Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-22T22:19:45.790Z Has data issue: false hasContentIssue false
  • English
  • Français

A branch-and-cut for the Non-Disjoint m-Ring-Star Problem

Published online by Cambridge University Press:  07 March 2014

Pierre Fouilhoux  and
Aurélien Questel
Pierre Fouilhoux
Affiliation:
Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu 75005 Paris, France.. pierre.fouilhoux@lip6.fr; aurelien.questel@lip6.fr
Aurélien Questel
Affiliation:
Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu 75005 Paris, France.. pierre.fouilhoux@lip6.fr; aurelien.questel@lip6.fr
Get access

Abstract

In this article we study the realistic network topology of Synchronous Digital Hierarchy (SDH) networks. We describe how providers fulfill customer connectivity requirements. We show that SDH Network design reduces to the Non-Disjoint m-Ring-Star Problem (NDRSP). We first show that there is no two-index integer formulation for this problem. We then present a natural 3-index formulation for the NDRSP together with some classes of valid inequalities that are used as cutting planes in a Branch-and-Cut approach. We propose a polyhedral study of a polytope associated with this formulation. Finally, we present our Branch-and-Cut algorithm and give some experimental results on both random and real instances.

Keywords

Realistic SDH networknon-disjointm-ring-star problempolyhedral approachbranch-and-cut algorithm
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 2: Isco 2012, guest editors Nelson Maculan, A. Ridha Mahjoub, Eduardo Uchoa , April 2014 , pp. 167 - 188
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Achterberg, T., SCIP: solving constraint integer programs. Math. Program. Comput. 1 (2009) 1–41. Google Scholar
Augerat, P., Belenguer, J.M., Benavent, E., Corberán, A. and Naddef, D., Separating capacity constraints in the CVRP using tabu search. Eur. J. Oper. Res. 106 (1998) 546–557. Google Scholar
Baïou, M. and Mahjoub, A.R., The Steiner traveling salesman polytope and related polyhedra. SIAM J. Opt. 13 (2002) 498. Google Scholar
Baldacci, R., Dell’Amico, M. and Gonzalez, J.S., The capacitated m-ring-star problem. Oper. Res. 55 (2007) 1147. Google Scholar
Baldacci, R., Hadjiconstantinou, E. and Mingozzi, A., An exact algorithm for the capacitated vehicle routing problem based on a two-commodity network flow formulation. Oper. Res. 52 (2004) 723–738. Google Scholar
Cornuejols, G. and Harche, F., Polyhedral study of the capacitated vehicle routing problem, on the p-median polytope. Math. Program. 60 (1991) 21–52. Google Scholar
Dezső, B., Jüttner, A. and Kovács, P., Lemon-an open source c++ graph template library. Electronic Notes in Theoretical Comput. Sci. 264 (2011) 23–45. Google Scholar
Fukasawa, R., Longo, H., Lysgaard, J., Aragão, M.P., Reis, M., Uchoa, E. and Werneck, R.F., Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Math. program. 106 (2006) 491–511. Google Scholar
M.R. Garey and D.S. Johnson, Computers and intractability. A guide to the theory of NP-completeness. A Series of Books in the Mathematical Sciences. WH Freeman and Company, San Francisco, Ca (1979).
Hoshino, E.A. and de Souza, C.C., A branch-and-cut-and-price approach for the capacitated m-ring-star problem. Discrete Appl. Math. 160 (2012) 2728–2741. Google Scholar
Kedad-Sidhoum, S. and Nguyen, V.H., An exact algorithm for solving the ring star problem. Optimization 59 (2010) 125–140. Google Scholar
Labbé, M., Laporte, G., Martin, I.R. and González, J.J.S., The ring star problem: Polyhedral analysis and exact algorithm. Networks 43 (2004) 177–189. Google Scholar
Laporte, G., The vehicle routing problem: An overview of exact and approximate algorithms. Eur. J. Oper. Res. 59 (1992) 345–358. Google Scholar
Letchford, A.N. and Salazar-Gonzalez, J.J.. Projection results for vehicle routing. Math. Program. 105 (2006) 251–274. Google Scholar
V. Hung Nguyen and M. Minoux, 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).
P. Soriano, C. Wynants, A. Seguin et al. Design and dimensionning of survivable SDH/SONET networks, in Telecommunications network planning (1999), pp. 147–167.