Abstract
In this paper, a new family of multivalued recurrent neural networks (MREM) is proposed. Its architecture, some computational properties and convergence is shown.
We also have generalized the function of energy of the Hopfield model by a new function of the outputs of neurons that we named “function of similarity” as it measures the resemblance between their outputs. When the function of similarity is the product function, the model proposed is identical to the binary Hopfield one.
This network shows a great versatility to represent, in an effective way, most of the combinatorial optimization problem [14]-[17] due to it usually incorporates some or all the restrictions of the problem generating only feasible states and avoiding the presence of parameters in the energy function, as other models do. When this interesting property is obtained, it also avoids the time-consuming task of fine tuning of parameters.
In order to prove its suitability, we have used as benchmark the symmetric Travelling Salesman Problem (TSP). The versatility of MREM allows to define some different updating rules based on effective heuristic algorithms that cannot be incorporated into others Hopfield models.
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References
Angéniol B., Vaubois, G. and Texier, J. Self-organizing feature maps and the T.S.P. Neural Networks, V. 1, pp. 289–93, 1988.
Aras, N. Oomen, B.J. and Altinel, I.K., The Kohonen network incorporating explicit statistics and its application to the T.S.P. Neural Networks, V. 12, pp. 1273–84, 1999.
Burke, L. I. and Damany, P., The guily net for the T.S.P. Computer and Operational Research, V. 19, pp. 255–65, 1992.
Croes, G. A. A method for solving T.S.P. Oper. Research, V. 6, pp 791–812, 1958.
Durbin, R. and Willshaw, D. An analogue approach to the T.S.P. using an elastic net methods, Nature, V. 326, 689–91, 1987.
M. H. Erdem & Y. Ozturk, A New family of Multivalued Networks, Neural Networks 9, 6, pp 979–89, 1996.
Zhi-Hong Guan, Guanrong Chen and Yi Qin, On equilibria, Stability, and Instability of Hopfield Neural Networks, IEEE Trans. N. N., V. 11, No 2, pp 534–41, 2000.
J.J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. National Academy of Sciences USA, 79, 2254–58, 1982.
J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Nat. Ac. of Sciences USA, 81, 3088–92, 1984.
J. J. Hopfield, & D.W. Tank, Neural computations of decisions in optimization problems, Biological Cybernetics, 52, 141–52, 1985.
Kohonen, T. Self-organizing maps. Berlin: Springer, 1994.
Kohring, G.A., On the Q-state Neuron Problem in Attractor Neural Networks. Neural Networks, V. 6, 573–81, 1993.
Li, S.Z., Improving convergence and solution quality of Hopfield-type neural networks with augmented Lagrange multipliers, IEEE Trans. N.N, V. 7, 1507–16, 1996.
E. Mérida Casermeiro, Red Neuronal recurrente multivaluada para el R. patrones y la opt. comb., Ph.D. dissertation. University of Málaga, Spain, (in spanish), 2000.
Mérida-Casermeiro, E., Galán-Marín, G., Muñoz-Pérez. J., An Efficient Multivalued Hopfield Network for the T.S.P. Neural Proccessing Letters 14, 203–16, 2001.
Enrique Mérida, José Muñoz and Rafaela Benítez, A Recurrent Multivalued Neural Network for the N-Queens Problem. LNCS, Vol 2084, 522–529, 2001.
Enrique Mérida-Casermeiro, José. Muñoz-Pérez and M.A. García-Bernal, An Associative Multivalued Recurrent Network. LNAI, Vol. 2527, 509–518, 2002.
Peng, M., Gupta, N. K. and Armitage, A. F., An investigation into the improvement of local minima of the Hopfield Network. Neural Networks 9, 1241–53, 1996.
Reinelt, G., TSPLIB-a T.S.P. library, ORSA J. on Computing 3, 376–84, 1991.
Wilson, V. & Pawley, G.S. On the stability of the TSP algorithm of Hopfield and Tank, Biological Cybernetics 58, pp 63–70, 1988.
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Mérida-Casermeiro, E., Muñoz-Pérez, J., Domínguez-Merino, E. (2003). An N-Parallel Multivalued Network: Applications to the Travelling Salesman Problem. In: Mira, J., Álvarez, J.R. (eds) Computational Methods in Neural Modeling. IWANN 2003. Lecture Notes in Computer Science, vol 2686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44868-3_52
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DOI: https://doi.org/10.1007/3-540-44868-3_52
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