模拟退火算法Matlab实现

叁歲伎倆 2022-01-27 06:23 292阅读 0赞

### 模拟退火算法Matlab实现 ###

*  瞎BB
 *  代码
 *   *  目标函数
     *  选择两个个体交配
     *  二进制转十进制
     *  适应度函数
     *  是否交叉或变异
     *  交叉
     *  变异
     *  生成随机初等行变换的单位矩阵
     *  主函数

# 瞎BB #

# 代码 #

## 目标函数 ##

function value=targetfun(x)
    value=200*exp(-0.05*x).*sin(x);

## 选择两个个体交配 ##

%select two individuals
    function seln=selection(population,cumsump)
    seln=zeros(1,2);
    for i=1:2
        r=rand;
        prand=cumsump-r;
        j=1;
        %stop when cumsump>r
        while prand(j)<0
            j=j+1;
        end
        seln(i)=j;
    end

## 二进制转十进制 ##

function x=transform2to10(population)
    BitLength=size(population,2);
    x=population(BitLength);
    for i=1:BitLength-1
        x=x+population(BitLength-i)*power(2,i);
    end

## 适应度函数 ##

function [fitvalue,cumsump]=fitness(population)
    global BitLength
    global boundsbegin
    global boundsend
    popsize=size(population,1);
    cumsump=zeros(1,popsize);
    fitvalue=zeros(1,popsize);
    for i=1:popsize
        x=transform2to10(population(i,:));
        %tansform to range of variable
        xx=boundsbegin+x.*(boundsend-boundsbegin)./(power((boundsend),BitLength)-1);
        fitvalue(i)=targetfun(xx);
    end
    %ensure fitvalue>0
    fitvalue=fitvalue'+230;
    fsum=sum(fitvalue);
    Pperpopulation=fitvalue/fsum;
    cumsump(1)=Pperpopulation(1);
    for i=2:popsize
        cumsump(i)=cumsump(i-1)+Pperpopulation(i);
    end
    cumsump=cumsump';

## 是否交叉或变异 ##

function pcc=IfCroIfMut(cro_or_mut)
    test(1:100)=0;
    l=ceil(rand()*cro_or_mut);
    test(1:l)=1;
    n=ceil(rand*100);
    pcc=test(n);

## 交叉 ##

function scro=crossover(population,seln,pc)
    %seln:two individuals
    BitLength=size(population,2);
    pcc=IfCroIfMut(pc);
    if pcc==1
        %generate a random position
        chb=round(rand*(BitLength-2))+1;
        %crossover
        scro(1,:)=[population(seln(1),1:chb) population(seln(2),chb+1:BitLength)];
        scro(2,:)=[population(seln(2),1:chb) population(seln(1),chb+1:BitLength)];
    else
        scro(1,:)=population(seln(1),:);
        scro(2,:)=population(seln(2),:);
    end

## 变异 ##

function snnew=mutation(snew,pmutation)
    BitLength=size(snew,2);
    snnew=snew;
    pmm=IfCroIfMut(pmutation);
    if pmm==1
        %generate a random position
        chb=round(rand*(BitLength-1))+1;
        %0to1 or 1to0
        snnew(chb)=abs(snew(chb)-1);
    end

## 生成随机初等行变换的单位矩阵 ##

function f=generate_random_eye(a)
    n=size(a);
    c1=ceil(rand*n);
    c2=ceil(rand*n);
    for i=1:20
        while c1==c2
            c1=ceil(rand*n);
            c2=ceil(rand*n);
        end
        temp=a(c1,:);
        a(c1,:)=a(c2,:);
        a(c2,:)=temp;
    end
    f=a;

## 主函数 ##

%max goal function value
    clc,clear
    global BitLength
    global boundsbegin
    global boundsend
    cro_mut_rate=0.01;
    %range of variable
    bounds=[-2 2];
    %begin of variable
    boundsbegin=bounds(:,1);
    %end of variable
    boundsend=bounds(:,2);
    precision=0.0001;
    %calc the BitLength
    BitLength=ceil(log2((boundsend-boundsbegin)'./precision));
    
    %init
    popsize=50;
    Generationmax=100;
    pcro=0.9;
    pmut=0.09;
    ymax=zeros(1,Generationmax+1);
    ymean=zeros(1,Generationmax+1);
    xmax=zeros(1,Generationmax+1);
    %generate random population
    population=round(rand(popsize,BitLength));
    %calc fitness return fitvalue and sum of probability
    [fitvalue,cumsump]=fitness(population);
    
    %main code
    Generation=1;
    tic
    while Generation<Generationmax+1
        for j=1:2:popsize
            %select twoindividual
            seln=selection(population,cumsump);
            %crossover
            scro=crossover(population,seln,pcro);
            scnew(j,:)=scro(1,:);
            scnew(j+1,:)=scro(2,:);
            %mutation
            smnew(j,:)=mutation(scnew(j,:),pmut);
            smnew(j+1,:)=mutation(scnew(j+1,:),pmut);
        end
        population=smnew;
        [fitvalue,cumsump]=fitness(population);
        [fmax,nmax]=max(fitvalue);
        fmean=mean(fitvalue);
        ymax(Generation)=fmax;
        ymean(Generation)=fmean;
        x=transform2to10(population(nmax,:));
        xx=boundsbegin+x.*(boundsend-boundsbegin)./(power((boundsend),BitLength)-1);
        xmax(Generation)=xx;
        Generation=Generation+1;
    end
    toc
    %Generation=Generation-1;
    Bestpopulation=xx;
    BestValue=targetfun(xx);
    
    %figure
    figure(1);
    hand1=plot(1:Generation,ymax);
    set(hand1,'linestyle','-','linewidth',1.8,'marker','*','markersize',6);
    hold on;
    hand2=plot(1:Generation,ymean);
    set(hand2,'color','r','linestyle','-','linewidth',1.8,'marker','h','markersize',6);
    %hold on;
    xlabel('Generation');ylabel('max/mean');xlim([1 Generationmax]);
    legend('fitness_max','fitness_mean');
    box off;hold off;