A Study into the Improvement of Binary Hopfield Networks for Map Coloring

Authors:
Gloria Galán-Marín;Enrique Mérida-Casermeiro;Domingo López-Rodríguez;Juan M. Ortiz-De-Lazcano-Lobato
Affiliations:
Department of Electronics and Electromechanical Engineering, University of Extremadura, Badajoz, Spain;Department of Applied Mathematics, University of Málaga, Málaga, Spain;Department of Applied Mathematics, University of Málaga, Málaga, Spain;Department of Computer Science and Artificial Intelligence, University of Málaga, Málaga, Spain
Venue:
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part II
Year:
2007

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Abstract

The map-coloring problem is a well known combinatorial optimization problem which frequently appears in mathematics, graph theory and artificial intelligence. This paper presents a study into the performance of some binary Hopfield networks with discrete dynamics for this classic problem. A number of instances have been simulated to demonstrate that only the proposed binary model provides optimal solutions. In addition, for large-scale maps an algorithm is presented to improve the local minima of the network by solving gradually growing submaps of the considered map. Simulation results for several n-region 4-color maps showed that the proposed neural algorithm converged to a correct colouring from at least 90% of initial states without the fine-tuning of parameters required in another Hopfield models.