【DE算法】差分进化算法原理及python代码

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差分进化算法DE与遗传算法GA非常类似，下面是差分进化算法的步骤。

算法步骤如下：

初始化
变异
交叉

d.选择

测试函数：

Rastrigr函数

全局最优点: ,

matlab代码如下：

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function DE(Gm,F0)
t0 = cputime;
%差分进化算法程序
%F0是变异率 %Gm 最大迭代次数
Gm = 10000;
F0 = 0.5;
Np = 100;
CR = 0.9; %交叉概率
G= 1; %初始化代数
D = 10; %所求问题的维数
Gmin = zeros(1,Gm); %各代的最优值
best_x = zeros(Gm,D); %各代的最优解
value = zeros(1,Np);
%产生初始种群
%xmin = -10; xmax = 100;%带负数的下界
xmin = -5.12;
xmax = 5.12;
function y = f(v)
%Rastrigr 函数
y = sum(v.^2 - 10.*cos(2.*pi.*v) + 10);
end
X0 = (xmax-xmin)*rand(Np,D) + xmin; %产生Np个D维向量
XG = X0;
%%%%%%%%%%%%%----这里未做评价，不判断终止条件----%%%%%%%%%%%%%%%%%%%%%%%%
XG_next_1= zeros(Np,D); %初始化
XG_next_2 = zeros(Np,D);
XG_next = zeros(Np,D);
while G <= Gm
G
%%%%%%%%%%%%%%%%%%%%%%%%----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);% [1,2,3,...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
[value_min,pos_min] = 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
[value_min,pos_min] = min(Gmin);
best_value = value_min
best_vector = best_x(pos_min,:)
fprintf('DE所耗的时间为：%f \n',cputime - t0);
%画出代数跟最优函数值之间的关系图
plot(trace(:,1),trace(:,2));
end

结果：

以上转载自：http://blog.csdn.net/hehainan_86/article/details/38685231

DE算法的求解步骤：
(1)基本参数的设置，包括NP， F， CR
(2)初始化种群
(3)计算种群适应度值
(4)终止条件不满足时，进行循环，依次执行变异、交叉、选择运算，直到终止运算。

DE算法的流程图：

以上转载自：http://blog.csdn.net/misayaaaaa/article/details/54407548

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