Novel Adaptive Velocity Clamping Methods in Particle Swarm Optimization with Benchmark Validation

Particle Swarm Optimization (PSO) is an effective population-based metaheuristic algorithm widely utilized in solving complex optimization problems across various disciplines. Despite its success, conventional PSO suffers from premature convergence and suboptimal exploration–exploitation balance due to its static velocity clamping mechanisms. To address this limitation, this study proposes and systematically evaluates two Adaptive Velocity Clamping strategies: Performance-Feedback Velocity Clamping (PFVC) and Position-Distance-Based Velocity Clamping (PDVC). Comprehensive benchmarking was conducted on three distinct optimization functions: Sphere (unimodal), Rosenbrock (complex unimodal), and Rastrigin (complex multimodal). Results demonstrated that both PFVC and PDVC significantly improved solution quality compared to conventional PSO, with PFVC achieving the most stable and accurate results across functions, particularly on multimodal problems such as Rastrigin, while PDVC provided competitive performance with consistently fast convergence. Convergence analyses further confirmed that adaptive strategies effectively mitigate premature convergence, substantially enhancing optimization robustness and efficiency. The findings underscore the practical value of Adaptive Velocity Clamping strategies in advancing PSO performance while offering useful insights for future research and real-world optimization applications.