Review of chaotic mapping enabled nature-inspired algorithms

Zheng-Ming Gao; Juan Zhao; Yu-Jun Zhang; Zheng-Ming Gao; Juan Zhao; Yu-Jun Zhang

doi:10.3934/mbe.2022383

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 8: 8215-8258. doi: 10.3934/mbe.2022383

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Research article

Review of chaotic mapping enabled nature-inspired algorithms

1.
School of computer engineering, Jingchu university of technology, Jingmen 448000, China
2.
School of electronics and information engineering, Jingchu university of technology, Jingmen 448000, China

Academic Editor: Xiaodong Huang

Received: 14 May 2022 Revised: 25 May 2022 Accepted: 26 May 2022 Published: 06 June 2022

Chaotic maps were frequently introduced to generate random numbers and used to replace the pseudo-random numbers distributed in Gauss distribution in computer engineering. These improvements in optimization were called the chaotic improved optimization algorithm, most of them were reported better in literature. In this paper, we collected 19 classical maps which could all generate pseudo-random numbers in an interval between 0 and 1. Four types of chaotic improvement to original optimization algorithms were summarized and simulation experiments were carried out. The classical grey wolf optimization (GWO) and sine cosine (SC) algorithms were involved in these experiments. The final simulation results confirmed an uncertainty about the performance of improvements applied in different algorithms, different types of improvements, or benchmark functions. However, Results confirmed that Bernoulli map might be a better choice for most time. The code related to this paper is shared with https://gitee.com/lvqing323/chaotic-mapping.
- chaotic maps,
- nature-inspired algorithms,
- benchmark functions,
- simulation experiments,
- chaotic improvements
Citation: Zheng-Ming Gao, Juan Zhao, Yu-Jun Zhang. Review of chaotic mapping enabled nature-inspired algorithms[J]. Mathematical Biosciences and Engineering, 2022, 19(8): 8215-8258. doi: 10.3934/mbe.2022383

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Abstract

Chaotic maps were frequently introduced to generate random numbers and used to replace the pseudo-random numbers distributed in Gauss distribution in computer engineering. These improvements in optimization were called the chaotic improved optimization algorithm, most of them were reported better in literature. In this paper, we collected 19 classical maps which could all generate pseudo-random numbers in an interval between 0 and 1. Four types of chaotic improvement to original optimization algorithms were summarized and simulation experiments were carried out. The classical grey wolf optimization (GWO) and sine cosine (SC) algorithms were involved in these experiments. The final simulation results confirmed an uncertainty about the performance of improvements applied in different algorithms, different types of improvements, or benchmark functions. However, Results confirmed that Bernoulli map might be a better choice for most time. The code related to this paper is shared with https://gitee.com/lvqing323/chaotic-mapping.

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