【VRP问题】基于帝国企鹅算法求解某乳制品企业冷链配送物流车辆调度优化研究附matlab代码

1 简介

2 部分代码

function [bestY,bestX,recording]=AFO2(x,y,option,data)%% Input% x----positions of initialized populaiton% y----fitnesses of initialized populaiton% option-----parameters set of the algorithm% data------Pre-defined parameters% This parameter is used for solving complex problems is passing case data%% outPut% bestY ----fitness of best individual% bestX ----position of best individual% recording ---- somme data was recorded in this variable%% initializationpe=option.pe;L=option.L;gap0=option.gap0;gap=gap0;dim=option.dim;maxIteration=option.maxIteration;recording.bestFit=zeros(maxIteration 1,1);recording.meanFit=zeros(maxIteration 1,1);numAgent=option.numAgent;At=randn(numAgent,dim);w2=option.w2; %weight of Moving strategy IIIw4=option.w4;%weight of Moving strategy IIIw5=option.w5;%weight of Moving strategy IIIpe=option.pe; % rate to judge Premature convergencegapMin=option.gapMin;dec=option.dec;ub=option.ub;lb=option.lb;v_lb=option.v_lb;v_ub=option.v_ub;fobj=option.fobj;count=1;%% center of population[y_c,position]=min(y);x_c=x(position(1)；At_c=At(position(1)；%% memory of populationy_m=y;x_m=x;%% update recordingrecording.bestFit(1)=y_c;recording.meanFit(1)=mean(y_m);%% main loopiter=1;while iter<=maxIteration    %Dmp(['AFO,iter:',num2str(iter),',minFit:',num2str(y_c)])    %% Moving Strategy I for center of population    if rem(iter, gap)==0 && dim<option.numAgent        c0=exp(-30*(iter-gap0)/maxIteration); % EQ.2-11        Dx=ones(1,dim);        Dx=c0*Dx/norm(Dx)*norm(v_ub-v_lb)/2; %EQ.2-12 % △x        Dx1=-Dx; %-△x        %  △x        for j=1:dim            tempX(j,:)=x_c;            tempX(j,j)=x_c(1,j) Dx(j);            if tempX(j,j)>ub(j)                tempX(j,j)=ub(j);                Dx(1,j)=tempX(j,j)-x_c(1,j);            end            if tempX(j,j)<lb(j)                tempX(j,j)=lb(j);                Dx(1,j)=tempX(j,j)-x_c(1,j);            end            tempY(j,:)=fobj(tempX(j,:),option,data);            if tempY(j)*y_c<0                g0(1,j)=(log(tempY(j))-log(y_c))./Dx(j); %EQ.2-18            else                temp=[tempY(j),y_c];                temp=temp min(temp) eps;                g0(1,j)=(log(temp(1))-log(temp(2)))./Dx(j);            end            g0(isnan(g0))=0;        end        G0=-g0(1,:)*norm(v_ub-v_lb)/2/norm(g(1)； % part of Eq 2-18        G0(1,G0(1,:)>v_ub)=G0(1,G0(1,:)>v_ub)/max(G0(1,G0(1,:)>v_ub))*max(v_ub(G0(1,:)>v_ub));        G0(1,G0(1,:)<v_lb)=G0(1,G0(1,:)<v_lb)/min(G0(1,G0(1,:)<v_lb))*min(v_lb(G0(1,:)<v_lb));        G01=G0;        % -△x        Dx=Dx1;        for j=1:dim            tempX(j dim,:)=x_c;            tempX(j dim,j)=x_c(1,j) Dx(j);            if tempX(j dim,j)>ub(j)                tempX(j dim,j)=ub(j);                Dx(1,j)=tempX(j,j)-x_c(1,j);            end            if tempX(j dim,j)<lb(j)                tempX(j dim,j)=lb(j);                Dx(1,j)=tempX(j,j)-x_c(1,j);            end            tempY(j dim,:)=fobj(tempX(j,:),option,data);            if tempY(j)*y_c<0                g0(1,j)=(log(tempY(j))-log(y_c))./Dx(j); %EQ.2-18            else                temp=[tempY(j),y_c];                temp=temp min(temp) eps;                g0(1,j)=(log(temp(1))-log(temp(2)))./Dx(j);            end            g0(isnan(g0))=0;
     
              end
       G0=-g0(1,:)*norm(v_ub-v_lb)/2/norm(g0(1,:)); % part of Eq 2-18
       G0(1,G0(1,:)>v_ub)=G0(1,G0(1,:)>v_ub)/max(G0(1,G0(1,:)>v_ub))*max(v_ub(G0(1,:)>v_ub));
       G0(1,G0(1,:)<v_lb)=G0(1,G0(1,:)<v_lb)/min(G0(1,G0(1,:)<v_lb))*min(v_lb(G0(1,:)<v_lb));
       G02=G0;
       G0=G01+G02; % part of Eq 2-18
       G0(isnan(G0))=0;
       if sum(G0)==0
       N=numAgent-2*dim;
       Dm=mean(x-repmat(x_c,numAgent,1));
       Dm=norm(Dm); %EQ.2-22
       if Dm<norm(v_ub-v_lb)/20*iter/maxIteration
       Dm=norm(v_ub-v_lb);
       end
       for j=2*dim+(1:N)
       G0=randn(1,dim);
       tempX(j,:)=x(i,:)+5*rand*G0./norm(G0)*Dm; %EQ.2-21
       tempX(j,tempX(j,:)<lb)=lb(tempX(j,:)<lb);
       tempX(j,tempX(j,:)>ub)=ub(tempX(j,:)>ub);
       tempY(j,:)=fobj(tempX(j,:),option,data);
       end
       else
       N=numAgent-2*dim;
       r1=exp(-10*(0:N-1)/(N-1));
       unitG=norm(Dx)/norm(G0); %EQ.2-19
       if unitG~=1
       r2=1:-(1-unitG)/(N-1):unitG;
       a=r1.*r2; %EQ.2-17
       else
       a=r1;
       end
       for j=2*dim+(1:N)
       tempX(j,:)=x_c+G0*a(j-2*dim); %EQ,2-20
       tempX(j,tempX(j,:)<lb)=lb(tempX(j,:)<lb);
       tempX(j,tempX(j,:)>ub)=ub(tempX(j,:)>ub);
       tempY(j,:)=fobj(tempX(j,:),option,data);
       end
       end
       [minY,no]=min(tempY);
       if minY<y_c
       y_c=tempY(no);
       x_c=tempX(no,:);
       end
       if rand>(no-dim*2)/(numAgent-dim*2)*(maxIteration-iter)/maxIteration
       gap=max(gapMin,gap-dec); %EQ.2-15
       end
       else
       R1=rand(numAgent,dim);
       R2=rand(numAgent,dim);
       R3=rand(numAgent,dim);
       Rn=rand(numAgent,dim);
       indexR1=ceil(rand(numAgent,dim)*numAgent);
       indexR2=ceil(rand(numAgent,dim)*numAgent);
       std0=exp(-20*iter/maxIteration)*(v_ub-v_lb)/2;
       std1=std(x_m); 
       % In order to use matrix operations, all individuals of the population are updated.
       % Although more individuals were updated, the running time of the algorithm dropped tremendously. 
       % This is because MATLAB is extremely good at matrix operations.
       % If you want to rewrite this code in another language, we suggest you refer to AFO1.
       % AFO2 is optimized for MATLAB and may not be suitable for your language.
       for j=1:dim
       x_m1(:,j)=x_m(indexR1(:,j),j);
       x_m2(:,j)=x_m(indexR2(:,j),j);
       y_m1(:,j)=y_m(indexR1(:,j));
       y_m2(:,j)=y_m(indexR2(:,j));
       AI(:,j)=R1(:,j).*sign(y_m1(:,j)-y_m2(:,j)).*(x_m1(:,j)-x_m2(:,j));
       if std1(j)<=std0(j)
       position=find(AI(:,j)==0);
       AI(position,j)=Rn(position,j)*(v_ub(j)-v_lb(j))/2;
       position=find(AI(:,j)~=0);
       AI(position,j)=R2(:,j).*sign(y_m1(:,j)-y_m2(:,j)).*sign(x_m1(:,j)-x_m2(:,j))*(v_ub(j)-v_lb(j))/2;
       end
       end
       for i=1:numAgent
       p =tanh(abs(y(i)-y_c)); %EQ.2-30
       if rand<p*(maxIteration-iter)/maxIteration
       % EQ 2-28
       At(i,:)=w2*At(i,:)+w4*R1(i,:).*(x_c-x(i,:))+w5*R2(i,:).*(x_m(i,:)-x(i,:));
       x(i,:)=x(i,:)+At(i,:); %EQ 2-29
       x(i,x(i,:)<lb)=lb(x(i,:)<lb);
       x(i,x(i,:)>ub)=ub(x(i,:)>ub);
       tempY(i,:)=y(i);
       y(i)=fobj(x(i,:),option,data);
       if tempY(i,:)<y(i)
       for j=1:dim
       r1=indexR1(i,j);
       r2=indexR2(i,j);
       v(i,j)=R3(i,j).*(x_m(r1,j)-x_m(r2,j))*-sign(y_m(r1)-y_m(r2));
       if std1(j)<=std0(j)
       if v(i,j)==0
       v(i,j)=randn*(v_ub(j)-v_lb(j))/2;
       else
       v(i,j)=rand.*sign(x_m(r1,j)-x_m(r2,j))*-sign(y_m(r1)-y_m(r2))*(v_ub(j)-v_lb(j))/2;
       end
       end
       end
       end
       else
       x(i,:)=x_c+AI(i,:);
       At(i,:)=AI(i,:);
       x(i,x(i,:)<lb)=lb(x(i,:)<lb);
       x(i,x(i,:)>ub)=ub(x(i,:)>ub);
       y(i)=fobj(x(i,:),option,data);
       end
       
       if y(i)<y_m(i)
       y_m(i)=y(i);
       x_m(i,:)=x(i,:);
       if y_m(i)<y_c
       y_c=y_m(i);
       x_c=x_m(i,:);
       At_c=At(i,:);
       end
       end
       end
       end
       % EQ.2-31
       if abs(y_c-recording.bestFit(iter))/abs(recording.bestFit(iter))<=pe
       count=count+1;
       else
       count=0;
       end
       %% 更新记录
       recording.bestFit(1+iter)=y_c;
       recording.meanFit(1+iter)=mean(y_m);
       % recording.std(1+iter)=mean(std(x_m));
       % recording.DC(1+iter)=norm(x_m-repmat(x_c,numAgent,1));
       % recording.x1(1+iter,:)=x(1,:);
       iter=iter+1;
       %%
       if count>L
       for i=1:numAgent
       x(i,:)=(ub-lb)*rand+lb;
       y(i)=fobj(x(i,:),option,data);
       if y(i)<y_m(i)
       y_m(i)=y(i);
       x_m(i,:)=x(i,:);
       if y_m(i)<y_c
       y_c=y_m(i);
       x_c=x_m(i,:);
       At_c=At(i,:);
       end
       end
       end
       count=0;
       recording.bestFit(1+iter)=y_c;
       recording.meanFit(1+iter)=mean(y_m);
       iter=iter+1;
       end
      end
      bestY=y_c;
      bestX=x_c;
      end
      %%
      ​
     

3 仿真结果

4 参考文献

[1]李娜. 单亲遗传算法的冷链物流车辆路径问题(VRP)优化研究[D]. 燕山大学.

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