非線性整數(shù)規(guī)劃的遺傳算法Matlab程序

1、非線性整數(shù)規(guī)劃的遺傳算法Matlab程序附圖通常,非線性整數(shù)規(guī)劃是一個(gè)具有指數(shù)復(fù)雜度的NP問(wèn)題,如果約束較為復(fù)雜,Matlab優(yōu)化工具箱和一些優(yōu)化軟件比方lingo等,常常無(wú)法應(yīng)用,即使能應(yīng)用也不能給出一個(gè)較為令人滿意的解.這時(shí)就需要針對(duì)問(wèn)題設(shè)計(jì)專(zhuān)門(mén)的優(yōu)化算法.下面舉一個(gè)遺傳算法應(yīng)用于非線性整數(shù)規(guī)劃的編程實(shí)例,供大家參考！模型的形式和適應(yīng)度函數(shù)定義如下：millE-3、口二工支三*j=i,2*,療_f=1,2t3,ws0或L適應(yīng)度函數(shù)為：而電不“內(nèi)工,manfEmO#/叼0抬/i-l/-I其中*=2即.工=2=2%門(mén)口一物-%,元=X=NZ/0X=0.3,02X忠13*J!eslj.l這是一個(gè)

2、具有200個(gè)01決策變量的多目標(biāo)非線性整數(shù)規(guī)劃,編寫(xiě)優(yōu)化的目標(biāo)函數(shù)如下,其中將多目標(biāo)轉(zhuǎn)化為單目標(biāo)采用簡(jiǎn)單的加權(quán)處理.functionFitness=FITNESSx,FARM,e,q,w%適應(yīng)度函數(shù)%輸入?yún)?shù)列表%x決策變量構(gòu)成的4X50的0-1矩陣%FARM細(xì)胞結(jié)構(gòu)存儲(chǔ)的當(dāng)前種群,它包含了個(gè)體x%e4X50的系數(shù)矩陣%q4X50的系數(shù)矩陣%w1X50的系數(shù)矩陣%gamma=0.98;N=length(FARM);%種群規(guī)模F1=zeros(1,N);F2=zeros(1,N);fori=1:Nxx=FARMi;ppp=(1-xx)+(1-q).*xx;F1(i)=sum(w.*prod(pp

3、p);F2(i)=sum(sum(e.*xx);endppp=(1-x)+(1-q).*x;f1=sum(w.*prod(ppp);f2=sum(sum(e.*x);Fitness=gamma*sum(min(sign(f1-F1);zeros(1,N)+(1-gamma)*sum(min(sign(f2-F2);zeros(1,N);針對(duì)問(wèn)題設(shè)計(jì)的遺傳算法如下,其中對(duì)模型約束的處理是重點(diǎn)考慮的地方functionXp,LC1,LC2,LC3,LC4=MYGA(M,N,Pm)%求解01整數(shù)規(guī)劃的遺傳算法%輸入?yún)?shù)列表%M遺傳進(jìn)化迭代次數(shù)%N種群規(guī)模%Pm變異概率%輸出參數(shù)列表%Xp最優(yōu)個(gè)體%L

4、C1子目標(biāo)1的收斂曲線%LC2子目標(biāo)2的收斂曲線%LC3平均適應(yīng)度函數(shù)的收斂曲線%LC4最優(yōu)適應(yīng)度函數(shù)的收斂曲線%參考調(diào)用格式Xp,LC1,LC2,LC3,LC4=MYGA(50,40,0.3)%第一步：載入數(shù)據(jù)和變量初始化loadeqw;%載入三個(gè)系數(shù)矩陣e,q,w%俞出變量初始化Xp=zeros(4,50);LC1=zeros(1,M);LC2=zeros(1,M);LC3=zeros(1,M);LC4=zeros(1,M);Best=inf;%第二步：隨機(jī)產(chǎn)生初始種群farm=cell(1,N);%用于存儲(chǔ)種群的細(xì)胞結(jié)構(gòu)k=0;whilek%以下是一個(gè)合法個(gè)體的產(chǎn)生過(guò)程x=zeros(4

5、,50);%x每一列的1的個(gè)數(shù)隨機(jī)決定fori=1:50R=rand;Col=zeros(4,1);ifR0.9RP=randperm(4);Col(RP(1:2)=1;elseRP=randperm(4);Col(RP(1:3)=1;endx(:,i)=Col;end%下面是檢查行和是否滿足約束的過(guò)程,對(duì)于不滿足約束的予以拋棄Temp1=sum(x,2);Temp2=find(Temp120);iflength(Temp2)=0k=k+1;farmk=x;endend%以下是進(jìn)化迭代過(guò)程counter=0;%設(shè)置迭代計(jì)數(shù)器whilecounter%第三步：交叉%交叉采用雙親雙子單點(diǎn)交叉new

6、farm=cell(1,2*N);%用于存儲(chǔ)子代的細(xì)胞結(jié)構(gòu)Ser=randperm(N);%兩兩隨機(jī)配對(duì)的配對(duì)表A=farmSer(1);%取出父代AB=farmSer(2);%取出父代BP0=unidrnd(49);%隨機(jī)選擇交叉點(diǎn)a=A(:,1:P0),B(:,(P0+1):end);%產(chǎn)生子代ab=B(:,1:P0),A(:,(P0+1):end);%產(chǎn)生子代bnewfarm2*N-1=a;%參加子代種群newfarm2*N=b;%以下循環(huán)是重復(fù)上述過(guò)程fori=1:(N-1)A=farmSer(i);B=farmSer(i+1);P0=unidrnd(49);a=A(:,1:P0),B

7、(:,(P0+1):end);b=B(:,1:P0),A(:,(P0+1):end);newfarm2*i-1=a;newfarm2*i=b;endFARM=farm,newfarm;%新舊種群合并%第四步：選擇復(fù)制FLAG=ones(1,3*N);%標(biāo)志向量,對(duì)是否滿足約束進(jìn)行標(biāo)記%以下過(guò)程是檢測(cè)新個(gè)體是否滿足約束fori=1:(3*N)x=FARMi;sum1=sum(x,1);sum2=sum(x,2);flag1=find(sum1=0);flag2=find(sum1=4);flag3=find(sum220);iflength(flag1)+length(flag2)+length

8、(flag3)0FLAG(i)=0;%如果不滿足約束,用0加以標(biāo)記endendNN=length(find(FLAG)=1);%滿足約束的個(gè)體數(shù)目,它一定大于等于NNEWFARM=cell(1,NN);%以下過(guò)程是剔除不滿主約束的個(gè)體kk=0;fori=1:(3*N)ifFLAG(i)=1kk=kk+1;NEWFARMkk=FARMi;endend%以下過(guò)程是計(jì)算并存儲(chǔ)當(dāng)前種群每個(gè)個(gè)體的適應(yīng)值SYZ=zeros(1,NN);syz=zeros(1,N);fori=1:NNx=NEWFARMi;SYZ(i)=FITNESS2(x,NEWFARM,e,q,w);%調(diào)用適應(yīng)值子函數(shù)endk=0;%下

9、面是選擇復(fù)制,選擇較優(yōu)的N個(gè)個(gè)體復(fù)制到下一代whilekminSYZ=min(SYZ);posSYZ=find(SYZ=minSYZ);POS=posSYZ(1);k=k+1;farmk=NEWFARMPOS;syz(k)=SYZ(POS);SYZ(POS)=inf;end%記錄和更新,更新最優(yōu)個(gè)體,記錄收斂曲線的數(shù)據(jù)minsyz=min(syz);meansyz=mean(syz);pos=find(syz=minsyz);LC3(counter+1)=meansyz;ifminsyzBest=minsyz;Xp=farmpos(1);endLC4(counter+1)=Best;ppp=(

10、1-Xp)+(1-q).*Xp;LC1(counter+1)=sum(w.*prod(ppp);LC2(counter+1)=sum(sum(e.*Xp);%第五步：變異fori=1:NifPmrand%是否變異由變異概率Pm限制AA=farmi;%取出一個(gè)個(gè)體POS=unidrnd(50);%隨機(jī)選擇變異位R=rand;Col=zeros(4,1);ifR0.9RP=randperm(4);Col(RP(1:2)=1;elseRP=randperm(4);Col(RP(1:3)=1;end卜面是判斷變異產(chǎn)生的新個(gè)體是否滿足約束,如果不滿足,此次變異無(wú)效AA(:,POS)=Col;Temp1=sum(AA,2);Temp2=find(Temp120);iflength(Temp2)=0farmi=AA;endendendcounter=counter+1end%第七步：繪收斂曲線圖figure(1);plot(LC1);xlabel(迭代次數(shù));ylabel(子目標(biāo)1的值)；title(子目標(biāo)1的收斂曲線);figure(2);plot(LC2);xlabel(迭代次數(shù));ylabel(子目標(biāo)2的值)；title(子目標(biāo)2的收斂曲線);figure(3);plot(LC3);xlabel(迭代次數(shù));ylabel(