AHPSO: Adaptive Hybrid Particle Swarm Optimization with Gradient Descent

A recent preprint on arXiv (2608.11258) presents Adaptive Hybrid Particle Swarm Optimization (AHPSO), a technique that incorporates gradient descent into Particle Swarm Optimization (PSO) while adapting to the diversity of the swarm. The authors contend that gradient injection is advantageous only when the swarm has located a basin with a smooth local structure, rather than being universally applicable. AHPSO employs a sigmoid function to adjust gradient influence based on swarm diversity, minimizing it during exploration and maximizing it during exploitation, thus negating the need for manual phase transitions. In budget-normalized tests, PSO outperformed AHPSO in 52.5% of 40 configurations, while AHPSO excelled in problems with smooth local basins (F8, F24-F27). In matched iterations across 29 functions (42 configurations, 14,700 runs), AHPSO-Adadelta achieved the top rank among nine methods, including CMA-ES (p = 9.75e-4). The study provides a clear understanding of when gradient injection is beneficial.