遗传算法十进制编码求函数F(i)=100*(x1^2-x2)^2+(1-x1)^2;极大值程序
%Generic Algorithm for function f(x1,x2) optimum
clear all;
close all;
Size=500;
CodeL=2;
MinX(1)=-2.048;
MaxX(1)=2.048;
MinX(2)=-2.048;
MaxX(2)=2.048;
E(:,1)=MinX(1)+(MaxX(1)-MinX(1))*rand(Size,1);
E(:,2)=MinX(2)+(MaxX(2)-MinX(2))*rand(Size,1);
G=200;
BsJ=0;
%*************** Start Running ***************
for kg=1:1:G
time(kg)=kg;
%****** Step 1 : Evaluate BestJ ******
for i=1:1:Size
xi=E(i,:);
x1=xi(1);
x2=xi(2);
F(i)=100*(x1^2-x2)^2+(1-x1)^2;
Ji=1./F;
BsJi(i)=min(Ji);
end
[OderJi,IndexJi]=sort(BsJi);
BestJ(kg)=OderJi(1);
BJ=BestJ(kg);
Ji=BsJi+1e-10; %Avoiding deviding zero
fi=F;
[Oderfi,Indexfi]=sort(fi); %Arranging fi small to bigger
Bestfi=Oderfi(Size); %Let Bestfi=max(fi)
BestS=E(Indexfi(Size),:); %Let BestS=E(m), m is the Indexfi belong to max(fi)
bfi(kg)=Bestfi;
kg
BestS
%****** Step 2 : Select and Reproduct Operation******
fi_sum=sum(fi);
fi_Size=(Oderfi/fi_sum)*Size;
fi_S=floor(fi_Size); % Selecting Bigger fi value
r=Size-sum(fi_S);
Rest=fi_Size-fi_S;
[RestValue,Index]=sort(Rest);
for i=Size:-1:Size-r+1
fi_S(Index(i))=fi_S(Index(i))+1; % Adding rest to equal Size
end
k=1;
for i=Size:-1:1 % Select the Sizeth and Reproduce firstly
for j=1:1:fi_S(i)
TempE(k,:)=E(Indexfi(i),:); % Select and Reproduce
k=k+1; % k is used to reproduce
end
end
%************ Step 3 : Crossover Operation ************
Pc=0.90;
for i=1:2:(Size-1)
temp=rand;
if Pc>temp %Crossover Condition
alfa=rand;
TempE(i,:)=alfa*E(i+1,:)+(1-alfa)*E(i,:);
TempE(i+1,:)=alfa*E(i,:)+(1-alfa)*E(i+1,:);
end
end
TempE(Size,:)=BestS;
E=TempE;
%************ Step 4: Mutation Operation **************
Pm=0.10-[1:1:Size]*(0.01)/Size; %Bigger fi,smaller Pm
Pm_rand=rand(Size,CodeL);
Mean=(MaxX + MinX)/2;
Dif=(MaxX-MinX);
for i=1:1:Size
for j=1:1:CodeL
if Pm(i)>Pm_rand(i,j) %Mutation Condition
TempE(i,j)=Mean(j)+Dif(j)*(rand-0.5);
end
end
end
%Guarantee TempE(Size,:) belong to the best individual
TempE(Size,:)=BestS;
E=TempE;
end
BestS
Bestfi
figure(1);
plot(time,BestJ,'k');
xlabel('Times');ylabel('Best J');
figure(2);
plot(time,bfi,'k');
xlabel('times');ylabel('Best F');
