Abstract
We present a new input-output function of the binary Hopfield neural network operating in a sequential mode and its application for solving combinatorial optimization problems. From convergence theorem for the binary network, we obtain the correct input-output function that satisfies the convergence conditions for any value of the self-conections. We also present performance comparison of different input-output functions through the N-queens problem. Our simulation results show that with our input-output function the network always reaches the global minimum in this problem. However, with McCulloch-Pitts or hysteresis McCulloch-Pitts functions the network is trapped in local minima.
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References
J. J. Hopfield and D. W. Tauk, “Neural computation of decisions in optimization problems”, Biol. Cybern., vol. 52, 1985, pp. 141–152.
J. J. Hopfield, “Neural Networks and physical systems with emergent collective computational abilities” in Proc. Ac. Academy Sci. USA, vol. 79, 1982, pp. 2554–2558.
Y. Takefuji, K. C. Lee, “An artificial hysteresis binary neuron: a model supressing the oscillatory behaviors of neural dynamics”, Biol. Cybern., vol. 64, 1991, pp. 353–356.
Y. Takefuji, K. C. Lee, “Artificial neural networks for four-colouring map problems and K-colorability problems”, IEEE Trans. Circuits Syst., vol. 38, 1991, pp. 326–333.
Y. Takefuji, “Neural Network Parallel computing”, Kluwer Academic Publishers, 1992.
N. Funabiki, Y. Takenaka, S. Nishikawa, “A maximum neural network approach for N-queens problem”, Biol. Cybern., vol. 76, 1997, pp. 251–255.
M. Ohta, A. Ogihara, K. Fukumaga, “Binary neural network with self-feedback and its application to N-queens problem”, IEICE Trans. inf. & syst., vol. E77-D, no. 4, 1994, pp. 459–465.
Mandzink, J., “Solving the N-queens problem with a binary Hopfield-type network”, Biol. Cybern., vol. 72, 1995, pp. 439–445.
Sun, Y., “A generalized updating rule for modified Hopfield neural network for quadratic optimization”, Neurocomputing, vol. 19, 1998, pp. 133–143.
M. Peng, N.k. Gupta, A.F. Armitage, “An investigation into the improvement of local minima of the Hopfield network”, Neural Networks, vol. 9, 1996, pp. 1241–1253.
M. Tateishi, S. Tamura, “Comments on ‘Artificial neural networks for four-colouring map problems and K-colorability problems”, IEEE Trans. Circuits Syst. I: Fundamental Theory Applical., vol. 41, 1994, pp. 248–249.
L. Wang, “Discrete-time convergence theory and updating rules for neural networks with energy functions”, IEEE Trans. Neural Networks, vol. 8, 1997, pp. 445–447.
C. K. Cheng, T. Lee, “On the convergence of Neural Network for higher order programming”, Proc. of International Joint Conference on Neural Networks, 1993, pp. 1507–1511.
J. K. Paik, A. K. Katsaggelos, “Image restoration using a modified Hopfield network”, IEEE Trans. Image Process., vol. 36(7), 1992, pp. 49–63.
Y. Sun, J. G. Li, S. Y. Yu, “Improvement on performance of modified Hopfield network for image restoration”, IEEE Trans. Image Process., vol. 5, 1995, pp. 688–692.
Y. T. Zhou, R. Chellappa, A. Vaid, B. K. Jenkins, “Image restoration using a neural networks”, IEEE Trans. Acoust. Speech Signal Process., vol. 36(7), 1988, pp. 1141–1151.
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Galán, G., Muñoz, J. (1999). A new input-output function for binary hopfield neural networks. In: Mira, J., Sánchez-Andrés, J.V. (eds) Foundations and Tools for Neural Modeling. IWANN 1999. Lecture Notes in Computer Science, vol 1606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098187
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DOI: https://doi.org/10.1007/BFb0098187
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