Optimization strategies for tuning the parameters of radial basis functions network models

In this paper the problem of tuning the parameters of the RBF networks by using optimization methods is investigated. Two modifications of the classical RBFN, called Reduced and Simplified RBFN are introduced and analysed in the paper. They have a smaller number of parameters. Three optimization strategies that perform one or two steps for tuning the parameters of the RBFN models are explained and investigated in the paper. They use the particle swarm optimization algorithm with constraints. The one-step Strategy 3 is a simultaneous optimization of all three groups of parameters, namely the Centers, Widths and the Weights of the RBFN. This strategy is used in the paper for performance evaluation of the Reduced and Simplified RBFN models. A test 2-dimensional example with high nonlinearity is used to create different RBFN models with different number of RBFs. It is shown that the Simplified RBFN models can achieve almost the same modelling accuracy as the Reduced RBFN models. This makes the Simplified RBFN models a preferable choice as a structure of the RBFN model.

1 Introduction

Radial Basis Function (RBF) Networks have been widely used for a long time as a power tool in modeling and simulation, because they are proven to be universal approximators of nonlinear input-output relationships with any complexity (Poggio, Girosi, 1990; Park, Sandberg, 1993). In fact, the RBF Network (RBFN) is a composite multi-input, single output model, consisting of a predetermined number of N RBFs, each of them performing the role of a local model (Pedrycz, Park, Oh, 2008). Then the aggregation of all the local models in the form of a weighted sum of their output produces the nonlinear output of the RBFN.