基于Matlab怎么实现鲸鱼优化算法

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！

1.鲸鱼优化算法建模

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：

1.1 包围猎物

1.2 螺旋狩猎

1.3 搜索猎物 

1.4 算法流程图

2.Matlab代码实现 

2.1 结果

2.2 代码

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 iterationsMax_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 AlGorithmfunction [Leader_score,Leader_pos,Convergence_curve]=WOABAT(SearchAgents_no,Max_iter,lb,ub,dim,fobj) % initialize position vector and score for the leaderLeader_pos=zeros(1,dim);Leader_score=inf; %change this to -inf for maximization problems  %Initialize the positions of search agentsPositions=initialization(SearchAgents_no,dim,ub,lb); Convergence_curve=zeros(1,Max_iter);  %bat algorithm additionQmin=0;         % Frequency minimuMQmax=2;         % Frequency maximumQ=zeros(SearchAgents_no,1);   % Frequencyv=zeros(SearchAgents_no,dim);   % Velocitiesr=0.5;A1=0.5;t=0;% Loop counter% summ=0;% Main loopwhile 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 functionsfunction 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              endend 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;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)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);endo=(1/500+sum(1./([1:25]+bS))).^(-1);end% F15function 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% F16function 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% F17function 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% F18function 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% F19function 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))));endend% F20function 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))));endend% F21function 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);endend % 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);endend% F23function 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);endend 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 agentsfunction 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 lbif Boundary_no==1    Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb;end % If each variable has a different lb and ubif 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;    endend

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