Matlab利用遺傳演演算法GA求解非連續函數問題詳解

%%%%%%%%%%%%%%%%%%%%實值遺傳演演算法求函數極值%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all;                           %清除所有變數
close all;                           %清圖
clc;                                 %清屏
D=10;                                %基因數目    
NP=100;                              %染色體數目
Xs=20;                               %上限          
Xx=-20;                              %下限
G=1000;                               %最大遺傳代數
f=zeros(D,NP);                       %初始種群賦空間
nf=zeros(D,NP);                      %子種群賦空間
Pc=0.8;                              %交叉概率
Pm=0.1;                              %變異概率
f=rand(D,NP)*(Xs-Xx)+Xx;             %隨機獲得初始種群
%%%%%%%%%%%%%%%%%%%%%%按適應度升序排列%%%%%%%%%%%%%%%%%%%%%%%
for np=1:NP
    MSLL(np)=func2(f(:,np));
end
[SortMSLL,Index]=sort(MSLL);                            
Sortf=f(:,Index);
%%%%%%%%%%%%%%%%%%%%%%%遺傳演演算法迴圈%%%%%%%%%%%%%%%%%%%%%%%%%%
for gen=1:G
    %%%%%%%%%%%%%%採用君主方案進行選擇交叉操作%%%%%%%%%%%%%%%%
    Emper=Sortf(:,1);                      %君主染色體
    NoPoint=round(D*Pc);                   %每次交叉點的個數
    PoPoint=randi([1 D],NoPoint,NP/2);   %交叉基因的位置
    nf=Sortf;
    for i=1:NP/2
        nf(:,2*i-1)=Emper;
        nf(:,2*i)=Sortf(:,2*i);
        for k=1:NoPoint
            nf(PoPoint(k,i),2*i-1)=nf(PoPoint(k,i),2*i);
            nf(PoPoint(k,i),2*i)=Emper(PoPoint(k,i));
        end
    end
    %%%%%%%%%%%%%%%%%%%%%%%%%%變異操作%%%%%%%%%%%%%%%%%%%%%%%%%
    for m=1:NP
        for n=1:D
            r=rand(1,1);
            if r<Pm
                nf(n,m)=rand(1,1)*(Xs-Xx)+Xx;
            end
        end
    end
    %%%%%%%%%%%%%%%%%%%%%子種群按適應度升序排列%%%%%%%%%%%%%%%%%%
    for np=1:NP 
          NMSLL(np)=func2(nf(:,np));   
    end
    [NSortMSLL,Index]=sort(NMSLL);           
    NSortf=nf(:,Index);
    %%%%%%%%%%%%%%%%%%%%%%%%%產生新種群%%%%%%%%%%%%%%%%%%%%%%%%%%
    f1=[Sortf,NSortf];                %子代和父代合併
    MSLL1=[SortMSLL,NSortMSLL];       %子代和父代的適應度值合併
    [SortMSLL1,Index]=sort(MSLL1);    %適應度按升序排列
    Sortf1=f1(:,Index);               %按適應度排列個體
    SortMSLL=SortMSLL1(1:NP);         %取前NP個適應度值
    Sortf=Sortf1(:,1:NP);             %取前NP個個體
    trace(gen)=SortMSLL(1);           %歷代最優適應度值
end
Bestf=Sortf(:,1);                     %最優個體 
trace(end)                            %最優值
figure
plot(trace)
xlabel('迭代次數')
ylabel('目標函數值')
title('適應度進化曲線')
%%%%%%%%%%%%%%%%%%%%%%%%%%%適應度函數%%%%%%%%%%%%%%%%%%%%%%%%%%%
function result=func2(x)
summ=sum(x.^2);
result=summ;
end