Nonlinear Map Optimization

Abstract

We propose a novel optimization algorithm which named Nonlinear Map-model Optimization (abbr. NMO) method. The NMO is classified as swarm intelligence (abbr. SI) optimizer and consists of some search individuals whose dynamics is driven by a simple nonlinear map. The search point distribution is controlled by the simple nonlinear map. Based on the theoretical analysis results about the dynamics of the particle swarm optimization, we set so that the searching point distribution of the NMO becomes an optimal distribution. Also, the simple nonlinear map generates a chaotic search point time series while keeping the search range. Such a time series can efficiently search within the search range. As a result, NMO can search along the valley of the evaluation function. Namely, NMO is considered to have a rotation invariance and a scaling invariance. In general, the computation amount of SI optimizer is proportional to the number of search elements included in the SI optimizer. However, the NMO requires only a few particles comparing with other swarm intelligence optimizers. Therefore, the computation amount is the smaller than the other methods. As the result, the search performance of the NMO exhibits better than Standard PSO 2011.