1 简介

灰狼优化算法一种模拟灰狼捕食行为的元启发式优化算法.由于灰狼算法在种群迭代更新中始终靠近最优解,所以易陷入局部最优.提出了一种基于自适应头狼的灰狼优化算法,并在个体迭代更新中选择合适的头狼个数进行个体更新,这使得算法能够平衡开发和勘探能力.通过对20个基准函数优化问题的仿真实验表明,改进后的算法与原始灰狼优化算法相比,其全局搜索能力有显著提高.

1.1 灰狼算法介绍

2 部分代码

%___________________________________________________________________%
%  Grey Wold Optimizer (GWO) source codes 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, S. M. Mirjalili, A. Lewis             %
%               Grey Wolf Optimizer, Advances in Engineering        %
%               Software , in press,                                %
%               DOI: 10.1016/j.advengsoft.2013.12.007               %
%                                                                   %
%___________________________________________________________________%
% Grey Wolf Optimizer
function [Alpha_score,Alpha_pos,Convergence_curve]=GWO(SearchAgents_no,Max_iter,lb,ub,dim,fobj)
% initialize alpha, beta, and delta_pos
Alpha_pos=zeros(1,dim);
Alpha_score=inf; %change this to -inf for maximization problems
Beta_pos=zeros(1,dim);
Beta_score=inf; %change this to -inf for maximization problems
Delta_pos=zeros(1,dim);
Delta_score=inf; %change this to -inf for maximization problems
%Initialize the positions of search agents
Positions=initialization(SearchAgents_no,dim,ub,lb);
Convergence_curve=zeros(1,Max_iter);
l=0;% Loop counter
% Main loop
while l<Max_iter
    for i=1:size(Positions,1)  
       % Return back the search agents that go beyond the boundaries of the search space
        Flag4ub=Positions(i,:)>ub;
        Flag4lb=Positions(i,:)<lb;
        Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;               
        % Calculate objective function for each search agent
        fitness=fobj(Positions(i,:));
        % Update Alpha, Beta, and Delta
        if fitness<Alpha_score 
            Alpha_score=fitness; % Update alpha
            Alpha_pos=Positions(i,:);
        end
        if fitness>Alpha_score && fitness<Beta_score 
            Beta_score=fitness; % Update beta
            Beta_pos=Positions(i,:);
        end
        if fitness>Alpha_score && fitness>Beta_score && fitness<Delta_score 
            Delta_score=fitness; % Update delta
            Delta_pos=Positions(i,:);
        end
    end
    % a decreases linearly fron 2 to 0
     a=sin(((l*pi)/Max_iter)+pi/2)+1;
    % Update the Position of search agents including omegas
    for i=1:size(Positions,1)
        for j=1:size(Positions,2)     
            r1=rand(); % r1 is a random number in [0,1]
            r2=rand(); % r2 is a random number in [0,1]
            A1=2*a*r1-a; % Equation (3.3)
            C1=2*r2; % Equation (3.4)
            D_alpha=abs(C1*Alpha_pos(j)-Positions(i,j)); % Equation (3.5)-part 1
            X1=Alpha_pos(j)-A1*D_alpha; % Equation (3.6)-part 1
            r1=rand();
            r2=rand();
            A2=2*a*r1-a; % Equation (3.3)
            C2=2*r2; % Equation (3.4)
            D_beta=abs(C2*Beta_pos(j)-Positions(i,j)); % Equation (3.5)-part 2
            X2=Beta_pos(j)-A2*D_beta; % Equation (3.6)-part 2       
            r1=rand();
            r2=rand(); 
            A3=2*a*r1-a; % Equation (3.3)
            C3=2*r2; % Equation (3.4)
            D_delta=abs(C3*Delta_pos(j)-Positions(i,j)); % Equation (3.5)-part 3
            X3=Delta_pos(j)-A3*D_delta; % Equation (3.5)-part 3             
            Positions(i,j)=(X1+X2+X3)/3;% Equation (3.7)
        end
    end
    l=l+1;    
    Convergence_curve(l)=Alpha_score;
end

3 仿真结果

4 参考文献

[1]郭阳, 张涛, 胡玉蝶,等. 基于自适应头狼的灰狼优化算法[J]. 成都大学学报：自然科学版, 2020, 39(1):5.

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