🤖 AI Summary
This work addresses the performance degradation in particle swarm optimization (PSO) caused by the indiscriminate incorporation of gradient information and proposes an Adaptive Hybrid PSO (AHPSO). The method provides the first principled characterization of when gradient injection is beneficial, activating gradients only within locally smooth basins. It further employs a sigmoid function to adaptively modulate the influence of gradient descent based on population diversity—suppressing gradients during exploration and enhancing them during exploitation—without manual intervention. Experimental results demonstrate that AHPSO significantly outperforms standard PSO on smooth local basin functions (F8, F24–F27) across 40 configurations. In an extensive iterative matching study involving 29 benchmark functions and 14,700 runs, AHPSO-Adadelta ranked first among nine competing methods (p = 9.75e⁻⁴).
📝 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.