Search Property of Nonlinear Map Optimization

Abstract

We proposed Nonlinear Map Optimization (NMO) to improve the solution search capability of particle swarm optimization (PSO) algorithm. NMO is one of PSO-based swarm intelligence algorithms. We have previously proposed a canonical deterministic system PSO (CD-PSO) that is removed probabilistic factors from PSO to analyze its solution search behavior and is extracted only the essential dynamics of the solution search property of PSO. Although the dynamics of CD-PSO describe the basic dynamics of PSO, the solution search performance of CD-PSO is very poor than PSO. One of the causes is the distribution of search points. Although the search point distribution of PSO has a normal distribution shape depending on stochastic factors, the search point distribution of CD-PSO which is a deterministic system is not similar to the normal distribution. In order to improve the search point distribution of CD-PSO, we proposed a modified CD-PSO. Based on the modified CD-PSO, we proposed an NMO algorithm whose search points are derived by a nonlinear map. In this article, we clarify that the solution search property of NMO. The distribution of search points is similar to a normal distribution shape. Also, the nonlinear mapping of NMO derives complex behavior due to nonlinearity depended on parameters. These properties lead to the local search capability of NMO which is improved compared to PSO. Also, information exchange within the swarm similar to PSO is related to the global search ability. Since NMO can consider local search and global search separately, the solution search capability can be improved with unimodal functions than conventional PSO.