Exploring the Impact of Random Distribution Choices on Particle Swarm Optimization: An Initial Analysis

Abstract

Particle Swarm Optimization (PSO) is a robust stochastic optimization algorithm for solving complex and constrained optimization problems. This paper aims to systematically investigate the influence of diverse random number distributions on the learning parameters of PSO and evaluate the algorithm's sensitivity based on these parameters. To this end, several exhaustive numerical experiments were conducted on several test functions, including asymmetric Sphere, Easom, and Csendes. Initially, appropriate random distributions were identified for the learning parameters and proceeded to compare these distributions using all potential combinations. The sensitivity of PSO to these parameters was evaluated using the mean best score, the relative proximity of the best particle to the theoretical optimum, and the average objective function evaluations. The most significant contribution of this research lies in the insights derived from the experimental data. The discovery was that highly skewed and long-tailed distributions such as Chi, Chi-square, Lomax, and Exponential often underperform. On the other hand, distributions that are bounded proportionally to the problem domain consistently surpass the performance of the standard uniform distribution. These findings significantly enhance the understanding of PSO algorithms and provide valuable guidelines for their practical deployment.