Alfonso Martinez-Estudillo, Francisco Martinez-Estudillo, Cesar Hervas-Martinez and Nicolas Garcia-Pedrajas,
Model Fitting by Evolutionary Computation Using Product Units, Preprint submitted to Elsevier Science, 29 December 2003

ABSTRACT

This paper presents a new model of evolution of neural networks based on potential basis function units. These nodes are usually called product units. The use of product units has two major advantages: these units are more powerful and they are easier to interpret. In contrast to the usual black-box model of a neural network based on sigmoidal functions, we can consider these networks as \grey-box" models. Nevertheless, the training of product unit based networks poses several problems, as local learning algorithms are not suitable for these networks due to the existence of many local minima in the error surface. In this paper, we propose a model of evolution of product unit based networks to overcome this diculty. The proposed model evolves both the weights and the structure of these networks by means of an algorithm based on evolutionary programming. The performance of the model is evaluated in a hard real-world problem of microbial growth modelling. Using the best obtained model we applied a heuristic approach to obtain rules of the behavior of the model with regard to the input variables. The error obtained over the generalization set is very interesting, when compared with standard sigmoidal-based neural networks.

Key words: Product units; Regression; Evolutionary Computation; Rule extraction