遺傳算法的Matlab實現(xiàn)講解

數(shù)學(xué)建模專題之

遺傳算法的MATLAB實現(xiàn)遺傳算法的Matlab實現(xiàn)講解ContentsIMatlab編程實現(xiàn)GA1Matlab函數(shù)調(diào)用實現(xiàn)GA2Matlab工具箱實現(xiàn)GA3遺傳算法的Matlab實現(xiàn)講解Matlab編程實現(xiàn)GA例1：計算目標(biāo)函數(shù)值函數(shù)

遺傳算法的Matlab實現(xiàn)講解主程序

%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(xiàn)GApop=initpop(popsize,chromlength);%隨機產(chǎn)生初始群體fori=1:Gene%20為迭代次數(shù)

[objvalue]=calobjvalue(pop,chromlength,Xmax,Xmin);%計算目標(biāo)函數(shù)

fitvalue=calfitvalue(objvalue);%計算群體中每個個體的適應(yīng)度

[newpop]=selection(pop,fitvalue);%復(fù)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(yīng)值最大的個體及其適應(yīng)值

x(i)=decodechrom(bestindividual,1,chromlength)*10/(2^chromlength-1);%最佳個體解碼

y(i)=bestfit+Cmin;%最佳個體適應(yīng)度

y_mean(i)=mean(fitvalue+Cmin);%第i代平均適應(yīng)度

pop=newpop;endfplot('2*x+10*sin(5*x)+7*cos(4*x)',[010])holdonplot(x,y,'r*')holdoff遺傳算法的Matlab實現(xiàn)講解初始化(編碼)

%initpop.m函數(shù)的功能是實現(xiàn)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(shù)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(chǎn)生每個單元為{0,1}行數(shù)為popsize，列數(shù)為chromlength的矩陣，%round對矩陣的每個單元進行取整。這樣產(chǎn)生的初始種群。Matlab編程實現(xiàn)GA遺傳算法的Matlab實現(xiàn)講解將二進制數(shù)轉(zhuǎn)化為十進制數(shù)

將二進制數(shù)轉(zhuǎn)化為十進制數(shù)%產(chǎn)生[2^n2^(n-1)...1]的行向量，然后求和，將二進制轉(zhuǎn)化為十進制functionpop2=decodebinary(pop)[px,py]=size(pop);%求pop行和列數(shù)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(xiàn)GA遺傳算法的Matlab實現(xiàn)講解計算目標(biāo)函數(shù)值

計算目標(biāo)函數(shù)值%calobjvalue.m函數(shù)的功能是實現(xiàn)目標(biāo)函數(shù)的計算，其公式采用本文示例仿真，可根據(jù)不同優(yōu)化問題予以修改。%遺傳算法子程序%Name:calobjvalue.m%實現(xiàn)目標(biāo)函數(shù)的計算function[objvalue]=calobjvalue(pop,chromlength,Xmax,Xmin)temp1=decodechrom(pop,1,chromlength);%將pop每行轉(zhuǎn)化成十進制數(shù)x=temp1*(Xmax-Xmin)/(2^chromlength-1);%將十進制域中的數(shù)轉(zhuǎn)化為變量域的數(shù)objvalue=2*x+10*sin(5*x)+7*cos(4*x);%計算目標(biāo)函數(shù)值Matlab編程實現(xiàn)GA遺傳算法的Matlab實現(xiàn)講解計算個體的適應(yīng)值

functionfitvalue=calfitvalue(objvalue)globalCmin;fitvalue=objvalue-Cmin;Matlab編程實現(xiàn)GA遺傳算法的Matlab實現(xiàn)講解選擇復(fù)制

function[newpop]=selection(pop,fitvalue)%程序中采用賭輪盤選擇法選擇實現(xiàn)totalfit=sum(fitvalue);%求適應(yīng)值之和fitvalue=fitvalue/totalfit;%單個個體被選擇的概率fitvalue=cumsum(fitvalue);%如fitvalue=[1234]，則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(xiàn)GA遺傳算法的Matlab實現(xiàn)講解交叉

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(xiàn)GA遺傳算法的Matlab實現(xiàn)講解變異

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(xiàn)GAifany(newpop(i,mpoint))==0newpop(i,mpoint)=1;elsenewpop(i,mpoint)=0;endelsenewpop(i,:)=pop(i,:);endend遺傳算法的Matlab實現(xiàn)講解求出群體中最大的適應(yīng)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(xiàn)GA或function[bestindividual,bestfit]=…best(pop,fitvalue)[bestfit,m_indx]=max(fitvalue);bestindividual=pop(m_indx,:);遺傳算法的Matlab實現(xiàn)講解結(jié)果見My_GA.m

Matlab編程實現(xiàn)GA遺傳算法的Matlab實現(xiàn)講解Matlab函數(shù)調(diào)用實現(xiàn)GAMatlab的GA函數(shù)

[xfval]=ga(@fitnessfun,nvars,[],[],[],[],[],[],[],options)；fitnessfcn—Fitnessfunctionnvars—NumberofvariablesfortheproblemAineq—MatrixforinequalityconstraintsBineq—VectorforinequalityconstraintsAeq—MatrixforequalityconstraintsBeq—VectorforequalityconstraintsLB—LowerboundonxUB—Upperboundonxnonlcon—NonlinearconstraintFunctionoptions—Optionsstructure遺傳算法的Matlab實現(xiàn)講解Matlab函數(shù)調(diào)用實現(xiàn)GAMatlab的GA函數(shù)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(...)遺傳算法的Matlab實現(xiàn)講解Matlab函數(shù)調(diào)用實現(xiàn)GAGA函數(shù)調(diào)用步驟第一步：編寫適應(yīng)度函數(shù)；第二步：對GA參數(shù)進行設(shè)置；options=gaoptimset(‘參數(shù)名’,參數(shù)值,…,‘參數(shù)名’,參數(shù)值)例:options=gaoptimset('PopulationSize',100)第三步：調(diào)用GA函數(shù)；[xfval]=ga(@fitnessfun,nvars)[xfvalexitflagoutputpopulationscores]=ga(@fitnessfcn,nvars)[xfval]=ga(@fitnessfun,nvars,[],[],[],[],[],[],[],options)；specifyanylinearequality,linearinequality,ornonlinearconstraints遺傳算法的Matlab實現(xiàn)講解Matlab函數(shù)調(diào)用實現(xiàn)GA調(diào)用GA函數(shù)求例1的最大值（見ga_eg1.m）第一步：編寫適應(yīng)度函數(shù)；functiony=fit1(x)y=-(2*x+10*sin(5*x)+7*cos(4*x));第二步：設(shè)置參數(shù)options=gaoptimset('PopulationSize',100,'PopulationType','doubleVector','PlotFcns',{@gaplotbestf,@gaplotbestindiv,@gaplotexpectation,@gaplotstopping})第三步：調(diào)用GA函數(shù)[xfval]=ga(@fit1,1,[],[],[],[],0,10,[],options);最后還原y=-1*fit1(x)%最小值還原為最大值figure;fplot('2*x+10*sin(5*x)+7*cos(4*x)',[010])holdonplot(x,y,'*')遺傳算法的Matlab實現(xiàn)講解

遺傳算法的GA工具箱實現(xiàn)：Matlab的GA工具箱(R2007)遺傳算法的Matlab實現(xiàn)講解Matlab的GA工具箱(R2010b)

遺傳算法的GA工具箱實現(xiàn)：遺傳算法的Matlab實現(xiàn)講解例二求下列優(yōu)化問題遺傳算法的Matlab實現(xiàn)講解Matlab函數(shù)調(diào)用實現(xiàn)調(diào)用GA函數(shù)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)遺傳算法的Matlab實現(xiàn)講解Matlab函數(shù)調(diào)用實現(xiàn)調(diào)用GA函數(shù)求解（見ga_eg2.m）

遺傳算法的Matlab實現(xiàn)講解遺傳算法的GA工具箱實現(xiàn)Matlab的GA工具箱(R2010b)遺傳算法的Matlab實現(xiàn)講解練習(xí)一在－5<=Xi<=5,i=1,2區(qū)間內(nèi)，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(shù)100，變異率0.1,交叉率0.7遺傳算法的Matlab實現(xiàn)講解ContentsIIGA求解多目標(biāo)優(yōu)化問題1GA優(yōu)化BP神經(jīng)網(wǎng)絡(luò)2GA求解TSP問題3遺傳算法的Matlab實現(xiàn)講解II-1GA求解多目標(biāo)優(yōu)化問題通常多目標(biāo)優(yōu)化，例如非線性整數(shù)規(guī)劃是一個具有指數(shù)復(fù)雜度的NP問題，如果約束較為復(fù)雜，Matlab優(yōu)化工具箱和一些優(yōu)化軟件比如lingo等，常常無法應(yīng)用，即使能應(yīng)用也不能給出一個較為令人滿意的解。