1 简介
In order to solve the problem that the butterflfly optimization algorithm (BOA) is prone to lowaccuracy and slow convergence, the trend of study is to hybridize two or more algorithms to obtain asuperior solution in the fifield of optimization problems. A novel hybrid algorithm is proposed, namelyHPSOBOA, and three methods are introduced to improve the basic BOA. Therefore, the initializationof BOA using a cubic one-dimensional map is introduced, and a nonlinear parameter control strategyis also performed. In addition, the particle swarm optimization (PSO) algorithm is hybridized withBOA in order to improve the basic BOA for global optimization. There are two experiments (including26 well-known benchmark functions) that were conducted to verify the effffectiveness of the proposedalgorithm. The comparison results of experiments show that the hybrid HPSOBOA converges quicklyand has better stability in numerical optimization problems with a high dimension compared withthe PSO, BOA, and other kinds of well-known swarm optimization algorithms.
2 部分代码
function [fmin,best_pos,Convergence_curve] = BOA(n,N_iter,Lb,Ub,dim,fobj)
% n is the population size
% N_iter represnets total number of iterations
p=0.6; % probabibility switch
power_exponent=0.1; %initial value of a
sensory_modality=0.01; %initial value of c
%Initialize the positions of search agents
Sol=initialization(n,dim,Ub,Lb);
for i=1:n
Fitness(i)=fobj(Sol(i,:));
end
% Find the current best_pos
[fmin,I]=min(Fitness);
best_pos=Sol(I,:);
S=Sol;
% Start the iterations -- Butterfly Optimization Algorithm
for t=1:N_iter
for i=1:n % Loop over all butterflies/solutions
%Calculate fragrance of each butterfly which is correlated with objective function
Fnew=fobj(S(i,:));
FP=(sensory_modality*(Fnew^power_exponent));
%Global or local search
if rand<p
dis = rand * rand * best_pos - Sol(i,:); %Eq. (2) in paper
S(i,:)=Sol(i,:)+dis*FP;
else
% Find random butterflies in the neighbourhood
epsilon=rand;
JK=randperm(n);
dis=epsilon*epsilon*Sol(JK(1),:)-Sol(JK(2),:);
S(i,:)=Sol(i,:)+dis*FP; %Eq. (3) in paper
end
% Check if the simple limits/bounds are OK
% S(i,:)=simplebounds(S(i,:),Lb,Ub);
Flag4Ub=S(i,:)>Ub;
Flag4Lb=S(i,:)<Lb;
S(i,:)=(S(i,:).*(~(Flag4Ub+Flag4Lb)))+Ub.*Flag4Ub+Lb.*Flag4Lb;
% Evaluate new solutions
Fnew=fobj(S(i,:)); %Fnew represents new fitness values
% If fitness improves (better solutions found), update then
if (Fnew<=Fitness(i))
Sol(i,:)=S(i,:);
Fitness(i)=Fnew;
end
% Update the current global best_pos
if Fnew<=fmin
best_pos=S(i,:);
fmin=Fnew;
end
end
Convergence_curve(t,1)=fmin;
%Update sensory_modality
sensory_modality=sensory_modality_NEW(sensory_modality, N_iter);
end
end
% % Boundary constraints
% function s=simplebounds(s,Lb,Ub)
% % Apply the lower bound
% ns_tmp=s;
% I=ns_tmp<Lb;
% ns_tmp(I)=Lb;
%
% % Apply the upper bounds
% J=ns_tmp>Ub;
% ns_tmp(J)=Ub;
% % Update this new move
% s=ns_tmp;
function y=sensory_modality_NEW(x,Ngen)
y=x+(0.025/(x*Ngen));
end
3 仿真结果
4 参考文献
[1]刘景森, 马义想, 李煜. 改进蝴蝶算法求解多维复杂函数优化问题[J]. 电子学报, 2021, 49(6):9.
[2] Zhang, M. , et al. "A Chaotic Hybrid Butterfly Optimization Algorithm with Particle Swarm Optimization for High-Dimensional Optimization Problems." Symmetry 12.11(2020):1800.
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