Population statistics for particle swarm optimization: Hybrid methods in noisy optimization problems

Particle swarm optimization (PSO) is a metaheuristic designed to find good solutions to optimization problems. However, when optimization problems are subject to noise, the quality of the resulting solutions significantly deteriorates, hence prompting the need to incorporate noise mitigation mechanisms into PSO. Based on the allocation of function evaluations, two opposite approaches are generally taken. On the one hand, resampling-based PSO algorithms incorporate resampling methods to better estimate the objective function values of the solutions at the cost of performing fewer iterations. On the other hand, single-evaluation PSO algorithms perform more iterations at the cost of dealing with very inaccurately estimated objective function values. In this paper, we propose a new approach in which hybrid PSO algorithms incorporate noise mitigation mechanisms from the other two approaches, and the quality of their results is better than that of the state of the art with a few exceptions. The performance of the algorithms is analyzed by means of a set of population statistics that measure different characteristics of the swarms throughout the search process. Amongst the hybrid PSO algorithms, we find a promising algorithm whose simplicity, flexibility and quality of results questions the importance of incorporating complex resampling methods into state-of-the-art PSO algorithms.