這篇文章主要介紹“基于Matlab怎么實現鯨魚優化算法”，在日常操作中，相信很多人在基于Matlab怎么實現鯨魚優化算法問題上存在疑惑，小編查閱了各式資料，整理出簡單好用的操作方法，希望對大家解答”基于Matlab怎么實現鯨魚優化算法”的疑惑有所幫助！接下來，請跟著小編一起來學習吧！

1.鯨魚優化算法建模

鯨魚優化算法(WOA)是澳大利亞學者Mirjaili等于2016年提出的群體智能優化算法，根據座頭鯨的捕獵行為實現優化搜索的目的。其中，每個鯨魚可以看作一個粒子，每個粒子作為不同的決策變量。WOA的實現過程主要包括包圍獵物、螺旋狩獵和隨機搜索3個階段，其數學模型如下：

1.1 包圍獵物

1.2螺旋狩獵

1.3搜索獵物

1.4 算法流程圖

2.Matlab代碼實現

2.1 結果

2.2 代碼

clearall
clc
SearchAgents_no=30;
Function_name='F1';%NameofthetestfunctionthatcanbefromF1toF23(Table1,2,3inthepaper)
%Max_iteration=500;%Maximumnumbefofiterations
Max_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])
%Drawsearchspace
subplot(1,2,1);
func_plot(Function_name);
title('Parameterspace')
xlabel('x_1');
ylabel('x_2');
zlabel([Function_name,'(x_1,x_2)'])

%Drawobjectivespace
subplot(1,2,2);
semilogy(WOABAT_cg_curve,'Color','r')
title('Objectivespace')
xlabel('Iteration');
ylabel('Bestscoreobtainedsofar');

axistight
gridon
boxon
legend('WOABAT')
%display(['ThebestsolutionobtainedbyWOABATis:',num2str(Best_pos)]);
display(['ThebestoptimalvalueoftheobjectivefuncitonfoundbyWOAis:',num2str(Best_score)]);

%display(num2str(Best_score));

%TheWhaleOptimizationAlgorithm
function[Leader_score,Leader_pos,Convergence_curve]=WOABAT(SearchAgents_no,Max_iter,lb,ub,dim,fobj)

%initializepositionvectorandscorefortheleader
Leader_pos=zeros(1,dim);
Leader_score=inf;%changethisto-infformaximizationproblems


%Initializethepositionsofsearchagents
Positions=initialization(SearchAgents_no,dim,ub,lb);

Convergence_curve=zeros(1,Max_iter);


%batalgorithmaddition
Qmin=0;%Frequencyminimum
Qmax=2;%Frequencymaximum
Q=zeros(SearchAgents_no,1);%Frequency
v=zeros(SearchAgents_no,dim);%Velocities
r=0.5;
A1=0.5;
t=0;%Loopcounter
%summ=0;
%Mainloop
whilet<Max_iter
fori=1:size(Positions,1)

%Returnbackthesearchagentsthatgobeyondtheboundariesofthesearchspace
Flag4ub=Positions(i,:)>ub;
Flag4lb=Positions(i,:)<lb;
Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;

%Calculateobjectivefunctionforeachsearchagent
fitness=fobj(Positions(i,:));

%Updatetheleader
iffitness<Leader_score%Changethisto>formaximizationproblem
Leader_score=fitness;%Updatealpha
Leader_pos=Positions(i,:);
end

end

a=2-t*((2)/Max_iter);%adecreaseslinearlyfron2to0inEq.(2.3)

%a2linearlydicreasesfrom-1to-2tocalculatetinEq.(3.12)
a2=-1+t*((-1)/Max_iter);

%UpdatethePositionofsearchagents
fori=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<0.5

ifabs(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
ifrand>r
%Thefactor0.001limitsthestepsizesofrandomwalks
z(i,:)=Leader_pos(j)+0.001*randn(1,dim);
end
%Evaluatenewsolutions
Fnew=fobj(z(i,:));
%Updateifthesolutionimproves,ornottooloud
if(Fnew<=fitness)&&(rand<A1)
Positions(i,:)=z(i,:);
fitness=Fnew;
end

elseifabs(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
ifrand>r
%Thefactor0.001limitsthestepsizesofrandomwalks
z(i,:)=Leader_pos(j)+0.001*randn(1,dim);
end
%Evaluatenewsolutions
Fnew=fobj(z(i,:));
%Updateifthesolutionimproves,ornottooloud
if(Fnew<=fitness)&&(rand<A1)
Positions(i,:)=z(i,:);
fitness=Fnew;
end
end

elseifp>=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;
[tLeader_score]


end

%Thisfunctiondrawthebenchmarkfunctions
functionfunc_plot(func_name)

[lb,ub,dim,fobj]=Get_Functions_details(func_name);

switchfunc_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=[];

fori=1:L
forj=1:L
ifstrcmp(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
ifstrcmp(func_name,'F15')==1
f(i,j)=fobj([x(i),y(j),0,0]);
end
ifstrcmp(func_name,'F19')==1
f(i,j)=fobj([x(i),y(j),0]);
end
ifstrcmp(func_name,'F20')==1
f(i,j)=fobj([x(i),y(j),0,0,0,0]);
end
ifstrcmp(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)


switchF
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

functiono=F1(x)
o=sum(x.^2);
end

%F2

functiono=F2(x)
o=sum(abs(x))+prod(abs(x));
end

%F3

functiono=F3(x)
dim=size(x,2);
o=0;
fori=1:dim
o=o+sum(x(1:i))^2;
end
end

%F4

functiono=F4(x)
o=max(abs(x));
end

%F5

functiono=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

functiono=F6(x)
o=sum(abs((x+.5)).^2);
end

%F7

functiono=F7(x)
dim=size(x,2);
o=sum([1:dim].*(x.^4))+rand;
end

%F8

functiono=F8(x)
o=sum(-x.*sin(sqrt(abs(x))));
end

%F9

functiono=F9(x)
dim=size(x,2);
o=sum(x.^2-10*cos(2*pi.*x))+10*dim;
end

%F10

functiono=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

functiono=F11(x)
dim=size(x,2);
o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1;
end

%F12

functiono=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

functiono=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

functiono=F14(x)
aS=[-32-1601632-32-1601632-32-1601632-32-1601632-32-1601632;,...
-32-32-32-32-32-16-16-16-16-160000016161616163232323232];

forj=1:25
bS(j)=sum((x'-aS(:,j)).^6);
end
o=(1/500+sum(1./([1:25]+bS))).^(-1);
end
%F15
functiono=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
%F16
functiono=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
functiono=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
functiono=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
functiono=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=1:4
o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
end
end
%F20
functiono=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=1:4
o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
end
end
%F21
functiono=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=1:5
o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
end
end

%F22

functiono=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=1:7
o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
end
end
%F23
functiono=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=1:10
o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
end
end

functiono=Ufun(x,a,k,m)
o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a));
end

%Thisfunctioninitializethefirstpopulationofsearchagents
functionPositions=initialization(SearchAgents_no,dim,ub,lb)

Boundary_no=size(ub,2);%numnberofboundaries

%Iftheboundariesofallvariablesareequalanduserenterasingle
%numberforbothubandlb
ifBoundary_no==1
Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb;
end

%Ifeachvariablehasadifferentlbandub
ifBoundary_no>1
fori=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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