材料多目標代碼fmaxga

function[BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation,options)%[BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)%Findsamaximumofafunctionofseveralvariables.%fmaxgasolvesproblemsoftheform:%maxF(X)subjectto:LB<=X<=UB%BestPop--------最優(yōu)的群體即為最優(yōu)的染色體群%Trace-----------最佳染色體所對應的目標函數(shù)值%FUN------------目標函數(shù)%LB--------------自變量下限%UB--------------自變量上限%eranum----------種群的代數(shù),取100--1000(默認1000)%popsize---------每一代種群的規(guī)模；此可取50--100(默認50)%pcross-----------交叉的概率,此概率一般取0.5--0.85之間較好(默認0.8)%pmutation------變異的概率,該概率一般取0.05-0.2左右較好(默認0.1)%options--------1×2矩陣,options(1)=0二進制編碼(默認0),option(1)~=0十進制編碼,option(2)設定求解%精度(默認1e-4)%%如測試Shaffer's(f=0.5-((sin(sqrt(x(1)^2+x(2)^2)))^2-0.5)/(1+0.001*(x(1)^2+x(2)^2))^2)函數(shù),自變量下限%%[-100,-100],上限[100,100],當x=[00]時,取得理想最優(yōu)MaxF6=1%運行得到相當好的結果:自變量為0.00033379-4.7684e-005時,最優(yōu)值1.000000%對應染色體是：10000000000000000001101111%1111111111111111T1=clock;ifnargin<3,error('FMAXGArequiresatleastthreeinputarguments');endifnargin==3,eranum=1000;popsize=50;pcross=0.8;pmutation=0.1;options=[01e-4];endifnargin==4,popsize=50;pcross=0.8;pmutation=0.1;options=[01e-4];endifnargin==5,pcross=0.8;pmutation=0.1;options=[01e-4];endifnargin==6,pmutation=0.1;options=[01e-4];endifnargin==7,options=[01e-4];endiffind((LB-UB)>0)error('數(shù)據(jù)輸入錯誤,請重新輸入(LB<UB):');ends=sprintf('程序運行需要約%.4f秒鐘時間,請稍等......',(eranum*popsize*40/(1000*50)));disp(s);bounds=[LB;UB]';bits=[];precision=options(2);%由求解精度確定二進制編碼長度bits=ceil(log2((bounds(:,2)-bounds(:,1))'./precision));[Pop]=initpop(popsize,bits);%初始化種群[m,n]=size(Pop);pm0=pmutation;BestPop=zeros(eranum,n);Trace=zeros(eranum,length(bits)+1);%分配初始解空間i=1;whilei<=eranumforj=1:mvalue(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%計算適應度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]=selectchrom(FUN,Pop,bounds,bits);%選擇[CrossOverPop]=CrossOver(selectpop,pcross);%交叉[NewPop]=Mutation(CrossOverPop,pmutation);%變異Pop=NewPop;%更新pmutation=pm0+(i^4)*(0.6-pm0)/(eranum^4);%隨著種群向前進化，逐步增大變異率p(i)=pmutation;i=i+1;endt=1:eranum;plot(t,Trace(:,1)');title('函數(shù)優(yōu)化的遺傳算法');xlabel('進化世代數(shù)(eranum)');ylabel('每一代最優(yōu)適應度(maxfitness)');[MaxFval,I]=max(Trace(:,1));X=Trace(I,(2:length(bits)+1));holdon;plot(I,MaxFval,'*');text(I+5,MaxFval,['FMAX='num2str(MaxFval)]);str1=sprintf('進化到%d代,自變量為%s時,得本次求解的最優(yōu)值%f\n對應染色體是：%s',...I,num2str(X),MaxFval,num2str(BestPop(I,:)));disp(str1);%figure(2);plot(t,p);%繪制變異值增大過程T2=clock;CostTime=T2-T1;ifCostTime(6)<0CostTime(6)=CostTime(6)+60;CostTime(5)=CostTime(5)-1;endifCostTime(5)<0CostTime(5)=CostTime(5)+60;CostTime(4)=CostTime(4)-1;end%像這種程序當然不考慮運行上小時啦str2=sprintf('程序運行耗時%d小時%d分鐘%.4f秒',CostTime(4),CostTime(5),CostTime(6));disp(str2);%初始化種群，采用二進制編碼function[pop]=initpop(popsize,bits)len=sum(bits);pop(1,:)=zeros(1,len);fori=2:popsize-1pop(i,:)=round(rand(1,len));endpop(popsize,:)=ones(1,len);%解碼function[fval]=b2f(bval,bounds,bits)%fval-表征各變量的十進制數(shù)%bval-表征各變量的二進制編碼串%bounds-各變量的取值范圍%bits-各變量的二進制編碼長度scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1);numV=size(bounds,1);cs=[0cumsum(bits)];fori=1:numVa=bval((cs(i)+1):cs(i+1));fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);end%計算各個體的適應度并采用輪盤賭進行選擇function[selectpop]=selectchrom(FUN,pop,bounds,bits)%采用輪盤賭選擇方法[m,n]=size(pop);fori=1:mfit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函數(shù)值為適應度endselectprob=fit/sum(fit);%選擇概率prob=cumsum(selectprob);%累計選擇概率sumprob=[0prob];fori=1:mselectpop(i,:)=pop(length(find(rand>=sumprob)),:);end%交叉操作function[NewPop]=CrossOver(OldPop,pcross)%OldPop為父代種群，pcross為交叉概率[m,n]=size(OldPop);r=rand(1,m);y1=find(r<pcross);y2=find(r>=pcross);len=length(y1);iflen>2&mod(len,2)==1%如果用來進行交叉的染色體的條數(shù)為奇數(shù)，將其調(diào)整為偶數(shù)y2(length(y2)+1)=y1(len);y1(len)=[];endiflength(y1)>=2fori=0:2:length(y1)-2[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));endendNewPop(y2,:)=OldPop(y2,:);function[children1,children2]=EqualCrossOver(parent1,parent2)%采用均勻交叉例：%父1：01110011010%父2：10101100101%掩碼：01100011010%交叉后新個體：%子1：11101111111%子2：00110000000L=length(parent1);hidecode=round(rand(1,L));%隨機生成掩碼，如hidecode=[01100011010];children1=zeros(1,L);children2=zeros(1,L);children1(find(hidecode==1))=parent1(find(hidecode==1));%掩碼為1，父1為子1提供基因children1(find(hidecode==0))=parent2(find(hidecode==0));%掩碼為0，父2為子1提供基因children2(find(hidecode==1))=parent2(find(hidecode==1));%掩碼為1，父2為子2提供基因children2(find(hidecode==0))=parent1(find(hidecode==0));%掩碼為0，父1為子2提供基因%變異操作function[NewPop]=Mutation(OldPop,pmutation)[m,n]=size(OldPop);r=rand(1,m);position=find(r<=pmutation);len=length(position);iflen>=1fori=1:lenk=unidrnd(n,1,1);%設置變異點數(shù)，一般設置1點forj=1:length(k)ifOldPop(position(i),k(j))==1OldPop(position(i),k(j))=0;elseOldPop(position(i),k(j))=1;end