基于Matlab怎么实现鲸鱼优化算法(matlab,开发技术)

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

clearallclcSearchAgents_no=30;Function_name='F1';%NameofthetestfunctionthatcanbefromF1toF23(Table1,2,3inthepaper)%Max_iteration=500;%MaximumnumbefofiterationsMax_iteration=500;%Loaddetailsoftheselectedbenchmarkfunction[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',[269240660290])%Drawsearchspacesubplot(1,2,1);func_plot(Function_name);title('Parameterspace')xlabel('x_1');ylabel('x_2');zlabel([Function_name,'(x_1,x_2)'])%Drawobjectivespacesubplot(1,2,2);semilogy(WOABAT_cg_curve,'Color','r')title('Objectivespace')xlabel('Iteration');ylabel('Bestscoreobtainedsofar');axistightgridonboxonlegend('WOABAT')%display(['ThebestsolutionobtainedbyWOABATis:',num2str(Best_pos)]);display(['ThebestoptimalvalueoftheobjectivefuncitonfoundbyWOAis:',num2str(Best_score)]);%display(num2str(Best_score));

%TheWhaleOptimizationAlgorithmfunction[Leader_score,Leader_pos,Convergence_curve]=WOABAT(SearchAgents_no,Max_iter,lb,ub,dim,fobj)%initializepositionvectorandscorefortheleaderLeader_pos=zeros(1,dim);Leader_score=inf;%changethisto-infformaximizationproblems%InitializethepositionsofsearchagentsPositions=initialization(SearchAgents_no,dim,ub,lb);Convergence_curve=zeros(1,Max_iter);%batalgorithmadditionQmin=0;%FrequencyminimumQmax=2;%FrequencymaximumQ=zeros(SearchAgents_no,1);%Frequencyv=zeros(SearchAgents_no,dim);%Velocitiesr=0.5;A1=0.5;t=0;%Loopcounter%summ=0;%Mainloopwhilet<Max_iterfori=1:size(Positions,1)%ReturnbackthesearchagentsthatgobeyondtheboundariesofthesearchspaceFlag4ub=Positions(i,:)>ub;Flag4lb=Positions(i,:)<lb;Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;%Calculateobjectivefunctionforeachsearchagentfitness=fobj(Positions(i,:));%Updatetheleaderiffitness<Leader_score%Changethisto>formaximizationproblemLeader_score=fitness;%UpdatealphaLeader_pos=Positions(i,:);endenda=2-t*((2)/Max_iter);%adecreaseslinearlyfron2to0inEq.(2.3)%a2linearlydicreasesfrom-1to-2tocalculatetinEq.(3.12)a2=-1+t*((-1)/Max_iter);%UpdatethePositionofsearchagentsfori=1:size(Positions,1)r1=rand();%r1isarandomnumberin[0,1]r2=rand();%r2isarandomnumberin[0,1]A=2*a*r1-a;C=2*r2;b=1;l=(a2-1)*rand+1;p=rand();forj=1:size(Positions,2)ifp<0.5ifabs(A)>=1rand_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,:);%%%%problemifrand>r%Thefactor0.001limitsthestepsizesofrandomwalksz(i,:)=Leader_pos(j)+0.001*randn(1,dim);end%EvaluatenewsolutionsFnew=fobj(z(i,:));%Updateifthesolutionimproves,ornottooloudif(Fnew<=fitness)&&(rand<A1)Positions(i,:)=z(i,:);fitness=Fnew;endelseifabs(A)<1Q(i)=Qmin+(Qmin-Qmax)*rand;v(i,:)=v(i,j)+(Positions(i,:)-Leader_pos(j))*Q(i);z(i,:)=Positions(i,:)+v(i,:);%%%%problemifrand>r%Thefactor0.001limitsthestepsizesofrandomwalksz(i,:)=Leader_pos(j)+0.001*randn(1,dim);end%EvaluatenewsolutionsFnew=fobj(z(i,:));%Updateifthesolutionimproves,ornottooloudif(Fnew<=fitness)&&(rand<A1)Positions(i,:)=z(i,:);fitness=Fnew;endendelseifp>=0.5distance2Leader=abs(Leader_pos(j)-Positions(i,j));%Eq.(2.5)Positions(i,j)=distance2Leader*exp(b.*l).*cos(l.*2*pi)+Leader_pos(j);endendendt=t+1;Convergence_curve(t)=Leader_score;[tLeader_score]end

%Thisfunctiondrawthebenchmarkfunctionsfunctionfunc_plot(func_name)[lb,ub,dim,fobj]=Get_Functions_details(func_name);switchfunc_namecase'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]endL=length(x);f=[];fori=1:Lforj=1:Lifstrcmp(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')==0f(i,j)=fobj([x(i),y(j)]);endifstrcmp(func_name,'F15')==1f(i,j)=fobj([x(i),y(j),0,0]);endifstrcmp(func_name,'F19')==1f(i,j)=fobj([x(i),y(j),0]);endifstrcmp(func_name,'F20')==1f(i,j)=fobj([x(i),y(j),0,0,0,0]);endifstrcmp(func_name,'F21')==1||strcmp(func_name,'F22')==1||strcmp(func_name,'F23')==1f(i,j)=fobj([x(i),y(j),0,0]);endendendsurfc(x,y,f,'LineStyle','none');end

function[lb,ub,dim,fobj]=Get_Functions_details(F)switchFcase'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;endend%F1functiono=F1(x)o=sum(x.^2);end%F2functiono=F2(x)o=sum(abs(x))+prod(abs(x));end%F3functiono=F3(x)dim=size(x,2);o=0;fori=1:dimo=o+sum(x(1:i))^2;endend%F4functiono=F4(x)o=max(abs(x));end%F5functiono=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%F6functiono=F6(x)o=sum(abs((x+.5)).^2);end%F7functiono=F7(x)dim=size(x,2);o=sum([1:dim].*(x.^4))+rand;end%F8functiono=F8(x)o=sum(-x.*sin(sqrt(abs(x))));end%F9functiono=F9(x)dim=size(x,2);o=sum(x.^2-10*cos(2*pi.*x))+10*dim;end%F10functiono=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%F11functiono=F11(x)dim=size(x,2);o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1;end%F12functiono=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%F13functiono=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%F14functiono=F14(x)aS=[-32-1601632-32-1601632-32-1601632-32-1601632-32-1601632;,...-32-32-32-32-32-16-16-16-16-160000016161616163232323232];forj=1:25bS(j)=sum((x'-aS(:,j)).^6);endo=(1/500+sum(1./([1:25]+bS))).^(-1);end%F15functiono=F15(x)aK=[.1957.1947.1735.16.0844.0627.0456.0342.0323.0235.0246];bK=[.25.51246810121416];bK=1./bK;o=sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2);end%F16functiono=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%F17functiono=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%F18functiono=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%F19functiono=F19(x)aH=[31030;.11035;31030;.11035];cH=[11.233.2];pH=[.3689.117.2673;.4699.4387.747;.1091.8732.5547;.03815.5743.8828];o=0;fori=1:4o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));endend%F20functiono=F20(x)aH=[103173.51.78;.051017.1814;33.51.710178;178.0510.114];cH=[11.233.2];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;fori=1:4o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));endend%F21functiono=F21(x)aSH=[4444;1111;8888;6666;3737;2929;5533;8181;6262;73.673.6];cSH=[.1.2.2.4.4.6.3.7.5.5];o=0;fori=1:5o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);endend%F22functiono=F22(x)aSH=[4444;1111;8888;6666;3737;2929;5533;8181;6262;73.673.6];cSH=[.1.2.2.4.4.6.3.7.5.5];o=0;fori=1:7o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);endend%F23functiono=F23(x)aSH=[4444;1111;8888;6666;3737;2929;5533;8181;6262;73.673.6];cSH=[.1.2.2.4.4.6.3.7.5.5];o=0;fori=1:10o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);endendfunctiono=Ufun(x,a,k,m)o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a));end

%ThisfunctioninitializethefirstpopulationofsearchagentsfunctionPositions=initialization(SearchAgents_no,dim,ub,lb)Boundary_no=size(ub,2);%numnberofboundaries%Iftheboundariesofallvariablesareequalanduserenterasingle%numberforbothubandlbifBoundary_no==1Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb;end%IfeachvariablehasadifferentlbandubifBoundary_no>1fori=1:dimub_i=ub(i);lb_i=lb(i);Positions(:,i)=rand(SearchAgents_no,1).*(ub_i-lb_i)+lb_i;endend