The topology of a neural network has a significant importance on the network's performance, Although this is well known, finding optimal configurations is still an open problem. This paper proposes a solution to this problem for Radial Basis Function (RBF) networks and General Regression Neural Network (GRNN) which is a kind of radial basis networks. In such networks, placement of centers has significant effect on the performance of network. The centers and widths of the hidden layer neuron basis functions are coded in a chromosome and these two critical parameters are determined by the optimization using genetic algorithms. Thyroid, iris and escherichia coli bacteria datasets are used to test the algorithm proposed in this study. The most important advantage of this algorithm is getting succesful results by using only a small part of a benchmark. Some numerical solution results indicate the applicability of the proposed approach. © Springer-Verlag Berlin Heidelberg 2006.