三個遺傳算法matlab程序實例

1、遺傳算法程序(一) :說明：fga.m為遺傳算法的主程序；采用二進制Gray編碼，采用基于輪盤賭法的非線性排 名選擇 , 均勻交叉 ,變異操作 ,而且還引入了倒位操作 !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

2、solves problems of the form：% max F(X) subject to： 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值% FUN- 目標函數% LB- 自變量下限% UB- 自變量上限% eranum- 種群的代數 ，取 100-1000(默認 200)% popsize- 每一代種群的規(guī)模；此可取50-200( 默認 100)% pcross- 交叉概率 ，一般取 0.5-0.85 之間較好 (默認 0.8)% pmutation - 初始變異概率 ，一般取 0.05-0.2 之間較好 (默

3、認 0.1)% pInversion - 倒位概率 ，一般取 0.050.3 之間較好 (默認 0.2)% 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)% T1=clock；if nargin0)error( 數據輸入錯誤 ,請重新輸入 (LBUB)：)；ends=sprintf(程序運行需要約 %.4f秒鐘時間，請稍等 ,(eranum*popsize/1000);disp(s)；global m n NewPop children1 children2 VarNum

4、 bounds=LB;UB;bits=;VarNum=size(bounds,1);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);% 由設定精度劃分區(qū)間 Pop=InitPopGray(popsize,bits);% 初始化種群m,n=size(Pop);NewPop=zeros(m,n);children1=zeros(1,n);children2=zeros(1,n);pm0=pMutation;BestPop=zeros(era num, n);% 分配

5、初始解空間 BestPop,TraceTrace=zeros(eranum,length(bits)+1);i=1;while i=eranumfor j=1:mvalue(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits);% 計算適應度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

6、(FUN,Pop,bounds,bits);% 非線性排名選擇 CrossOverPop=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum);%采用多點交叉和均勻交叉，且逐步增大均勻交叉的概率%round(unidrnd(eranum-i)/eranum)MutationPop=Mutation(CrossOverPop,pMutation,VarNum);% 變異 InversionPop=Inversion(MutationPop,pInversion);% 倒位Pop=In vers ion Pop;% 更新pMutati

7、o n=pmO+(iA4)*(pCross/3-pmO)/(era nu mM);%隨著種群向前進化，逐步增大變異率至1/2 交叉率p(i)=pMutation;i=i+1;endt=1:eranum;plot(t,Trace(:,1);title(函數優(yōu)化的遺傳算法);xlabel(進化世代數(era nu m);ylabel(每一代最優(yōu)適應度(maxfitness);MaxFval,I=max(Trace(:,1);X=Trace(I,(2:length(bits)+1);hold on; plot(I,MaxFval,*);text(I+5,MaxFval,FMAX= num2str(M

8、axFval);str1=sprintf ( 進化到 %d 代 ,自變量為 %s 時,得本次求解的最優(yōu)值 %fn 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;elapsed_time=T2-T1;if elapsed_time(6)0elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;endif elapsed_time(5)1 時,b(i)=

9、mod(a(i-1)+a(i),2)%其中原二進制串：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%解碼function fval = b2f(bval,bounds,bits)% fval - 表征各變量的十進制數% 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=(bou nds(:,2)-bou n

10、ds(:,1)./(24bits-1); %The range of the variables numV=size(bounds,1);cs=0 cumsum(bits);for i=1:numVa=bval(cs(i)+1):cs(i+1);fval(i)=sum(2.A(size(a,2)-1:-1:0).*a)*scale(i)+bou nds(i,1);end%選擇操作%采用基于輪盤賭法的非線性排名選擇%各個體成員按適應值從大到小分配選擇概率：%P(i)=(q/1-(1-q)An)*(1-q)9,其中 P(O)PP(n), sum(P(i)=1function selectpop=N

11、onlinearRankSelect(FUN,pop,bounds,bits)global m nselectpop=zeros(m,n);fit=zeros(m,1);for i=1:mfit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits);% 以函數值為適應值做排名依據 endselectprob=fit/sum(fit);% 計算各個體相對適應度 (0,1)q=max(selectprob);% 選擇最優(yōu)的概率 x=zeros(m,2);x(:,1)=m:-1:1;y x(:,2)=sort(selectprob);r=q/(1-(1-q)Am)

12、;%標準分布基值newfit(x(:,2)=r*(1-q).A(x(:,1)-1);% 生成選擇概率newfit=cumsum(newfit);% 計算各選擇概率之和 rNums=sort(rand(m,1);fitIn=1;newIn=1;while newIn=mif rNums(newIn)newfit(fitIn) selectpop(newIn,:)=pop(fitIn,:); newIn=newIn+1;elsefitIn=fitIn+1;endend%交叉操作function NewPop=CrossOver(OldPop,pCross,opts)%OldPop 為父代種群， p

13、cross 為交叉概率 global m n NewPopr=rand(1,m); y1=find(r=pCross); len=length(y1);if len2&mod(len,2)=1% 如果用來進行交叉的染色體的條數為奇數，將其調整為偶數 y2(length(y2)+1)=y1(len);y1(len)=;endif length(y1)=2for i=0:2:length(y1)-2if opts=0NewPop(y1(i+1),:),NewPop(y1(i+2),:)=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:); else

14、NewPop(y1(i+1),:),NewPop(y1(i+2),:)=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:); endendendNewPop(y2,:)=OldPop(y2,:);%采用均勻交叉function children1,children2=EqualCrossOver(parent1,parent2)global n children1 children2hidecode=round(rand(1,n);% 隨機生成掩碼 crossposition=find(hidecode=1);holdposition=fin

15、d(hidecode=0); children1(crossposition)=parent1(crossposition);% 掩碼為 1，父 1 為子 1 提供基因 children1(holdposition)=parent2(holdposition);% 掩碼為 0，父 2 為子 1 提供基因 children2(crossposition)=parent2(crossposition);% 掩碼為 1，父 2 為子 2 提供基因 children2(holdposition)=parent1(holdposition);% 掩碼為 0，父 1 為子 2 提供基因%采用多點交叉，交叉

16、點數由變量數決定function Children1,Children2=MultiPointCross(Parent1,Parent2)global n Children1 Children2 VarNumChildren1=Parent1;Children2=Parent2;Points=sort(unidrnd(n,1,2*VarNum);for i=1:VarNumChildren1(Points(2*i-1):Points(2*i)=Parent2(Points(2*i-1):Points(2*i);Children2(Points(2*i-1):Points(2*i)=Parent

17、1(Points(2*i-1):Points(2*i);end%變異操作function NewPop=Mutation(OldPop,pMutation,VarNum) global m n NewPop r=rand(1,m); position=find(r=1for i=1:lenk=unidrnd(n,1,VarNum); % 設置變異點數，一般設置 1 點 for j=1:length(k)if OldPop(position(i),k(j)=1 OldPop(position(i),k(j)=0;elseOldPop(position(i),k(j)=1;endendendend

18、NewPop=OldPop;%倒位操作function NewPop=Inversion(OldPop,pInversion)global m n NewPopNewPop=OldPop;r=rand(1,m);PopIn=find(r=1for i=1:lend=sort(unidrnd(n,1,2);if d(1)=1&d(2)=nNewPop(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

19、)=OldPop(PopIn(i),d(2)+1:n); endend end遺傳算法程序（二）function youhuafunD=code;N=50; % Tunable maxgen=50;% Tunablecrossrate=0.5; %Tunable muterate=0.08; %Tunable generation=1;num = length(D); fatherrand=randint(num,N,3); score = zeros(maxgen,N); while generation1450)|(min(F2)=900)error(DATA property F2 ex

20、ceed its range (900,1450) end% get group property F1 of data, according to F2 value F4=zeros(size(F1);for ite=11:-1:1 index=find(F2best.max_fadvance_k=advance_k+1; x_better(advance_k)=fitness.x; best.max_f=max(f); best.popus=popus; best.x=fitness.x;endif mod(advance_k,SPEEDUP_INTER)=0RANGE=minmax(x_

21、better);RANGEadvance=0;endendreturn;function popus=init% 初始化M=50;%種群個體數目N=30;%編碼長度popus=round(rand(M,N);return;function fitness=fit(popus,RANGE)% 求適應度M,N=size(popus);fitn ess=zeros(M,1);% 適應度f=zeros(M,1);% 函數值A=RANGE(1);B=RANGE(2);初始取值范圍0 255for m=1:Mx=0;for n=1:Nx=x+popus(m, n)*(2( n-1);endx=x*(B-A

22、)/(2AN)+A;for k=1:5 f(m,1)=f(m,1)-(k*sin(k+1)*x+k);endendf_std=(f-min(f)./(max(f)-min(f);% 函數值標準化 fitness.f=f;fitness.f_std=f_std;fitness.x=x;return;function picked=choose(popus,fitness)% 選擇 f=fitness.f;f_std=fitness.f_std;M,N=size(popus);choose_N=3; picked=zeros(choose_N,2); p=zeros(M,1);%選擇 choose

23、_N 對雙親 %記錄選擇好的雙親%選擇概率d_order=zeros(M,1);%把父代個體按適應度從大到小排序f_t=sort(f,descend);% 將適應度按降序排列for k=1:Mx=find(f=f_t(k);% 降序排列的個體序號 d_order(k)=x(1);endfor m=1:Mpopus_t(m,:)=popus(d_order(m),:);endpopus=popus_t;f=f_t;p=f_std./sum(f_std);%選擇概率c_p=cumsum(p);%累積概率for cn=1:choose_Npicked(cn,1)=roulette(c_p); % 輪盤賭picked(cn,2)=roulette(c_p); % 輪盤賭 popus=intercross(popus,picked(cn,:);% 雜交 endpopus=aberrance(popus,picked);% 變異 return;function popus=interc