The emergence of scaling laws search dynamics in a particle swarm optimization

This paper investigates the search dynamics of a fundamental particle swarm optimization (PSO) algorithm via gathering and analyzing the data of the search area during the optimization process. The PSO algorithm exhibits a distinct performance when optimizing different functions, which induces the emergence of different search dynamics during the optimization process. The simulation results show that the performance is tightly related to the search dynamics which results from the interaction between the PSO algorithm and the landscape of the solved problems. The Lévy type scaling laws search dynamics emerges from the process in which the PSO algorithm shows good performance, while the Brownian dynamics appears after the algorithm has stagnated due to the premature convergence. The Lévy dynamics characterized by a large number of intensive local searches punctuated by long-range transfers is an indicator of good performance, which allows the algorithm to achieve an efficient balance between exploration and exploitation so as to improve the search efficiency.