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1、遗传算法程序(一):说明：馆a.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!functionBestPop,Trace=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)%BestPop,Trace=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)%Findsamaximumofafunctionofseveralvariables.%fmaxgasolvesproblemsofthefo
2、rm:%maxF(X)subjectto: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
3、)=0二进制编码(默认0),option(1)=0十进制编%码,option设定求解精度(默认1e-4)%T1=clock；ifnargin0)error(数据输入错误，请重新输入(LBUB):);ends=sprintf(程序运行需要约%.4f秒钟时间,请稍等,(eranum*popsize/1000);disp(s);globalmnNewPopchildren1children2VarNumbounds=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(:
4、,2)-bounds(:,1)./precision);%由设定精度划分区间Pop=lnitPopGray(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;whilei=eranumforj=1:mvalue(j)=feval(FUN(1,:),(b2f(Pop(
5、j,:),bounds,bits);%计算适应度endMaxValue,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，
6、且逐步增大均匀交叉的概率%round(unidrnd(eranum-i)/eranum)MutationPop=Mutation(CrossOverPop,pMutation,VarNum);%变异lnversionPop=lnversion(MutationPop,plnversion);%到位Pop=lnversionPop;%更新pMutation=pmO+(S4)*(pCross/3-pmO)/(eranumA4);%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
7、化的遗传算法);xlabel(进化世代数(eranum);ylabel(每一代最优适应度(maxfitness);MaxFval,l=max(Trace(:,1);X=Trace(l,(2:length(bits)+1);holdon;plot(l,MaxFval,*);text(l+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
8、制变异值增大过程T2=clock;elapsed_time=T2-T1;ifelapsed_time(6)Oelapsed_time(6)=elapsed_time(6)+6O;elapsed_time(5)=elapsed_time(5)-1;endifelapsed_time(5)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);%Thewholeoneencodingindividua
9、l%解码functionfval=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)./(24bits-1);%TherangeofthevariablesnumV=size(bounds,1);cs=0cumsum(bits);fori=1:numVa=bval(cs(i)+1):cs(i+1);fval(i)=sum(24(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1)
10、;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)An)*(1-q)N,其中P(0)P(1).P(n),sum(P(i)=1functionselectpop=NonlinearRankSelect(FUN,pop,bounds,bits)globalmnselectpop=zeros(m,n);fit=zeros(m,1);fori=1:mfit(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);
11、%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;yx(:,2)=sort(selectprob);r=q/(1-(1-q)Am);%标准分布基值newfit(x(:,2)=r*(1-q)4(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;whilenewIn=mifrNums(newIn)newfit(fitIn)selectpop(newIn,:)=pop(fitIn,:);new
12、In=newIn+1;elsefitIn=fitIn+1;endend%交叉操作functionNewPop=CrossOver(OldPop,pCross,opts)%OldPop为父代种群，pcross为交叉概率globalmnNewPopr=rand(1,m);y1=find(r=pCross);len=length(y1);iflen2&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)=;endiflength(y1)=2fori=0:2:length(y1)-2ifopts=0NewPop(y1(i+1),:),NewPop(y1(i+2),:)=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:);elseNewPop(y1(i+1),:),NewPop(y1(i+2),:)=Multi
