【多目标优化求解】基于matlab蜻蜓算法求解多目标优化问题【含Matlab源码 477期】

唐伯虎

　　
一、简介
　　蜻蜓算法(Dragonfly Algorithm)是由Seyedali Mirjalili在2015年提出的一种新兴群智能算法。Reynoldz指出三个关于蜂群体行为准则：分离度、对齐度与聚合度。分离度是指相邻个体间保持适当距离，以免碰撞；对齐度是指速度和方向与相邻个体对齐；聚合度是指个体飞向相邻区域中心。蜻蜓主要目标都是生存，Seyedali Mirjalili提出五个因素影响蜻蜓算法的位置更新：分离，列队，聚集，捕食，逃离。数学模型如下：



二、源代码

%___________________________________________________________________%
%  Multi-Objective Dragonfly Algorithm (MODA) source codes demo   %
%               version 1.0               %
%                                   %
%  Developed in MATLAB R2011b(7.13)                 %
%                                   %
%  Author and programmer: Seyedali Mirjalili            %
%                                   %
%     e-Mail: ali.mirjalili@gmail.com               %
%         seyedali.mirjalili@griffithuni.edu.au       %
%                                   %
%     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、运行结果

四、备注
　　版本：2014a