matlab练习程序（演化策略ES）

% 算法步骤如下：
% 1.设定种群个体数和需要迭代的次数。
% 2.选择父代中的个体按照公式:
% z1=sqrt(-2*ln(u1))*sin(2*pi*u2)*m，
% z2=sqrt(-2*ln(u1))*cos(2*pi*u2)*m
% 这里u1,u2都是随机值，m是控制因子，演化次数越多m，
% m越小，父代通过与z1，z2相加得到后代。
% 3.计算后代的适应性。
% 4.选择后代中最优的适应性作为全局最优适应性。

%% matlab 代码开始
clc;
clear all;
close all;
%% 绘出所求函数图形
[x,y] = meshgrid(-100:100,-100:100);
sigma = 50;
img = (1/(2*pi*sigma^2))*exp(-(x.^2 + y.^2)/(2*sigma^2));
mesh(img);
axis([-100,100,-100,100,2e-5,8e-5]);
hold on
%% 初始化种群
pop_size = 20;%种群规模
pop = struct([]);
iterative = 100;
for i = 1:pop_size
pop(i).x = -100 + 200*rand();
pop(i).y = -100 + 200*rand();
pop(i).fit = compute_fit(pop(i));
end
pop_best = pop(1);

%% 演化开始
p1 = plot3(pop_best.x +100,pop_best.y+100,pop_best.fit,'k.','markersize',30);
for i = 1:iterative
set(p1, 'xdata',pop_best.x+100,'ydata',pop_best.y+100,'zdata',pop_best.fit)
drawnow
pause(.1)
[pop,pop_best] = select_and_combin(pop,pop_best,pop_size,i,iterative);
end

function [new_pop,pop_best] = select_and_combin(pop,pop_best,pop_size,k,iterative)
mul = (iterative - k) / iterative;
new_pop = pop;
% z1=sqrt(-2*ln(u1))*sin(2*pi*u2)*m，
% z2=sqrt(-2*ln(u1))*cos(2*pi*u2)*m
for i = 1:pop_size
%随机数
u1 = rand();
u2 = rand();
z1 = sqrt(-2*log(u1))*sin(2*pi*u2)*mul;
z2 = sqrt(-2*log(u1))*cos(2*pi*u2)*mul;
%变异
new_pop(i).x = pop(i).x + z1;
new_pop(i).y = pop(i).y + z2;
%计算适应值
new_pop(i).fit = compute_fit(new_pop(i));
if new_pop(i).fit < pop(i).fit
new_pop(i) = pop(i);
end
if pop_best.fit < new_pop(i).fit
pop_best = pop(i);
end
end
end

function re = compute_fit(pop)
x = pop.x;
y = pop.y;
sigma = 50;
if x < -100 || x > 100 || y < -100 || y > 100
re = 0;
else
re =(1/(2*pi*sigma^2))*exp(-(x^2 + y ^2)/(2 * sigma^2));
end

 http://www.cnblogs.com/tiandsp/p/3165388.html