Divergence-Guided Particle Swarm Optimization

Kleyton Da Costa, Bernardo Modenesi

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∈{10,30,50}, each with 30 independent runs, show that DPSO frequently outperforms standard PSO on multimodal problems, with improvements of 2-8× on functions such as Pinter, Ackley, and Levy, and up to 5× 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.