數學建模專題之

遺傳算法的MATLAB實現精選pptContentsIMatlab編程實現GA1Matlab函數調用實現GA2Matlab工具箱實現GA3精選pptMatlab編程實現GA例1：計算目標函數值函數

精選ppt主程序

%遺傳算法主程序functionMy_GAglobalCmin;Cmin=-10^6;popsize=50;%群體大小Gene=20;chromlength=20;%字符串長度〔個體長度〕pc=0.8;%交叉概率pm=0.01;%變異概率Xmax=10;Xmin=0;Matlab編程實現GApop=initpop(popsize,chromlength);%隨機產生初始群體fori=1:Gene%20為迭代次數[objvalue]=calobjvalue(pop,chromlength,Xmax,Xmin);%計算目標函數fitvalue=calfitvalue(objvalue);%計算群體中每個個體的適應度[newpop]=selection(pop,fitvalue);%復制[newpop]=crossover(newpop,pc);%交叉[newpop]=mutation(newpop,pm);%變異[bestindividual,bestfit]=best(pop,fitvalue);%求出群體中適應值最大的個體及其適應值x(i)=decodechrom(bestindividual,1,chromlength)*10/(2^chromlength-1);%最正確個體解碼y(i)=bestfit+Cmin;%最正確個體適應度y_mean(i)=mean(fitvalue+Cmin);%第i代平均適應度pop=newpop;endfplot('2*x+10*sin(5*x)+7*cos(4*x)',[010])holdonplot(x,y,'r*')holdoff精選ppt初始化(編碼)

%initpop.m函數的功能是實現群體的初始化，popsize表示群體的大小，chromlength表示染色體的長度(二值數的長度)，%長度大小取決于變量的二進制編碼的長度(在本例中取20位)。%Name:initpop.mfunctionpop=initpop(popsize,chromlength)pop=round(rand(popsize,chromlength));%rand隨機產生每個單元為{0,1}行數為popsize，列數為chromlength的矩陣，%round對矩陣的每個單元進行取整。這樣產生的初始種群。Matlab編程實現GA精選ppt將二進制數轉化為十進制數

將二進制數轉化為十進制數%產生[2^n2^(n-1)...1]的行向量，然后求和，將二進制轉化為十進制functionpop2=decodebinary(pop)[px,py]=size(pop);%求pop行和列數fori=1:py pop1(:,i)=2.^(py-i).*pop(:,i);endpop2=sum(pop1,2);%求pop1的每行之和functionpop2=decodechrom(pop,spoint,length)pop1=pop(:,spoint:spoint+length-1);pop2=decodebinary(pop1);Matlab編程實現GA精選ppt計算目標函數值

計算目標函數值%calobjvalue.m函數的功能是實現目標函數的計算，其公式采用本文例如仿真，可根據不同優化問題予以修改。%遺傳算法子程序%Name:calobjvalue.m%實現目標函數的計算function[objvalue]=calobjvalue(pop,chromlength,Xmax,Xmin)temp1=decodechrom(pop,1,chromlength);%將pop每行轉化成十進制數x=temp1*(Xmax-Xmin)/(2^chromlength-1);%將十進制域中的數轉化為變量域的數objvalue=2*x+10*sin(5*x)+7*cos(4*x);%計算目標函數值Matlab編程實現GA精選ppt計算個體的適應值

functionfitvalue=calfitvalue(objvalue)globalCmin;fitvalue=objvalue-Cmin;Matlab編程實現GA精選ppt選擇復制

function[newpop]=selection(pop,fitvalue)%程序中采用賭輪盤選擇法選擇實現totalfit=sum(fitvalue);%求適應值之和fitvalue=fitvalue/totalfit;%單個個體被選擇的概率fitvalue=cumsum(fitvalue);%如fitvalue=[1234]，那么cumsum(fitvalue)=[13610][px,py]=size(pop);ms=sort(rand(px,1));%從小到大排列fitin=1;newin=1;whilenewin<=px%蒙特卡洛方法抽樣if(ms(newin))<fitvalue(fitin)newpop(newin,:)=pop(fitin,:);newin=newin+1;elsefitin=fitin+1;endendMatlab編程實現GA精選ppt交叉

function[newpop]=crossover(pop,pc)[px,py]=size(pop);newpop=ones(size(pop));fori=1:2:px-1if(rand<pc)cpoint=round(rand*py);newpop(i,:)=[pop(i,1:cpoint),pop(i+1,cpoint+1:py)];newpop(i+1,:)=[pop(i+1,1:cpoint),pop(i,cpoint+1:py)];elsenewpop(i,:)=pop(i);newpop(i+1,:)=pop(i+1);endendMatlab編程實現GA精選ppt變異

function[newpop]=mutation(pop,pm)[px,py]=size(pop);newpop=ones(size(pop));fori=1:pxif(rand<pm)mpoint=round(rand*py);ifmpoint<=0mpoint=1;endnewpop(i,:)=pop(i,:);

Matlab編程實現GAifany(newpop(i,mpoint))==0newpop(i,mpoint)=1;elsenewpop(i,mpoint)=0;endelsenewpop(i,:)=pop(i,:);endend精選ppt求出群體中最大的適應值及其個體

function[bestindividual,bestfit]…=best(pop,fitvalue)[px,py]=size(pop);bestindividual=pop(1,:);bestfit=fitvalue(1);fori=2:pxiffitvalue(i)>bestfitbestindividual=pop(i,:);bestfit=fitvalue(i);endendMatlab編程實現GA或function[bestindividual,bestfit]=…best(pop,fitvalue)[bestfit,m_indx]=max(fitvalue);bestindividual=pop(m_indx,:);精選ppt結果見My_GA.m

Matlab編程實現GA精選pptMatlab函數調用實現GAMatlab的GA函數

[xfval]=ga(@fitnessfun,nvars,[],[],[],[],[],[],[],options)；fitnessfcn—Fitnessfunctionnvars—NumberofvariablesfortheproblemAineq—MatrixforinequalityconstraintsBineq—VectorforinequalityconstraintsAeq—MatrixforequalityconstraintsBeq—VectorforequalityconstraintsLB—LowerboundonxUB—Upperboundonxnonlcon—NonlinearconstraintFunctionoptions—Optionsstructure精選pptMatlab函數調用實現GAMatlab的GA函數x=ga(fitnessfcn,nvars)x=ga(fitnessfcn,nvars,A,b)x=ga(fitnessfcn,nvars,A,b,Aeq,beq)x=ga(fitnessfcn,nvars,A,b,Aeq,beq,LB,UB)x=ga(fitnessfcn,nvars,A,b,Aeq,beq,LB,UB,nonlcon)x=ga(fitnessfcn,nvars,A,b,Aeq,beq,LB,UB,nonlcon,options)x=ga(problem)[x,fval]=ga(...)[x,fval,exitflag]=ga(...)精選pptMatlab函數調用實現GAGA函數調用步驟第一步：編寫適應度函數；第二步：對GA參數進行設置；options=gaoptimset(‘參數名’,參數值,…,‘參數名’,參數值)例:options=gaoptimset('PopulationSize',100)第三步：調用GA函數；[xfval]=ga(@fitnessfun,nvars)[xfvalexitflagoutputpopulationscores]=ga(@fitnessfcn,nvars)[xfval]=ga(@fitnessfun,nvars,[],[],[],[],[],[],[],options)；specifyanylinearequality,linearinequality,ornonlinearconstraints精選pptMatlab函數調用實現GA調用GA函數求例1的最大值〔見ga_eg1.m〕第一步：編寫適應度函數；functiony=fit1(x)y=-(2*x+10*sin(5*x)+7*cos(4*x));第二步：設置參數options=gaoptimset('PopulationSize',100,'PopulationType','doubleVector','PlotFcns',{@gaplotbestf,@gaplotbestindiv,@gaplotexpectation,@gaplotstopping})第三步：調用GA函數[xfval]=ga(@fit1,1,[],[],[],[],0,10,[],options);最后復原y=-1*fit1(x)%最小值復原為最大值figure;fplot('2*x+10*sin(5*x)+7*cos(4*x)',[010])holdonplot(x,y,'*')精選ppt

遺傳算法的GA工具箱實現：Matlab的GA工具箱(R2007)精選pptMatlab的GA工具箱(R2021b)

遺傳算法的GA工具箱實現：精選ppt例二求以下優化問題精選pptMatlab函數調用實現調用GA函數求解〔見ga_eg2.m〕

functionga_eg2A=[11;-12;21];b=[2;2;3];lb=zeros(2,1);[x,fval,exitflag]=ga(@lincontest6,2,A,b,[],[],lb);mesh_lincontest6;holdon;plot3(x(1),x(2),fval,'r*');

functionmesh_lincontest6m=10;n=1000;x=-n:m:n;y=-n:m:n;z=0.5*(ones(length(x),1)*x).^2+(ones(length(y),1)*y).^2...-(ones(length(x),1)*x).*(ones(length(y),1)*y)-2*(ones(...length(x),1)*x)-6*(ones(length(y),1)*y);mesh(x,y,z)精選pptMatlab函數調用實現調用GA函數求解〔見ga_eg2.m〕

精選ppt遺傳算法的GA工具箱實現Matlab的GA工具箱(R2021b)精選ppt練習一在－5<=Xi<=5,i=1,2區間內，求解f(x1,x2)=-20*exp(0.2*sqrt(0.5*(x1.^2+x2.^2)))-exp(0.5*(cos(2*pi*x1)+cos(2*pi*x2)))+22.71282的最小值。要求：種群大小20，最大代數100，變異率0.1,交叉率0.7精選pptContentsIIGA求解多目標優化問題1GA優化BP神經網絡2GA求解TSP問題3精選pptII-1