多目标优化蚱蜢优化算法（Matlab代码实现）

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目录

​​💥1 概述​​

​​📚2 运行结果​​

​​🎉3 参考文献​​

​​🌈4 Matlab代码实现​​

💥1 概述

本工作提出了一种新的多目标算法，其灵感来自自然界中蚱蜢群的导航。首先使用数学模型来模拟游泳中个体的相互作用，包括吸引力、排斥力和舒适区。然后提出了一种机制，使用该模型在单目标搜索空间中近似全局最优值。然后，将存档和目标选择技术集成到算法中，以估计多目标问题的帕累托最优前沿。为了对所提算法的性能进行基准测试，利用了一组不同的标准多目标测试问题。将结果与进化多目标优化文献中最受好评和最新的算法进行了比较，使用三个性能指标定量和图形定性。结果表明，所提算法在得到的帕累托最优解的精度及其分布方面能够提供极具竞争力的结果。

📚2 运行结果

主函数代码：

clc;
 clear;
 close all;% Change these details with respect to your problem%%%%%%%%%%%%%%
 ObjectiveFunction=@ZDT1;
 dim=5;
 lb=0;
 ub=1;
 obj_no=2;if size(ub,2)==1
     ub=ones(1,dim)*ub;
     lb=ones(1,dim)*lb;
 end
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 flag=0;
 if (rem(dim,2)~=0)
     dim = dim+1;
     ub = [ub, 1];
     lb = [lb, 0];
     flag=1;
 end max_iter=100;
 N=200;
 ArchiveMaxSize=100;Archive_X=zeros(100,dim);
 Archive_F=ones(100,obj_no)*inf;Archive_member_no=0;
%Initialize the positions of artificial whales
 GrassHopperPositions=initialization(N,dim,ub,lb);TargetPosition=zeros(dim,1);
 TargetFitness=inf*ones(1,obj_no);cMax=1;
 cMin=0.00004;
 %calculate the fitness of initial grasshoppersfor iter=1:max_iter
     for i=1:N
         
         Flag4ub=GrassHopperPositions(:,i)>ub';
         Flag4lb=GrassHopperPositions(:,i)<lb';
         GrassHopperPositions(:,i)=(GrassHopperPositions(:,i).*(~(Flag4ub+Flag4lb)))+ub'.*Flag4ub+lb'.*Flag4lb;
         
         GrassHopperFitness(i,:)=ObjectiveFunction(GrassHopperPositions(:,i)');
         if dominates(GrassHopperFitness(i,:),TargetFitness)
             TargetFitness=GrassHopperFitness(i,:);
             TargetPosition=GrassHopperPositions(:,i);
         end
         
     end
     
     [Archive_X, Archive_F, Archive_member_no]=UpdateArchive(Archive_X, Archive_F, GrassHopperPositions, GrassHopperFitness, Archive_member_no);
     
     if Archive_member_no>ArchiveMaxSize
         Archive_mem_ranks=RankingProcess(Archive_F, ArchiveMaxSize, obj_no);
         [Archive_X, Archive_F, Archive_mem_ranks, Archive_member_no]=HandleFullArchive(Archive_X, Archive_F, Archive_member_no, Archive_mem_ranks, ArchiveMaxSize);
     else
         Archive_mem_ranks=RankingProcess(Archive_F, ArchiveMaxSize, obj_no);
     end
     
     Archive_mem_ranks=RankingProcess(Archive_F, ArchiveMaxSize, obj_no);
     index=RouletteWheelSelection(1./Archive_mem_ranks);
     if index==-1
         index=1;
     end
     TargetFitness=Archive_F(index,:);
     TargetPosition=Archive_X(index,:)';
     
     c=cMax-iter*((cMax-cMin)/max_iter); % Eq. (3.8) in the paper
     
     for i=1:N
         
         temp= GrassHopperPositions;
         
         for k=1:2:dim
             S_i=zeros(2,1);
             for j=1:N
                 if i~=j
                     Dist=distance(temp(k:k+1,j), temp(k:k+1,i));
                     r_ij_vec=(temp(k:k+1,j)-temp(k:k+1,i))/(Dist+eps);
                     xj_xi=2+rem(Dist,2);
                        
                     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Eq. (3.2) in the paper 
                     s_ij=((ub(k:k+1)' - lb(k:k+1)') .*c/2)*S_func(xj_xi).*r_ij_vec;
                     S_i=S_i+s_ij;
                     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
                 end
             end
             S_i_total(k:k+1, :) = S_i;
             
         end
         
         X_new=c*S_i_total'+(TargetPosition)'; % Eq. (3.7) in the paper
         GrassHopperPositions_temp(i,:)=X_new';
     end
     % GrassHopperPositions
     GrassHopperPositions=GrassHopperPositions_temp';
     
     display(['At the iteration ', num2str(iter), ' there are ', num2str(Archive_member_no), ' non-dominated solutions in the archive']);
 end if (flag==1)
     TargetPosition = TargetPosition(1:dim-1);
 endfigure
Draw_ZDT1();
hold on
plot(Archive_F(:,1),Archive_F(:,2),'ro','MarkerSize',8,'markerfacecolor','k');
legend('True PF','Obtained PF');
 title('MOGOA');set(gcf, 'pos', [403   466   230   200])

🎉3 参考文献

​​🌈​​4 Matlab代码实现及文章讲解