This paper discusses using genetic algorithms (GA) to optimize the structure of radial basis probabilistic neural networks (RBPNN), including how to select hidden centers of the first hidden layer and to determine the controlling parameter of Gaussian kernel functions. In the process of constructing the genetic algorithm, a novel encoding method is proposed for optimizing the RBPNN structure. This encoding method can not only make the selected hidden centers sufficiently reflect the key distribution characteristic in the space of training samples set and reduce the hidden centers number as few as possible, but also simultaneously determine the optimum controlling parameters of Gaussian kernel functions matching the selected hidden centers. Additionally, we also constructively propose a new fitness function so as to make the designed RBPNN as simple as possible in the network structure in the case of not losing the network performance. Finally, we take the two benchmark problems of discriminating two-spiral problem and classifying the iris data, for example, to test and evaluate this designed GA. The experimental results illustrate that our designed GA can significantly reduce the required hidden centers number, compared with the recursive orthogonal least square algorithm (ROLSA) and the modified K-means algorithm (MKA). In particular, by means of statistical experiments it was proved that the optimized RBPNN by our designed GA, have still a better generalization performance with respect to the ones by the ROLSA and the MKA, in spite of the network scale having been greatly reduced. Additionally, our experimental results also demonstrate that our designed GA is also suitable for optimizing the radial basis function neural networks (RBFNN).
