Abstract
In this paper we present a neural network model and new formulation for the p-median problem. The effectiveness and efficiency of our algorithm under varying problem sizes are analyzed in comparison to conventional heuristic methods. The results for small-scale problems (less than 100 points) indicate that our implementation of algorithm is effective. Furthermore, we also have applied our algorithm to solve large-scale problems, demonstrating that a simple recurrent neural network, with an adapted formulation of the problem, can generate good solutions in a few seconds.
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References
E. Bartezzaghi, A. Colorni (1981), “A search tree algorithm for plant location problems”, European Journal of Operational Research 7, 371–379
M. J. Canós, C. Ivorra, V. Liern (1999), “An exact algorithm for the fuzzy problem pmediates”, European Journal of Operational Research 116, 80–86
N. Christofides, J. E. Beasley (1982), “A tree search algorithm for the problem pmediates”, European Journal of Operational Research 10, 196–204
L. Cooper (1963), “Location-Allocation Problems”, Operations Research 11, 331–343
E. Dominguez, J. Muñoz (2001), “Solving the m-median problem with a neural network”, Proc. of IX CAEPIA (Conference of the Spanish Associations for the Artificial Intelligence) Gijon, Spain
Zvi Drezner (ed.) (1995), “Facility location: To survey of applications and methods”, Springer
Zvi Drezner, Jeffery Guyse (1999), “Application of decision analysis to the Weber facility location problem”, European Journal of Operational Research 116, 69–79
G. Galán Marín, J. Muñoz Pérez (1999), “A Net n-parallel Competitive Neuronal for Combinatory Optimization”, Proc. of VIII CAEPIA (Conference of the Spanish Asociations for the Artificial Intelligence) Murcia, Spain, vol. 1, 98–106
G. Galán Marín, J. Muñoz Pérez (1999), “A Design of a Neuronal Network for the resolution of the problem of the Four Colors”, Have Ibero-American of Artificial Intelligence 8, 6–17
G. Galán Marín, J. Muñoz Pérez (2000), “An improved Neural Network Algorithm for the Bipatite Subgraph Problem”, Proc. of International Conference on Computational Intelligence and Neuroscience, Atlantic City, NJ USES
G. Galán Marín, J. Muñoz Pérez (2000), “Finding Near-Maximum Cliques with Competitive Hopfield Networks”, Proc. of International ICSC Symposium on Neural Computation, Berlin, Germany
G. Galán Marín, J. Muñoz Pérez (2001), “Design and Analysis of Maximum Hopfield Networks”, IEEE Trans. On Neural Networks 12 (2), 329–339
Roberto D. Galvao (1980), “A dual-bounded algorithm for the problem p-mediates”, Operations Research
M. R. Garey, D. S. Johnson (1979), “Computers and intractability: To guide to the theory of NP-completeness”, W.H. Freeman and Co., New York
S. L. Hakimi (1964), “Optimum locations of switching centers and absolute centers and medians of to graph”, Operations Research 12, 450–459
S. L. Hakimi (1965), “Optimum distribution of switching centers in to communication network and some related graph theoretic problems”, Operations Research 13, 462–475
P. Hanjoul, D. Peeters (1985), “A comparison of two dual-based procedures for solving the p-median problem”, European Journal of Operational Research 20, 386–396
Pierre Hansen, Nenad Mladenovic, Eric Taillard (1998), “Heuristic solution of the multisource Weber problem ace to problem p-mediates”, Operations Research Letters 22, 55–62
J. J. Hopfield, D.W. Tank (1985), “Neural computation of decisions in optimization problems”, Biological Cybernetics 52, 141–152
Michelle Hribar, Mark S. Daskin (1997), “A dynamic programming heuristic for the problem p-mediates”, European Journal of Operational Research 101, 499–508
Kariv O. and Hakimi S. L. (1979) “An Algorithmic Approach to Network Location Problem. Part 2: The p-Median”. SIAM J. Appl. Math., Vol. 37, pp. 539–560.
Love, Robert F., Morris, James G. and Wesolowsky, George O. (1998) “Facilities Location Models & Methods”, North-Holland
S. Lozano, F. Guerrero, L. Onieva, J. Larrañeta (1998), “Kohonen maps for solving to class of location-allocation problems”, European Journal of Operational Research 108, 106–117
Subhash C. Narula, Ugonnaya I. Ogbu, Haakon M. Samuelsson (1977), “An algorithm for the problem p-mediates”, Operations Research 25, 709–713
M. Ohlemüller (1997), “Taboo search for large location-allocation problems”, Journal of the Operational Research Society 48, 745–750
C. ReVelle, R. Swain (1970), “Central facilities location”, Geographical Analysis, 2, 30–42
M. B. Teitz, P. Bart (1968), “Heuristic methods for estimating the generalized vertex median of a weighted graph”, Operations Research 16, 955–961
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Dominguez Merino, E., Muñoz Perez, J. (2002). An Efficient Neural Network Algorithm for the p-Median Problem. In: Garijo, F.J., Riquelme, J.C., Toro, M. (eds) Advances in Artificial Intelligence — IBERAMIA 2002. IBERAMIA 2002. Lecture Notes in Computer Science(), vol 2527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36131-6_47
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DOI: https://doi.org/10.1007/3-540-36131-6_47
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