差分演进法
本帖最后由 matlab的旋律 于 2015-3-26 15:32 编辑clear all
close all
clc
t = cputime;
Gm = 10000;%Gm 最大迭代次数
F0 = 0.5;%变异率
Np = 100;
CR = 0.9;%交叉概率
G= 1; %初始化迭代数
D = 10; %所求问题的维数
Gmin = zeros(1,Gm); %迭代的最优值
best_x = zeros(Gm,D); %迭代的最优解
value = zeros(1,Np);
%产生初始种群
xmin = -10;
xmax = 100;%带负数的下界
X0 = (xmax-xmin)*rand(Np,D) + xmin;%产生Np个D维向量
XG = X0;
XG_next_1= zeros(Np,D); %初始化
XG_next_2 = zeros(Np,D);
XG_next = zeros(Np,D);
while G <= Gm
%%%%%%%%%%%%%%%%%%%%%%%%变异操作
for i = 1:Np
%产生j,k,p三个不同的数
a = 1;
b = Np;
dx = randperm(b-a+1) + a- 1;
j = dx(1);
k = dx(2);
p = dx(3);
%要保证与i不同
if j == i
j= dx(4);
else if k == i
k = dx(4);
else if p == i
p = dx(4);
end
end
end
%变异算子
suanzi = exp(1-Gm/(Gm + 1-G));
F = F0*2.^suanzi;
%变异的个体来自三个随机父代
son = XG(p,:) + F*(XG(j,:) - XG(k,:));
for j = 1: D
if son(1,j) >xmin& son(1,j) < xmax %防止变异超出边界
XG_next_1(i,j) = son(1,j);
else
XG_next_1(i,j) = (xmax - xmin)*rand(1) + xmin;
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%---交叉操作
for i = 1: Np
randx = randperm(D);% 的随机序列
for j = 1: D
if rand > CR & randx(1) ~= j % CR = 0.9
XG_next_2(i,j) = XG(i,j);
else
XG_next_2(i,j) = XG_next_1(i,j);
end
end
end
%%%%%%%%%%%%%%%%%%----选择操作---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i = 1:Np
if f(XG_next_2(i,:)) < f(XG(i,:))
XG_next(i,:) = XG_next_2(i,:);
else
XG_next(i,:) = XG(i,:);
end
end
%找出最小值
for i = 1:Np
value(i) = f(XG_next(i,:));
end
= min(value);
%第G代中的目标函数的最小值
Gmin(G) = value_min;
%保存最优的个体
best_x(G,:) = XG_next(pos_min,:);
XG = XG_next;
trace(G,1) = G;
trace(G,2) = value_min;
G = G + 1;
end
= min(Gmin);
disp(['迭代次数为:',num2str(G)])
disp(['最优解为:',num2str(best_x(pos_min,:))])
disp(['函数值为:',num2str(value_min)])
fprintf('DE所耗的时间为：%f \n',cputime - t);
%画出迭代次数跟最优函数值之间的关系图
plot(trace(:,1),trace(:,2),'r-*');
xlabel('迭代次数')
ylabel('最优函数值')
function f = f(x)
%测试函数
f = sum(x.^2-10*cos(2.*pi*x)+10);
end
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测试函数
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