Genetic multivariate polynomials: An alternative tool to neural networks

Abstract

One of the basic problems of applied mathematics is to find a synthetic expression (model) which captures the essence of a system given a (necessarily) finite sample which reflects selected characteristics. When the model considers several independent variables its mathematical treatment may become burdensome or even downright impossible from a practical standpoint, In this paper we explore the utilization of an efficient genetic algorithm to select the "best" subset of multivariate monomials out of a full polynomial of the form F(v 1,..., v n) = Σ i1=0g1...Σ ingnc i1...i nv 1i1...v ni n (where gi denotes the maximum desired degree for the i-th independent variable). This regression problem has been tackled with success using neural networks (NN). However, the "black box" characteristic of such models is frequently cited as a major drawback. We show that it is possible to find a polynomial model for an arbitrary set of data, From selected practical cases we argue that, despite the restrictions of a polynomial basis, our Genetic Multivariate Polynomials (GMP) compete with the NN approach without the mentioned limitation. We show how to treat constrained functions as unconstrained ones using GMPs. © Springer-Verlag Berlin Heidelberg 2005.