Adaptive Hybrid Particle Swarm Optimization with Gradient Descent
Aryan Gurudeo
cs.AI, cs.NE
Submitted: 2026-08-07
Updated: 2026-08-13
Comments: 11 pages, 8 figures, 8 tables, 25 references. 14,700+ independent optimization runs
License: http://creativecommons.org/licenses/by/4.0/
The gist: Gradient injection helps Particle Swarm Optimization (PSO) only when the swarm has identified a basin with smooth local structure, not universally.
Terminology
Abstract
Gradient injection helps Particle Swarm Optimization (PSO) only when the swarm has identified a basin with smooth local structure, not universally. We propose Adaptive Hybrid PSO (AHPSO), which uses a sigmoid function on swarm diversity to automatically modulate gradient influence: near-zero during exploration, near-maximum during exploitation, with no manual phase-switching. Under budget-normalized comparison (PSO given equivalent total function evaluations), PSO wins 52.5% of 40 configurations versus AHPSO's 20% (p = 7.0e-5, Friedman). AHPSO retains advantage specifically on problems with smooth local basins (F8, F24-F27) where directed descent outperforms undirected sampling even at equal cost. Under iteration-matched comparison across 29 functions (42 configurations, 14,700 runs), AHPSO-Adadelta ranks first of 9 methods including CMA-ES (p = 9.75e-4). The contribution is a principled characterization of when gradient injection provides value in swarm-based search, not a claim of universal superiority.
Sources
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