【灰狼算法】基于Iterative映射和单纯形法改进灰狼优化算法求解单目标优化问题

1 简介

为了解决基本灰狼优化算法(GWO)依赖初始种群和求解精度不高的问题,提出一种基于Iterative映射和单纯形法的改进灰狼优化算法(SMIGWO).该算法利用混沌Iterative映射产生初始灰狼种群,增强全局搜索过程中的种群多样性;采用逆不完全Γ函数更新收敛因子,以平衡算法的全局搜索和局部搜索能力;利用单纯形法的反射,扩张和收缩操作对当前较差个体进行改进,避免算法陷入局部最优.对10个测试函数进行仿真实验,数值结果表明,与基本GWO算法,改进的灰狼优化算法求解精度更高,稳定性更好.

2 部分代码

%___________________________________________________________________%
% Grey Wolf Optimizer (GWO) source codes version 1.0 %
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% Developed in MATLAB R2011b(7.13) %
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% Author and programmer: Seyedali Mirjalili %
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% e-Mail: ali.mirjalili@gmail.com %
% seyedali.mirjalili@griffithuni.edu.au %
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% 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=2-l*((2)/Max_iter); % a decreases linearly fron 2 to 0
% 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]王梦娜, 王秋萍, 王晓峰. 基于Iterative映射和单纯形法的改进灰狼优化算法[J]. 计算机应用, 2018, 38(A02):6.

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