Exploring the Optimized Hyperparameter Values Based on Mathematical Models for PSO

In recent years, numerous swarm intelligence optimization algorithms have emerged for tackling diverse optimization problems. However, the determination of several hyperparameters remains a critical challenge. Take Particle Swarm Optimization (PSO) as an example: while it has demonstrated superior optimization performance in various applications, setting the weights for inertial velocity, the particle's best-known position, and the swarm's best-known position poses a significant hurdle. Hence, this study introduces an analytical framework aimed at examining the optimized mean fitness function value through mathematical models encompassing a range of fitness functions. Moreover, this framework facilitates the determination of optimized hyperparameter values associated with lower mean fitness function values. Experimental findings indicate that employing the proposed method for hyperparameter determination leads to enhanced convergence efficiency and decreased mean fitness function values.