Abstract
In this paper, we propose novel adaptation rules for the self-organizing map to solve the prize-collecting traveling salesman problem (PC-TSP). The goal of the PC-TSP is to find a cost-efficient tour to collect prizes by visiting a subset of a given set of locations. In contrast with the classical traveling salesman problem, where all given locations must be visited, locations in the PC-TSP may be skipped at the cost of some additional penalty. Using the self-organizing map, locations for the final solution may be selected during network adaptation, and locations where visitation would be more expensive than their penalty can be avoided. We have applied the proposed self-organizing map learning procedure to autonomous data collection problems, where the proposed approach provides results competitive with an existing combinatorial solver.
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References
Applegate, D., Bixby, R., Chvátal, V., Cook, W.: CONCORDE TSP Solver (2003), http://www.tsp.gatech.edu/concorde.html (cited October 20, 2013)
Applegate, D., Bixby, R., Chvátal, V., Cook, W.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton (2007)
Archer, A., Bateni, M., Hajiaghayi, M., Karloff, H.: Improved approximation algorithms for prize-collecting steiner tree and tsp. In: IEEE Symposium on Foundations of Computer Science (2009)
Ausiello, G., Bonifaci, V., Leonardi, S., Marchetti-Spaccamala, A.: Prize-collecting traveling salesman and related problems. In: Gonzalez, T.F. (ed.) Handbook of Approximation Algorithms and Metaheuristics. CRC Press (2007)
Balas, E.: The prize collecting traveling salesman problems. Networks 19, 621–636 (1989)
Bienstock, D., Goemans, M., Simchi-Levi, D., Williamson, D.: A note on the prize collecting traveling salesman problem. Mathematical Programming 59, 413–420 (1993)
Cochrane, E.M., Beasley, J.E.: The co-adaptive neural network approach to the Euclidean travelling salesman problem. Neural Networks 16(10), 1499–1525 (2003)
Créput, J.C., Koukam, A.: A memetic neural network for the Euclidean traveling salesman problem. Neurocomputing 72(4-6), 1250–1264 (2009)
Faigl, J.: Approximate Solution of the Multiple Watchman Routes Problem with Restricted Visibility Range. IEEE Transactions on Neural Networks 21(10), 1668–1679 (2010)
Faigl, J., Přeučil, L.: Self-Organizing Map for the Multi-Goal Path Planning with Polygonal Goals. In: Honkela, T. (ed.) ICANN 2011, Part I. LNCS, vol. 6791, pp. 85–92. Springer, Heidelberg (2011)
Goemans, M., Williamson, D.P.: A general approximation technique for constrained forest problems. SIAM J. Computing 24(2), 296–317 (1995)
Helsgaun, K.: An Effective Implementation of the Lin-Kernighan Traveling Salesman Heuristic. European Journal of Operational Research 126(1) (2000)
Hollinger, G., Mitra, U., Sukhatme, G.: Autonomous data collection from underwater sensor networks using acoustic communication. In: IROS, pp. 3564–3570. IEEE (2011)
Somhom, S., Modares, A., Enkawa, T.: A self-organising model for the travelling salesman problem. Journal of the Operational Research Society, 919–928 (1997)
Tucci, M., Raugi, M.: Stability analysis of self-organizing maps and vector quantization algorithms. In: IJCNN, pp. 1–5 (2010)
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Faigl, J., Hollinger, G.A. (2014). Self-Organizing Map for the Prize-Collecting Traveling Salesman Problem. In: Villmann, T., Schleif, FM., Kaden, M., Lange, M. (eds) Advances in Self-Organizing Maps and Learning Vector Quantization. Advances in Intelligent Systems and Computing, vol 295. Springer, Cham. https://doi.org/10.1007/978-3-319-07695-9_27
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DOI: https://doi.org/10.1007/978-3-319-07695-9_27
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07694-2
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