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

  • Gloria Galán-Marín
  • Enrique Mérida-Casermeiro
  • Domingo López-Rodríguez
  • Juan M. Ortiz-de-Lazcano-Lobato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4432)


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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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Gloria Galán-Marín
    • 1
  • Enrique Mérida-Casermeiro
    • 2
  • Domingo López-Rodríguez
    • 2
  • Juan M. Ortiz-de-Lazcano-Lobato
    • 3
  1. 1.Department of Electronics and Electromechanical Engineering, University of Extremadura, BadajozSpain
  2. 2.Department of Applied Mathematics, University of Málaga, MálagaSpain
  3. 3.Department of Computer Science and Artificial Intelligence, University of Málaga, MálagaSpain

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