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

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