# Adaptive Hybrid Particle Swarm Optimization with Gradient Descent

arXiv: https://arxiv.org/abs/2608.11258 · HTML: https://mlsanity.com/paper/2608.11258/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 26 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 1 of 1)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)

## Abstract (arXiv)

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.