| Issue |
RAIRO-Oper. Res.
Volume 48, Number 2, April-June 2014
Isco 2012, guest editors Nelson Maculan, A. Ridha Mahjoub, Eduardo Uchoa
|
|
|---|---|---|
| Page(s) | 167 - 188 | |
| DOI | https://doi.org/10.1051/ro/2014006 | |
| Published online | 07 March 2014 | |
A branch-and-cut for the Non-Disjoint m-Ring-Star Problem
Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu 75005
Paris, France.
pierre.fouilhoux@lip6.fr; aurelien.questel@lip6.fr
Received:
11
September
2013
Accepted:
28
November
2013
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.
Mathematics Subject Classification: 90B10 / 90C10 / 90C57 / 90C90
Key words: Realistic SDH network / non-disjointm-ring-star problem / polyhedral approach / branch-and-cut algorithm
© EDP Sciences, ROADEF, SMAI, 2014
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