Using Genetic Algorithms to Optimize Wavelet Neural Networks Parameters for Function Approximation

Abstract

This paper deals with the problem of function approximation from a given set of input/output data. This paper presents a new approach for solving the problem of function approximation from a given set of I/O data using Wavelet Neural Networks (WNN) and Genetic Algorithms (GAs). GAs has the property of global optimal search algorithm and WNNs are universal approximations, it’s achieved faster convergence than Radial Basis Function Neural Networks (RBFN) and avoids stocking in local minimum. This approach is based on a new efficient method of optimizing WNNs parameters using GAs, it uses GA to optimize scale parameter Aj and the translation parameter Bj of the WNN such that each individual of the population represents scale parameter and translation parameter of WNNs. Orthogonal least squares (OLS) is used to optimize weights w of WNNs. Finally Levenberg–Marquardt Algorithm (LMA) is used to train the WNN to speed up the training process. The performance of the proposed approach has been evaluated on cases of one and two dimensions. The results show that the function approximation using GAs to optimize WNN parameters can achieve better normalized-root-mean-square-error than those achieved by traditional algorithms that use RBFN