Divergence-Guided Particle Swarm Optimization

TL;DR

Divergence-guided PSO (DPSO) enhances standard Particle Swarm Optimization by incorporating a divergence-based repulsion mechanism, significantly improving performance on multimodal functions while maintaining efficiency.

Contribution

This paper introduces a divergence-guided modification to PSO that improves exploration in multimodal landscapes through a principled, kernel-based repulsion mechanism.

Findings

DPSO outperforms standard PSO on multimodal benchmark functions by 2-8 times.

DPSO reduces run-to-run variance by up to 5 times.

The method incurs minimal overhead and adds only one hyperparameter.

Abstract

Particle Swarm Optimization (PSO) is susceptible to premature convergence when the swarm collapses around the global best, particularly on multimodal landscapes in higher dimensions. We propose Divergence-guided PSO (DPSO), which augments the velocity update with a modulation term that repels particles whose personal bests have converged near the global best. The repulsion is gated by a Gaussian similarity kernel, which we prove is equivalent to an exponentially decaying function of the KL divergence between Gaussian-embedded personal and global bests, connecting the mechanism to the family of $f$-divergences and providing a principled basis for kernel design. Experiments on 36 benchmark functions (15 unimodal, 21 multimodal) across dimensions $D \in \{10, 30, 50\}$, each with 30 independent runs, show that DPSO frequently outperforms standard PSO on multimodal problems, with improvements of 2-8$\times$ on functions such as Pinter, Ackley, and Levy, and up to 5$\times$ reduction in run-to-run variance. On unimodal landscapes the modulation term is counterproductive, confirming that DPSO targets the exploration-exploitation trade-off rather than offering a universal improvement. The method adds one hyperparameter, incurs 15--25\% wall-clock overhead, and does not increase the asymptotic per-iteration complexity of PSO. The project code is available here: https://github.com/Kleyt0n/dpso