Optimization of Radial Basis Function Neural Networks Parameters using Genetic Algorithms: Applied on Function Approximation

Abstract

This paper deals with the problem of function approximation from a given set of input/output (I/O) data. The problem consists of analyzing training examples, so that we can predict the output of a model given new inputs. We present a new approach for solving the problem of function approximation of I/O data using Radial Basis Function Neural Networks (RBFNNs) and Genetic Algorithms (GAs). This approach is based on a new efficient method of optimizing RBFNNs parameters using GA, this approach uses GA to optimize centres c and radii r of RBFNNs, such that each individual of the population represents centres and radii of RBFNNs. Singular value decomposition (SVD) is used to optimize weights w of RBFNNs. The GA initial population performed by using Enhanced Clustering Algorithm for Function Approximation (ECFA) to initialize the RBF centres c and k-nearest neighbor to initialize the radii r. The performance of the proposed approach has been evaluated on cases of one and two dimensions. The results show that the function approximation using GA to optimize RBFNNs parameters can achieve better normalizedroot-mean square-error than those achieved by traditional algorithms.