学步园

参考：《智能控制》作者刘金琨，电子工业出版社

利用遗传算法求取Rosenbrock函数的最大值

该函数有两个局部极大值点，分别是f(2.048,-2.048)=3897.7342,  f(-2.048,-2.048)=3905.9262;其中后者为全局最大点

Matlab程序：

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

%Parameters
Size=80; % 80个群
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;
    %****** 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****** 选择算子
    fi_sum=sum(fi);
    fi_Size=(Oderfi/fi_sum)*Size;

    fi_S=floor(fi_Size);        %Selecting Bigger fi value

    kk=1;                       %选择贡献比较大的
    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 ************ 交叉算子
    pc=0.60;
    n=ceil(20*rand);% rand，随时变化的单个数据
    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); %对没有交叉的某个群体，matlab语法设置该行数据为0
                TempE(i+1,j)=E(i,j);
            end
        end
    end
    TempE(Size,:)=BestS; %保留最好的一个
    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; % 保留最好的
    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');