Growing RBF networks for function approximation by a DE-based method

Abstract

The Differential Evolution (DE) algorithm is a floating-point encoded Evolutionary Algorithm for global optimization. It has been demonstrated to be an efficient, effective, and robust optimization method especially for problems containing continuous variables. The paper concerns applying a DE-based method to perform function approximation using Gaussian Radial Basis Function (RBF) networks with variable widths. This method selects centres and decides weights of the networks heuristically, then uses the Differential Evolution algorithm for local and global tuning iteratively to find the widths of RBFs. The method is demonstrated by training networks that approximate a set of functions. The Mean Square Error from the desired outputs to the actual network outputs is applied as the objective function to be minimized. A comparison of the net performances with other approaches reported in the literature has been performed. The proposed approach effectively overcomes the problem of how many radial basis functions to use. The obtained initial results suggest that the Differential Evolution based method is an efficient approach in approximating functions with growing radial basis function networks and the resulting network generally improves the approximation results reported for continuous mappings. © Springer-Verlag 2004.