A Chaotic Hybrid Butterfly Optimization Algorithm with Particle Swarm Optimization for High-Dimensional Optimization Problems

Mengjian Zhang,Jing Yang,Daoyin Long,Tao Qin

doi:10.3390/sym12111800

Abstract

In order to solve the problem that the butterfly optimization algorithm (BOA) is prone to low accuracy and slow convergence, the trend of study is to hybridize two or more algorithms to obtain a superior solution in the field of optimization problems. A novel hybrid algorithm is proposed, namely HPSOBOA, and three methods are introduced to improve the basic BOA. Therefore, the initialization of BOA using a cubic one-dimensional map is introduced, and a nonlinear parameter control strategy is also performed. In addition, the particle swarm optimization (PSO) algorithm is hybridized with BOA in order to improve the basic BOA for global optimization. There are two experiments (including 26 well-known benchmark functions) that were conducted to verify the effectiveness of the proposed algorithm. The comparison results of experiments show that the hybrid HPSOBOA converges quickly and has better stability in numerical optimization problems with a high dimension compared with the PSO, BOA, and other kinds of well-known swarm optimization algorithms.

Highlights

The butterfly optimization algorithm (BOA) was proposed by Arora and Singh in 2018 [1].The method and concept of this algorithm was proposed [2] firstly at the 2015 International Conference on Signal Processing, Computing and Control (2015 ISPCC)
The comparison results of experiments show that the hybrid HPSOBOA converges quickly and has better stability in numerical optimization problems with a high dimension compared with the particle swarm optimization (PSO), BOA, and other kinds of well-known swarm optimization algorithms
In order to improve the ability of the algorithm for high-dimensional optimization problems that we proposed, the method for hybrid the meta-heuristic algorithms, which combines the basic PSO and BOA, and the chaotic theory, is used in the improved method

Summary

Introduction

The butterfly optimization algorithm (BOA) was proposed by Arora and Singh in 2018 [1].The method and concept of this algorithm was proposed [2] firstly at the 2015 International Conference on Signal Processing, Computing and Control (2015 ISPCC). The butterfly optimization algorithm (BOA) was proposed by Arora and Singh in 2018 [1]. After the algorithm was proposed, the authors have performed many studies on BOA. Arora and Singh [3] proposed an improved butterfly optimization algorithm with ten chaotic maps for solving three engineering optimization problems. Arora and Singh [4] proposed a new hybrid optimization algorithm which combines the standard BOA with Artificial Bee Colony (ABC) algorithm. Arora and Singh [5] used the BOA to solve the node localization in wireless sensor networks and compared the results with the particle swarm optimization (PSO) algorithm and firefly algorithm (FA). Arora et al [6] proposed a modified butterfly optimization algorithm for solving the mechanical design optimization problems.

Methods

Results

Conclusion