A Bayesian Interpretation of the Particle Swarm Optimization and Its Kernel Extension

Peter Andras

doi:10.1371/journal.pone.0048710

Abstract

Particle swarm optimization is a popular method for solving difficult optimization problems. There have been attempts to formulate the method in formal probabilistic or stochastic terms (e.g. bare bones particle swarm) with the aim to achieve more generality and explain the practical behavior of the method. Here we present a Bayesian interpretation of the particle swarm optimization. This interpretation provides a formal framework for incorporation of prior knowledge about the problem that is being solved. Furthermore, it also allows to extend the particle optimization method through the use of kernel functions that represent the intermediary transformation of the data into a different space where the optimization problem is expected to be easier to be resolved–such transformation can be seen as a form of prior knowledge about the nature of the optimization problem. We derive from the general Bayesian formulation the commonly used particle swarm methods as particular cases.

Highlights

Particle swarm optimization (PSO) is a heuristic optimization method that was proposed in the mid-1990s following inspiration from social problem solving [1]
Summary In principle the advantage of the Bayesian approach is that we take into account the full distribution of likelihoods of finding the optimal solution at any admissible solution parameter vector
The Bayesian approach to PSO described here provides a general insight into how PSO algorithms work in principle

Summary

Introduction

Particle swarm optimization (PSO) is a heuristic optimization method that was proposed in the mid-1990s following inspiration from social problem solving (e.g. collaborative foraging by flocking birds) [1]. Ð2Þ where xi(0) and vi(0)are the original solution parameter and velocity vectors, xbi and xgare the solution parameters found so far that are the best among those found by particle i and the best among those found by all particles, w is the inertial factor, Q and g are attraction parameters of the optimization process and rQ and rg are random numbers drawn from the uniform distribution over (0,1) Another common variant of the equations was proposed around 2000 [13], [14] with the aim to improve the convergence and avoid the divergence of the search paths of particles. We demonstrate the performance of the proposed Bayesian variants of the PSO algorithm using a set of commonly used test functions [19]

Related Works

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Discussion and Conclusions