On how percolation threshold affects PSO performance

TL;DR

This paper investigates how the percolation threshold influences the topology and performance of particle swarm optimization, revealing that smaller neighborhood radii near the threshold improve results and reduce complexity.

Contribution

It introduces the application of percolation theory to PSO neighborhood topology, highlighting the impact of the percolation threshold on algorithm performance and complexity.

Findings

Lower radius values near the percolation threshold improve PSO results.

Using the percolation threshold reduces computational complexity.

Percolation theory provides a universal measure for comparing PSO topologies.

Abstract

Statistical evidence of the influence of neighborhood topology on the performance of particle swarm optimization (PSO) algorithms has been shown in many works. However, little has been done about the implications could have the percolation threshold in determining the topology of this neighborhood. This work addresses this problem for individuals that, like robots, are able to sense in a limited neighborhood around them. Based on the concept of percolation threshold, and more precisely, the disk percolation model in 2D, we show that better results are obtained for low values of radius, when individuals occasionally ask others their best visited positions, with the consequent decrease of computational complexity. On the other hand, since percolation threshold is a universal measure, it could have a great interest to compare the performance of different hybrid PSO algorithms.