NSGA-Ⅱ算法Matlab实现（测试函数为ZDT1）

function NSGAII()
clc;format compact;tic;hold on
    
%---初始化/参数设定
 
    generations=100;                                %迭代次数
    popnum=100;                                     %种群大小(须为偶数)
    poplength=30;                                   %个体长度
    minvalue=repmat(zeros(1,poplength),popnum,1);   %个体最小值
    maxvalue=repmat(ones(1,poplength),popnum,1);    %个体最大值    
    population=rand(popnum,poplength).*(maxvalue-minvalue)+minvalue;    %产生新的初始种群
    
%---开始迭代进化
 
    for gene=1:generations                      %开始迭代
        
%-------交叉 
 
        newpopulation=zeros(popnum,poplength);  %子代种群
        for i=1:popnum/2                        %交叉产生子代
            k=randperm(popnum);                 %从种群中随机选出两个父母,不采用二进制联赛方法
            beta=(-1).^round(rand(1,poplength)).*abs(randn(1,poplength))*1.481; %采用正态分布交叉产生两个子代
            newpopulation(i*2-1,:)=(population(k(1),:)+population(k(2),:))/2+beta.*(population(k(1),:)-population(k(2),:))./2;    %产生第一个子代           
            newpopulation(i*2,:)=(population(k(1),:)+population(k(2),:))/2-beta.*(population(k(1),:)-population(k(2),:))./2;      %产生第二个子代
        end
        
%-------变异        
 
        k=rand(size(newpopulation));    %随机选定要变异的基因位
        miu=rand(size(newpopulation));  %采用多项式变异
        temp=k<1/poplength & miu<0.5;   %要变异的基因位
        newpopulation(temp)=newpopulation(temp)+(maxvalue(temp)-minvalue(temp)).*((2.*miu(temp)+(1-2.*miu(temp)).*(1-(newpopulation(temp)-minvalue(temp))./(maxvalue(temp)-minvalue(temp))).^21).^(1/21)-1);        %变异情况一
        newpopulation(temp)=newpopulation(temp)+(maxvalue(temp)-minvalue(temp)).*(1-(2.*(1-miu(temp))+2.*(miu(temp)-0.5).*(1-(maxvalue(temp)-newpopulation(temp))./(maxvalue(temp)-minvalue(temp))).^21).^(1/21));  %变异情况二
        
%-------越界处理/种群合并        
 
        newpopulation(newpopulation>maxvalue)=maxvalue(newpopulation>maxvalue); %子代越上界处理
        newpopulation(newpopulation<minvalue)=minvalue(newpopulation<minvalue); %子代越下界处理
        newpopulation=[population;newpopulation];                               %合并父子种群
        
%-------计算目标函数值        
 
        functionvalue=zeros(size(newpopulation,1),2);           %合并后种群的各目标函数值,这里的问题是ZDT1
        functionvalue(:,1)=newpopulation(:,1);                  %计算第一维目标函数值
        g=1+9*sum(newpopulation(:,2:poplength),2)./(poplength-1);
        functionvalue(:,2)=g.*(1-(newpopulation(:,1)./g).^0.5); %计算第二维目标函数值
        
%-------非支配排序        
 
        fnum=0;                                             %当前分配的前沿面编号
        cz=false(1,size(functionvalue,1));                  %记录个体是否已被分配编号
        frontvalue=zeros(size(cz));                         %每个个体的前沿面编号
        [functionvalue_sorted,newsite]=sortrows(functionvalue);    %对种群按第一维目标值大小进行排序
        while ~all(cz)                                      %开始迭代判断每个个体的前沿面,采用改进的deductive sort
            fnum=fnum+1;
            d=cz;
            for i=1:size(functionvalue,1)
                if ~d(i)
                    for j=i+1:size(functionvalue,1)
                        if ~d(j)
                            k=1;                            
                            for m=2:size(functionvalue,2)
                                if functionvalue_sorted(i,m)>functionvalue_sorted(j,m)
                                    k=0;
                                    break
                                end
                            end
                            if k
                                d(j)=true;
                            end
                        end
                    end
                    frontvalue(newsite(i))=fnum;
                    cz(i)=true;
                end
            end
        end
        
%-------计算拥挤距离/选出下一代个体        
 
        fnum=0;                                                                 %当前前沿面
        while numel(frontvalue,frontvalue<=fnum+1)<=popnum                      %判断前多少个面的个体能完全放入下一代种群
            fnum=fnum+1;
        end        
        newnum=numel(frontvalue,frontvalue<=fnum);                              %前fnum个面的个体数
        population(1:newnum,:)=newpopulation(frontvalue<=fnum,:);               %将前fnum个面的个体复制入下一代                       
        popu=find(frontvalue==fnum+1);                                          %popu记录第fnum+1个面上的个体编号
        distancevalue=zeros(size(popu));                                        %popu各个体的拥挤距离
        fmax=max(functionvalue(popu,:),[],1);                                   %popu每维上的最大值
        fmin=min(functionvalue(popu,:),[],1);                                   %popu每维上的最小值
        for i=1:size(functionvalue,2)                                           %分目标计算每个目标上popu各个体的拥挤距离
            [~,newsite]=sortrows(functionvalue(popu,i));
            distancevalue(newsite(1))=inf;
            distancevalue(newsite(end))=inf;
            for j=2:length(popu)-1
                distancevalue(newsite(j))=distancevalue(newsite(j))+(functionvalue(popu(newsite(j+1)),i)-functionvalue(popu(newsite(j-1)),i))/(fmax(i)-fmin(i));
            end
        end                                      
        popu=-sortrows(-[distancevalue;popu]')';                                %按拥挤距离降序排序第fnum+1个面上的个体
        population(newnum+1:popnum,:)=newpopulation(popu(2,1:popnum-newnum),:);	%将第fnum+1个面上拥挤距离较大的前popnum-newnum个个体复制入下一代        
    end
 
%---程序输出    
 
    fprintf('已完成,耗时%4s秒\n',num2str(toc));          %程序最终耗时
    output=sortrows(functionvalue(frontvalue==1,:));    %最终结果:种群中非支配解的函数值
    plot(output(:,1),output(:,2),'*b');                 %作图
    axis([0,1,0,1]);xlabel('F_1');ylabel('F_2');title('ZDT1')
end