遗传算法Matlab源代码(共10页).doc

精选优质文档-倾情为你奉上function X,MaxFval,BestPop,Trace=fga(FUN,bounds,MaxEranum,PopSize,options,pCross,pMutation,pInversion)% X,MaxFval,BestPop,Trace=fga(FUN,bounds,MaxEranum,PopSize,options,pCross,pMutation,pInversion)% Finds a maximum of a function of several variables.% fga solves problems of the form: % max F(X) subject to: LB <= X <= UB (LB=bounds(:,1),UB=bounds(:,2) % X - 最优个体对应自变量值% MaxFval - 最优个体对应函数值% BestPop - 最优的群体即为最优的染色体群% Trace - 每代最佳个体所对应的目标函数值% FUN - 目标函数% bounds - 自变量范围% MaxEranum - 种群的代数,取50-500(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;%检验初始参数if nargin<2, error('FMAXGA requires at least three input arguments'); endif nargin=2, MaxEranum=150;PopSize=100;options=1 1e-4;pCross=0.85;pMutation=0.1;pInversion=0.25;endif nargin=3, PopSize=100;options=1 1e-4;pCross=0.85;pMutation=0.1;pInversion=0.25;endif nargin=4, options=1 1e-4;pCross=0.85;pMutation=0.1;pInversion=0.25;endif nargin=5, pCross=0.85;pMutation=0.1;pInversion=0.25;endif nargin=6, pMutation=0.1;pInversion=0.25;endif nargin=7, pInversion=0.25;endif (options(1)=0|options(1)=1)&find(bounds(:,1)-bounds(:,2)>0) error('数据输入错误,请重新输入:');end% 定义全局变量global m n NewPop children1 children2 VarNum% 初始化种群和变量precision = options(2);bits = ceil(log2(bounds(:,2)-bounds(:,1)' ./ precision);%由设定精度划分区间VarNum = size(bounds,1);Pop = InitPop(PopSize,bounds,bits,options);%初始化种群m,n = size(Pop);fit = zeros(1,m);NewPop = zeros(m,n);children1 = zeros(1,n);children2 = zeros(1,n);pm0 = pMutation;BestPop = zeros(MaxEranum,n);%分配初始解空间BestPop,TraceTrace = zeros(1,MaxEranum);Lb = ones(PopSize,1)*bounds(:,1)'Ub = ones(PopSize,1)*bounds(:,2)'%二进制编码采用多点交叉和均匀交叉，并逐步增大均匀交叉概率%浮点编码采用离散交叉（前期）、算术交叉（中期）、AEA重组（后期）OptsCrossOver = ones(1,MaxEranum)*options(1);. round(unidrnd(2*(MaxEranum-1:MaxEranum)/MaxEranum)'%浮点编码时采用两种自适应变异和一种随机变异（自适应变异发生概率为随机变异发生的2倍）OptsMutation = ones(1,MaxEranum)*options(1);unidrnd(5,1,MaxEranum)'if options(1)=3 D=zeros(n); CityPosition=bounds; D = sqrt(CityPosition(:, ones(1,n) - CityPosition(:, ones(1,n)').2 +. (CityPosition(:,2*ones(1,n) - CityPosition(:,2*ones(1,n)').2 );end%=% 进化主程序 %=eranum = 1;H=waitbar(0,'Please wait.');while(eranum<=MaxEranum) for j=1:m if options(1)=1 %eval('fit(j)=' FUN '(Pop(j,:);');%但执行字符串速度比直接计算函数值慢 fit(j)=feval(FUN,Pop(j,:);%计算适应度 elseif options(1)=0 %eval('fit(j)=' FUN '(b2f(Pop(j,:),bounds,bits);'); fit(j)=feval(FUN,(b2f(Pop(j,:),bounds,bits); else fit(j)=-feval(FUN,Pop(j,:),D); end end Maxfit,fitIn=max(fit);%得到每一代最大适应值 Meanfit(eranum)=mean(fit); BestPop(eranum,:)=Pop(fitIn,:); Trace(eranum)=Maxfit; if options(1)=1 Pop=(Pop-Lb)./(Ub-Lb);%将定义域映射到0,1：Lb,Ub->0,1 ,Pop->(Pop-Lb)./(Ub-Lb) end switch round(unifrnd(0,eranum/MaxEranum)%进化前期尽量使用实行锦标赛选择，后期逐步增大非线性排名选择 case 0 selectpop=TournamentSelect(Pop,fit,bits);%锦标赛选择 case 1 selectpop=NonlinearRankSelect(Pop,fit,bits);%非线性排名选择 end CrossOverPop=CrossOver(selectpop,pCross,OptsCrossOver(eranum,:);%交叉 MutationPop=Mutation(CrossOverPop,fit,pMutation,VarNum,OptsMutation(eranum,:); %变异 InversionPop=Inversion(MutationPop,pInversion);%倒位 %更新种群 if options(1)=1 Pop=Lb+InversionPop.*(Ub-Lb);%还原Pop else Pop=InversionPop; end pMutation=pm0+(eranum3)*(pCross/2-pm0)/(eranum4); %逐步增大变异率至1/2交叉率 percent=num2str(round(100*eranum/MaxEranum); waitbar(eranum/MaxEranum,H,'Evolution complete ',percent,'%'); eranum=eranum+1;endclose(H);% 格式化输出进化结果和解的变化情况t=1:MaxEranum;plot(t,Trace,t,Meanfit);legend('解的变化','种群的变化');title('函数优化的遗传算法');xlabel('进化世代数');ylabel('每一代最优适应度');MaxFval,MaxFvalIn=max(Trace);if options(1)=1|options(1)=3 X=BestPop(MaxFvalIn,:);elseif options(1)=0 X=b2f(BestPop(MaxFvalIn,:),bounds,bits);endhold on; plot(MaxFvalIn,MaxFval,'*');text(MaxFvalIn+5,MaxFval,'FMAX=' num2str(MaxFval);str1=sprintf(' Best generation:n %dnn Best X:n %snn MaxFvaln %fn',. MaxFvalIn,num2str(X),MaxFval);disp(str1);% -计时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 str2=sprintf('elapsed_timen %d (h) %d (m) %.4f (s)',elapsed_time(4),elapsed_time(5),elapsed_time(6);disp(str2);%=% 遗传操作子程序 %=% - 初始化种群 -% 采用浮点编码和二进制Gray编码(为了克服二进制编码的Hamming悬崖缺点)function initpop=InitPop(popsize,bounds,bits,options)numVars=size(bounds,1);%变量数目rang=(bounds(:,2)-bounds(:,1)'%变量范围if options(1)=1 initpop=zeros(popsize,numVars); initpop=(ones(popsize,1)*rang).*(rand(popsize,numVars)+(ones(popsize,1)*bounds(:,1)');elseif options(1)=0 precision=options(2);%由求解精度确定二进制编码长度 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 individualelse for i=1:popsize initpop(i,:)=randperm(numVars);%为Tsp问题初始化种群 endend% - 二进制串解码 -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 NewPop=NonlinearRankSelect(OldPop,fit,bits)global m n NewPopfit=fit'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=0 cumsum(newfit);%计算各选择概率之和rNums=rand(m,1);newIn=1;while(newIn<=m) NewPop(newIn,:)=OldPop(length(find(rNums(newIn)>newfit),:); newIn=newIn+1;end% - 锦标赛选择(含精英选择) -function NewPop=TournamentSelect(OldPop,fit,bits)global m n NewPopnum=floor(m./2.(1:10);num(find(num=0)=;L=length(num);a=sum(num);b=m-a;PopIn=1;while(PopIn<=L) r=unidrnd(m,num(PopIn),2PopIn); LocalMaxfit,In=max(fit(r),2); SelectIn=r(In-1)*num(PopIn)+1:num(PopIn)'); NewPop(sum(num(1:PopIn)-num(PopIn)+1:sum(num(1:PopIn),:)=OldPop(SelectIn,:); PopIn=PopIn+1; r=;In=;LocalMaxfit=; end if b>1 NewPop(sum(num)+1):(sum(num)+b-1),:)=OldPop(unidrnd(m,1,b-1),:); end GlobalMaxfit,I=max(fit);%保留每一代中最佳个体 NewPop(end,:)=OldPop(I,:); % - 交叉操作 -function NewPop=CrossOver(OldPop,pCross,opts)global m n NewPop r=rand(1,m);y1=find(r<pCross);y2=find(r>=pCross);len=length(y1);if len=1|(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)=;endi=0;if length(y1)>=2 if opts(1)=1%浮点编码交叉 while(i<=length(y1)-2) NewPop(y1(i+1),:)=OldPop(y1(i+1),:); NewPop(y1(i+2),:)=OldPop(y1(i+2),:); if opts(2)=0&n>1%discret crossover Points=sort(unidrnd(n,1,2); NewPop(y1(i+1),Points(1):Points(2)=OldPop(y1(i+2),Points(1):Points(2); NewPop(y1(i+2),Points(1):Points(2)=OldPop(y1(i+1),Points(1):Points(2); elseif opts(2)=1%arithmetical crossover Points=round(unifrnd(0,pCross,1,n); CrossPoints=find(Points=1); r=rand(1,length(CrossPoints); NewPop(y1(i+1),CrossPoints)=r.*OldPop(y1(i+1),CrossPoints)+(1-r).*OldPop(y1(i+2),CrossPoints); NewPop(y1(i+2),CrossPoints)=r.*OldPop(y1(i+2),CrossPoints)+(1-r).*OldPop(y1(i+1),CrossPoints); else %AEA recombination Points=round(unifrnd(0,pCross,1,n); CrossPoints=find(Points=1); v=unidrnd(4,1,2); NewPop(y1(i+1),CrossPoints)=(floor(10v(1)*OldPop(y1(i+1),CrossPoints)+. 10v(1)*OldPop(y1(i+2),CrossPoints)-floor(10v(1)*OldPop(y1(i+2),CrossPoints)/10v(1); NewPop(y1(i+2),CrossPoints)=(floor(10v(2)*OldPop(y1(i+2),CrossPoints)+. 10v(2)*OldPop(y1(i+1),CrossPoints)-floor(10v(2)*OldPop(y1(i+1),CrossPoints)/10v(2); end i=i+2; end elseif opts(1)=0%二进制编码交叉 while(i<=length(y1)-2) if opts(2)=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 i=i+2; end else %Tsp问题次序杂交 for i=0:2:length(y1)-2 xPoints=sort(unidrnd(n,1,2); NewPop(y1(i+1) y1(i+2),xPoints(1):xPoints(2)=OldPop(y1(i+2) y1(i+1),xPoints(1):xPoints(2); %NewPop(y1(i+2),xPoints(1):xPoints(2)=OldPop(y1(i+1),xPoints(1):xPoints(2); temp=OldPop(y1(i+1),xPoints(2)+1:n) OldPop(y1(i+1),1:xPoints(2); for del1i=xPoints(1):xPoints(2) temp(find(temp=OldPop(y1(i+2),del1i)=; end NewPop(y1(i+1),(xPoints(2)+1):n)=temp(1:(n-xPoints(2); NewPop(y1(i+1),1:(xPoints(1)-1)=temp(n-xPoints(2)+1):end); temp=OldPop(y1(i+2),xPoints(2)+1:n) OldPop(y1(i+2),1:xPoints(2); for del2i=xPoints(1):xPoints(2) temp(find(temp=OldPop(y1(i+1),del2i)=; end NewPop(y1(i+2),(xPoints(2)+1):n)=temp(1:(n-xPoints(2); NewPop(y1(i+2),1:(xPoints(1)-1)=temp(n-xPoints(2)+1):end); end endendNewPop(y2,:)=OldPop(y2,:);% -二进制串均匀交叉算子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% -二进制串多点交叉算子function Children1,Children2=MultiPointCross(Parent1,Parent2)%交叉点数由变量数决定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,fit,pMutation,VarNum,opts)global m n NewPopNewPop=OldPop;r=rand(1,m);MutIn=find(r<=pMutation);L=length(MutIn);i=1;if opts(1)=1%浮点变异 maxfit=max(fit); upfit=maxfit+0.05*abs(maxfit); if opts(2)=1|opts(2)=3 while(i<=L)%自适应变异（自增或自减） Point=unidrnd(n); T=(1-fit(MutIn(i)/upfit)2; q=abs(1-randT); %if q>1%按严格数学推理来说，这段程序是不能缺少的 % q=1 %end p=OldPop(MutIn(i),Point)*(1-q); if unidrnd(2)=1 NewPop(MutIn(i),Point)=p+q; else NewPop(MutIn(i),Point)=p; end i=i+1; end elseif opts(2)=2|opts(2)=4%AEA变异（任意变量的某一位变异） while(i<=L) Point=unidrnd(n); T=(1-abs(upfit-fit(MutIn(i)/upfit)2; v=1+unidrnd(1+ceil(10*T); %v=1+unidrnd(5+ceil(10*eranum/MaxEranum); q=mod(floor(OldPop(MutIn(i),Point)*10v),10); NewPop(MutIn(i),Point)=OldPop(MutIn(i),Point)-(q-unidrnd(9)/10v; i=i+1; end else while(i<=L) Point=unidrnd(n); if round(rand) NewPop(MutIn(i),Point)=OldPop(MutIn(i),Point)*(1-rand); else NewPop(MutIn(i),Point)=OldPop(MutIn(i),Point)+(1-OldPop(MutIn(i),Point)*rand; end i=i+1; end end elseif opts(1)=0%二进制串变异 if L>=1 while i<=L k=unidrnd(n,1,VarNum); %设置变异点数(=变量数) for j=1:length(k) if NewPop(MutIn(i),k(j)=1 NewPop(MutIn(i),k(j)=0; else NewPop(MutIn(i),k(j)=1; end end i=i+1; end endelse%Tsp变异 if opts(2)=1|opts(2)=2|opts(2)=3|opts(2)=4 numMut=ceil(pMutation*m); r=unidrnd(m,numMut,2); LocalMinfit,In=min(fit(r),2); SelectIn=r(In-1)*numMut+1:numMut'); while(i<=numMut) mPoints=sort(unidrnd(n,1,2); if mPoints(1)=mPoints(2) NewPop(SelectIn(i),1:mPoints(1)-1)=OldPop(SelectIn(i),1:mPoints(1)-1); NewPop(SelectIn(i),mPoints(1):mPoints(2)-1)=OldPop(SelectIn(i),mPoints(1)+1:mPoints(2); NewPop(SelectIn(i),mPoints(2)=OldPop(SelectIn(i),mPoints(1); NewPop(SelectIn(i),mPoints(2)+1:n)=OldPop(SelectIn(i),mPoints(2)+1:n); else NewPop(SelectIn(i),:)=OldPop(SelectIn(i),:); end i=i+1; end else r=rand(1,m); MutIn=find(r<=pMutation); L=length(MutIn); while i<=L mPoin