Abstract
In this article we study the realistic network topology of Synchronous Digital Hierarchy (SDH) networks. In such a network, a customer must be a node of a ring. We first show that there is no two-index integer formulation for this problem. We then present a mathematical model for the NDRSP along with some classes of valid inequalities that are used as cutting planes in a Branch-and-Cut approach. We also study the dominant polytope of the NDRSP and introduce several polyhedral results. Finally, we present our Branch-and-Cut algorithm and give some experimental results on both random and real instances.
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References
Achterberg, T.: SCIP: solving constraint integer programs. Mathematical Programming Computation 1(1), 1–41 (2009)
Augerat, P., Belenguer, J.M., Benavent, E., Corberán, A., Naddef, D.: Separating capacity constraints in the CVRP using tabu search. European Journal of Operational Research 106(2-3), 546–557 (1998)
Baïou, M., Mahjoub, A.R.: The Steiner traveling salesman polytope and related polyhedra. SIAM Journal on Optimization 13, 498 (2002)
Baldacci, R., Dell’Amico, M., Gonzalez, J.S.: The capacitated m-ring-star problem. Operations Research 55(6), 1147 (2007)
Baldacci, R., Hadjiconstantinou, E., Mingozzi, A.: An exact algorithm for the capacitated vehicle routing problem based on a two-commodity network flow formulation. Operations Research, 723–738 (2004)
Cornuejols, G., Harche, F.: Polyhedral study of the capacitated vehicle routing problem, on the p-median polytope. Mathematical Programming 60(1-3), 21–52 (1991)
Fukasawa, R., Longo, H., Lysgaard, J., Aragão, M.P., Reis, M., Uchoa, E., Werneck, R.F.: Robust Branch-and-Cut-and-price for the capacitated vehicle routing problem. Mathematical programming 106(3), 491–511 (2006)
Kedad-Sidhoum, S., Nguyen, V.H.: An exact algorithm for solving the ring star problem. Optimization 59(1), 125–140 (2010)
Labbé, M., Laporte, G., Martin, I.R., González, J.J.S.: The ring star problem: Polyhedral analysis and exact algorithm. Networks 43(3), 177–189 (2004)
Laporte, G.: The vehicle routing problem: An overview of exact and approximate algorithms. European Journal of Operational Research 59(3), 345–358 (1992)
Letchford, A.N., Salazar-Gonzalez, J.J.: Projection results for vehicle routing. Mathematical Programming 105(2), 251–274 (2006)
Nguyen, V.H., Minoux, M.: New formulation for the sonet/sdh network design problem. In: Congrès de la Société Française de Recherche Opérationnelle et d’Aide à la Décision (2006)
Fouilhoux, P., Questel, A.: The Non-Disjoint m-Ring-Star Problem: application to SDH network design. In: International Network Optimization Conference (2011)
Soriano, P., Wynants, C., Gendreau, M., Fortz, B.: Design and dimensionning of survivable SDH/SONET networks. In: Telecommunications Network Planning, p. 147 (1999)
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Fouilhoux, P., Questel, A. (2012). The Non-Disjoint m-Ring-Star Problem: Polyhedral Results and SDH/SONET Network Design. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds) Combinatorial Optimization. ISCO 2012. Lecture Notes in Computer Science, vol 7422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32147-4_10
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DOI: https://doi.org/10.1007/978-3-642-32147-4_10
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