混合策略改进的哈里斯鹰优化算法-附matlab代码

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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;end​end​% F1​function o = F1(x)o=sum(x.^2);end​% F2​function 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​% F3​function o = F3(x)dim=size(x,2);o=0;for i=1:dim    o=o+sum(x(1:i))^2;endend​% F4​function o = F4(x)o=max(abs(x));end​% F5​function 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​% F6​function o = F6(x)o=sum(abs((x+.5)).^2);end​% F7​function o = F7(x)dim=size(x,2);o=sum([1:dim].*(x.^4))+rand;end​% F8​function o = F8(x)dim = size(x, 2);o = sum([1:dim].*(x.^2));end​% F9​function o = F9(x)o=sum(abs(x.*sin(x)+0.1*x));end​% F10​function o = F10(x)dim = size(x, 2);o = 0;for i = 1:dim    o = o+abs(x(i))^(i+1);endend​% F11​function 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​% F12​function 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​​% F13​function o = F13(x)o=sum(-x.*sin(sqrt(abs(x))));end​% F14​function o = F14(x)dim=size(x,2);o=sum(x.^2-10*cos(2*pi.*x))+10*dim;end​% F15​function 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​% F16​function o = F16(x)dim=size(x,2);o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1;end​% F17​function 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​% F18​function 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​% F19​function o = F19(x)o = 418.9829*size(x, 2)-sum(x.*sin(sqrt(abs(x))));end​% F20​function 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​% F21​function o = F21(x)o = -(1+cos(12*sqrt(x(1)^2+x(2)^2)))/(0.5*(x(1)^2+x(2)^2)+2);end​% F22​function o = F22(x)o = 0.26*(x(1)^2+x(2)^2)-0.48*x(1)*x(2);end​% F23​function 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% F24​function 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​% F25​function 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​% F26​function 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​% F27​function 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​% F28​function 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​% F29​function 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​% F30​function 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​% F31​function 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​% F32​function 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​% F33​function 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​% F34​function 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​% F35​function 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;endend​function 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.

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