Matlab调用遗传工具箱复现论文模型求解部分

原文转载自：https://blog.csdn.net/robert_chen1988/article/details/52431594

论文来源：

https://www.sciencedirect.com/science/article/pii/S0045782599003898

function [xm,fv]=GAEOQ1
%%初始目标函数与约束条件
%求解变量t, k, 目标函数 f,约束条件 g1
syms t k z;
f=100/t+25*(25*t+k*10*sqrt(1+1.25*t))+100*10*sqrt(1+1.25*t)*int((z-k)*normpdf(z,0,1),z,k,inf)/t;
tmin=1e-2;
tmax=4;
kmin=0;
kmax=2;
g1=1-200*sqrt(2+0.75*t)*int((z-k)*normpdf(z,0,1),z,k,inf)/(50*t);%%将约束标准化，将右端变为1
NP=50; %进化多少代

%%初始化种群，种群长度40
size=20;
E=zeros(20,5); %前两列为初始解，第三列为适应函数值，第四列记录是否为可行解，第五列记录违背约束条件的差值
E(:,1)=tmin+(tmax-tmin)*rand(size,1);
E(:,2)=kmin+(kmax-kmin)*rand(size,1);
fv=inf;%初始最优值为无穷大的值
D=zeros(NP,4);%用来记录每代的最优解,平均值，最差解,最优解是否为可行解

%%计算适应函数罚函数值，判断是否为可行解
for i=1:size
     B=zeros(1,1);
     B(1)=subs(g1,[t,k],E(i,(1:2)));
     if B(1)>=0
        E(i,4)=1;
        E(i,3)=subs(f,[t,k],E(i,(1:2)));
     else
        E(i,4)=0;
        E(i,3)=0;
     end
     if B(1)>=0
        B(1)=0;
     else
        B(1)=abs(B(1));
     end
     E(i,5)=B(1);
end
fmax=max(E(:,3));
for i=1:size
if E(i,4)<1e-6
    E(i,3)=fmax+E(i,5);
    end
end

%%遗传进化   %%到这步适应值还没出错
for g=1:NP    %%原来错误在这里，这个k跟前面的k重复了
     %%竞标赛选择  %%小生态技术
     M=zeros(size,2);%用来存储优胜者的中间矩阵
         for i=1:size
             %A=randperm(size,6);
             %dij1=sqrt(0.5*(E(A(1),1)-E(A(2),1))^2);  %%小生态技术,只有单界时小生态技术没法用
             %dij2=sqrt(0.5*(E(A(1),1)-E(A(3),1))^2);
             %dij3=sqrt(0.5*(E(A(1),1)-E(A(4),1))^2);
             %dij4=sqrt(0.5*(E(A(1),1)-E(A(5),1))^2);
             %dij5=sqrt(0.5*(E(A(1),1)-E(A(6),1))^2);
             %if dij1<0.1
                 %if E(A(1),3)<=E(A(2),3)
                     %M(i,:)=E(A(1),(1:2));
                 %else
                     %M(i,:)=E(A(2),(1:2));  
                 %end
                 %continue;
             %elseif dij2<0.1
                 %if E(A(1),3)<=E(A(3),3)
                     %M(i,:)=E(A(1),(1:2));
                 %else
                     %M(i,:)=E(A(3),(1:2));  
                 %end
                 %continue;
             %elseif dij3<0.1
                 %if E(A(1),3)<=E(A(4),3)
                     %M(i,:)=E(A(1),(1:2));
                 %else
                     %M(i,:)=E(A(4),(1:2));  
                 %end
                 %continue;
             %elseif dij4<0.1
                 %if E(A(1),3)<=E(A(5),3)
                     %M(i,:)=E(A(1),(1:2));
                 %else
                     %M(i,:)=E(A(5),(1:2));  
                 %end
                 %continue;
             %elseif dij5<0.1
                 %if E(A(1),3)<=E(A(6),3)
                     %M(i,:)=E(A(1),(1:2));
                 %else
                     %M(i,:)=E(A(6),(1:2));  
                 %end
             %else
                 %M(i,:)=E(A(1),(1:2));
             %end 
         %end
             A=randperm(size,2);
             if E(A(1),3)<=E(A(2),3)
                 M(i,:)=E(A(1),(1:2));
             else
                 M(i,:)=E(A(2),(1:2));
             end
         end

%%模拟二进制交叉生成后代
         for j=1:size/2
             if rand()>=0.5
                 A=randperm(size,2);
                 c=rand();
                 x2=max(M(A(1),1),M(A(2),1));
                 x1=min(M(A(1),1),M(A(2),1));
                 beita1_t=1+2*(x1-tmin)/(x2-x1);
                 rfa_t=2-beita1_t^(-2);
                 if c<=1/rfa_t
                     beita2_t=sqrt(rfa_t*c);
                 else
                     beita2_t=sqrt(1/(2-rfa_t*c));
                 end
                 E(2*j-1,1)=0.5*(x1+x2-beita2_t*(x2-x1));
                 E(2*j,1)=0.5*(x1+x2+beita2_t*(x2-x1));
             end
     %%只在可行解时出错是怎么回事？是不是变异的原因，已纠正
             if rand()>0.5
                 c=rand();
                 x2=max(M(A(1),2),M(A(2),2));
                 x1=min(M(A(1),2),M(A(2),2));
                 beita1_t=1+2*(x1-kmin)/(x2-x1);
                 rfa_t=2-beita1_t^(-2);
                 if c<=1/rfa_t
                     beita2_t=sqrt(rfa_t*c);
                 else
                     beita2_t=sqrt(1/(2-rfa_t*c));
                 end
                 E(2*j-1,2)=0.5*(x1+x2-beita2_t*(x2-x1));
                 E(2*j,2)=0.5*(x1+x2+beita2_t*(x2-x1));
             end
         end

%%变异，变异会不会导致可行解不可行?单下界时不用变异,设置判断条件防止过界
         for i=1:size
             nita=100+g;
             pm=1/size+g*(1-1/size)/NP;
             if rand()<pm
                 u=rand();
                 %x=E(i,1);
                 x=E(i,1);%%
                 deltamax=1;
                 if u<=0.5
                     delta_2=(2*u)^(1/(nita+1))-1;
                 else
                     delta_2=1-(2*(1-u))^(1/(nita+1));
                 end
                 if x+delta_2*deltamax>=tmin
                     E(i,1)=x+delta_2*deltamax;
                 end
             end
    
             if rand()<pm
                 u=rand();
                 x=E(i,2);
                 deltamax=1;
                 if u<=0.5
                     delta_1=(2*u)^(1/(nita+1))-1;
                 else
                     delta_1=1-(2*(1-u))^(1/(nita+1));
                 end
                 if x+delta_1*deltamax>=kmin
                     E(i,2)=x+delta_1*deltamax;
                 end
             end
         end
     %%计算子代罚函数值，判断是否满足可行解
     for i=1:size
         B(1)=subs(g1,[t,k],E(i,(1:2)));
         if B(1)>=0
             E(i,4)=1;
             E(i,3)=subs(f,[t,k],E(i,(1:2)));%%跟直接算的结果不一样，也跟EOQ得到的结果不一样 eval出错的原因
         else
             E(i,4)=0;
             E(i,3)=0;
         end
         if B(1)>=0
             B(1)=0;
         else
             B(1)=abs(B(1));
         end
         E(i,5)=B(1);
     end
     for i=1:size
         if E(i,4)<1e-6
             E(i,3)=fmax+E(i,5);
         end
     end      
     [Q,IX]=sort(E,1);
     %Q=vpa(Q,4);%%
     D(g,1)=Q(1,3);
     D(g,2)=mean(Q(:,3));
     D(g,3)=Q(size,3);
     D(g,4)=E(IX(1,3),4);
     if Q(1,3)<fv && D(g,4)==1
         fv=Q(1,3);
         xm=E(IX(1,3),(1:2));
         xm=[xm,E(IX(1,3),4)];
     end
end

%画图
k=1;
for i=1:NP
     if D(i,4)==1
         N(k,:)=D(i,:);
         k=k+1;
     end
end
        
plot(N(:,1),'r*');
hold on
plot(N(:,2),'b+');
hold on

plot(N(:,3),'ms');

legend('最优值','平均值','最差值');
hold off

end

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