WOA.rar_WOA_algorithm_promisedpxe

%_________________________________________________________________________% % Whale Optimization Algorithm (WOA) source codes demo 1.0 % % % % Developed in MATLAB R2011b(7.13) % % % % Author and programmer: Seyedali Mirjalili % % % % e-Mail: [email protected] % % [email protected] % % % % Homepage: http://www.alimirjalili.com % % % % Main paper: S. Mirjalili, A. Lewis % % The Whale Optimization Algorithm, % % Advances in Engineering Software , in press, % % DOI: http://dx.doi.org/10.1016/j.advengsoft.2016.01.008 % % % %_________________________________________________________________________% % This function containts full information and implementations of the benchmark % functions in Table 1, Table 2, and Table 3 in the paper % lb is the lower bound: lb=[lb_1,lb_2,...,lb_d] % up is the uppper bound: ub=[ub_1,ub_2,...,ub_d] % dim is the number of variables (dimension of the problem) function [lb,ub,dim,fobj] = Get_Functions_details(F) switch F case 'F1' fobj = @F1; lb=-100; ub=100; dim=30; case 'F2' fobj = @F2; lb=-10; ub=10; dim=30; case 'F3' fobj = @F3; lb=-100; ub=100; dim=30; case 'F4' fobj = @F4; lb=-100; ub=100; 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=-500; ub=500; dim=30; case 'F9' fobj = @F9; lb=-5.12; ub=5.12; dim=30; case 'F10' fobj = @F10; lb=-32; ub=32; dim=30; case 'F11' fobj = @F11; lb=-600; ub=600; dim=30; case 'F12' fobj = @F12; lb=-50; ub=50; dim=30; case 'F13' fobj = @F13; lb=-50; ub=50; dim=100; case 'F14' fobj = @F14; lb=-65.536; ub=65.536; dim=2; case 'F15' fobj = @F15; lb=-5; ub=5; dim=4; case 'F16' fobj = @F16; lb=-5; ub=5; dim=2; case 'F17' fobj = @F17; lb=[-5,0]; ub=[10,15]; dim=2; case 'F18' fobj = @F18; lb=-2; ub=2; dim=2; case 'F19' fobj = @F19; lb=0; ub=1; dim=3; case 'F20' fobj = @F20; lb=0; ub=1; dim=6; case 'F21' fobj = @F21; lb=0; ub=10; dim=4; case 'F22' fobj = @F22; lb=0; ub=10; dim=4; case 'F23' fobj = @F23; lb=0; ub=10; dim=4; end end % F1 function o = F1(x) o=sum(x.^2); end % F2 function o = F2(x) o=sum(abs(x))+prod(abs(x)); end % F3 function o = F3(x) dim=size(x,2); o=0; for i=1:dim o=o+sum(x(1:i))^2; end end % 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) o=sum(-x.*sin(sqrt(abs(x)))); end % F9 function o = F9(x) dim=size(x,2); o=sum(x.^2-10*cos(2*pi.*x))+10*dim; end % F10 function o = F10(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 % F11 function o = F11(x) dim=size(x,2); o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1; end % F12 function o = F12(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 % F13 function o = F13(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 % F14 function o = 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); end o=(1/500+sum(1./([1:25]+bS))).^(-1); end % F15 function o = 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; o=sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2); end % F16 function o = F16(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 % F17 function o = F17(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 % F18 function o = F18(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 % F19 function o = 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]; o=0; for i=1:4 o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2)))); end end % F20 function o = 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]; o=0; for i=1:4 o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2)))); end end % F21 function o = 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]; o=0; for i=1:5 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end % F22 function o = 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]; o=0; for i=1:7 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end % F23 function o = 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]; o=0; for i=1:10 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end function o=Ufun(x,a,k,m) o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a)); end