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这篇文章主要介绍“基于Matlab怎么实现鲸鱼优化算法”，在日常操作中，相信很多人在基于Matlab怎么实现鲸鱼优化算法问题上存在疑惑，小编查阅了各式资料，整理出简单好用的操作方法，希望对大家解答”基于Matlab怎么实现鲸鱼优化算法”的疑惑有所帮助！接下来，请跟着小编一起来学习吧！
鲸鱼优化算法(WOA)是澳大利亚学者Mirjaili等于2016年提出的群体智能优化算法，根据座头鲸的捕猎行为实现优化搜索的目的。其中，每个鲸鱼可以看作一个粒子，每个粒子作为不同的决策变量。WOA的实现过程主要包括包围猎物、螺旋狩猎和随机搜索3个阶段，其数学模型如下：
clear all
clc
SearchAgents_no=30;
Function_name='F1'; % Name of the test function that can be from F1 to F23 (Table 1,2,3 in the paper)
% Max_iteration=500; % Maximum numbef of iterations
Max_iteration=500;
% Load details of the selected benchmark function
[lb,ub,dim,fobj]=Get_Functions_details(Function_name);
[Best_score,Best_pos,WOABAT_cg_curve]=WOABAT(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);
figure('Position',[269 240 660 290])
%Draw search space
subplot(1,2,1);
func_plot(Function_name);
title('Parameter space')
xlabel('x_1');
ylabel('x_2');
zlabel([Function_name,'( x_1 , x_2 )'])
%Draw objective space
subplot(1,2,2);
semilogy(WOABAT_cg_curve,'Color','r')
title('Objective space')
xlabel('Iteration');
ylabel('Best score obtained so far');
axis tight
grid on
box on
legend('WOABAT')
%display(['The best solution obtained by WOABAT is : ', num2str(Best_pos)]);
display(['The best optimal value of the objective funciton found by WOA is : ', num2str(Best_score)]);
%display( num2str(Best_score));% The Whale Optimization Algorithm function [Leader_score,Leader_pos,Convergence_curve]=WOABAT(SearchAgents_no,Max_iter,lb,ub,dim,fobj) % initialize position vector and score for the leader Leader_pos=zeros(1,dim); Leader_score=inf; %change this to -inf for maximization problems %Initialize the positions of search agents Positions=initialization(SearchAgents_no,dim,ub,lb); Convergence_curve=zeros(1,Max_iter); %bat algorithm addition Qmin=0; % Frequency minimum Qmax=2; % Frequency maximum Q=zeros(SearchAgents_no,1); % Frequency v=zeros(SearchAgents_no,dim); % Velocities r=0.5; A1=0.5; t=0;% Loop counter % summ=0; % Main loop while t<Max_iter for i=1:size(Positions,1) % Return back the search agents that go beyond the boundaries of the search space Flag4ub=Positions(i,:)>ub; Flag4lb=Positions(i,:)<lb; Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb; % Calculate objective function for each search agent fitness=fobj(Positions(i,:)); % Update the leader if fitness<Leader_score % Change this to > for maximization problem Leader_score=fitness; % Update alpha Leader_pos=Positions(i,:); end end a=2-t*((2)/Max_iter); % a decreases linearly fron 2 to 0 in Eq. (2.3) % a2 linearly dicreases from -1 to -2 to calculate t in Eq. (3.12) a2=-1+t*((-1)/Max_iter); % Update the Position of search agents for i=1:size(Positions,1) r1=rand(); % r1 is a random number in [0,1] r2=rand(); % r2 is a random number in [0,1] A=2*a*r1-a; C=2*r2; b=1; l=(a2-1)*rand+1; p = rand(); for j=1:size(Positions,2) if p<0.5 if abs(A)>=1 rand_leader_index = floor(SearchAgents_no*rand()+1); X_rand = Positions(rand_leader_index, :); Q(i)=Qmin+(Qmin-Qmax)*rand; v(i,:)=v(i,j)+(X_rand(j)-Leader_pos(j))*Q(i); z(i,:)= Positions(i,:)+ v(i,:); %%%% problem if rand>r % The factor 0.001 limits the step sizes of random walks z (i,:)=Leader_pos(j)+0.001*randn(1,dim); end % Evaluate new solutions Fnew=fobj(z(i,:)); % Update if the solution improves, or not too loud if (Fnew<=fitness) && (rand<A1) Positions(i,:)=z(i,:); fitness=Fnew; end elseif abs(A)<1 Q(i)=Qmin+(Qmin-Qmax)*rand; v(i,:)=v(i,j)+(Positions(i,:)-Leader_pos(j))*Q(i); z(i,:)= Positions(i,:)+ v(i,:); %%%% problem if rand>r % The factor 0.001 limits the step sizes of random walks z (i,:)=Leader_pos(j)+0.001*randn(1,dim); end % Evaluate new solutions Fnew=fobj(z(i,:)); % Update if the solution improves, or not too loud if (Fnew<=fitness) && (rand<A1) Positions(i,:)=z(i,:); fitness=Fnew; end end elseif p>=0.5 distance2Leader=abs(Leader_pos(j)-Positions(i,j)); % Eq. (2.5) Positions(i,j)=distance2Leader*exp(b.*l).*cos(l.*2*pi)+Leader_pos(j); end end end t=t+1; Convergence_curve(t)=Leader_score; [t Leader_score] end
% This function draw the benchmark functions function func_plot(func_name) [lb,ub,dim,fobj]=Get_Functions_details(func_name); switch func_name case 'F1' x=-100:2:100; y=x; %[-100,100] case 'F2' x=-100:2:100; y=x; %[-10,10] case 'F3' x=-100:2:100; y=x; %[-100,100] case 'F4' x=-100:2:100; y=x; %[-100,100] case 'F5' x=-200:2:200; y=x; %[-5,5] case 'F6' x=-100:2:100; y=x; %[-100,100] case 'F7' x=-1:0.03:1; y=x %[-1,1] case 'F8' x=-500:10:500;y=x; %[-500,500] case 'F9' x=-5:0.1:5; y=x; %[-5,5] case 'F10' x=-20:0.5:20; y=x;%[-500,500] case 'F11' x=-500:10:500; y=x;%[-0.5,0.5] case 'F12' x=-10:0.1:10; y=x;%[-pi,pi] case 'F13' x=-5:0.08:5; y=x;%[-3,1] case 'F14' x=-100:2:100; y=x;%[-100,100] case 'F15' x=-5:0.1:5; y=x;%[-5,5] case 'F16' x=-1:0.01:1; y=x;%[-5,5] case 'F17' x=-5:0.1:5; y=x;%[-5,5] case 'F18' x=-5:0.06:5; y=x;%[-5,5] case 'F19' x=-5:0.1:5; y=x;%[-5,5] case 'F20' x=-5:0.1:5; y=x;%[-5,5] case 'F21' x=-5:0.1:5; y=x;%[-5,5] case 'F22' x=-5:0.1:5; y=x;%[-5,5] case 'F23' x=-5:0.1:5; y=x;%[-5,5] end L=length(x); f=[]; for i=1:L for j=1:L if strcmp(func_name,'F15')==0 && strcmp(func_name,'F19')==0 && strcmp(func_name,'F20')==0 && strcmp(func_name,'F21')==0 && strcmp(func_name,'F22')==0 && strcmp(func_name,'F23')==0 f(i,j)=fobj([x(i),y(j)]); end if strcmp(func_name,'F15')==1 f(i,j)=fobj([x(i),y(j),0,0]); end if strcmp(func_name,'F19')==1 f(i,j)=fobj([x(i),y(j),0]); end if strcmp(func_name,'F20')==1 f(i,j)=fobj([x(i),y(j),0,0,0,0]); end if strcmp(func_name,'F21')==1 || strcmp(func_name,'F22')==1 ||strcmp(func_name,'F23')==1 f(i,j)=fobj([x(i),y(j),0,0]); end end end surfc(x,y,f,'LineStyle','none'); end
function [lb,ub,dim,fobj] = Get_Functions_details(F) switch F case 'F1' fobj = @F1; lb=-100; ub=100; % dim=30; 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=30; 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
% This function initialize the first population of search agents function Positions=initialization(SearchAgents_no,dim,ub,lb) Boundary_no= size(ub,2); % numnber of boundaries % If the boundaries of all variables are equal and user enter a single % number for both ub and lb if Boundary_no==1 Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb; end % If each variable has a different lb and ub if Boundary_no>1 for i=1:dim ub_i=ub(i); lb_i=lb(i); Positions(:,i)=rand(SearchAgents_no,1).*(ub_i-lb_i)+lb_i; end end
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