A Pad$ \acute{e} $ approximation and intelligent population shrinkage chicken swarm optimization algorithm for solving global optimization and engineering problems

Tianbao Liu; Yue Li; Xiwen Qin; Tianbao Liu; Yue Li; Xiwen Qin

doi:10.3934/mbe.2024041

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 984-1016. doi: 10.3934/mbe.2024041

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Research article

A Pad$ \acute{e} $ approximation and intelligent population shrinkage chicken swarm optimization algorithm for solving global optimization and engineering problems

School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, Jilin, China

Academic Editor: Yang Kuang

Received: 18 November 2023 Revised: 09 December 2023 Accepted: 13 December 2023 Published: 22 December 2023

Bio-inspired optimization algorithms are competitive solutions for engineering design problems. Chicken swarm optimization (CSO) combines the advantages of differential evolution and particle swarm optimization, drawing inspiration from the foraging behavior of chickens. However, the CSO algorithm may perform poorly in the face of complex optimization problems because it has a high risk of falling into a local optimum. To address these challenges, a new CSO called chicken swarm optimization combining Pad$ \acute{e} $ approximate, random learning and population reduction techniques (PRPCSO) was proposed in this work. First, a Pad$ \acute{e} $ approximate strategy was combined to help agents converge to the approximate real solution area quickly. Pad$ \acute{e} $ approximate was grounded in a rational function aligning with the power series expansion of the approximated function within a defined number of terms. The fitting function used in this strategy employs the above rational function and the extreme points are calculated mathematically, which can significantly improve the accuracy of the solution. Second, the random learning mechanism encouraged agents to learn from other good agents, resulting in better local exploitation capability compared to traditional CSO. This mechanism has a special idea that when it comes to selecting random individuals, it selects from the same type of high-performing agents, rather than selecting them completely at random. Third, a new intelligent population size shrinking strategy was designed to dynamically adjust the population size to prevent premature convergence. It considers fitness function calls and variations in recent optimal solutions creatively. To validate the algorithm's efficacy, PRPCSO was rigorously tested across 23 standard test functions and six kinds of practical engineering problems. We then compared PRPCSO with several mainstream algorithms, and the results unequivocally established PRPCSO's superior performance in most instances, highlighting its substantial practical utility in real engineering applications.
- chicken swarm optimization,
- Pad$ \acute{e} $ approximate,
- random learning mechanism,
- intelligent population size shrinkage,
- engineering optimization
Citation: Tianbao Liu, Yue Li, Xiwen Qin. A Pad$ \acute{e} $ approximation and intelligent population shrinkage chicken swarm optimization algorithm for solving global optimization and engineering problems[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 984-1016. doi: 10.3934/mbe.2024041

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Abstract

Bio-inspired optimization algorithms are competitive solutions for engineering design problems. Chicken swarm optimization (CSO) combines the advantages of differential evolution and particle swarm optimization, drawing inspiration from the foraging behavior of chickens. However, the CSO algorithm may perform poorly in the face of complex optimization problems because it has a high risk of falling into a local optimum. To address these challenges, a new CSO called chicken swarm optimization combining Pad$ \acute{e} $ approximate, random learning and population reduction techniques (PRPCSO) was proposed in this work. First, a Pad$ \acute{e} $ approximate strategy was combined to help agents converge to the approximate real solution area quickly. Pad$ \acute{e} $ approximate was grounded in a rational function aligning with the power series expansion of the approximated function within a defined number of terms. The fitting function used in this strategy employs the above rational function and the extreme points are calculated mathematically, which can significantly improve the accuracy of the solution. Second, the random learning mechanism encouraged agents to learn from other good agents, resulting in better local exploitation capability compared to traditional CSO. This mechanism has a special idea that when it comes to selecting random individuals, it selects from the same type of high-performing agents, rather than selecting them completely at random. Third, a new intelligent population size shrinking strategy was designed to dynamically adjust the population size to prevent premature convergence. It considers fitness function calls and variations in recent optimal solutions creatively. To validate the algorithm's efficacy, PRPCSO was rigorously tested across 23 standard test functions and six kinds of practical engineering problems. We then compared PRPCSO with several mainstream algorithms, and the results unequivocally established PRPCSO's superior performance in most instances, highlighting its substantial practical utility in real engineering applications.

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