遗传算法求解函数最大值(matlab).doc

遗传算法求解函数F(x1，x2)=100*(x1^2-x2)^2+(1-x1)^2;
的最大值(MATLAB)

%Generic Algorithm for function f(x1,x2) optimum （最大值）
clear all;
close all;

%Parameters
Size=80;
G=100;
CodeL=10;

umax=2.048;
umin=-2.048;

E=round(rand(Size,2*CodeL)); %Initial Code

%Main Program
for k=1:1:G
time(k)=k;

for s=1:1:Size
m=E(s,:);
y1=0;y2=0;

%Uncoding
m1=m(1:1:CodeL);
for i=1:1:CodeL
y1=y1+m1(i)*2^(i-1);
end
x1=(umax-umin)*y1/1023+umin;
m2=m(CodeL+1:1:2*CodeL);
for i=1:1:CodeL
y2=y2+m2(i)*2^(i-1);
end
x2=(umax-umin)*y2/1023+umin;

F(s)=100*(x1^2-x2)^2+(1-x1)^2;
end

Ji=1./(F+1);
%****** Step 1 : Evaluate BestJ ******
BestJ(k)=min(Ji);

fi=F; %Fitness Function
[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(k)=Bestfi;

%****** 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 (取整)

kk=1;
for i=1:1:Size
for j=1:1:fi_S(i) %Select and Reproduce
TempE(kk,:)=E(Indexfi(i),:);
kk=kk+1; %kk is used to reproduce
end
end

%************ Step 3 : Crossover Operation ************
pc=0.60;
n=ceil(20*rand);
for i=1:2:(Size-1)
temp=rand;
if pc>temp %Crossover Condition
for j=n:1:20
TempE(i,j)=E(i+1,j);
TempE(i+1,j)=E(i,j);
end
end
end
TempE(Size,:)=BestS;
E=TempE;

%************ Step 4: Mutation Operation **************
%pm=0.001;
%pm=0.001-[1:1:Size]*(0.001)/Size; %Bigger fi, smaller Pm
%pm=0.0; %No mutation
pm=0.1; %Big mutation

for i=1:1:Size
for j=1:1:2*CodeL
temp=rand;
if pm>temp %Mutation Condition
if TempE(i,j)==0
TempE(i,j)=1;
else
TempE(i,j)=0;
end
end
end
end

%Guarantee TempPop(30,:) is the code belong to the best individual(max(fi))
TempE(Size,:)=BestS;
E=TempE;
end

Max_Value=Bestfi
BestS
x1
x2
figure(1);
plot(time,BestJ);
xlabel('Times');ylabel('Best J');
figure(2);
plot(time,bfi);
xlabel('times');ylabel('Best F');

轐行绒果︚

Map_Falue =

3.9059e+ 03

BestS =
0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 Р0

ɸ1 =
 -2&0480
x2 =

-2.0080