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⛄ 内容介绍
在最近的研究中,一种名为秃鹰搜索算法(Cuckoo Search Algorithm)的优化算法已经引起了广泛的关注。这种算法受到了自然界中秃鹰的繁殖行为的启发,通过模拟秃鹰寻找巢穴和替换其他鸟类鸟蛋的行为,来搜索最优解。
然而,传统的秃鹰搜索算法在解决复杂问题时可能会遇到一些困难。为了克服这些问题,研究人员提出了一种改进的算法,即融合自适应惯性权重和柯西变异的秃鹰搜索算法(CBES)。
这种改进的算法引入了自适应惯性权重和柯西变异两个重要的概念。自适应惯性权重可以使算法在搜索过程中具有更好的全局搜索能力和局部搜索能力。柯西变异则可以增加算法的多样性,从而更好地避免陷入局部最优解。
CBES算法的基本步骤与传统的秃鹰搜索算法类似。首先,生成一组初始解作为种群。然后,根据适应度函数对种群进行评估,并根据柯西变异和自适应惯性权重来更新解的位置。最后,通过迭代多次来寻找最优解。
通过在不同的测试函数上进行实验,研究人员发现CBES算法相比于传统的秃鹰搜索算法具有更好的搜索性能和收敛性能。这表明CBES算法在解决复杂问题时具有更大的潜力。
总之,融合自适应惯性权重和柯西变异的秃鹰搜索算法(CBES)是一种有效的优化算法,可以用于解决各种复杂问题。通过引入自适应惯性权重和柯西变异的概念,CBES算法能够更好地平衡全局搜索和局部搜索能力,从而提高搜索性能。我们期待未来进一步的研究和应用,以探索CBES算法在实际问题中的潜力。
⛄ 部分代码
%################################################################################################%% Designed and Developed by Dr. Gaurav Dhiman (http://dhimangaurav.com/) %% Doi: https://doi.org/10.1016/j.engappai.2019.03.021 %% Link: https://www.sciencedirect.com/science/article/abs/pii/S0952197619300715 %% Title: STOA: A bio-inspired based optimization algorithm for industrial engineering problems %% Authors: Gaurav Dhiman and Amandeep Kaur %%################################################################################################%function [lowerbound,upperbound,dimension,fitness] = fun_info(F)switch F case 'F1' fitness = @F1; lowerbound=-100; upperbound=100; dimension=30; case 'F2' fitness = @F2; lowerbound=-10; upperbound=10; dimension=30; case 'F3' fitness = @F3; lowerbound=-100; upperbound=100; dimension=30; case 'F4' fitness = @F4; lowerbound=-100; upperbound=100; dimension=30; case 'F5' fitness = @F5; lowerbound=-30; upperbound=30; dimension=30; case 'F6' fitness = @F6; lowerbound=-100; upperbound=100; dimension=30; case 'F7' fitness = @F7; lowerbound=-1.28; upperbound=1.28; dimension=30; case 'F8' fitness = @F8; lowerbound=-500; upperbound=500; dimension=30; case 'F9' fitness = @F9; lowerbound=-5.12; upperbound=5.12; dimension=30; case 'F10' fitness = @F10; lowerbound=-32; upperbound=32; dimension=30; case 'F11' fitness = @F11; lowerbound=-600; upperbound=600; dimension=30; case 'F12' fitness = @F12; lowerbound=-50; upperbound=50; dimension=30; case 'F13' fitness = @F13; lowerbound=-50; upperbound=50; dimension=30; case 'F14' fitness = @F14; lowerbound=-65.536; upperbound=65.536; dimension=2; case 'F15' fitness = @F15; lowerbound=-5; upperbound=5; dimension=4; case 'F16' fitness = @F16; lowerbound=-5; upperbound=5; dimension=2; case 'F17' fitness = @F17; lowerbound=[-5,0]; upperbound=[10,15]; dimension=2; case 'F18' fitness = @F18; lowerbound=-2; upperbound=2; dimension=2; case 'F19' fitness = @F19; lowerbound=0; upperbound=1; dimension=3; case 'F20' fitness = @F20; lowerbound=0; upperbound=1; dimension=6; case 'F21' fitness = @F21; lowerbound=0; upperbound=10; dimension=4; case 'F22' fitness = @F22; lowerbound=0; upperbound=10; dimension=4; case 'F23' fitness = @F23; lowerbound=0; upperbound=10; dimension=4; endend% F1function R = F1(x)R=sum(x.^2);end% F2function R = F2(x)R=sum(abs(x))+prod(abs(x));end% F3function R = F3(x)dimension=size(x,2);R=0;for i=1:dimension R=R+sum(x(1:i))^2;endend% F4function R = F4(x)R=max(abs(x));end% F5function R = F5(x)dimension=size(x,2);R=sum(100*(x(2:dimension)-(x(1:dimension-1).^2)).^2+(x(1:dimension-1)-1).^2);end% F6function R = F6(x)R=sum(abs((x+.5)).^2);end% F7function R = F7(x)dimension=size(x,2);R=sum([1:dimension].*(x.^4))+rand;end% F8function R = F8(x)R=sum(-x.*sin(sqrt(abs(x))));end% F9function R = F9(x)dimension=size(x,2);R=sum(x.^2-10*cos(2*pi.*x))+10*dimension;end% F10function R = F10(x)dimension=size(x,2);R=-20*exp(-.2*sqrt(sum(x.^2)/dimension))-exp(sum(cos(2*pi.*x))/dimension)+20+exp(1);end% F11function R = F11(x)dimension=size(x,2);R=sum(x.^2)/4000-prod(cos(x./sqrt([1:dimension])))+1;end% F12function R = F12(x)dimension=size(x,2);R=(pi/dimension)*(10*((sin(pi*(1+(x(1)+1)/4)))^2)+sum((((x(1:dimension-1)+1)./4).^2).*...(1+10.*((sin(pi.*(1+(x(2:dimension)+1)./4)))).^2))+((x(dimension)+1)/4)^2)+sum(Ufun(x,10,100,4));end% F13function R = F13(x)dimension=size(x,2);R=.1*((sin(3*pi*x(1)))^2+sum((x(1:dimension-1)-1).^2.*(1+(sin(3.*pi.*x(2:dimension))).^2))+...((x(dimension)-1)^2)*(1+(sin(2*pi*x(dimension)))^2))+sum(Ufun(x,5,100,4));end% F14function R = F14(x)aS=[-32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32;,...-32 -32 -32 -32 -32 -16 -16 -16 -16 -16 0 0 0 0 0 16 16 16 16 16 32 32 32 32 32];for j=1:25 bS(j)=sum((x'-aS(:,j)).^6);endR=(1/500+sum(1./([1:25]+bS))).^(-1);end% F15function R = F15(x)aK=[.1957 .1947 .1735 .16 .0844 .0627 .0456 .0342 .0323 .0235 .0246];bK=[.25 .5 1 2 4 6 8 10 12 14 16];bK=1./bK;R=sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2);end% F16function R = F16(x)R=4*(x(1)^2)-2.1*(x(1)^4)+(x(1)^6)/3+x(1)*x(2)-4*(x(2)^2)+4*(x(2)^4);end% F17function R = F17(x)R=(x(2)-(x(1)^2)*5.1/(4*(pi^2))+5/pi*x(1)-6)^2+10*(1-1/(8*pi))*cos(x(1))+10;end% F18function R = F18(x)R=(1+(x(1)+x(2)+1)^2*(19-14*x(1)+3*(x(1)^2)-14*x(2)+6*x(1)*x(2)+3*x(2)^2))*... (30+(2*x(1)-3*x(2))^2*(18-32*x(1)+12*(x(1)^2)+48*x(2)-36*x(1)*x(2)+27*(x(2)^2)));end% F19function R = F19(x)aH=[3 10 30;.1 10 35;3 10 30;.1 10 35];cH=[1 1.2 3 3.2];pH=[.3689 .117 .2673;.4699 .4387 .747;.1091 .8732 .5547;.03815 .5743 .8828];R=0;for i=1:4 R=R-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));endend% F20function R = F20(x)aH=[10 3 17 3.5 1.7 8;.05 10 17 .1 8 14;3 3.5 1.7 10 17 8;17 8 .05 10 .1 14];cH=[1 1.2 3 3.2];pH=[.1312 .1696 .5569 .0124 .8283 .5886;.2329 .4135 .8307 .3736 .1004 .9991;....2348 .1415 .3522 .2883 .3047 .6650;.4047 .8828 .8732 .5743 .1091 .0381];R=0;for i=1:4 R=R-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));endend% F21function R = F21(x)aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];R=0;for i=1:5 R=R-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);endend% F22function R = F22(x)aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];R=0;for i=1:7 R=R-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);endend% F23function R = F23(x)aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6];cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];R=0;for i=1:10 R=R-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);endendfunction R=Ufun(x,a,k,m)R=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a));end
⛄ 运行结果编辑
编辑
⛄ 参考文献
[1]丁容,高建瓴,张倩.融合自适应惯性权重和柯西变异的秃鹰搜索算法[J].小型微型计算机系统, 2023, 44(5):910-915.