【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

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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 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(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])

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三、运行结果

四、备注

版本：2014a