一、簡介

蜻蜓演算法(Dragonfly Algorithm)是由Seyedali Mirjalili在2015年提出的一種新興群智慧演算法。Reynoldz指出三個關於蜂群體行為準則：分離度、對齊度與聚合度。分離度是指相鄰個體間保持適當距離，以免碰撞；對齊度是指速度和方向與相鄰個體對齊；聚合度是指個體飛向相鄰區域中心。蜻蜓主要目標都是生存，Seyedali Mirjalili提出五個因素影響蜻蜓演算法的位置更新：分離，列隊，聚集，捕食，逃離。數學模型如下：

二、原始碼

%___________________________________________________________________%
%  Multi-Objective Dragonfly Algorithm (MODA) source codes demo     %
%                           version 1.0                             %
%                                                                   %
%  Developed in MATLAB R2011b(7.13)                                 %
%                                                                   %
%  Author and programmer: Seyedali Mirjalili                        %
%                                                                   %
%         e-Mail: [email protected]                           %
%                 [email protected]             %
%                                                                   %
%       Homepage: http://www.alimirjalili.com                       %
%                                                                   %
%   Main paper:                                                     %
%                                                                   %
%   S. Mirjalili, Dragonfly algorithm: a new meta-heuristic         %
%   optimization technique for solving single-objective, discrete,  %
%   and multi-objective problems, Neural Computing and Applications %
%   DOI: http://dx.doi.org/10.1007/s00521-015-1920-1                %
%___________________________________________________________________%

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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Initial parameters of the MODA algorithm
max_iter=100;
N=100;
ArchiveMaxSize=100;

Archive_X=zeros(100,dim);
Archive_F=ones(100,obj_no)*inf;

Archive_member_no=0;

r=(ub-lb)/2;
V_max=(ub(1)-lb(1))/10;

Food_fitness=inf*ones(1,obj_no);
Food_pos=zeros(dim,1);

Enemy_fitness=-inf*ones(1,obj_no);
Enemy_pos=zeros(dim,1);

X=initialization(N,dim,ub,lb);
fitness=zeros(N,2);

DeltaX=initialization(N,dim,ub,lb);
iter=0;

position_history=zeros(N,max_iter,dim);

for iter=1:max_iter
    
    r=(ub-lb)/4+((ub-lb)*(iter/max_iter)*2);
    
    w=0.9-iter*((0.9-0.2)/max_iter);
    
    my_c=0.1-iter*((0.1-0)/(max_iter/2));
    if my_c<0
        my_c=0;
    end
    
    if iter<(3*max_iter/4)
        s=my_c;             % Seperation weight
        a=my_c;             % Alignment weight
        c=my_c;             % Cohesion weight
        f=2*rand;           % Food attraction weight
        e=my_c;             % Enemy distraction weight
    else
        s=my_c/iter;        % Seperation weight
        a=my_c/iter;        % Alignment weight
        c=my_c/iter;        % Cohesion weight
        f=2*rand;           % Food attraction weight
        e=my_c/iter;        % Enemy distraction weight
    end
    
    for i=1:N %Calculate all the objective values first
        Particles_F(i,:)=ObjectiveFunction(X(:,i)');
        if dominates(Particles_F(i,:),Food_fitness)
            Food_fitness=Particles_F(i,:);
            Food_pos=X(:,i);
        end
        
        if dominates(Enemy_fitness,Particles_F(i,:))
            if all(X(:,i)<ub') && all( X(:,i)>lb')
                Enemy_fitness=Particles_F(i,:);
                Enemy_pos=X(:,i);
            end
        end
    end
    
    [Archive_X, Archive_F, Archive_member_no]=UpdateArchive(Archive_X, Archive_F, X, Particles_F, 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);
    
    % Chose the archive member in the least population area as foods
    % to improve coverage
    index=RouletteWheelSelection(1./Archive_mem_ranks);
    if index==-1
        index=1;
    end
    Food_fitness=Archive_F(index,:);
    Food_pos=Archive_X(index,:)';
       
    % Chose the archive member in the most population area as enemies
    % to improve coverage
    index=RouletteWheelSelection(Archive_mem_ranks);
    if index==-1
        index=1;
    end
    Enemy_fitness=Archive_F(index,:);
    Enemy_pos=Archive_X(index,:)';
    
    for i=1:N
        index=0;
        neighbours_no=0;
        
        clear Neighbours_V
        clear Neighbours_X
        % Find the neighbouring solutions
        for j=1:N
            Dist=distance(X(:,i),X(:,j));
            if (all(Dist<=r) && all(Dist~=0))
                index=index+1;
                neighbours_no=neighbours_no+1;
                Neighbours_V(:,index)=DeltaX(:,j);
                Neighbours_X(:,index)=X(:,j);
            end
        end
        
        % Seperation%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        % Eq. (3.1)
        S=zeros(dim,1);
        if neighbours_no>1
            for k=1:neighbours_no
                S=S+(Neighbours_X(:,k)-X(:,i));
            end
            S=-S;
        else
            S=zeros(dim,1);
        end
        
        % Alignment%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        % Eq. (3.2)
        if neighbours_no>1
            A=(sum(Neighbours_V')')/neighbours_no;
        else
            A=DeltaX(:,i);
        end
        
        % Cohesion%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        % Eq. (3.3)
        if neighbours_no>1
            C_temp=(sum(Neighbours_X')')/neighbours_no;
        else
            C_temp=X(:,i);
        end
        
        C=C_temp-X(:,i);
        
        % Attraction to food%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        % Eq. (3.4)
        Dist2Attraction=distance(X(:,i),Food_pos(:,1));
        if all(Dist2Attraction<=r)
            F=Food_pos-X(:,i);
            iter;
        else
            F=0;
        end
        
        % Distraction from enemy%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        % Eq. (3.5)
        Dist=distance(X(:,i),Enemy_pos(:,1));
        if all(Dist<=r)
            E=Enemy_pos+X(:,i);
        else
            E=zeros(dim,1);
        end
        
        for tt=1:dim
            if X(tt,i)>ub(tt)
                X(tt,i)=lb(tt);
                DeltaX(tt,i)=rand;
            end
            if X(tt,i)<lb(tt)
                X(tt,i)=ub(tt);
                DeltaX(tt,i)=rand;
            end
        end
        
        
        if any(Dist2Attraction>r)
            if neighbours_no>1
                for j=1:dim
                    DeltaX(j,i)=w*DeltaX(j,i)+rand*A(j,1)+rand*C(j,1)+rand*S(j,1);
                    if DeltaX(j,i)>V_max
                        DeltaX(j,i)=V_max;
                    end
                    if DeltaX(j,i)<-V_max
                        DeltaX(j,i)=-V_max;
                    end
                    X(j,i)=X(j,i)+DeltaX(j,i);
                end
 

三、執行結果

四、備註

版本：2014a
完整程式碼或代寫加1564658423