An Efficient Multivalued Hopfield Network for the Traveling Salesman Problem

Authors:
E. Mérida-Casermeiro;G. Galán-Marín;J. Muñoz-Pérez
Affiliations:
Department of Applied Mathematics, University of Málaga, Campus de Teatinos s/n, 29071-Málaga, Spain;Department of Electronics and Electromechanical Engineering, University of Extremadura, Escuela de Ingenierías Industriales, Avda. de Elvas s/n, 06071-Badajoz, Spain. E-mail: gloriagm ...;Department of Computer Science, University of Málaga, Campus de Teatinos s/n, 29071-Málaga, Spain. E-mail: munozp@lcc.uma.es
Venue:
Neural Processing Letters
Year:
2001

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Abstract

In this Letter we show that discrete multivalued Hopfield-type neural networks enable a relatively easy formulation of the Traveling Salesman Problem compared to the traditional Hopfield model. Thus, with the multivalued representation the network can be easily confined to feasible solutions, avoiding the need to tune any parameter. An investigation into the performance of the network has led us to define updating rules based on simple effective heuristic algorithms, a technique that can not be usually incorporated into standard Hopfield models. Simulation results for Euclidean Traveling Salesman Problems taken from the data library TSPLIB [11] indicate that this multivalued neural approach is superior to the best neural network currently reported for this problem.