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

Particle Swarm Optimization (PSO) is a metaheuristic whose performance deteriorates significantly when utilized on optimization problems subject to noise. On these problems, particles eventually fail to distinguish good from bad solutions because their objective values are corrupted by noise. Specifically, the effect of noise causes particles to suffer from deception when they do not select their true neighborhood best solutions, from blindness when they ignore better solutions, and from disorientation when they prefer worse solutions. Resampling methods reduce the presence of these conditions by re-evaluating the solutions multiple times and better estimating their true objective values with a sample mean over the evaluations. PSO with Equal Resampling (PSO-ER) finds better solutions than the regular PSO thanks mainly to the reduction of deception and blindness, as has been found by utilizing a set of population statistics that track the presence of these conditions throughout the search process. However, the solutions of PSO-ER have been reported to be worse than those of state-of-the-art resampling-based PSO algorithms, and the underlying reasons are not known because the population statistics for such algorithms have never been computed. In this article, we study the population statistics for a new extension to PSO-ER that further reduces the presence of blindness, and for state-of-the-art resampling-based PSO algorithms. Experiments on 20 large-scale benchmark functions subject to different levels of noise show that our new algorithm succeeds at reducing blindness and finding better solutions than PSO-ER. However, the population statistics for state-of-the-art resampling-based PSO algorithms show that their particles suffer even less from deception, blindness and disorientation, and therefore find much better solutions.