Stochastic stability analysis of particle swarm optimization with pseudo random number assignment strategy

• Published in: European journal of operational research Vol. 305; no. 2; pp. 562 - 593
• Main Author: Chih, Mingchang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2023
• Subjects: Metaheuristics; Particle swarm optimization; Pseudo-random number assignment strategy; Stability analysis; Stochastic process theory; Stochastic process theory; Stability analysis; Metaheuristics; Particle swarm optimization; Pseudo-random number assignment strategy
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2022.06.009

•We propose a novel idea by introducing PRN assignment strategies into PSO method.•The stability of the PSO under different PRN assignment strategies is studied.•The stability analysis is conducted using stochastic process theory.•The correlation caused by PRN has no effect on the unbiasedness of the expectation.•But it would reduce or increase the variance of the particle dynamics. Particle swarm optimization (PSO) is a population-based optimization method and has been successfully applied to solve many real-world problems. This method belongs to the stochastic optimization method and is mainly driven by two random streams utilized in the stochastic search mechanism, namely, individual (cognition) and social randomness effects. To our best knowledge, no research work has been conducted about the manipulation of the random stream assignment for stochastic search mechanism in the PSO algorithm. In this work, the influences of controlling randomness in the searching scheme of PSO is studied by introducing different pseudo random number (PRN) assignment strategies. The order-1 and order-2 stability analyses for particle dynamics under different PRN assignment strategies are also conducted to understand the influences. Stability analysis is carried out using the stochastic process theory. Our results show that the correlation caused by PRN has no effect on the unbiasedness of the expectation of particle position, but it would reduce or increase the variance of particle dynamics. Second, the convergent conditions of the PSO system under different PRN assignment strategies and the corresponding parameter selection ranges are provided. Finally, an empirical analysis via experimental simulations evaluated by six common swarm diversity measures, eight benchmark test functions, and two parameter tuples is presented.