实数编码的遗传算法与MATLAB

（一）函数示例

Z=x.^2-10*cos(2*pi*x)+10+y.^2-10*cos(2*pi*y)+10

（二）MATLAB的实现
1）GAss(主函数)

clc
clear
x=-5.12:0.01:5.12;
y=-5.12:0.01:5.12;
[X,Y]=meshgrid(x,y);
Z=X.^2-10*cos(2*pi*X)+10+Y.^2-10*cos(2*pi*Y)+10;
mesh(X,Y,Z)

%%%%%%%%%%%%%%%初始化种群%%%%%%%%%%%
N=50;dim=2;B=5.12;Pc=0.75;pm=0.3
Po=-B+rand(N,2)*2*B;
%%%%%%%%%%%%函数评价%%%%%%%%%%%%%%%
for it=1:10
    for i=1:N
        fit(i)=GAmb(Po(i,1),Po(i,2));
    end
    [ymax,ind1]=max(fit);
    figure(1)
    set(gca,'nextplot','replace');
    mesh(X,Y,Z)
    hold on
    plot3(Po(:,1),Po(:,2),fit,'b*')
    plot3(Po(ind1,1),Po(ind1,2),fit(ind1),'mo')
    %%%%%%%%%%%%%%选择%%%%%%%%%%%%%%%
    p=fit/sum(fit); %%计算比例概率
    Lp(1)=fit(1);
    for i=2:N
        Lp(i)=Lp(i-1)+fit(i); %%计算累积概率
    end
    for i=1:N
        ind=find((Lp-rand)>0); %%找出轮盘赌选择的指标
        Co(i)=ind(1);
        nPo(i,:)=Po(ind(1),:); %%将对应指标的染色体取出来赋值给新的种群
    end
    %%%%%%%%%%%%%%交叉%%%%%%%%%%%%%%%%%%
    for i=1:2:N
        [x1,y1]=GAjc(nPo(i,:),nPo(i+1,:),Pc);
        Nnpo(i,:)=x1;
        Nnpo(i+1,:)=y1;
    end
    %%%%%%%%%%%%%%变异%%%
    for i=1:N
        Npo(i,:)=GAby(Nnpo(i,:),pm);
    end
    %%%%%%%%%%%%%%%%%%%%%
    %保留最好的个体
    Npo(1,:)=Po(ind1,:);
    Npo(41:N,:)=-B+rand(10,2)*2*B;%%避免早熟
    %%新的种群要赋值给原来的变量
    Po=Npo;
end

2）GAmb(目标函数)

function    z1=GAmb(x1,y1)
z1=x1^2-10*cos(2*pi*x1)+10+y1^2-10*cos(2*pi*y1)+10;

3)GAjc(交叉函数)

function  [x1,y1]=GAjc(x,y,Pc)
if  rand<Pc
lameda1=0.4;
x1=lameda1*x+(1-lameda1)*y;
y1=lameda1*y+(1-lameda1)*x;
else
   x1=x; 
   y1=y;
 end

4)GAby(变异函数)

function x=GAby(x,pm)
if rand<pm
    x=x+[(1-2*rand)*10e-3  (1-2*rand)*10e-3 ];
end

5）结果图例