A Cautionary Note on Poli's Stability Condition for Particle Swarm Optimization
Daniel von Eschwege, Andries Petrus Engelbrecht · 2023
Particle swarm optimization (PSO) is a swarm intelligence algorithm that finds candidate solutions by iteratively updating the positions of particles in a swarm. PSO performance depends on the use of a suitable control parameter (CP) configuration, which governs the trade-off between exploration and exploitation in the swarm. Various methods of adapting or tuning CPs exist, but many result in exploding particle velocities and an unstable search process. Poli's stability condition ensures convergence in the mathematical limit, and is often used to inform CP configuration. However, this study shows that since it does not place any practical convergence constraints, it cannot be used to guarantee a stable search process. Velocity explosion occurs nonetheless and can lead to floating-point overflow and numerical instability. The investigation into various CP configurations across diverse functions and measurements of particle velocities provides empirical evidence of velocity explosion, and cautions against the assumption that enforcing Poli's criterion guarantees stability. The findings underline the need for comprehensive understanding of CP tuning and stability conditions in PSO, as well as the crucial role of empirical evidence in evaluating the real-world performance of swarm intelligence algorithms.