mymulti.m

关于两个目标函数的

clear;
clc;
%下面为一个含有两个优化目标的多目标优化问题：利用并列选择法求解
%Function f1=f(x)                   %第一目标函数
%f1=x(:,1).*x(:,1)/4+x(:,2).*x(:,2)/4;
%Function f2=f(x)                   %第二目标函数
%f2=x(:,1).*(1-x(:,2))+10;
%定义遗传算法参数
NIND=100;                          %个体数目(Number of individuals)
MAXGEN=50;                         %最大遗传代数(Maximum number of generations)
NVAR=2;                            %变量个数
PRECI=20;                          %变量的二进制位数(Precision of variables)
GGAP=0.9                           %代沟(Generation gap)
trace1=[ ];trace2=[ ];trace3=[ ];  %性能跟踪
%建立区域描述器(Build field descriptor)——采用矩阵复制函数rep建立矩阵FieldD，描述染色体的表示和解释
FieldD=[rep([PRECI],[1,NVAR]);[1,1;4,2];rep([1;0;1;1],[1,NVAR])];
Chrom=crtbp(NIND,NVAR*PRECI);      %初始种群
v=bs2rv(Chrom,FieldD);             %初始种群十进制转换
gen=1
while gen < MAXGEN,
    [NIND,N]=size(Chrom);
    M=fix(NIND/2);
    ObiV1=f1(v(1:M,:));            %分组后第一目标函数值
    FitnV1=ranking(ObiV1);        %分配适应度值(Assign fitness values)
    SelCh1=select('sus',Chrom(1:M,:),FitnV1,GGAP);     % 选择
    ObiV2=f2(v(M+1:NIND,:));            %分组后第二目标函数值
    FitnV2=ranking(ObiV2);        %分配适应度值(Assign fitness values)
    SelCh2=select('sus',Chrom(M+1:NIND,:),FitnV2,GGAP);     %选择
    SelCh=[SelCh1;SelCh2];          %合并
    SelCh=recombin('xovsp',SelCh,0.7); %重组
    Chrom=mut(SelCh);                %变异
    v=bs2rv(Chrom,FieldD);
    trace1(gen,1)=min(f1(v));
    trace1(gen,2)=sum(f1(v))/length(f1(v));
    trace2(gen,1)=min(f2(v));
    trace2(gen,2)=sum(f2(v))/length(f2(v));
    trace3(gen,1)=min(f1(v)+f2(v));
    trace3(gen,2)=sum(f1(v))/length(f1(v))+sum(f2(v))/length(f2(v));
    gen=gen+1;
end
figure(1);clf;
plot(trace1(:,1));hold on;
plot(trace1(:,2),'-.');
plot(trace1(:,1),'.');
plot(trace1(:,2),'.');grid;
legend('解的变化','种群均值的变化')
xlabel('迭代次数');ylabel('目标函数值');
figure(2);clf;
plot(trace2(:,1));hold on;
plot(trace2(:,2),'-.');
plot(trace2(:,1),'.');
plot(trace2(:,2),'.');grid;
legend('解的变化','种群均值的变化')
xlabel('迭代次数');ylabel('目标函数值');
figure(3);clf;
plot(trace3(:,1));hold on;
plot(trace3(:,2),'-.');
plot(trace3(:,1),'.');
plot(trace3(:,2),'.');grid;
legend('解的变化','种群均值的变化')
xlabel('迭代次数');ylabel('目标函数值');
figure(4);clf;
plot(f1(v));hold on;
plot(f2(v),'r-.');grid;