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A branch-and-cut for the Non-Disjoint m-Ring-StarProblem

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

Abstract

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

Keywords

Realistic SDH networknon-disjointm-ring-star problempolyhedral approachbranch-and-cut algorithm

Information

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

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