Refined Velocity–Position Dynamics in Particle Swarm Optimization: A Survey of Recent Mathematical Innovations - Perkasa, Sigit Dani; Jasmine, Senit Araminta (Peneliti Teknologi Teknik Indonesia, 2025)
Particle Swarm Optimization (PSO) remains a pivotal metaheuristic for complex optimization, yet its canonical form faces persistent challenges, including premature convergence and inefficacy in dynamic or high-dimensional landscapes. This survey examines recent advancements in refining PSO’s velocity-position dynamics, emphasizing adaptive mechanisms that enhance exploration-exploitation balance, ensure stability in noisy measurement environments, preserve swarm diversity in discrete search spaces, and maintain robustness under changing problem conditions. Evaluation results on standardized benchmark functions and targeted applications—such as crack detection in bridge structural health monitoring, real-time photovoltaic panel solar tracking, and high-dimensional gene-expression feature selection—demonstrate convergence speeds up to 4-times faster, reliable scaling to over 150 dimensions, and task success rates exceeding 98%. However, these refinements incur moderate runtime overhead and require more intensive hyperparameter tuning, posing challenges for large-scale or real-time deployments. Building on the limitations of static parameter settings and theoretical gaps in dynamic adaptation, the study advocates for future research into hybrid metaheuristic frameworks, automated self-tuning strategies, and rigorous theoretical convergence guarantees. This synthesis bridges mathematical innovation with practical insights, guiding researchers in developing next-generation, self-adaptive PSO variants for contemporary optimization demands.