{"id":45748,"date":"2025-07-30T01:01:26","date_gmt":"2025-07-29T17:01:26","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/45748.html"},"modified":"2025-07-30T01:01:26","modified_gmt":"2025-07-29T17:01:26","slug":"%e5%a4%9a%e6%9c%ba%e5%99%a8%e4%ba%ba%e8%b7%af%e5%be%84%e8%a7%84%e5%88%92%e7%9a%84%e5%a4%9a%e7%ad%96%e7%95%a5%e8%87%aa%e9%80%82%e5%ba%94%e5%b7%ae%e5%88%86%e6%ad%a3%e4%bd%99%e5%bc%a6%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/45748.html","title":{"rendered":"\u591a\u673a\u5668\u4eba\u8def\u5f84\u89c4\u5212\u7684\u591a\u7b56\u7565\u81ea\u9002\u5e94\u5dee\u5206\u6b63\u4f59\u5f26\u7b97\u6cd5\uff0cMulti-robot path planning\u591a\u673a\u5668\u4eba\u8def\u5f84\u89c4\u5212\u3002\u9644\u4ee3\u7801"},"content":{"rendered":"

1\u3001\u7b80\u4ecb<\/h4>\n

\u6700\u8fd1\u8fdb\u884c\u4e86\u4f7f\u7528\u5404\u79cd\u5143\u542f\u53d1\u5f0f\u7b97\u6cd5\u8fdb\u884c\u591a\u673a\u5668\u4eba\u8def\u5f84\u89c4\u5212\u7684\u7814\u7a76\u3002\u5176\u4e2d\u4e00\u79cd\u7b97\u6cd5\u6b63\u5f26\u4f59\u5f26\u7b97\u6cd5（SCA）\u4e0d\u80fd\u5728\u8def\u5f84\u89c4\u5212\u95ee\u9898\u4e2d\u4ea7\u751f\u4ee4\u4eba\u6ee1\u610f\u7684\u7ed3\u679c，\u7531\u4e8e\u5355\u4e00\u7684\u66f4\u65b0\u7b56\u7565\u3002\u6709\u5fc5\u8981\u91c7\u7528\u591a\u79cd\u66f4\u65b0\u7b56\u7565，\u5e76\u9488\u5bf9\u66f4\u5e7f\u6cdb\u7684\u95ee\u9898\u63d0\u9ad8\u5176\u6027\u80fd\u3002\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u591a\u7b56\u7565\u81ea\u9002\u5e94\u5fae\u5206\u6b63\u5f26\u4f59\u5f26\u7b97\u6cd5（sdSCA），\u5b83\u4f7f\u7528\u7b56\u7565\u6c60，\u5e76\u5141\u8bb8\u66f4\u9891\u7e41\u5730\u9009\u62e9\u7b56\u7565，\u4ece\u800c\u5bfc\u81f4\u66f4\u597d\u7684\u89e3\u51b3\u65b9\u6848，\u5c06sdSCA\u5e94\u7528\u4e8e\u5177\u6709\u9759\u6001\u548c\u52a8\u6001\u969c\u788d\u7269\u7684\u590d\u6742\u73af\u5883\u4e2d\u7684\u5728\u7ebf\u591a\u673a\u5668\u4eba\u8def\u5f84\u89c4\u5212\u3002<\/p>\n

2\u3001\u57fa\u672c\u6b63\u5f26\u4f59\u5f26\u7b97\u6cd5(SCA)<\/h4>\n

SCA\u662fMirjalili\u4e8e2016\u5e74\u63d0\u51fa\u7684\u57fa\u4e8e\u6570\u5b66\u7684\u5148\u8fdb\u5143\u542f\u53d1\u5f0f\u7b97\u6cd5\u3002\u8be5\u7b97\u6cd5\u5728\u66f4\u65b0\u89e3\u65f6\u91c7\u7528\u6b63\u5f26\u548c\u4f59\u5f26\u51fd\u6570\u6784\u5efa\u7684\u65b9\u7a0b，\u8fd9\u4e9b\u4e09\u89d2\u51fd\u6570\u80fd\u6709\u6548\u5229\u7528\u4e24\u4e2a\u4e0d\u540c\u89e3\u4e4b\u95f4\u7684\u7a7a\u95f4(Mirjalili, 2016)\u3002\u7b97\u6cd5\u6d41\u7a0b\u5982\u4e0b：\u9996\u5148\u901a\u8fc7\u5f0f(1)\u968f\u673a\u751f\u6210\u521d\u59cb\u79cd\u7fa4：<\/p>\n

Xi=Xmin+(Xmax\u2212Xmin)\u2005\u200arand(1,D),i\u2208{1,2,\u2026,PS}(1)X_i = X_{min} + (X_{max} – X_{min}) \\\\; rand(1, D), \\\\quad i \\\\in \\\\{1, 2, \\\\ldots, PS\\\\} \\\\tag{1}<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>X<\/span><\/span>min<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>(<\/span>X<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>X<\/span><\/span>min<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>r<\/span>an<\/span>d<\/span>(<\/span>1<\/span>,<\/span><\/span>D<\/span>)<\/span>,<\/span><\/span><\/span>i<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>PS<\/span>}<\/span><\/span><\/span>(<\/span>1<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2dXiX_i<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u5019\u9009\u89e3ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>，XminX_{min}<\/span><\/span>X<\/span><\/span>min<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548cXmaxX_{max}<\/span><\/span>X<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5206\u522b\u8868\u793a\u89e3\u7684\u4e0a\u4e0b\u754c，DD<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u548cPSPS<\/span><\/span>PS<\/span><\/span><\/span><\/span><\/span>\u5206\u522b\u4ee3\u8868\u95ee\u9898\u7ef4\u5ea6\u548c\u79cd\u7fa4\u89c4\u6a21\u3002\u79cd\u7fa4\u7ecf\u9002\u5e94\u5ea6\u51fd\u6570\u8bc4\u4f30\u540e\u5f00\u59cb\u8fed\u4ee3\u8fc7\u7a0b，\u89e3\u901a\u8fc7\u5f0f(2)\u66f4\u65b0：<\/p>\n

Xit+1={Xit+r1\u2005\u200asin\u2061(r2)\u2005\u200a\u2223r3\u2005\u200aXbestt\u2212Xit\u2223\u5982\u679c\u00a0r4<0.5Xit+r1\u2005\u200acos\u2061(r2)\u2005\u200a\u2223r3\u2005\u200aXbestt\u2212Xit\u2223\u5426\u5219(2)X^{t+1}_i =
\n\\\\begin{cases}
\nX^t_i + r_1 \\\\; \\\\sin(r_2) \\\\; |r_3 \\\\; X^t_{best} – X^t_i| & \\\\text{\u5982\u679c } r_4 < 0.5 \\\\\\\\
\nX^t_i + r_1 \\\\; \\\\cos(r_2) \\\\; |r_3 \\\\; X^t_{best} – X^t_i| & \\\\text{\u5426\u5219}
\n\\\\end{cases} \\\\tag{2}<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span><\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>sin<\/span>(<\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2223<\/span>r<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>b<\/span>es<\/span>t<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>cos<\/span>(<\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2223<\/span>r<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>b<\/span>es<\/span>t<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5982\u679c<\/span>\u00a0<\/span><\/span>r<\/span><\/span>4<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span>0.5<\/span><\/span><\/span><\/span>\u5426\u5219<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5f0f\u4e2dXit+1X^{t+1}_i<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u7b2ct+1t+1<\/span><\/span>t<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u4ee3\u5019\u9009\u89e3ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>，XitX^t_i<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e3a\u7b2ctt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u4ee3\u5019\u9009\u89e3ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>，XbesttX^t_{best}<\/span><\/span>X<\/span><\/span>b<\/span>es<\/span>t<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u7b2ctt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u4ee3\u79cd\u7fa4\u4e2d\u7684\u6700\u4f18\u89e3\u3002r1r_1<\/span><\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u901a\u8fc7\u5f0f(3)\u8ba1\u7b97：<\/p>\n

r1=a\u2212taT(3)r_1 = a – t \\\\frac{a}{T} \\\\tag{3}<\/span><\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>t<\/span><\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>3<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2dtt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u4e3a\u5f53\u524d\u8fed\u4ee3\u6b21\u6570，TT<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span>\u4e3a\u6700\u5927\u8fed\u4ee3\u6b21\u6570，aa<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span>\u4e3a\u5e38\u6570\u3002r2r_2<\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001r3r_3<\/span><\/span>r<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548cr4r_4<\/span><\/span>r<\/span><\/span>4<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5206\u522b\u4e3a[0,2\u03c0]\u3001[0,2]\u548c[0,1]\u8303\u56f4\u5185\u7684\u968f\u673a\u6570\u3002\u65b0\u79cd\u7fa4\u7ecf\u9002\u5e94\u5ea6\u51fd\u6570\u8bc4\u4f30\u540e\u7ee7\u7eed\u8fed\u4ee3\u76f4\u81f3\u6ee1\u8db3\u505c\u6b62\u6761\u4ef6，\u6700\u7ec8\u8f93\u51fa\u6700\u4f18\u89e3\u3002\u6700\u5c0f\u5316\u95ee\u9898\u7684SCA\u4f2a\u4ee3\u7801\u89c1\u7b97\u6cd51\u3002
\n\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

3\u3001\u591a\u7b56\u7565\u81ea\u9002\u5e94\u5dee\u5206\u6b63\u5f26\u4f59\u5f26\u7b97\u6cd5(sdSCA)<\/h4>\n

\u57fa\u4e8e\u79cd\u7fa4\u7684\u5143\u542f\u53d1\u5f0f\u7b97\u6cd5\u9996\u5148\u751f\u6210\u968f\u673a\u521d\u59cb\u79cd\u7fa4，\u7ecf\u9002\u5e94\u5ea6\u51fd\u6570\u8bc4\u4f30\u540e\u5f00\u59cb\u8fed\u4ee3\u66f4\u65b0\u8fc7\u7a0b\u3002\u591a\u6570\u7b97\u6cd5\u4e2d，\u79cd\u7fa4\u5019\u9009\u89e3\u901a\u5e38\u91c7\u7528\u5355\u4e00\u66f4\u65b0\u7b56\u7565，\u8fed\u4ee3\u7ed3\u675f\u65f6\u8f93\u51fa\u6700\u4f18\u89e3\u3002\u7136\u800c\u5355\u4e00\u66f4\u65b0\u7b56\u7565\u4f1a\u9650\u5236\u7b97\u6cd5\u641c\u7d22\u6027\u80fd\u3002SCA\u4f5c\u4e3a\u57fa\u4e8e\u79cd\u7fa4\u7684\u7b97\u6cd5，\u5176\u539f\u59cb\u66f4\u65b0\u7b56\u7565\u5982\u5f0f(2)\u6240\u793a\u3002\u4e3a\u7a81\u7834\u8fd9\u4e00\u9650\u5236，\u672c\u6587\u5728SCA\u539f\u6709\u7b56\u7565\u57fa\u7840\u4e0a\u5f15\u5165\u5dee\u5206\u7b56\u7565，\u63d0\u51fa\u65b0\u578b\u591a\u7b56\u7565\u81ea\u9002\u5e94\u5dee\u5206\u6b63\u5f26\u4f59\u5f26\u7b97\u6cd5(sdSCA)\u3002\u8be5\u7b97\u6cd5\u4e2d，\u6bcf\u4e2a\u5019\u9009\u89e3\u901a\u8fc7\u8f6e\u76d8\u8d4c\u6982\u7387\u8ba1\u7b97\u81ea\u4e3b\u9009\u62e9\u66f4\u65b0\u7b56\u7565（\u975e\u968f\u673a\u9009\u62e9），\u7b97\u6cd5\u81ea\u9002\u5e94\u5b66\u4e60\u4ea7\u751f\u66f4\u4f18\u7ed3\u679c\u7684\u7b56\u7565，\u4ece\u800c\u63d0\u5347\u57fa\u7840SCA\u7684\u641c\u7d22\u6027\u80fd\u3002\u6240\u63d0\u7b97\u6cd5\u5728\u57fa\u7840SCA\u66f4\u65b0\u65b9\u7a0b\u5916\u65b0\u589e\u4e09\u79cd\u5dee\u5206\u7b56\u7565，\u5206\u522b\u5982\u5f0f(4)\u3001\u5f0f(5)\u548c\u5f0f(6)\u6240\u793a：<\/p>\n

Xit+1={XR1t+F(XR2t\u2212XR3t)\u82e5rand<CRXit\u5426\u5219(4)X_{i}^{t+1}=\\\\begin{cases}
\nX_{R_{1}}^{t}+F\\\\left(X_{R_{2}}^{t}-X_{R_{3}}^{t}\\\\right) & \\\\text{\u82e5}rand<CR\\\\\\\\
\nX_{i}^{t} & \\\\text{\u5426\u5219}
\n\\\\end{cases} \\\\tag{4}<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span><\/span><\/span>X<\/span><\/span>R<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>F<\/span><\/span>(<\/span><\/span>X<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>X<\/span><\/span>R<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u82e5<\/span><\/span>r<\/span>an<\/span>d<\/span><\/span><<\/span><\/span>CR<\/span><\/span><\/span><\/span>\u5426\u5219<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>4<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Xit+1={Xit+F(Xbestt\u2212Xit+XR1t\u2212XR2t)\u82e5rand<CRXit\u5426\u5219(5)X_{i}^{t+1}=\\\\begin{cases}
\nX_{i}^{t}+F\\\\left(X_{best}^{t}-X_{i}^{t}+X_{R_{1}}^{t}-X_{R_{2}}^{t}\\\\right) & \\\\text{\u82e5}rand<CR\\\\\\\\
\nX_{i}^{t} & \\\\text{\u5426\u5219}
\n\\\\end{cases} \\\\tag{5}<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span><\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>F<\/span><\/span>(<\/span><\/span>X<\/span><\/span>b<\/span>es<\/span>t<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>X<\/span><\/span>R<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>X<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u82e5<\/span><\/span>r<\/span>an<\/span>d<\/span><\/span><<\/span><\/span>CR<\/span><\/span><\/span><\/span>\u5426\u5219<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>5<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Xit+1=Xit+L(XR1t\u2212Xit)+F(XR2t\u2212XR3t)(6)X_{i}^{t+1}=X_{i}^{t}+L\\\\left(X_{R_{1}}^{t}-X_{i}^{t}\\\\right)+F\\\\left(X_{R_{2}}^{t}-X_{R_{3}}^{t}\\\\right) \\\\tag{6}<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>L<\/span><\/span>(<\/span><\/span>X<\/span><\/span>R<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>X<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>F<\/span><\/span>(<\/span><\/span>X<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>X<\/span><\/span>R<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>(<\/span>6<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2dXR1tX_{R_{1}}^{t}<\/span><\/span>X<\/span><\/span>R<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001XR2tX_{R_{2}}^{t}<\/span><\/span>X<\/span><\/span>R<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548cXR3tX_{R_{3}}^{t}<\/span><\/span>X<\/span><\/span>R<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e3a\u7b2ctt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u4ee3\u968f\u673a\u9009\u53d6\u7684\u4e09\u4e2a\u5019\u9009\u89e3，FF<\/span><\/span>F<\/span><\/span><\/span><\/span><\/span>\u4e3a\u7f29\u653e\u56e0\u5b50，LL<\/span><\/span>L<\/span><\/span><\/span><\/span><\/span>\u4e3a[0,1]\u8303\u56f4\u5185\u7684\u968f\u673a\u6570，CRCR<\/span><\/span>CR<\/span><\/span><\/span><\/span><\/span>\u4e3a\u4ea4\u53c9\u7387\u3002<\/p>\n

\u7b97\u6cd5\u6d41\u7a0b\u8bf4\u660e：\u9996\u5148\u7531\u5f0f(2)\u3001(4)-(6)\u6784\u5efa\u5305\u542b\u56db\u79cd\u5dee\u5206\u7b56\u7565\u7684\u7b56\u7565\u6c60，\u521d\u59cb\u9636\u6bb5\u5404\u7b56\u7565\u9009\u62e9\u6982\u7387\u5747\u8bbe\u4e3a25%\u3002\u901a\u8fc7\u5f0f(1)\u968f\u673a\u751f\u6210\u521d\u59cb\u79cd\u7fa4\u540e，\u5404\u5019\u9009\u89e3\u91c7\u7528\u8f6e\u76d8\u8d4c\u6280\u672f\u9009\u62e9\u7b56\u7565\u3002\u7ecf\u9002\u5e94\u5ea6\u51fd\u6570\u8bc4\u4f30\u540e\u5f00\u59cb\u8fed\u4ee3，\u5019\u9009\u89e3\u6309\u5404\u81ea\u7b56\u7565\u66f4\u65b0，\u540c\u65f6\u66f4\u65b0\u7b56\u7565\u9009\u62e9\u8ba1\u6570\u5668\u3002\u65b0\u79cd\u7fa4\u8bc4\u4f30\u540e，\u6309\u5f0f(7)\u8ba1\u7b97\u5404\u7b56\u7565\u66f4\u65b0\u6982\u7387：<\/p>\n

pkt+1=ckt\u2211i=1NSci,k\u2208{1,2,\u2026,NS}(7)p_{k}^{t+1}=\\\\frac{c_{k}^{t}}{\\\\sum_{i=1}^{NS}c_{i}}, \\\\quad k\\\\in\\\\{1,2,\\\\ldots,NS\\\\} \\\\tag{7}<\/span><\/span>p<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span>i<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>NS<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>c<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>c<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span>k<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>NS<\/span>}<\/span><\/span><\/span>(<\/span>7<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5f0f\u4e2dpkt+1p_{k}^{t+1}<\/span><\/span>p<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>t<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u7b2ct+1t+1<\/span><\/span>t<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u4ee3\u7b56\u7565kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u7684\u9009\u62e9\u6982\u7387，cktc_{k}^{t}<\/span><\/span>c<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e3a\u7b2ctt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span>\u4ee3\u7b56\u7565kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u7684\u8ba1\u6570\u5668，NSNS<\/span><\/span>NS<\/span><\/span><\/span><\/span><\/span>\u4e3a\u7b56\u7565\u603b\u6570\u3002\u57fa\u4e8e\u66f4\u65b0\u6982\u7387，\u5019\u9009\u89e3\u518d\u6b21\u901a\u8fc7\u8f6e\u76d8\u8d4c\u8c03\u6574\u7b56\u7565\u9009\u62e9，\u76f4\u81f3\u6ee1\u8db3\u505c\u6b62\u6761\u4ef6\u3002\u6700\u5c0f\u5316\u95ee\u9898\u7684sdSCA\u6d41\u7a0b\u56fe\u89c1\u7b97\u6cd52\u548c\u56fe2\u3002
\n\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

4\u3001\u591a\u673a\u5668\u4eba\u5728\u7ebf\u8def\u5f84\u89c4\u5212\u5efa\u6a21<\/h4>\n

\u591a\u673a\u5668\u4eba\u5728\u7ebf\u8def\u5f84\u89c4\u5212\u662f\u4e00\u4e2a\u6700\u5c0f\u5316\u95ee\u9898，\u65e8\u5728\u4f7f\u673a\u5668\u4eba\u5728\u590d\u6742\u73af\u5883\u4e2d\u9010\u6b65\u5230\u8fbe\u76ee\u6807\u70b9，\u540c\u65f6\u4ee5\u6700\u5c0f\u6210\u672c\u907f\u514d\u4e0e\u9759\u6001\/\u52a8\u6001\u969c\u788d\u7269\u53ca\u5176\u4ed6\u673a\u5668\u4eba\u78b0\u649e(Toufan & Nitzade, 2020)\u3002\u672c\u6587\u9488\u5bf9\u5706\u5f62\u540c\u6784\u591a\u673a\u5668\u4eba\u7cfb\u7edf\u8fdb\u884c\u5728\u7ebf\u8def\u5f84\u89c4\u5212\u4eff\u771f，\u673a\u5668\u4eba\u4e0b\u4e00\u4f4d\u7f6e\u53ef\u901a\u8fc7\u5f0f(8)-(9)\u8ba1\u7b97：<\/p>\n

xin=xic+vicos\u2061(\u03b8i)(8)x_{i}^{n} = x_{i}^{c}+v_{i}\\\\cos\\\\left(\\\\theta_{i}\\\\right) \\\\tag{8}<\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>c<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>v<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>cos<\/span><\/span>(<\/span>\u03b8<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>(<\/span>8<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\nyin=yic+visin\u2061(\u03b8i)(9)y_{i}^{n} = y_{i}^{c}+v_{i}\\\\sin\\\\left(\\\\theta_{i}\\\\right) \\\\tag{9}<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>c<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>v<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>sin<\/span><\/span>(<\/span>\u03b8<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>(<\/span>9<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d(xin,yin)(x_{i}^{n},y_{i}^{n})<\/span><\/span>(<\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u8868\u793a\u673a\u5668\u4ebaii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u7684\u4e0b\u4e00\u4f4d\u7f6e\u5750\u6807，(xic,yic)(x_{i}^{c},y_{i}^{c})<\/span><\/span>(<\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>c<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>c<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u4e3a\u5f53\u524d\u4f4d\u7f6e\u5750\u6807，viv_{i}<\/span><\/span>v<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u03b8i\\\\theta_{i}<\/span><\/span>\u03b8<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5206\u522b\u4e3a\u673a\u5668\u4ebaii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u7684\u901f\u5ea6\u548c\u89d2\u5ea6\u3002\u901f\u5ea6\u5b9a\u4e49\u4e3a\u5355\u6b65\u79fb\u52a8\u8ddd\u79bb，\u901a\u8fc7\u6bcf\u6b65\u4f18\u5316\u786e\u5b9a\u673a\u5668\u4eba\u4e0b\u4e00\u4f4d\u7f6e，\u8be5\u4f18\u5316\u57fa\u4e8e\u6240\u6709\u673a\u5668\u4eba\u7684\u901f\u5ea6\u548c\u89d2\u5ea6\u53c2\u6570\u3002\u9996\u5148\u5728\u901f\u5ea6\u8303\u56f4[vmin,vmax][v_{min},v_{max}]<\/span><\/span>[<\/span>v<\/span><\/span>min<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>v<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span>\u548c\u89d2\u5ea6\u8303\u56f4[\u03b8min,\u03b8max][\\\\theta_{min},\\\\theta_{max}]<\/span><\/span>[<\/span>\u03b8<\/span><\/span>min<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03b8<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span>\u5185\u521b\u5efa\u5c40\u90e8\u641c\u7d22\u7a7a\u95f4，\u7136\u540e\u786e\u5b9a\u8be5\u7a7a\u95f4\u4e2d\u6700\u53ef\u884c\u4e0b\u4e00\u4f4d\u7f6e\u7684\u901f\u5ea6\u548c\u89d2\u5ea6\u3002\u673a\u5668\u4eba\u6301\u7eed\u79fb\u52a8\u81f3\u76ee\u6807\u70b9，\u6240\u6709\u673a\u5668\u4eba\u7684\u901f\u5ea6\u548c\u89d2\u5ea6\u4f5c\u4e3a\u6574\u4f53\u8fdb\u884c\u4f18\u5316\u3002\u7531\u4e8e\u4f18\u5316\u57fa\u4e8e\u8fd9\u4e24\u4e2a\u8fd0\u52a8\u7279\u6027，\u95ee\u9898\u7ef4\u5ea6DD<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u4e0e\u673a\u5668\u4eba\u6570\u91cfNRN^{R}<\/span><\/span>N<\/span><\/span>R<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6210\u6b63\u6bd4，\u5373D=NR\u00d72D=N^{R}\\\\times2<\/span><\/span>D<\/span><\/span>=<\/span><\/span><\/span><\/span>N<\/span><\/span>R<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u3002\u4e3b\u9002\u5e94\u5ea6\u51fd\u6570\u5982\u5f0f(10)\u6240\u793a：<\/p>\n

KaTeX parse error: Invalid delimiter type 'ordgroup' at position 61: \u2026_{i}\\\\right)\\\\big{\u0332|\u0332}\u0332i\\\\in \\\\left\\\\{1,\\\\\u2026<\/span><\/p>\n

\u4e3b\u9002\u5e94\u5ea6\u51fd\u6570\u8bc4\u4f30\u4ee5\u4e0b\u56db\u4e2a\u51c6\u5219：<\/p>\n