Critical Parameters in Particle Swarm Optimisation

TL;DR

This paper analyzes the stability of particle swarm optimization using dynamical systems theory, revealing how parameter choices influence convergence and divergence, and showing optimal performance near the stability boundary.

Contribution

It provides an analytical framework linking PSO parameters to stability, guiding optimal parameter selection for better performance.

Findings

Optimal performance occurs near the stability boundary.

Analytical results predict convergence and divergence conditions.

Simulation results confirm theoretical predictions.

Abstract

Particle swarm optimisation is a metaheuristic algorithm which finds reasonable solutions in a wide range of applied problems if suitable parameters are used. We study the properties of the algorithm in the framework of random dynamical systems which, due to the quasi-linear swarm dynamics, yields analytical results for the stability properties of the particles. Such considerations predict a relationship between the parameters of the algorithm that marks the edge between convergent and divergent behaviours. Comparison with simulations indicates that the algorithm performs best near this margin of instability.