Evaluating Convergence Rates in Particle Swarm Optimization: Insights from Gradient-Perturbation and Dual-Binary Approaches

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Résumé

This paper investigates the convergence properties of two Particle Swarm Optimization (PSO) algorithms:
the Gradient-Perturbation PSO and the Dual-Binary PSO. We introduce a novel evaluation criterion that
quantifies the rate of convergence using a stochastic dynamic averaging approach, enabling a more precise
analysis of the algorithms’ performance over time. Our theoretical contributions include explicit convergence
bounds under mild assumptions, supported by rigorous probabilistic analysis. Through extensive experiments
on benchmark optimization functions, we demonstrate that the proposed algorithms achieve competitive
convergence speeds compared to standard PSO variants. These findings highlight the practical value and
theoretical robustness of the new criterion in evaluating and enhancing PSO-based methods.

Mots-clés

Approximation; stochastic modelling; gradient perturbation; optimization.