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⛄ 内容介绍
针对原始哈里斯鹰优化算法(HHO)存在的收敛精度低,收敛速度慢,易陷入局部最优等不足,提出了一种基于混合策略的改进哈里斯鹰优化算法(HSHHO).首先,在种群初始化阶段引入Sobol序列,生成均匀分布的种群,提高种群的多样性,有利于提高算法的收敛速度;其次,引入limit阈值,令算法在一定迭代次数没有获得更优值后执行全局探索操作,提高算法跳出局部最优解的能力,改善HHO在迭代后期只执行开发阶段而易陷入局部最优的缺陷;最后,提出一种动态的反向学习机制,提高算法的收敛精度以及跳出局部最优的能力.在9个基准函数和6个CEC2017函数上进行测试,与其他多种优化算法,HHO变体作对比,验证所提出策略的有效性,并进行Wilcoxon符号秩检验,Friedman检验和Quade检验等非参数检验.实验结果表明, HSHHO在收敛速度,寻优精度和统计测试方面具有较为优秀的性能
⛄ 部分代码
function [lb,ub,dim,fobj] = Get_Functions_details(F)switch F case 'F1' fobj = @F1; lb=-100; ub=100; dim=10; case 'F2' fobj = @F2; lb=-10; ub=10; dim=10; case 'F3' fobj = @F3; lb=-100; ub=100; dim=30; case 'F4' fobj = @F4; lb=-10; ub=10; dim=30; case 'F5' fobj = @F5; lb=-30; ub=30; dim=30; case 'F6' fobj = @F6; lb=-100; ub=100; dim=30; case 'F7' fobj = @F7; lb=-1.28; ub=1.28; dim=30; case 'F8' fobj = @F8; lb=-10; ub=10; dim=10; case 'F9' fobj = @F9; lb=-10; ub=10; dim=10; case 'F10' fobj = @F10; lb=-1; ub=1; dim=30; case 'F11' fobj = @F11; lb=-100; ub=100; dim=30; case 'F12' fobj = @F12; lb=-10; ub=10; dim=10; case 'F13' fobj = @F13; lb=-500; ub=500; dim=30; case 'F14' fobj = @F14; lb=-5.12; ub=5.12; dim=10; case 'F15' fobj = @F15; lb=-32; ub=32; dim=10; case 'F16' fobj = @F16; lb=-600; ub=600; dim=10; case 'F17' fobj = @F17; lb=-50; ub=50; dim=30; case 'F18' fobj = @F18; lb=-50; ub=50; dim=30; case 'F19' fobj = @F19; lb=-500; ub=500; dim=30; case 'F20' fobj = @F20; lb=-5; ub=5; dim=4; case 'F21' fobj = @F21; lb=-5.12; ub=5.12; dim=2; case 'F22' fobj = @F22; lb=-10; ub=10; dim=2; case 'F23' fobj = @F23; lb=-100; ub=100; dim=2; case 'F24' fobj = @F24; lb=-65.536; ub=65.536; dim=2; case 'F25' fobj = @F25; lb=-5; ub=5; dim=4; case 'F26' fobj = @F26; lb=-5; ub=5; dim=2; case 'F27' fobj = @F27; lb=[-5,0]; ub=[10,15]; dim=2; case 'F28' fobj = @F28; lb=-2; ub=2; dim=2; case 'F29' fobj = @F29; lb=0; ub=1; dim=3; case 'F30' fobj = @F30; lb=0; ub=1; dim=6; case 'F31' fobj = @F31; lb=0; ub=10; dim=4; case 'F32' fobj = @F32; lb=0; ub=10; dim=4; case 'F33' fobj = @F33; lb=0; ub=10; dim=4; case 'F34' fobj = @F34; lb=-100; ub=100; dim=2; case 'F35' fobj = @F35; lb=-4; ub=5; dim=30;endend% F1function o = F1(x)o=sum(x.^2);end% F2function o = F2(x)o=sum(abs(x))+prod(abs(x));% o = ((sin(sqrt(sum(x.^2))))^2-0.5)/(1+0.001*sum(x.^2))+0.5;end% F3function o = F3(x)dim=size(x,2);o=0;for i=1:dim o=o+sum(x(1:i))^2;endend% F4function o = F4(x)o=max(abs(x));end% F5function o = F5(x)dim=size(x,2);o=sum(100*(x(2:dim)-(x(1:dim-1).^2)).^2+(x(1:dim-1)-1).^2);end% F6function o = F6(x)o=sum(abs((x+.5)).^2);end% F7function o = F7(x)dim=size(x,2);o=sum([1:dim].*(x.^4))+rand;end% F8function o = F8(x)dim = size(x, 2);o = sum([1:dim].*(x.^2));end% F9function o = F9(x)o=sum(abs(x.*sin(x)+0.1*x));end% F10function o = F10(x)dim = size(x, 2);o = 0;for i = 1:dim o = o+abs(x(i))^(i+1);endend% F11function o = F11(x)dim=size(x,2);o = 0;for i = 1:dim o = o+(10^6)^((i-1)/(dim-1))*x(i)^2;endend% F12function o = F12(x)dim = size(x, 2);p = 0; o = sum(x.^2);for i = 1:dim p = p+0.5*i*x(i);endo = o+p^2+p^4;end% F13function o = F13(x)o=sum(-x.*sin(sqrt(abs(x))));end% F14function o = F14(x)dim=size(x,2);o=sum(x.^2-10*cos(2*pi.*x))+10*dim;end% F15function o = F15(x)dim=size(x,2);o=-20*exp(-.2*sqrt(sum(x.^2)/dim))-exp(sum(cos(2*pi.*x))/dim)+20+exp(1);end% F16function o = F16(x)dim=size(x,2);o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1;end% F17function o = F17(x)dim=size(x,2);o=(pi/dim)*(10*((sin(pi*(1+(x(1)+1)/4)))^2)+sum((((x(1:dim-1)+1)./4).^2).*...(1+10.*((sin(pi.*(1+(x(2:dim)+1)./4)))).^2))+((x(dim)+1)/4)^2)+sum(Ufun(x,10,100,4));end% F18function o = F18(x)dim=size(x,2);o=.1*((sin(3*pi*x(1)))^2+sum((x(1:dim-1)-1).^2.*(1+(sin(3.*pi.*x(2:dim))).^2))+...((x(dim)-1)^2)*(1+(sin(2*pi*x(dim)))^2))+sum(Ufun(x,5,100,4));end% F19function o = F19(x)o = 418.9829*size(x, 2)-sum(x.*sin(sqrt(abs(x))));end% F20function o = F20(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;o=sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2);end% F21function o = F21(x)o = -(1+cos(12*sqrt(x(1)^2+x(2)^2)))/(0.5*(x(1)^2+x(2)^2)+2);end% F22function o = F22(x)o = 0.26*(x(1)^2+x(2)^2)-0.48*x(1)*x(2);end% F23function o = F23(x)o = 0.5+((sin(sqrt(x(1)^2+x(2)^2))^2)-0.5)/(1+0.001*(x(1)^2+x(2)^2)^2);end% F24function o = F24(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);endo=(1/500+sum(1./([1:25]+bS))).^(-1);end% F25function o = F25(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;o=sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2);end% F26function o = F26(x)o=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% F27function o = F27(x)o=(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% F28function o = F28(x)o=(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% F29function o = F29(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];o=0;for i=1:4 o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));endend% F30function o = F30(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];o=0;for i=1:4 o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));endend% F31function o = F31(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];o=0;for i=1:5 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);endend% F32function o = F32(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];o=0;for i=1:7 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);endend% F33function o = F33(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];o=0;for i=1:10 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);endend% F34function o = F34(x)o = x(1)^2+2*x(2)^2-0.3*cos(3*pi*x(1))-0.4*cos(4*pi*x(2))+0.7;end% F35function o = F35(x)o = 0;for i = 1:floor(size(x, 2)/4) o = o+(x(4*i-3)+10*x(4*i-2))^2+5*(x(4*i-1)-x(4*i))^2+(x(4*i-2)-2*x(4*i-1))^4+10*(x(4*i-3)-x(4*i))^4;endendfunction o=Ufun(x,a,k,m)o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a));end
⛄ 运行结果
⛄ 参考文献
[1]张海林,陈泯融.基于混合策略的改进哈里斯鹰优化算法[J].计算机系统应用, 2023, 32(1):166-178.
