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. © Springer-Verlag Berlin Heidelberg 2007.
Citation
G. Galán-Marín, E. Mérida-Casermeiro, D. López-Rodríguez, et al. “A Study into the Improvement of Binary Hopfield Networks for Map Coloring”. In: Adaptive and Natural Computing Algorithms, 8th International Conference, ICANNGA 2007, Warsaw, Poland, April 11-14, 2007, Proceedings, Part II. Ed. by B. Beliczynski, A. Dzielinski, M. Iwanowski and B. Ribeiro. Vol. 4432 LNCS. Lecture Notes in Computer Science PART 2. cited By 3; Conference of 8th International Conference on Adaptive and Natural Computing Algorithms, ICANNGA 2007 ; Conference Date: 11 April 2007 Through 14 April 2007; Conference Code:71057. Warsaw: Springer Verlag, 2007, pp. 98-106. DOI: 10.1007/978-3-540-71629-7_12. URL: https://doi.org/10.1007/978-3-540-71629-7_12.
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Papers citing this work
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- Yuxin Ding (2012). Artificial Higher Order Neural Networks for Modeling Combinatorial Optimization Problems. IGI Global eBooks DOI
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- Yuxin Ding, Ye Li, Min Xiao, et al. (2010). A high order neural network to solve N-queens problem. DOI