Convergence analysis of particle swarm optimization using stochastic Lyapunov functions and quantifier elimination

TL;DR

This paper investigates the stability and convergence of particle swarm optimization by employing stochastic Lyapunov functions and quantifier elimination, leading to an improved understanding of PSO stability regions.

Contribution

It introduces a novel approach combining stochastic Lyapunov functions and quantifier elimination to analyze PSO convergence and stability.

Findings

Reevaluation of PSO stability regions

Extension of stability analysis under stagnation assumptions

A computational procedure for convergence analysis

Abstract

This paper adds to the discussion about theoretical aspects of particle swarm stability by proposing to employ stochastic Lyapunov functions and to determine the convergence set by quantifier elimination. We present a computational procedure and show that this approach leads to reevaluation and extension of previously know stability regions for PSO using a Lyapunov approach under stagnation assumptions.