差分進化算法DE



差分進化算法DE與遺傳算法GA非常類似，下面是差分進化算法的步驟：

算法步驟如下：

1. 初始化

2. 變異
   

3. 交叉

d.選擇

測試函數：

Rastrigr函數  

                 

全局最優點: ,       

matlab代碼如下：

function DE(Gm,F0)

t0 = cputime;
%差分進化算法程序
%F0是變異率 %Gm 最大迭代次數
Gm = 10000;
F0 = 0.5;
Np = 100;
CR = 0.9;  %交叉概率
G= 1; %初始化代數
D = 10; %所求問題的維數
Gmin = zeros(1,Gm); %各代的最優值
best_x = zeros(Gm,D); %各代的最優解
value = zeros(1,Np);

%產生初始種羣
%xmin = -10; xmax = 100;%帶負數的下界
xmin = -5.12;
xmax = 5.12;
function y = f(v)
    %Rastrigr 函數
y = sum(v.^2 - 10.*cos(2.*pi.*v) + 10);
end

X0 = (xmax-xmin)*rand(Np,D) + xmin;  %產生Np個D維向量
XG = X0;

%%%%%%%%%%%%%----這裏未做評價，不判斷終止條件----%%%%%%%%%%%%%%%%%%%%%%%%

XG_next_1= zeros(Np,D); %初始化
XG_next_2 = zeros(Np,D);
XG_next = zeros(Np,D);

while G <= Gm 
G 
%%%%%%%%%%%%%%%%%%%%%%%%----變異操作----%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    for i = 1:Np
        %產生j,k,p三個不同的數
        a = 1;
        b = Np;
        dx = randperm(b-a+1) + a- 1;
        j = dx(1);
        k = dx(2);
        p = dx(3);
        %要保證與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
        
        %變異算子
        suanzi = exp(1-Gm/(Gm + 1-G));
        F = F0*2.^suanzi;
        %變異的個體來自三個隨機父代
       
        son = XG(p,:) + F*(XG(j,:) - XG(k,:));       
        for j = 1: D
            if son(1,j) >xmin  & son(1,j) < xmax %防止變異超出邊界
                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]的隨機序列   
        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
    
    %%%%%%%%%%%%%%%%%%----選擇操作---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    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代中的目標函數的最小值
    Gmin(G) = value_min;   
    %保存最優的個體
    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所耗的時間爲：%f \n',cputime - t0);
  %畫出代數跟最優函數值之間的關係圖  
  plot(trace(:,1),trace(:,2));
  
end

結果：