Abstract
There exist several neural networks models for solving NP-hard combinatorial optimization problems. Hopfield networks and self-organizing maps are the two main neural approaches studied. Criticism of these approaches includes the tendency of the Hopfield network to produce infeasible solutions and the lack of generalization of the self-organizing approaches. This paper presents a new bidirectional neural model for solving clustering problems. Bidirectional associative memory (BAM) is the best bidirectional neural architecture known. Typically, this model has ever been used for information storage. In this paper we propose a new neural model with this bidirectional neural architecture for optimization problems, concretely clustering problems. A sample theoretical clustering problem as the p-median problem is used to test the performance of the proposed neural approach against genetic algorithms and traditional heuristic techniques.
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References
Alp, O., Erkut, E., Drezner, Z.: An efficient genetic algorithm for the p-median problem. Annals of Operations Research 122, 21–42 (2003)
Bai-Ling, Z., Bing-Zheng, X., Chung-Ping, K.: Performance analysis of the bidirectional associative memory and an improved model from the matched-filtering viewpoint. IEEE Transactions on Neural Networks 4(5), 864–872 (1993)
Bartezzaghi, E., Colorni, A.: A search tree algorithm for plant location problems. European Journal of Operational Research 7, 371–379 (1981)
Christofides, N., Beasley, J.E.: A tree search algorithm for the problem pmediates. European Journal of Operational Research 10, 196–204 (1982)
Densham, P., Rusthon, G.: A more efficient heuristic for solving large pmedian problems. Paper in Regional Science 71, 207–239 (1992)
Drezner, Z., Guyse, J.: Application of decision analysis to the Weber facility location problem. European Journal of Operational Research 116, 69–79 (1999)
Drezner, Z., Hamacher, H.W.: Facility location: applications and theory. Springer, Heidelberg (2003)
Durbin, R., Willshaw, D.: An analogue approach to the travelling salesman problem using an elastic net method. Nature 326, 689–691 (1987)
Favata, F., Walker, R.: A study of the application of the Kohonen-type neural networks to the travelling salesman problem. Biological Cybernetics 64, 463–468 (1991)
Galvao, R.D.: A dual-bounded algorithm for the problem p-mediates. Operations Research 28, 1112–1121 (1980)
Gee, A.H., Prager, R.W.: Limitations of neural networks for solving traveling salesman problems. IEEE Transactions on Neural Networks 6(1), 280–282 (1995)
Hanjoul, P., Peeters, D.: A comparison of two dual-based procedures for solving the p-median problem. European Journal of Operational Research 20, 386–396 (1985)
Hansen, P., Mladenovic, N.: Variable neighborhood search for the p-median problem. Location Science 5(4), 141–152 (1997)
Hopfield, J., Tank, D.: Neural computation of decisions in optimization problems. Biological Cybernetics 52, 141–152 (1985)
Hribar, M., Daskin, M.S.: A dynamic programming heuristic for the problem p-mediates. European Journal of Operational Research 101, 499–508 (1997)
Hung, D.L., Wang, J.: Digital hardware realization of a recurrent neural network for solving the assignment problem. Neurocomputing 51, 447–461 (2003)
Kariv, O., Hakimi, S.L.: An Algorithmic Approach to Network Location Problem. Part 2: The p-Median. SIAM J. Appl. Math. 37, 539–560 (1979)
Khumawala, B.M.: An efficient branch and bound algorithm for the warehouse location problem. Management Science 18(12), 718–731 (1972)
Kosko, B.: Bidirectional associative memories. IEEE Transactions on Systems, Man and Cybernetics 18(1), 49–60 (1988)
Kung, S.: Digital neural networks, New Jersey (USA). Prentice-Hall, Englewood Cliffs (1993)
Rolland, E., Schilling, D., Current, J.P.: An efficient tabu search procedure for the p-median problem. European Journal of Operational Research 96, 329–342 (1997)
Rosing, K.E., ReVelle, C.S.: Heuristic concentration: two stage solution construction. European Journal of Operational Research 97, 75–86 (1997)
Shams, S., Gaudiot, J.-L.: Implementing regularly structured neural networks on the DREAM machine. IEEE Transactions on Neural Networks 6(2), 407–421 (1995)
Smith, K., Palaniswani, M., Krishnamoorthy, M.: Neural techniques for combinatorial optimization with applications. IEEE Transactions on Neural Networks 9(6), 1301–1318 (1998)
Smith, K.: An argument for abandoning the travelling salesman problem as a neural-network benchmark. IEEE Transactions on Neural Networks 7(6), 1542–1544 (1996)
Teitz, M.B., Bart, P.: Heuristic methods for estimating the generalized vertex median of a weighted graph. Operations Research 16, 955–961 (1968)
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Domínguez, E., Muñoz, J. (2004). Bidirectional Neural Network for Clustering Problems. In: Lemaître, C., Reyes, C.A., González, J.A. (eds) Advances in Artificial Intelligence – IBERAMIA 2004. IBERAMIA 2004. Lecture Notes in Computer Science(), vol 3315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30498-2_79
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DOI: https://doi.org/10.1007/978-3-540-30498-2_79
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