{"id":64839,"date":"2026-01-24T08:16:44","date_gmt":"2026-01-24T00:16:44","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/64839.html"},"modified":"2026-01-24T08:16:44","modified_gmt":"2026-01-24T00:16:44","slug":"%e7%81%b0%e7%8b%bc%e4%bc%98%e5%8c%96%ef%bc%88gwo%ef%bc%89%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/64839.html","title":{"rendered":"\u7070\u72fc\u4f18\u5316\uff08GWO\uff09\u7b97\u6cd5"},"content":{"rendered":"

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u7070\u72fc\u4f18\u5316\u7b97\u6cd5（Grey Wolf Optimizer, GWO）\u662f\u7531Seyedali Mirjalili\u7b49\u4eba\u4e8e2014\u5e74\u63d0\u51fa\u7684\u4e00\u79cd\u5143\u542f\u53d1\u5f0f\u4f18\u5316\u7b97\u6cd5，\u5176\u7075\u611f\u6e90\u4e8e\u81ea\u7136\u754c\u7070\u72fc\u7fa4\u4f53\u7684\u793e\u4f1a\u7b49\u7ea7\u7ed3\u6784\u4e0e\u534f\u4f5c\u72e9\u730e\u884c\u4e3a\u3002\u4f5c\u4e3a\u4e00\u79cd\u7fa4\u4f53\u667a\u80fd\u7b97\u6cd5，GWO\u4e0d\u4f9d\u8d56\u95ee\u9898\u7684\u5177\u4f53\u6570\u5b66\u6027\u8d28，\u5177\u6709\u53c2\u6570\u8bbe\u7f6e\u7b80\u5355\u3001\u6536\u655b\u901f\u5ea6\u5feb\u3001\u5168\u5c40\u641c\u7d22\u80fd\u529b\u5f3a\u7b49\u4f18\u52bf，\u5728\u5de5\u7a0b\u4f18\u5316\u3001\u673a\u5668\u5b66\u4e60\u3001\u8d44\u6e90\u8c03\u5ea6\u7b49\u591a\u4e2a\u9886\u57df\u5f97\u5230\u5e7f\u6cdb\u5e94\u7528\u3002<\/p>\n

\u4e00\u3001\u6838\u5fc3\u601d\u60f3：\u7070\u72fc\u7684\u793e\u4f1a\u7b49\u7ea7\u4e0e\u72e9\u730e\u884c\u4e3a<\/h3>\n

GWO\u7684\u6838\u5fc3\u7684\u662f\u6a21\u62df\u7070\u72fc\u7fa4\u4f53\u7684\u4e24\u5927\u6838\u5fc3\u7279\u5f81\u2014\u2014\u4e25\u683c\u7684\u793e\u4f1a\u7b49\u7ea7\u5236\u5ea6\u548c\u9ad8\u6548\u7684\u534f\u4f5c\u72e9\u730e\u7b56\u7565，\u5c06\u641c\u7d22\u4ee3\u7406（\u7b97\u6cd5\u4e2d\u7684\u201c\u7070\u72fc\u201d）\u4e0e\u4f18\u5316\u95ee\u9898\u7684\u5019\u9009\u89e3\u5bf9\u5e94，\u901a\u8fc7\u7fa4\u4f53\u534f\u4f5c\u9010\u6b65\u903c\u8fd1\u6700\u4f18\u89e3\u3002
\n1.\u793e\u4f1a\u7b49\u7ea7\u7ed3\u6784
\n\u7b97\u6cd5\u5c06\u7070\u72fc\u79cd\u7fa4\u5206\u4e3a\u56db\u4e2a\u7b49\u7ea7，\u5404\u7b49\u7ea7\u627f\u62c5\u4e0d\u540c\u89d2\u8272，\u5171\u540c\u5f15\u5bfc\u79cd\u7fa4\u641c\u7d22\u65b9\u5411：
\n\u2022\u03b1\u72fc（\u5934\u72fc）：\u79cd\u7fa4\u6700\u9ad8\u9886\u5bfc\u8005，\u5bf9\u5e94\u4f18\u5316\u95ee\u9898\u4e2d\u7684\u5f53\u524d\u6700\u4f18\u89e3，\u8d1f\u8d23\u51b3\u7b56\u72e9\u730e\u65b9\u5411\u3001\u4f11\u606f\u5730\u70b9\u7b49\u6838\u5fc3\u884c\u4e3a，\u662f\u79cd\u7fa4\u641c\u7d22\u7684\u6838\u5fc3\u5bfc\u5411\u3002
\n\u2022\u03b2\u72fc（\u526f\u72fc）：\u7b49\u7ea7\u4ec5\u6b21\u4e8e\u03b1\u72fc，\u4f5c\u4e3a\u03b1\u72fc\u7684\u987e\u95ee\u4e0e\u63a5\u73ed\u4eba，\u534f\u52a9\u7ba1\u7406\u79cd\u7fa4\u5e76\u53c2\u4e0e\u51b3\u7b56，\u5bf9\u5e94\u6b21\u4f18\u89e3，\u4e3a\u79cd\u7fa4\u641c\u7d22\u63d0\u4f9b\u8f85\u52a9\u5bfc\u5411\u3002
\n\u2022\u03b4\u72fc（\u652f\u914d\u72fc）：\u7b2c\u4e09\u7b49\u7ea7\u7070\u72fc，\u5305\u62ec\u4fa6\u5bdf\u5175\u3001\u54e8\u5175\u3001\u6355\u730e\u8005\u7b49，\u670d\u4ece\u03b1\u548c\u03b2\u72fc\u7684\u6307\u4ee4，\u540c\u65f6\u652f\u914d\u03c9\u72fc，\u5bf9\u5e94\u7b2c\u4e09\u4f18\u89e3，\u8865\u5145\u79cd\u7fa4\u641c\u7d22\u7684\u591a\u6837\u6027\u3002
\n\u2022\u03c9\u72fc（\u666e\u901a\u72fc）：\u6700\u4f4e\u7b49\u7ea7，\u6570\u91cf\u6700\u591a，\u5b8c\u5168\u670d\u4ece\u4e0a\u5c42\u7070\u72fc，\u5bf9\u5e94\u5176\u4f59\u5019\u9009\u89e3，\u8ddf\u968f\u03b1\u3001\u03b2\u3001\u03b4\u72fc\u7684\u65b9\u5411\u66f4\u65b0\u4f4d\u7f6e，\u662f\u79cd\u7fa4\u641c\u7d22\u7684\u4e3b\u8981\u6267\u884c\u7fa4\u4f53\u3002
\n\u7b97\u6cd5\u59cb\u7ec8\u8ffd\u8e2a\u03b1\u3001\u03b2\u3001\u03b4\u4e09\u53ea\u6700\u4f18\u7070\u72fc\u7684\u4f4d\u7f6e，\u5229\u7528\u5b83\u4eec\u7684\u4fe1\u606f\u5f15\u5bfc\u6574\u4e2a\u79cd\u7fa4（\u5c24\u5176\u662f\u03c9\u72fc）\u7684\u641c\u7d22\u65b9\u5411，\u907f\u514d\u5355\u4e00\u6700\u4f18\u89e3\u5bfc\u81f4\u7684\u5c40\u90e8\u6536\u655b\u95ee\u9898\u3002
\n2.\u72e9\u730e\u884c\u4e3a\u6a21\u62df
\nGWO\u5c06\u7070\u72fc\u72e9\u730e\u8fc7\u7a0b\u62c6\u89e3\u4e3a\u5305\u56f4\u3001\u8ffd\u6355\u3001\u653b\u51fb\u4e09\u4e2a\u9636\u6bb5，\u901a\u8fc7\u6570\u5b66\u6a21\u578b\u8f6c\u5316\u4e3a\u7b97\u6cd5\u7684\u641c\u7d22\u673a\u5236：
\n\u2022\u5305\u56f4\u9636\u6bb5：\u7070\u72fc\u53d1\u73b0\u730e\u7269\u540e，\u901a\u8fc7\u7fa4\u4f53\u534f\u4f5c\u9010\u6b65\u7f29\u5c0f\u5305\u56f4\u5708\u3002\u7b97\u6cd5\u4e2d\u8868\u73b0\u4e3a\u6240\u6709\u7070\u72fc\u5411\u03b1\u3001\u03b2\u3001\u03b4\u72fc\u7684\u4f4d\u7f6e\u9760\u62e2，\u7f29\u5c0f\u641c\u7d22\u8303\u56f4，\u903c\u8fd1\u6f5c\u5728\u6700\u4f18\u89e3\u3002
\n\u2022\u8ffd\u6355\u9636\u6bb5：\u7531\u03b1\u3001\u03b2\u3001\u03b4\u72fc\u4e3b\u5bfc\u72e9\u730e\u65b9\u5411，\u03c9\u72fc\u8ddf\u968f\u9886\u5bfc\u8005\u79fb\u52a8，\u901a\u8fc7\u8c03\u6574\u4f4d\u7f6e\u8ffd\u8e2a\u201c\u730e\u7269\u201d（\u6700\u4f18\u89e3）\u3002\u6b64\u9636\u6bb5\u901a\u8fc7\u53c2\u6570\u8c03\u63a7\u5e73\u8861\u5168\u5c40\u63a2\u7d22\u4e0e\u5c40\u90e8\u5f00\u53d1\u3002
\n\u2022\u653b\u51fb\u9636\u6bb5：\u5f53\u730e\u7269\u505c\u6b62\u79fb\u52a8（\u6700\u4f18\u89e3\u8d8b\u4e8e\u7a33\u5b9a）\u65f6，\u7070\u72fc\u53d1\u8d77\u653b\u51fb\u3002\u7b97\u6cd5\u4e2d\u5bf9\u5e94\u63a7\u5236\u53c2\u6570a\u51cf\u5c0f\u81f3\u63a5\u8fd10，\u79cd\u7fa4\u4f4d\u7f6e\u6536\u655b\u5230\u6700\u4f18\u89e3\u9644\u8fd1，\u5b8c\u6210\u5c40\u90e8\u7cbe\u7ec6\u5316\u641c\u7d22\u3002<\/p>\n

\u4e8c\u3001\u6570\u5b66\u6a21\u578b\u4e0e\u6838\u5fc3\u516c\u5f0f<\/h3>\n

GWO\u901a\u8fc7\u8ddd\u79bb\u5411\u91cf\u3001\u4f4d\u7f6e\u66f4\u65b0\u5411\u91cf\u53ca\u6700\u7ec8\u4f4d\u7f6e\u66f4\u65b0\u65b9\u7a0b，\u5c06\u72e9\u730e\u884c\u4e3a\u91cf\u5316\u4e3a\u53ef\u8ba1\u7b97\u7684\u6570\u5b66\u6a21\u578b，\u6838\u5fc3\u516c\u5f0f\u5982\u4e0b：
\n1.\u8ddd\u79bb\u5411\u91cf（D）
\n\u7528\u4e8e\u8ba1\u7b97\u5f53\u524d\u7070\u72fc\u4e0e\u03b1\u3001\u03b2\u3001\u03b4\u72fc（\u730e\u7269\u4ee3\u7406）\u4e4b\u95f4\u7684\u8ddd\u79bb，\u53cd\u6620\u4e2a\u4f53\u4e0e\u6700\u4f18\u89e3\u7684\u63a5\u8fd1\u7a0b\u5ea6：
\nD = |C \u00b7 X\u209a(t) – X(t)|
\n\u5176\u4e2d：Xp(t)X_p(t)<\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u03b1\u3001\u03b2\u3001\u03b4\u72fc\u5728\u7b2ct\u4ee3\u7684\u4f4d\u7f6e（\u730e\u7269\u4f4d\u7f6e\u4ee3\u7406）；X(t)X(t)<\/span><\/span>X<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5f53\u524d\u7070\u72fc\u5728\u7b2ct\u4ee3\u7684\u4f4d\u7f6e；C=2\u22c5r2C = 2 \\\\cdot r_2<\/span><\/span>C<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u7cfb\u6570\u5411\u91cf，r2r_2<\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f(0,1)\u533a\u95f4\u5185\u7684\u968f\u673a\u5411\u91cf，\u7528\u4e8e\u5f15\u5165\u968f\u673a\u6027，\u589e\u5f3a\u5168\u5c40\u641c\u7d22\u80fd\u529b，\u907f\u514d\u7b97\u6cd5\u9677\u5165\u5c40\u90e8\u6700\u4f18\u3002
\n2.\u4f4d\u7f6e\u66f4\u65b0\u5411\u91cf（A）
\n\u63a7\u5236\u7070\u72fc\u7684\u641c\u7d22\u884c\u4e3a（\u63a2\u7d22\u6216\u5f00\u53d1），\u5176\u53d6\u503c\u51b3\u5b9a\u7070\u72fc\u662f\u8fdc\u79bb\u8fd8\u662f\u9760\u8fd1\u9886\u5bfc\u8005：
\nA = 2 \u00b7 a \u00b7 r\u2081 – a
\n\u5176\u4e2d：aa<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6536\u655b\u63a7\u5236\u53c2\u6570，\u4ece2\u7ebf\u6027\u51cf\u5c0f\u81f30（\u968f\u8fed\u4ee3\u6b21\u6570\u589e\u52a0）；r1r_1<\/span><\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f(0,1)\u533a\u95f4\u5185\u7684\u968f\u673a\u5411\u91cf\u3002\u5f53\u2223A\u2223>1|A| > 1<\/span><\/span>\u2223<\/span>A<\/span>\u2223<\/span><\/span>><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u65f6，\u7070\u72fc\u503e\u5411\u4e8e\u63a2\u7d22\u65b0\u533a\u57df（\u8fdc\u79bb\u9886\u5bfc\u8005）；\u5f53\u2223A\u2223<1|A| < 1<\/span><\/span>\u2223<\/span>A<\/span>\u2223<\/span><\/span><<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u65f6，\u7070\u72fc\u503e\u5411\u4e8e\u5f00\u53d1\u5c40\u90e8\u533a\u57df（\u9760\u8fd1\u9886\u5bfc\u8005）\u3002
\n3.\u6700\u7ec8\u4f4d\u7f6e\u66f4\u65b0\u65b9\u7a0b
\n\u7531\u4e8e\u7b97\u6cd5\u65e0\u6cd5\u9884\u77e5\u771f\u5b9e\u6700\u4f18\u89e3，\u901a\u8fc7\u03b1\u3001\u03b2\u3001\u03b4\u72fc\u7684\u4f4d\u7f6e\u52a0\u6743\u5e73\u5747，\u5f15\u5bfc\u5176\u4ed6\u7070\u72fc\u66f4\u65b0\u4f4d\u7f6e，\u517c\u987e\u641c\u7d22\u7cbe\u5ea6\u4e0e\u591a\u6837\u6027：
\nX\u2081 = X_\u03b1 – A\u2081 \u00b7 |C\u2081 \u00b7 X_\u03b1 – X|；X\u2082 = X_\u03b2 – A\u2082 \u00b7 |C\u2082 \u00b7 X_\u03b2 – X|；X\u2083 = X_\u03b4 – A\u2083 \u00b7 |C\u2083 \u00b7 X_\u03b4 – X|；X(t+1) = (X\u2081 + X\u2082 + X\u2083)\/3
\n\u5176\u4e2d：X1\u3001X2\u3001X3X_1\u3001X_2\u3001X_3<\/span><\/span>X<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<\/span>X<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<\/span>X<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5206\u522b\u4e3a\u5f53\u524d\u7070\u72fc\u5411\u03b1\u3001\u03b2\u3001\u03b4\u72fc\u9760\u62e2\u540e\u7684\u6f5c\u5728\u4f4d\u7f6e；X(t+1)X(t+1)<\/span><\/span>X<\/span>(<\/span>t<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7b2ct+1\u4ee3\u7070\u72fc\u7684\u6700\u7ec8\u4f4d\u7f6e，\u901a\u8fc7\u4e09\u8005\u5e73\u5747\u5e73\u8861\u591a\u65b9\u5411\u5f15\u5bfc，\u63d0\u5347\u89e3\u7684\u7a33\u5b9a\u6027\u3002<\/p>\n

\u4e09\u3001\u7b97\u6cd5\u6d41\u7a0b<\/h3>\n

GWO\u7684\u5b9e\u73b0\u6d41\u7a0b\u7b80\u6d01，\u6838\u5fc3\u6b65\u9aa4\u53ef\u5206\u4e3a\u521d\u59cb\u5316\u3001\u8fed\u4ee3\u4f18\u5316\u4e0e\u7ed3\u679c\u8f93\u51fa\u4e09\u90e8\u5206，\u5177\u4f53\u5982\u4e0b：
\n1.\u79cd\u7fa4\u521d\u59cb\u5316：\u8bbe\u5b9a\u7b97\u6cd5\u53c2\u6570（\u7070\u72fc\u6570\u91cf\u3001\u6700\u5927\u8fed\u4ee3\u6b21\u6570\u3001\u641c\u7d22\u7a7a\u95f4\u4e0a\u4e0b\u754clb\/ub\u3001\u95ee\u9898\u7ef4\u5ea6dim），\u968f\u673a\u751f\u6210N\u53ea\u7070\u72fc\u7684\u521d\u59cb\u4f4d\u7f6e，\u6784\u6210\u521d\u59cb\u79cd\u7fa4（\u5019\u9009\u89e3\u96c6\u5408）\u3002
\n2.\u9002\u5e94\u5ea6\u8bc4\u4f30：\u8ba1\u7b97\u6bcf\u53ea\u7070\u72fc\u7684\u76ee\u6807\u51fd\u6570\u503c（\u9002\u5e94\u5ea6），\u8bc4\u4f30\u5019\u9009\u89e3\u7684\u4f18\u52a3\u3002
\n3.\u66f4\u65b0\u9886\u5bfc\u8005：\u6839\u636e\u9002\u5e94\u5ea6\u6392\u5e8f，\u7b5b\u9009\u51fa\u5f53\u524d\u6700\u4f18（\u03b1）\u3001\u6b21\u4f18（\u03b2）\u3001\u7b2c\u4e09\u4f18（\u03b4）\u7070\u72fc，\u8bb0\u5f55\u5176\u4f4d\u7f6e\u4e0e\u9002\u5e94\u5ea6\u503c\u3002
\n4.\u53c2\u6570\u66f4\u65b0：\u6839\u636e\u5f53\u524d\u8fed\u4ee3\u6b21\u6570，\u7ebf\u6027\u66f4\u65b0\u6536\u655b\u63a7\u5236\u53c2\u6570a（\u4ece2\u9012\u51cf\u81f30），\u5e76\u540c\u6b65\u8ba1\u7b97A\u3001C\u5411\u91cf\u3002
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\n2.\u7f3a\u9677
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\u4e94\u3001\u5e94\u7528\u9886\u57df\u4e0e\u6539\u8fdb\u65b9\u5411<\/h3>\n

1.\u5178\u578b\u5e94\u7528
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\n\u2022\u673a\u5668\u5b66\u4e60：\u7279\u5f81\u9009\u62e9\u3001\u6a21\u578b\u53c2\u6570\u8c03\u4f18（\u5982\u795e\u7ecf\u7f51\u7edc\u6743\u91cd\u4f18\u5316），\u63d0\u5347\u6a21\u578b\u7cbe\u5ea6\u4e0e\u6cdb\u5316\u80fd\u529b\u3002
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\n2.\u6539\u8fdb\u65b9\u5411
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\u516d\u3001\u603b\u7ed3<\/h3>\n

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