三个遗传算法matlab程序实例

遗传算法程序（一）:

   说明: fga.m 为遗传算法的主程序; 采用二进制Gray编码,采用基于轮盘赌法的非线性排名选择, 均匀交叉,变异操作,而且还引入了倒位操作!

function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)

% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)

% Finds a maximum of a function of several variables.

% fmaxga solves problems of the form:

%      max F(X) subject to: LB <= X <= UB                           

% BestPop       - 最优的群体即为最优的染色体群

% Trace         - 最佳染色体所对应的目标函数值

% FUN           - 目标函数

% LB            - 自变量下限

% UB            - 自变量上限

% eranum        - 种群的代数,取100--1000(默认200)

% popsize       - 每一代种群的规模；此可取50--200(默认100)

% pcross        - 交叉概率,一般取0.5--0.85之间较好(默认0.8)

% pmutation     - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)

% pInversion    - 倒位概率,一般取0.05－0.3之间较好(默认0.2)

% options       - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编

%码,option(2)设定求解精度(默认1e-4)

%

% ------------------------------------------------------------------------



T1=clock;

if nargin<3, error('FMAXGA requires at least three input arguments'); end

if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end

if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end

if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end

if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end

if nargin==7, pInversion=0.15;options=[0 1e-4];end

if find((LB-UB)>0)

   error('数据输入错误,请重新输入(LB<UB):');

end

s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));

disp(s);



global m n NewPop children1 children2 VarNum



bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);

precision=options(2);%由求解精度确定二进制编码长度

bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间

[Pop]=InitPopGray(popsize,bits);%初始化种群

[m,n]=size(Pop);

NewPop=zeros(m,n);

children1=zeros(1,n);

children2=zeros(1,n);

pm0=pMutation;

BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace

Trace=zeros(eranum,length(bits)+1);

i=1;

while i<=eranum

    for j=1:m

        value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度

    end

    [MaxValue,Index]=max(value);

    BestPop(i,:)=Pop(Index,:);

    Trace(i,1)=MaxValue;

    Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);

    [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择

[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));

%采用多点交叉和均匀交叉，且逐步增大均匀交叉的概率

    %round(unidrnd(eranum-i)/eranum)

    [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异

    [InversionPop]=Inversion(MutationPop,pInversion);%倒位

    Pop=InversionPop;%更新

pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);

%随着种群向前进化，逐步增大变异率至1/2交叉率

    p(i)=pMutation;

    i=i+1;

end

t=1:eranum;

plot(t,Trace(:,1)');

title('函数优化的遗传算法');xlabel('进化世代数(eranum)');ylabel('每一代最优适应度(maxfitness)');

[MaxFval,I]=max(Trace(:,1));

X=Trace(I,(2:length(bits)+1));

hold on; plot(I,MaxFval,'*');

text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);

str1=sprintf  ('进化到 %d 代 ,自变量为 %s 时,得本次求解的最优值 %f\n对应染色体是：%s',I,num2str(X),MaxFval,num2str(BestPop(I,:)));

disp(str1);

%figure(2);plot(t,p);%绘制变异值增大过程

T2=clock;

elapsed_time=T2-T1;

if elapsed_time(6)<0

    elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;

end

if elapsed_time(5)<0

    elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;

end %像这种程序当然不考虑运行上小时啦

str2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));

disp(str2);

%初始化种群

%采用二进制Gray编码,其目的是为了克服二进制编码的Hamming悬崖缺点

function [initpop]=InitPopGray(popsize,bits)

len=sum(bits);

initpop=zeros(popsize,len);%The whole zero encoding individual

for i=2:popsize-1

    pop=round(rand(1,len));

    pop=mod(([0 pop]+[pop 0]),2);

    %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)

    %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)

    initpop(i,:)=pop(1:end-1);

end

initpop(popsize,:)=ones(1,len);%The whole one encoding individual









%解码



function [fval] = b2f(bval,bounds,bits)

% fval   - 表征各变量的十进制数

% bval   - 表征各变量的二进制编码串

% bounds - 各变量的取值范围

% bits   - 各变量的二进制编码长度

scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables

numV=size(bounds,1);

cs=[0 cumsum(bits)];

for i=1:numV

a=bval((cs(i)+1):cs(i+1));

fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);

end









%选择操作

%采用基于轮盘赌法的非线性排名选择

%各个体成员按适应值从大到小分配选择概率：

%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1



function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)

global m n

selectpop=zeros(m,n);

fit=zeros(m,1);

for i=1:m

    fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据

end

selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)

q=max(selectprob);%选择最优的概率

x=zeros(m,2);

x(:,1)=[m:-1:1]';

[y x(:,2)]=sort(selectprob);

r=q/(1-(1-q)^m);%标准分布基值

newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率

newfit=cumsum(newfit);%计算各选择概率之和

rNums=sort(rand(m,1));

fitIn=1;newIn=1;

while newIn<=m

    if rNums(newIn)<newfit(fitIn)

        selectpop(newIn,:)=pop(fitIn,:);

        newIn=newIn+1;

    else

        fitIn=fitIn+1;

    end

end









%交叉操作

function [NewPop]=CrossOver(OldPop,pCross,opts)

%OldPop为父代种群，pcross为交叉概率

global m n NewPop

r=rand(1,m);

y1=find(r<pCross);

y2=find(r>=pCross);

len=length(y1);

if len>2&mod(len,2)==1%如果用来进行交叉的染色体的条数为奇数，将其调整为偶数

    y2(length(y2)+1)=y1(len);

    y1(len)=[];

end

if length(y1)>=2

   for i=0:2:length(y1)-2

       if opts==0

           [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));

       else

           [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));

       end

   end    

end

NewPop(y2,:)=OldPop(y2,:);



%采用均匀交叉

function [children1,children2]=EqualCrossOver(parent1,parent2)



global n children1 children2

hidecode=round(rand(1,n));%随机生成掩码

crossposition=find(hidecode==1);

holdposition=find(hidecode==0);

children1(crossposition)=parent1(crossposition);%掩码为1，父1为子1提供基因

children1(holdposition)=parent2(holdposition);%掩码为0，父2为子1提供基因

children2(crossposition)=parent2(crossposition);%掩码为1，父2为子2提供基因

children2(holdposition)=parent1(holdposition);%掩码为0，父1为子2提供基因



%采用多点交叉，交叉点数由变量数决定



function [Children1,Children2]=MultiPointCross(Parent1,Parent2)



global n Children1 Children2 VarNum

Children1=Parent1;

Children2=Parent2;

Points=sort(unidrnd(n,1,2*VarNum));

for i=1:VarNum

    Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));

    Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));

end









%变异操作

function [NewPop]=Mutation(OldPop,pMutation,VarNum)



global m n NewPop

r=rand(1,m);

position=find(r<=pMutation);

len=length(position);

if len>=1

   for i=1:len

       k=unidrnd(n,1,VarNum); %设置变异点数，一般设置1点

       for j=1:length(k)

           if OldPop(position(i),k(j))==1

              OldPop(position(i),k(j))=0;

           else

              OldPop(position(i),k(j))=1;

           end

       end

   end

end

NewPop=OldPop;









%倒位操作



function [NewPop]=Inversion(OldPop,pInversion)



global m n NewPop

NewPop=OldPop;

r=rand(1,m);

PopIn=find(r<=pInversion);

len=length(PopIn);

if len>=1

    for i=1:len

        d=sort(unidrnd(n,1,2));

        if d(1)~=1&d(2)~=n

           NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);

           NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));

           NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);

       end

   end

end

遗传算法程序（二）:

function youhuafun



D=code;

N=50;         % Tunable

maxgen=50;     % Tunable

crossrate=0.5; %Tunable

muterate=0.08; %Tunable

generation=1;  

num = length(D);

fatherrand=randint(num,N,3);

score = zeros(maxgen,N);

while generation<=maxgen

   ind=randperm(N-2)+2; % 随机配对交叉

   A=fatherrand(:,ind(1:(N-2)/2));

   B=fatherrand(:,ind((N-2)/2+1:end));

%     多点交叉

   rnd=rand(num,(N-2)/2);

   ind=rnd   tmp=A(ind);

   A(ind)=B(ind);

   B(ind)=tmp;



% % 两点交叉

%     for kk=1:(N-2)/2

%         rndtmp=randint(1,1,num)+1;

%         tmp=A(1:rndtmp,kk);

%         A(1:rndtmp,kk)=B(1:rndtmp,kk);

%         B(1:rndtmp,kk)=tmp;

%     end

   fatherrand=[fatherrand(:,1:2),A,B];

   

   % 变异

   rnd=rand(num,N);

   ind=rnd   [m,n]=size(ind);

   tmp=randint(m,n,2)+1;

   tmp(:,1:2)=0;

   fatherrand=tmp+fatherrand;

   fatherrand=mod(fatherrand,3);

%     fatherrand(ind)=tmp;

   

   %评价、选择

   scoreN=scorefun(fatherrand,D);% 求得N个个体的评价函数

   score(generation,:)=scoreN;

   [scoreSort,scoreind]=sort(scoreN);

   sumscore=cumsum(scoreSort);

   sumscore=sumscore./sumscore(end);

   childind(1:2)=scoreind(end-1:end);

   for k=3:N

       tmprnd=rand;

       tmpind=tmprnd       difind=[0,diff(tmpind)];

       if ~any(difind)

           difind(1)=1;

       end

       childind(k)=scoreind(logical(difind));

   end

   fatherrand=fatherrand(:,childind);    

   generation=generation+1;

end

% score

maxV=max(score,[],2);

minV=11*300-maxV;

plot(minV,'*');title('各代的目标函数值');

F4=D(:,4);

FF4=F4-fatherrand(:,1);

FF4=max(FF4,1);

D(:,5)=FF4;

save DData D





function D=code

load youhua.mat

% properties F2 and F3

F1=A(:,1);

F2=A(:,2);

F3=A(:,3);

if (max(F2)>1450)||(min(F2)<=900)

   error('DATA property F2 exceed it''s range (900,1450]')

end

% get group property F1 of data, according to F2 value

F4=zeros(size(F1));

for ite=11:-1:1

   index=find(F2<=900+ite*50);

   F4(index)=ite;

end

D=[F1,F2,F3,F4];



function ScoreN=scorefun(fatherrand,D)

F3=D(:,3);

F4=D(:,4);

N=size(fatherrand,2);

FF4=F4*ones(1,N);

FF4rnd=FF4-fatherrand;

FF4rnd=max(FF4rnd,1);

ScoreN=ones(1,N)*300*11;

% 这里有待优化

for k=1:N

   FF4k=FF4rnd(:,k);

   for ite=1:11

       F0index=find(FF4k==ite);

       if ~isempty(F0index)

           tmpMat=F3(F0index);

           tmpSco=sum(tmpMat);

           ScoreBin(ite)=mod(tmpSco,300);

       end

   end

   Scorek(k)=sum(ScoreBin);

end

ScoreN=ScoreN-Scorek;

遗传算法程序（三）：

%IAGA

function best=ga

clear

MAX_gen=200;            %最大迭代步数

best.max_f=0;           %当前最大的适应度

STOP_f=14.5;            %停止循环的适应度

RANGE=[0 255];          %初始取值范围[0 255]

SPEEDUP_INTER=5;       %进入加速迭代的间隔

advance_k=0;            %优化的次数



popus=init;             %初始化

for gen=1:MAX_gen

    fitness=fit(popus,RANGE);       %求适应度

    f=fitness.f;

    picked=choose(popus,fitness);   %选择

    popus=intercross(popus,picked); %杂交

    popus=aberrance(popus,picked); %变异

    if max(f)>best.max_f

        advance_k=advance_k+1;

        x_better(advance_k)=fitness.x;

        best.max_f=max(f);

        best.popus=popus;

        best.x=fitness.x;

    end

    if mod(advance_k,SPEEDUP_INTER)==0

        RANGE=minmax(x_better);

       

        RANGE

       

        advance=0;

    end

end

return;

function popus=init%初始化

M=50;%种群个体数目

N=30;%编码长度

popus=round(rand(M,N));

return;



function fitness=fit(popus,RANGE)%求适应度

[M,N]=size(popus);

fitness=zeros(M,1);%适应度

f=zeros(M,1);%函数值

A=RANGE(1);B=RANGE(2);%初始取值范围[0 255]



for m=1:M

    x=0;

    for n=1:N

        x=x+popus(m,n)*(2^(n-1));

    end

    x=x*((B-A)/(2^N))+A;

    for k=1:5

        f(m,1)=f(m,1)-(k*sin((k+1)*x+k));

    end

end

f_std=(f-min(f))./(max(f)-min(f));%函数值标准化

fitness.f=f;fitness.f_std=f_std;fitness.x=x;

return;



function picked=choose(popus,fitness)%选择

f=fitness.f;f_std=fitness.f_std;

[M,N]=size(popus);

choose_N=3;                 %选择choose_N对双亲

picked=zeros(choose_N,2);   %记录选择好的双亲

p=zeros(M,1);               %选择概率

d_order=zeros(M,1);



%把父代个体按适应度从大到小排序

f_t=sort(f,'descend');%将适应度按降序排列

for k=1:M

    x=find(f==f_t(k));%降序排列的个体序号

    d_order(k)=x(1);

end

for m=1:M

    popus_t(m,:)=popus(d_order(m),:);

end

popus=popus_t;

f=f_t;



p=f_std./sum(f_std);                    %选择概率

c_p=cumsum(p)';                          %累积概率



for cn=1:choose_N

    picked(cn,1)=roulette(c_p); %轮盘赌

    picked(cn,2)=roulette(c_p); %轮盘赌

    popus=intercross(popus,picked(cn,:));%杂交

end

popus=aberrance(popus,picked);%变异

return;



function popus=intercross(popus,picked) %杂交

[M_p,N_p]=size(picked);

[M,N]=size(popus);

for cn=1:M_p

    p(1)=ceil(rand*N);%生成杂交位置

    p(2)=ceil(rand*N);

    p=sort(p);

    t=popus(picked(cn,1),p(1):p(2));

    popus(picked(cn,1),p(1):p(2))=popus(picked(cn,2),p(1):p(2));

    popus(picked(cn,2),p(1):p(2))=t;

end

return;

function popus=aberrance(popus,picked) %变异

P_a=0.05;%变异概率

[M,N]=size(popus);

[M_p,N_p]=size(picked);

U=rand(1,2);



for kp=1:M_p

    if U(2)>=P_a        %如果大于变异概率，就不变异

        continue;

    end

    if U(1)>=0.5

        a=picked(kp,1);

    else

        a=picked(kp,2);

    end

    p(1)=ceil(rand*N);%生成变异位置

    p(2)=ceil(rand*N);

    if popus(a,p(1))==1%0 1变换

        popus(a,p(1))=0;

    else

        popus(a,p(1))=1;

    end

    if popus(a,p(2))==1

        popus(a,p(2))=0;

    else

        popus(a,p(2))=1;

    end

end

return;



function picked=roulette(c_p) %轮盘赌

[M,N]=size(c_p);

M=max([M N]);

U=rand;

if U<c_p(1)

    picked=1;

    return;

end

for m=1:(M-1)

    if U>c_p(m) & U<c_p(m+1)

        picked=m+1;

        break;

    end

end

全方位的两点杂交、两点变异的改进的加速遗传算法（IAGA）

今天的文章三个遗传算法matlab程序实例分享到此就结束了，感谢您的阅读。