【优化算法】多目标蝗虫优化算法（MOGOA）

一、简介

\ 1 GOA数学模型\ \ \ \ 2 GOA迭代模型\ \ \ 3 GOA算法的基本流程\ \ \ 4 GOA缺点\ \

二、源代码

``` 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;

ArchiveX=zeros(100,dim); ArchiveF=ones(100,obj_no)*inf;

Archivememberno=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 grasshoppers

for 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); end

figure

Draw_ZDT1();

hold on

plot(ArchiveF(:,1),ArchiveF(:,2),'ro','MarkerSize',8,'markerfacecolor','k');

legend('True PF','Obtained PF'); title('MOGOA');

set(gcf, 'pos', [403 466 230 200])

```

三、运行结果

四、备注

版本：2014a