遗传算法程序源代码matlab.doc

遗传算法程序 matlab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0.050.3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'); endif nargin=3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=0 1e-4;endif nargin=4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=0 1e-4;endif nargin=5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=0 1e-4;endif nargin=6, pMutation=0.1;pInversion=0.15;options=0 1e-4;endif nargin=7, pInversion=0.15;options=0 1e-4;endif find(LB-UB)>0) error('数据输入错误,请重新输入(LB<UB):');ends=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 VarNumbounds=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,TraceTrace=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);%采用多点交叉与均匀交叉，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+(i4)*(pCross/3-pm0)/(eranum4);%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;endt=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 %fn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;endif 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 individualfor 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);endinitpop(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 variablesnumV=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)=1function selectpop=NonlinearRankSelect(FUN,pop,bounds,bits)global m nselectpop=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endselectprob=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);%计算各选择概率之与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; endend%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 NewPopr=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)=;endif 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 endNewPop(y2,:)=OldPop(y2,:);%采用均匀交叉function children1,children2=EqualCrossOver(parent1,parent2)global n children1 children2hidecode=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 VarNumChildren1=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 NewPopr=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 endendNewPop=OldPop;%倒位操作function NewPop=Inversion(OldPop,pInversion)global m n NewPopNewPop=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 endend第 13 页