An N-parallel multivalued network: Applications to the travelling salesman problem

Abstract

In this paper, a new family of multivalued recurrent neural networks (MREM) is proposed. Its architecture, some computational properties and convergence is shown. We also have generalized the function of energy of the Hopfield model by a new function of the outputs of neurons that we named "function of similarity" as it measures the resemblance between their outputs. When the function of similarity is the product function, the model proposed is identical to the binary Hopfield one. This network shows a great versatility to represent, in an effective way, most of the combinatorial optimization problem [14-17] due to it usually incorporates some or all the restrictions of the problem generating only feasible states and avoiding the presence of parameters in the energy function, as other models do. When this interesting property is obtained, it also avoids the time-consuming task of fine tuning of parameters. In order to prove its suitability, we have used as benchmark the symmetric !ravelling Salesman Problem (TSP). The versatility of MREM allows to define some different updating rules based on effective heuristic algorithms that cannot be incorporated into others Hopfield models. © Springer-Verlag Berlin Heidelberg 2003.