Histogram particle swarm optimization (HistPSO): Evolving non-parametric acceleration distributions

Abstract

Particle swarm optimization (PSO) is a biologically-inspired optimization algorithm, which has evolved over time and has been extensively studied and meta-optimized. To solve an optimization problem, the algorithm sends a plethora of particles into the search space, each particle searching for, ideally, the global optima. The velocity of these particles are determined by three components: a social component; a personal component, and a momentum component. The social and personal components of the standard PSO rely on a uniform-random distribution. There has been work on changing this distribution from being uniform-random to Gaussian; this paper aims at generalizing this distribution. Through use of another PSO, the distributions are learned over a set of objective functions, resulting in the proposed algorithm HistPSO. A novel approach is used to represent the distributions as piecewise uniform distributions on sub-intervals of the [0, c] interval where is either c or 2 depending whether the distribution represents the personal or social component of the PSO velocity equation. HistPSO is then tested on two other objective functions on which it had not been trained, as well as the three objective functions from which it learned. The results are then compared with a meta-optimized version of the standard PSO algorithm and the two results are compared to find that HistPSO performs comparably, and in some cases outperforms the meta-optimized standard PSO.