遗传算法程序 matlab

遗传算法程序 matlab 作者：KINGTT 来源：转载 发布时间：2008-7-17 9:10:02 减小字体 增大字体 本程序收集于网络，本人并未进行过运行，如有问题请与作者联系，如有侵权请告之 遗传算法程序: 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