059\u308b\u591a\u76ee\u7684\u6700\u9069\u5316\u554f\u984c(Multi-objective Optimization Problem\uff0c\u4ee5\u4e0bMOP) \u3068\u306a\u308b\u3053\u3068\u304c\u591a\u304f\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u3048\u3070\uff0c\u81ea\u52d5\u8eca\u306e\u8a2d\u8a08\u306b\u304a\u3044\u3066\u306f\uff0c\u8d70\u884c\u6027\u80fd\u3068\u4fa1\u683c\u306e\u9593\u306b\u306f\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306e\u95a2\u4fc2\u304c\u3042\u308a\uff0c\u8d70\u884c\u6027\u80fd\u306e\u9ad8\u3044\u81ea\u52d5\u8eca\u306f\u9ad8\u4fa1\u683c\u306b\uff0c\u4f4e\u4fa1\u683c\u306a\u81ea\u52d5\u8eca\u306f\u8d70\u884c\u6027\u80fd\u3092\u843d\u3068\u3055\u3056\u308b\u3092\u5f97\u307e\u305b\u3093\uff0e\u3053\u306e\u3088\u3046\u306b\u4e00\u65b9\u3092\u8ffd\u6c42\u3059\u308c\u3070\u4ed6\u65b9\u3092\u72a0\u7272\u306b\u305b\u3056\u308b\u3092\u5f97\u306a\u3044\u80cc\u53cd\u306e\u72b6\u614b\u30fb\u95a2\u4fc2\u306b\u3042\u308b\u76ee\u7684\u3092\u540c\u6642\u306b\u6700\u9069\u5316\u3059\u308b\u554f\u984c\u304c\u591a\u76ee\u7684\u6700\u9069\u5316\u554f\u984c\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5358\u4e00\u76ee\u7684\u6700\u9069\u5316\u3068\u306e\u9055\u3044\u306f\uff0c\u8907\u6570\u306e\u76ee\u7684\u95a2\u6570\u3092\u540c\u6642\u306b\u6700\u9069\u5316\u3059\u308b\u3068\u3053\u308d\u306b\u3042\u308a\u307e\u3059\uff0e\u591a\u76ee\u7684\u6700\u9069\u5316\u554f\u984c\u3067\u306f\uff0c\u305d\u308c\u305e\u308c\u306e\u76ee\u7684\u95a2\u6570\u306e\u9593\u306b\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306e\u95a2\u4fc2\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u591a\u3044\u305f\u3081\uff0c\u3059\u3079\u3066\u306e\u76ee\u7684\u95a2\u6570\u3092\u540c\u6642\u306b\u6700\u5927\u5316(\u3082\u3057\u304f\u306f\u6700\u5c0f\u5316)\u3059\u308b\u5358\u4e00\u306e\u89e3\u306f\u4e00\u822c\u7684\u306b\u5b58\u5728\u305b\u305a\uff0c\u76ee\u7684\u95a2\u6570\u7a7a\u9593\u3067\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306e\u95a2\u4fc2\u3092\u793a\u3059\u30d1\u30ec\u30fc\u30c8\u6700\u9069\u89e3\u96c6\u5408(Pareto-Optimal Solutions\uff0c\u4ee5\u4e0bPOS)\u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\uff0e\u30d1\u30ec\u30fc\u30c8\u6700\u9069\u89e3\u96c6\u5408\u306e\u5206\u5e03\u306b\u3088\u3063\u3066\uff0c\u305d\u306e\u76ee\u7684\u95a2\u6570\u9593\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u3092\u628a\u63e1\u3059\u308b\u3053\u3068\u304c\u591a\u76ee\u7684\u6700\u9069\u5316\u306e\u30b4\u30fc\u30eb\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">EA\u306f\uff0c\u89e3\u96c6\u56e3\u3092\u7528\u3044\u305f\u591a\u70b9\u89e3\u63a2\u7d22\u6cd5\u3067\u3042\u308b\u305f\u3081\u4e00\u5ea6\u306e\u63a2\u7d22\u3067\u591a\u6570\u306e\u30d1\u30ec\u30fc\u30c8\u6700\u9069\u89e3\u96c6\u5408\u3092\u540c\u6642\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u53ef\u80fd\u306a\u70b9\u3067\u591a\u76ee\u7684\u6700\u9069\u5316\u554f\u984c\u306e\u6709\u7528\u306a\u89e3\u6cd5\u624b\u6bb5\u3068\u3055\u308c\u3066\u3044\u307e\u3059\uff0e1985\u5e74\uff0cSchaffer\u3089\u306b\u3088\u308bVector Evaluated Genetic Algorithm(VEGA)\u306e\u63d0\u6848\u306b\u59cb\u307e\u308a\uff0c\u4eca\u65e5\u307e\u3067MOP \u306e\u89e3\u6cd5\u306bEA\u3092\u7528\u3044\u308b\u591a\u76ee\u7684\u9032\u5316\u578b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0(Multi-objective Evolutionary Algorithm\uff0c\u4ee5\u4e0bMOEA) \u306e\u7814\u7a76\u304c\u92ed\u610f\u9032\u3081\u3089\u308c\u3066\u304d\u307e\u3057\u305f\uff0e\u6628\u4eca\u3067\u306f\uff0c\u9032\u5316\u578b\u8a08\u7b97\u306e\u9078\u629e\u306e\u969b\u306b\uff0c\u30d1\u30ec\u30fc\u30c8\u652f\u914d\u306e\u6982\u5ff5\u3092\u7528\u3044\u3066\u89e3\u306e\u512a\u52a3\u95a2\u4fc2\u3092\u6c7a\u5b9a\u3059\u308bNSGA-II, SPEA2\u306a\u3069\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306ePOS\u63a2\u7d22\u6027\u80fd\u306e\u9ad8\u3055\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3061\u3089\u306e\u30da\u30fc\u30b8\u3067\u306fEA\uff0cMOP\uff0cMOEA\u306b\u3064\u3044\u3066\u7c21\u5358\u306b\u7d39\u4ecb\u3057\uff0c\u6700\u5f8c\u306b\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fb\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u884c\u3044\u307e\u3059\uff0e<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u9032\u5316\u8a08\u7b97<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u751f\u7269\u306f\u74b0\u5883\u306b\u5bfe\u3059\u308b\u9069\u5fdc\u5ea6\u306e\u9ad8\u3044\u500b\u4f53\u307b\u3069\uff0c\u305d\u306e\u500b\u4f53\u304c\u6301\u3064\u907a\u4f1d\u5b50\u3092\u5f8c\u306e\u4e16\u4ee3\u306b\u53d7\u3051\u7d99\u304c\u308c\u308b\u3088\u3046\u306b\u5897\u6b96\u3068\u6dd8\u6c70\u3092\u7e70\u308a\u8fd4\u3057\uff0c\u9032\u5316\u3057\u3066\u3044\u304f\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u307e\u3059\uff0e\u3053\u306e\u751f\u7269\u306e\u9032\u5316\u306e\u904e\u7a0b\u306b\u304a\u3051\u308b\uff0c\u81ea\u7136\u6dd8\u6c70\uff0c\u907a\u4f1d\u7684\u64cd\u4f5c\u306e\u4ed5\u7d44\u307f\u3092\u6a21\u5023\u3057\u3066\u89e3\u63a2\u7d22\u3092\u884c\u3046\u8a08\u7b97\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304cEA\u306b\u306a\u308a\u307e\u3059\uff0eEA\u3067\u306f\uff0c\u6700\u9069\u5316\u554f\u984c\u306e\u89e3\u3092\u500b\u4f53\u306e\u907a\u4f1d\u5b50\u3068\u3057\u3066\u8868\u73fe\u3057\uff0c\u8a55\u4fa1\u95a2\u6570\u3092\u7528\u3044\u3066\u3059\u3079\u3066\u306e\u500b\u4f53\u306b\u8a55\u4fa1\u5024\u3092\u4e0e\u3048\u307e\u3059\uff0e\u8a55\u4fa1\u5024\u306b\u57fa\u3065\u3044\u3066\u6b21\u4e16\u4ee3\u306e\u89aa\u3068\u306a\u308b\u500b\u4f53\u304c\u9078\u629e\u3055\u308c\uff0c\u89aa\u500b\u4f53\u306e\u6301\u3064\u907a\u4f1d\u5b50\u60c5\u5831\u3092\uff0c\u907a\u4f1d\u7684\u64cd\u4f5c\u306b\u3088\u3063\u3066\u7d44\u307f\u63db\u307e\u3059\uff0e\u3053\u308c\u3089\u3092\u7e70\u308a\u8fd4\u3059\u3053\u3068\u306b\u3088\u308a\uff0c\u9ad8\u3044\u8a55\u4fa1\u5024\u3092\u793a\u3057\u305f\u500b\u4f53\u306e\u907a\u4f1d\u5b50\u60c5\u5831(\u89e3)\u3092\u624b\u304c\u304b\u308a\u306b\uff0c\u500b\u4f53\u96c6\u56e3\u3092\u7528\u3044\u3066\u3055\u3089\u306b\u9ad8\u3044\u8a55\u4fa1\u5024\u3092\u793a\u3059\u500b\u4f53\u306e\u63a2\u7d22\u3092\u5b9f\u73fe\u3057\u307e\u3059\uff0e\u3053\u308c\u307e\u3067\uff0c EA \u306b\u3088\u308b\u6700\u9069\u5316\u554f\u984c\u306e\u89e3\u6cd5\u3067\u306f\uff0c\u4e3b\u306b\u5358\u4e00\u76ee\u7684\u95a2\u6570\u306e\u6700\u9069\u5316\u306e\u691c\u8a0e\u304c\u591a\u6570\u884c\u308f\u308c\u3066\u304d\u307e\u3057\u305f\uff0e<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u591a\u76ee\u7684\u6700\u9069\u5316\u554f\u984c<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u610f\u601d\u6c7a\u5b9a\u306a\u3069\u306e\u5b9f\u4e16\u754c\u306e\u554f\u984c\u3067\u306f\uff0c\u6700\u9069\u5316\u3059\u3079\u304d\u76ee\u7684\u95a2\u6570\u304c1\u3064\u3060\u3051\u3067\u3042\u308b\u3053\u3068\u306f\u7a00\u3067\uff0c\u8907\u6570\u306e\u76ee\u7684\u95a2\u6570\u304c\u4e92\u3044\u306b\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306e\u95a2\u4fc2\u3068\u306a\u3063\u3066\u5b58\u5728\u3059\u308b\u591a\u76ee\u7684\u6700\u9069\u5316\u554f\u984c(MOP)\u3068\u306a\u308a\u307e\u3059\uff0eMOP\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e\u3053\u3053\u3067\u306f\u6700\u5927\u5316\u3092\u8003\u616e\u3059\u308b\u3053\u3068\u306b\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\left\\{\\begin{array}{l}  \\text{Maximize} &amp; \\boldsymbol{f}( \\boldsymbol{x})=(f_1( \\boldsymbol{x}),f_2( \\boldsymbol{x}),\\cdots, f_m(\\boldsymbol{x})) \\\\  \\text{subject to} &amp; \\boldsymbol{x} \\in \\mathcal{F} \\end{array}\\right.$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3059\u306a\u308f\u3061\uff0c\u591a\u76ee\u7684\u6700\u9069\u5316\u3068\u306f\u3002\\(m\\)\u7a2e\u985e\u306e\u76ee\u7684\u95a2\u6570 \\( f_{i}(i=1,2,\\cdots,m) \\)\u304b\u3089\u306a\u308b\u30d9\u30af\u30c8\u30eb\u8a55\u4fa1\u95a2\u6570 \\(\\boldsymbol{f}\\)\u306b\u3064\u3044\u3066\uff0c\u89e3\u7a7a\u9593\\(\\mathcal{S}\\)\u306e\u5b9f\u884c\u53ef\u80fd\u9818\u57df \\( \\mathcal{F}\\) \\((\\mathcal{F}\\subseteq\\mathcal{S})\\)\u5185\u306e\u6c7a\u5b9a\u5909\u6570\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{x}\\)\u3092\u7528\u3044\u3066\\(f_{i}\\)\u306e\u5024\u3092\u6700\u5927\u306b\u3059\u308b\u3053\u3068\u3068\u8a00\u3048\u307e\u3059\uff0e\u6b21\u306b\u89e3\u306e\u652f\u914d\u306b\u3064\u3044\u3066\u5b9a\u7fa9\u3057\u307e\u3059\uff0e\\(\\boldsymbol{x},\\boldsymbol{y}\\in\\mathcal{F}\\)\u306b\u5bfe\u3057\u3066\uff0c<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$${\\forall} i \\in {1, 2,\\cdots , m} : f_i(\\boldsymbol{x}) \\ge f_i( \\boldsymbol{ y}) \\quad \\wedge \\quad {\\exists} i \\in {1,2,\\cdots,m}:f_{i}( \\boldsymbol{ x})&gt;f_{i}( \\boldsymbol{y})$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u304c\u6210\u7acb\u3059\u308b\u3068\u304d\uff0c\\(\\boldsymbol{x}\\)\u306f \\(\\boldsymbol{y}\\) \u3092\u652f\u914d\u3059\u308b(\\({\\boldsymbol{f}(\\boldsymbol{x})\\succeq \\boldsymbol{f}(\\boldsymbol{y})}\\))\u3068\u3044\u3044\u307e\u3059\uff0e\u8fd1\u5e74\u306eMOEA\u306f\uff0c\u89e3\u306e\u652f\u914d\u3092\u7528\u3044\u3066\u89e3\u96c6\u56e3\u5185\u3067\u306e\u89e3\u306e\u512a\u52a3\u3092\u6c7a\u3081\u307e\u3059\uff0e\u3064\u307e\u308a\u591a\u304f\u306e\u89e3\u3092\u652f\u914d\u3057\u3066\u3044\u308b\u89e3\u307b\u3069\uff0c\u6b21\u306e\u4e16\u4ee3\u306b\u81ea\u8eab\u306e\u907a\u4f1d\u7684\u60c5\u5831\u3092\u6b8b\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u308f\u3051\u3067\u3059\uff0e\u307e\u305f\uff0c\u3053\u306e\u652f\u914d\u3092\u7528\u3044\u3066POS\u3092\uff0c<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\mathcal{P} = \\{ \\boldsymbol{x}\\in \\mathcal F {\\rm~} | {\\rm~} { \\neg \\exists} { \\boldsymbol{ y} \\in \\mathcal F: f( \\boldsymbol{ y}) \\succeq f( \\boldsymbol{ x}) }\\}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u306e\u69d8\u306b\u5b9a\u7fa9\u3057\u307e\u3059\uff0e\u3064\u307e\u308a\uff0cPOS\u306f\u3069\u306e\u89e3\u306b\u3082\u652f\u914d\u3055\u308c\u306a\u3044\u89e3\u96c6\u5408\u3067\u3042\u308b\u3068\u3044\u3048\u307e\u3059\uff0eMOEA\u3067\u306f\u89e3\u96c6\u56e3\u5185\u306e\u652f\u914d\u3055\u308c\u306a\u3044\u89e3\u96c6\u5408\u3092\u6700\u7d42\u7684\u306b\u89e3\u3068\u3057\u3066\u5c0e\u51fa\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u9032\u5316\u8a08\u7b97\u306b\u3088\u308b\u591a\u76ee\u7684\u6700\u9069\u5316<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">EA\u306f\u89e3\u96c6\u56e3\u3092\u7528\u3044\u308b\u591a\u70b9\u63a2\u7d22\u3067\u3042\u308b\u305f\u3081\uff0c\u4e00\u5ea6\u306e\u63a2\u7d22\u3067\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u3092\u306a\u3059\u30d1\u30ec\u30fc\u30c8\u6700\u9069\u89e3\u96c6\u5408(Pareto Optimal Solutions: POS) \u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e\u3053\u306e\u305f\u3081MOP\u306e\u89e3\u6cd5\u306bEA\u3092\u7528\u3044\u308b\u591a\u76ee\u7684\u9032\u5316\u578b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0(Multi-objective Evolutionary Algorithm: MOEA)\u306f\uff0c\u52b9\u7387\u826f\u304fMOP\u3092\u89e3\u6cd5\u3059\u308b\u6709\u529b\u306a\u624b\u6bb5\u3068\u3057\u3066\u6ce8\u76ee\u3055\u308c\uff0c\u69d8\u3005\u306a\u5fdc\u7528\u4f8b\u304c\u5831\u544a\u3055\u308c\u3066\u3044\u307e\u3059\uff0e\u8fd1\u5e74\uff0cPOS\u63a2\u7d22\u6027\u80fd\u304c\u9ad8\u3044\u3068\u3055\u308c\u308bNSGA-II(Nondominated Sorting Genetic Algorithm II)\u3068\u547c\u3070\u308c\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">NSGA-II\u3067\u306f\uff0c\\(t\\)\u4e16\u4ee3\u306e\u89aa\u96c6\u56e3\\(P_t\\)\u3068\u5b50\u96c6\u56e3\\(Q_t\\)\u3092\u5408\u308f\u305b\u305f\\(P_t \\cup Q_t\\)\u306b\u3064\u3044\u3066\uff0c\u96c6\u56e3\u5185\u306e\u5404\u500b\u4f53\u3092\u652f\u914d\u3055\u308c\u306a\u3044\u30ec\u30d9\u30eb\u3067\u500b\u4f53\u3092\u30e9\u30f3\u30af\u4ed8\u3051\u3057\uff0c\u30d5\u30ed\u30f3\u30c8\u3068\u547c\u3070\u308c\u308b\u3044\u304f\u3064\u304b\u306e\u968e\u5c64\u306b\u5206\u985e\u3057\u3066\u89aa\u500b\u4f53\u306e\u9078\u629e\u306b\u53cd\u6620\u3055\u305b\u307e\u3059\uff0e\u4e0a\u4f4d\u30d5\u30ed\u30f3\u30c8\u304b\u3089\u9806\u306b\u534a\u6570\u306e\u500b\u4f53\u3092\u9078\u3073\uff0c\u6b21\u4e16\u4ee3\u306e\u89aa\u96c6\u56e3\\(P_{t+1}\\)\u3068\u3059\u308b\uff0e\u3053\u306e\u969b\uff0c\u540c\u4e00\u30d5\u30ed\u30f3\u30c8\u306b\u5b58\u5728\u3059\u308b\u89e3\u306e\u512a\u52a3\u306f\uff0cCrowding Distance (CD)\u3068\u547c\u3070\u308c\u308b\u76ee\u7684\u95a2\u6570\u7a7a\u9593\u306b\u304a\u3051\u308b\u89e3\u306e\u6df7\u96d1\u5ea6\u3092\u8003\u616e\u3057\u3066\u6c7a\u5b9a\u3057\u307e\u3059\uff0eCD\u306b\u3088\u308b\u89e3\u306e\u53d6\u6368\u9078\u629e\u3067\u306f\uff0c\u5404\u76ee\u7684\u95a2\u6570\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u8a55\u4fa1\u5024\u3068\u3057\u3066\u6301\u3064\u500b\u4f53\u3092\u7d76\u5bfe\u7684\u306b\u512a\u9047\u3059\u308b\u4ed5\u7d44\u307f\u304c\u3042\u308a\uff0c\u89e3\u96c6\u56e3\u306b\u591a\u69d8\u6027\u3092\u751f\u307f\u51fa\u3059\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\uff0e\u652f\u914d\u30e9\u30f3\u30af\u3068\u89e3\u306e\u6df7\u96d1\u5ea6\u306b\u57fa\u3065\u304f\u30d0\u30a4\u30ca\u30ea\u30fc\u30c8\u30fc\u30ca\u30e1\u30f3\u30c8\u9078\u629e\u306b\u3088\u3063\u3066\\(P_{t+1}\\)\u304b\u3089\u89aa\u500b\u4f53\u3092\u9078\u3073\uff0c\u3053\u308c\u3089\u306b\u4ea4\u53c9\uff0c\u7a81\u7136\u5909\u7570\u3092\u65bd\u3057\u3066\u5b50\u500b\u4f53\u3092\u751f\u6210\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/06\/nsgaii.jpg\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b9f\u9a13<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">0\/1\u591a\u76ee\u7684\u30ca\u30c3\u30d7\u30b6\u30c3\u30af\u554f\u984c<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">NSGA-II\u3092\u7528\u3044\u3066\u591a\u76ee\u76840\/1\u30ca\u30c3\u30d7\u30b6\u30c3\u30af\u554f\u984c\u3092\u89e3\u304f\u30c7\u30e2\u52d5\u753b\u3092\u4ee5\u4e0b\u306b\u63b2\u8f09\u3057\u307e\u3059\uff0eZitzler\u5148\u751f\u306eWEB\u30da\u30fc\u30b8\u304b\u3089\u30c6\u30b9\u30c8\u554f\u984c\u3092\u63a1\u7528\u3055\u305b\u3066\u3044\u305f\u3060\u304d\u307e\u3057\u305f\uff0e<span class=\"has-inline-color has-nv-c-2-color\"><strong>\u8d64<\/strong><\/span>\u306e\u30d7\u30ed\u30c3\u30c8\u304c\u6c42\u3081\u308b\u3079\u304d\u771f\u306ePOS\uff0c<strong>\u9ed2<\/strong>\u306e\u30d7\u30ed\u30c3\u30c8\u304c\u89e3\u96c6\u56e3\u306b\u306a\u308a\u307e\u3059\uff0e\u76ee\u7684\u95a2\u6570\u7a7a\u9593\u306b\u304a\u3051\u308b\u89e3\u96c6\u56e3\u306e\u9032\u5316\u3092\u6642\u7cfb\u5217\u7684\u306b\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u9762\u767d\u3044\u3068\u601d\u3044\u307e\u3059\uff0e<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/06\/KP.gif\" alt=\"\"\/><\/figure><\/div>\n\n\n\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<h4 class=\"wp-block-heading\">\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u8a2d\u5b9a<\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li>\u89e3\u96c6\u56e3\u30b5\u30a4\u30ba \\(N=100\\)<\/li><li>\u4ea4\u53c9\u6cd5\uff1a\u4e8c\u70b9\u4ea4\u53c9<\/li><li>\u4ea4\u53c9\u7387\uff1a1.0<\/li><li>\u7a81\u7136\u5909\u7570\u6cd5\uff1a\u30d3\u30c3\u30c8\u53cd\u8ee2<\/li><li>\u7a81\u7136\u5909\u7570\u7387\uff1a0.01<\/li><li>\u4e16\u4ee3\u6570\uff1a1500<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h4 class=\"wp-block-heading\">\u591a\u76ee\u76840\/1\u30ca\u30c3\u30d7\u30b6\u30c3\u30af\u554f\u984c\u306e\u30d1\u30e9\u30e1\u30fc\u30bf<\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li>\u30a2\u30a4\u30c6\u30e0\u6570 \\(n=100\\)<\/li><li>\u30ca\u30c3\u30d7\u30b6\u30c3\u30af(\u76ee\u7684)\u6570 \\(m=2\\)<\/li><li>\u5b9f\u884c\u53ef\u80fd\u7387 \\(\\phi=0.5\\)<\/li><\/ul>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u591a\u76ee\u7684\u9023\u7d9a\u95a2\u6570\u6700\u9069\u5316 DTLZ1<\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/06\/DTLZ1.gif\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u591a\u76ee\u7684\u9023\u7d9a\u95a2\u6570\u6700\u9069\u5316 DTLZ2<\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/nic.lab.uec.ac.jp\/wp-content\/uploads\/2021\/06\/DTLZ2.gif\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u7814\u7a76\u7d39\u4ecb\u7a0b\u5ea6\u3067\u306f\u3042\u308a\u307e\u3057\u305f\u304c\uff0c\u9032\u5316\u578b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u7528\u3044\u305f\u591a\u76ee\u7684\u6700\u9069\u5316\u306b\u3064\u3044\u3066\u7c21\u5358\u306b\u8aac\u660e\uff0c\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fb\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u305f\u3081\u306e\u30c7\u30e2\u52d5\u753b\u3092\u63b2\u8f09\u3055\u305b\u3066\u3044\u305f\u3060\u304d\u307e\u3057\u305f\uff0e\u5c11\u3057\u3067\u3082\u8208\u5473\u3092\u6301\u3063\u3066\u3044\u305f\u3060\u3051\u305f\u3089\u5e78\u3044\u3067\u3059\uff0e<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>J. H. Holland, &#8221;&#8217;Adaptation in Natural and Artificial Systems&#8221;&#8217;, University of Michigan Press, 1975.))((D. E. Goldberg, &#8221;&#8217;Genetic Algorithms in Search, Optimization &amp; Machine Learning&#8221;&#8217;, Addision-wesley, Reading, 1989.<\/li><li>K. Deb, S. Agrawal, A. Pratap and T. Meyarivan, &#8220;A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II&#8221;, &#8221;&#8217;KanGAL report 200001&#8221;&#8217;, 2000.<\/li><li>K. Deb, &#8221;&#8217;Multi-Objective Optimization using Evolutionary Algorithms&#8221;&#8217;, Jhon Wiley &amp; Sons, 2001.<\/li><li>C. A. C. Coello, D. A. V. Veldhuizen, and G. Lamont, &#8221;&#8217;Evolutionary Algorithms for Solving Multi-Objective Problems&#8221;&#8217;, Boston, Kluwer Academic Publishers, 2002.<\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u306f\u3058\u3081\u306b \u751f\u7269\u306e\u907a\u4f1d\u3068\u9032\u5316\u306e\u904e\u7a0b\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3066\u69cb\u7bc9\u3055\u308c\u305f\u9032\u5316\u578b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0(Evolutionary Algorithms\uff0c\u4ee5\u4e0bEA) \u306f\uff0c\u63a2\u7d22\uff0c\u5b66\u7fd2\uff0c\u6700\u9069\u5316\uff0c\u5206\u985e\u306a\u3069\u306e\u624b\u6bb5\u3068\u3057\u3066\uff0c\u5e45\u5e83\u3044\u5206\u91ce\u3067\u6709\u7528\u6027\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\uff0eE&hellip;&nbsp;<a href=\"https:\/\/nic.lab.uec.ac.jp\/index.php\/emo\/\" rel=\"bookmark\">\u7d9a\u304d\u3092\u8aad\u3080 &raquo;<span class=\"screen-reader-text\">\u9032\u5316\u8a08\u7b97\u306b\u3088\u308b\u591a\u76ee\u7684\u6700\u9069\u5316<\/span><\/a><\/p>\n","protected":false},"author":1,"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-719","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/pages\/719","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\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/comments?post=719"}],"version-history":[{"count":47,"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/pages\/719\/revisions"}],"predecessor-version":[{"id":1047,"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/pages\/719\/revisions\/1047"}],"wp:attachment":[{"href":"https:\/\/nic.lab.uec.ac.jp\/index.php\/wp-json\/wp\/v2\/media?parent=719"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}