A New Family of Multivalued Networks

Abstract

This paper introduces a new family of multivalued neural networks. We have interpreted the Hopfield network as encoding the same/different information of elements of binary patterns in the connections and developed a scheme which encodes bigger/smaller information of multivalued patterns in the connections with the aid of signum function. The model can be constructed as an autoassociative memory (multivalued counterpart of Hopfield) or heteroassociative memory (multivalued counterpart of BAM). We have used Lyapunov stability analysis in showing the stability of networks. In simulations the energy surface topography of the model is compared to that of Hopfield. Also, asymptotic stability and basin of attraction of the stored patterns are examined. The proposed model can also be used in solving the optimization problems. Mapping a problem on to the network is relatively easy compared to the Hopfield model because of the multivalued representation. Very good results are obtained in traveling salesperson problem simulations. Copyright © 1996 Elsevier Science Ltd.