Optimum design using radial basis function networks by adaptive range genetic algorithms (determination of radius in radial basis function networks)

Abstract

We use the radial basis function (RBF) network to approximate the fitness function of genetic algorithms and try to obtain approximate optimum results. A RBF is a kind of neural network that is composed of a number of radial basis functions in a Gaussian distribution. When the positions of the basis functions and their radii are given, the learning system of the RBF is summarized in the calculation of the inverse matrix. Thus, the learning system is quite simple and very rapid. There are two important issues in a RBF: one is to place the basis functions and to give data, and the other is to give an appropriate radius to each radial basis function. For the first issue, we have proposed a data distribution and basis function distribution method, together with adaptive-range genetic algorithms (ARange GAs). In this study, we focus our attention on the second problem. For that purpose, we give an oval distribution for the basis functions and assume that every basis function has the same oval radius. In this way, we can reduce the number of radius functions as we reduce the number of design variables. We show the effectiveness of the proposed method through a benchmark problem.