ga.m

基于遗传算法的函数优化,利用遗传算法求解函数极值。

clc;
clear;close all;
v = 2*rand(50,22)-1;
v=hardlim(v);
[N,L] = size(v); ger = 200; 
pc = 0.5; pm = 0.01; updatef=-100;c=0;updatec=zeros(1,size(v,2));

disp(sprintf('Number of generations: %d',ger));
disp(sprintf('Population size: %d',N));
disp(sprintf('Crossover probability: %.3f',pc));
disp(sprintf('Mutation probability: %.3f',pm));

f='-1*(x.^2+y.^2)';

% General parameters & Initial operations
sol1=1; vmfit = []; it = 1; vx = []; C = [];updatef=-10
x = decod(v(:,1:11),11); y = decod(v(:,12:end),11);
fit = eval(f);

% Generations
t0 = clock;
while it <= ger 
% Selection 轮盘赌
for i=1:N
    sp(i)=(fit(i)+3)/sum(fit+3);%
end

for i=2:N
   sp(i)=sp(i-1)+sp(i);
end
for i=1:N
   p=rand(1); sindex=1;
   while p > sp(sindex) 
      sindex=sindex+1; %寻找要选择个体的位置
   end
   newv(i,:)=v(sindex,:); 
end
for i=1:N
   v(i,:)=newv(i,:);%用选择出的个体构成的种群替代旧的种群
end
% Crossver
for i=1:N
   cindex(i)=i;
end
for i=1:N %产生要配对的父代的序号；经过N次顺序调换，将原有顺序打乱，使相邻两个个体作为交叉的父代
   point=unidrnd(N-i+1);
   temp=cindex(i);
   cindex(i)=cindex(i+point-1);
   cindex(i+point-1)=temp;
end
for i=1:2:N
   p=rand(1);
   if(p<pc)
      point=unidrnd(L-1)+1;%1<point<L 产生交叉点
      for j=point:(L-1) %交叉
         ch=v(cindex(i),j);
         v(cindex(i),j)=v(cindex(i+1),j); %cindex中相邻的两个为两个父代的序号
         v(cindex(i+1),j)=ch;
      end
   end
end
% Mutation
M=rand(N,L)<=pm;%产生（N，L）维的01矩阵，为1的位置进行变异
v=v-2.*(v.*M)+M;
% Evaluatefitness & Evolution
x = decod(v(:,1:11),11); y = decod(v(:,12:end),11); fit = eval(f);
[sol1,indb1] = max(fit); 
if updatef>=sol1
   sol1=updatef;
   v(indb1,:)=updatec;
end
updatef=sol1;
updatec=v(indb1,:);
[sol2,indb2] = min(fit);
v(indb2,:) = v(indb1,:);
x = decod(v(:,1:11),11); y = decod(v(:,12:end),11); fit = eval(f);

media = mean(fit);
vx = [vx sol1]; vmfit = [vmfit media];
    if rem(it,1) == 0 | it == 10,
       if c~=1
          disp(sprintf('Gen.: %d  x: %2.5f  y: %2.5f  Av: %2.2f  f(x,y): %2.40f',it,x(indb1),y(indb1),media,sol1));
      else
          disp(sprintf('Gen.: %d   Av: %2.2f  f(x,y): %2.5f',it,media,sol1));
      end
	end;
	it = it + 1;
end;
T = etime(clock,t0); %F = flops - f0;
X=x;Y=y;
x = x(indb1); y = y(indb1); fx = sol1; P = v;
disp(sprintf('the total time is %2.4f',T));

 disp(sprintf('Maximum found [f(x,y)]: [%.2f]',fx));
%       xx=vx;yy=vmfit;
      figure(2); plot(vx,'r'); 
      title('f(x,y) x Mean'); xlabel('Generations'); ylabel('f(x,y)');
      hold on; plot(vmfit,'k:'); legend('best','mean',0);hold off;