差分进化算法

差分进化算法(DE)是一种新兴的进化计算技术，它是由 Storn 等人于1995年提出，其最初的设想是用于解决切比雪夫多项式问题，后来成为解决复杂优化问题的有效技术。

    差分进化算法的操作如下:

    (1)初始化

    (2)变异

    (3)交叉

    (4)选择

    (5)边界条件处理

   差分进化算法流程图:

   

  matlab仿真实例:

  求函数f(x,y)=3cos(xy)+x+y的最小值，其中x的取值范围为[-4,4], y的取值范围为[-4,4](多个局部极值的函数)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%差分进化算法求函数极值%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clear all;close all;clc;NP=20;     %种群数量D=2;       %变量的维数G=100;     %最大进化代数F=0.5;     %变异算子CR=0.1;    %交叉算子Xs=4;      %上限Xx=-4;     %下限%%%%%%%%%%%%%%%%%%%%%%%%%%%%%赋初值%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%x=zeros(D,NP);       %初始种群v=zeros(D,NP);       %变异种群u=zeros(D,NP);       %选择种群x=rand(D,NP)*(Xs-Xx)+Xx;         %赋初值%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%计算目标函数%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%for m=1:NP   Ob(m)=func2(x(:,m));endtrace(1)=min(Ob);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%差分进化循环%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%for gen=1:G     %%%%%%%%%%%%%%%%%%%%%%变异操作%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     %%%%%%%%%%%%%%%%%%%%%%%%r1,r2,r3和m互不相同%%%%%%%%%%%%%%%%%%%%%%     for m=1:NP        r1=randint(1,1,[1,NP]);        while(r1==m)          r1=randint(1,1,[1,NP]);        end         r2=randint(1,1,[1,NP]);         while(r2==m)|(r2==r1)          r2=randint(1,1,[1,NP]);         end        r3=randint(1,1,[1,NP]);         while((r3==m)|(r3==r1)|(r3==r2))          r3=randint(1,1,[1,NP]);         end         v(:,m)=x(:,r1)+F*(x(:,r2)-x(:,r3));     end          %%%%%%%%%%%%%%%%%%%%%%交叉操作%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     r=randint(1,1,[1,NP]);     for n=1:D         cr=rand(1);         if(cr<CR)|(n==r)           u(n,:)=v(n,:);         else            u(n,:)=x(n,:);         end     end          %%%%%%%%%%%%%%%%%%%%%%边界条件的处理%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     %%%%%%%%%%%%%%%%%%%%%%边界吸收%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     for n=1:D       for m=1:NP           if u(n,m)<Xx               u(n,m)=Xx;           end           if u(n,m)>Xs               u(n,m)=Xs;           end       end     end     %%%%%%%%%%%%%%%%%%%%%%选择操作%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     for m=1:NP         Ob1(m)=func2(u(:,m));     end         for m=1:NP        if Ob1(m)<Ob(m)      %小于先前的目标值            x(:,m)=u(:,m);        end    end    for m=1:NP       Ob(m)=func2(x(:,m));    end    trace(gen+1)=min(Ob);end    [SortOb,Index]=sort(Ob);    x=x(:,Index);    X=x(:,1);          %最优变量    Y=min(Ob);         %最优值   disp('最优变量');   disp(X);   disp('最优值');   disp(Y);  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%画图%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  figure  plot(trace);  %plot(X,Y,'-ro');  xlabel('迭代次数');  ylabel('目标函数值');  title('DE目标函数曲线');    

%%%%%%%%%%%%%%%%%%%%%%%%%%%%适应度函数计算%%%%%%%%%%%%%%%%%%%%%%%%%%%%  function value=func2(x)  value=3*cos(x(1)*x(2))+x(1)+x(2);  end

运行效果如下: