A Study into the Improvement of Binary Hopfield Networks for Map Coloring
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- Galán-Marín G., Mérida-Casermeiro E., López-Rodríguez D., Ortiz-de-Lazcano-Lobato J.M. (2007) A Study into the Improvement of Binary Hopfield Networks for Map Coloring. In: Beliczynski B., Dzielinski A., Iwanowski M., Ribeiro B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2007. Lecture Notes in Computer Science, vol 4432. Springer, Berlin, Heidelberg
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.
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