Overview and Computational Analysis of PSO Variants for Solving Systems of Nonlinear Equations

Abstract

AbstractThe problem of solving systems of nonlinear equations is one of great difficulty, especially as the scale of these systems grow. Traditional numerical methods rely on selecting good initial estimates for the roots and refine them iteratively, which is not a simple task, especially with large systems of nonlinear equations. Particle swarm optimization (PSO), in turn, is a nature-inspired metaheuristic algorithm for finding the minimum of a function for which multiple improvements and different hybridizations have been proposed. These modifications range from dynamically choosing parameters and topologies to hybridization with other population-based optimization algorithms. All of these modifications have the goal of improving the basic algorithm, and a broader comparison between these proposals is necessary to further understand what might be the path forward in achieving better and more exact results. In this paper, after a brief overview of PSO-based algorithms for nonlinear equation systems, several PSO variants are tested on a number of problems in order to find the solution to non-trivial systems of nonlinear equations. Each variant was tested 100 times on each problem, in order to produce enough samples for a legitimate comparison.KeywordsComputational intelligenceParticle swarm optimizationPSO variantsNonlinear equation systems