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On the Facial Structure of the Constrained-Routing and Spectrum Assignment Polyhedron: Part II

Diarrassouba, Ibrahima; Hadhbi, Youssouf; Mahjoub, Ali Ridha (2021), On the Facial Structure of the Constrained-Routing and Spectrum Assignment Polyhedron: Part II. https://basepub.dauphine.psl.eu/handle/123456789/22207

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Type
Document de travail / Working paper
Date
2021
Series title
Preprint Lamsade
Published in
Paris
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Author(s)
Diarrassouba, Ibrahima
Hadhbi, Youssouf
Mahjoub, Ali Ridha
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
The constrained-routing and spectrum assignment (C-RSA) problem is a key issue when dimensioning and designing an optical network. Given an optical network G and a multiset of traffic demand K, it aims at determining for each traffic demand k ∈ K a path and an interval of contiguous slots while satisfying technological constraints and optimizing some linear objective function(s). In this paper, we introduce an integer linear programming formulation based on the so-called cut formulation for the C-RSA problem. We describe several valid inequalities for the associated polytope, and further give necessary and sufficient conditions under which these inequalities are facet defining. Based on these results, we develop a branch-and-cut algorithm to solve the problem.
Subjects / Keywords
Optical networks; constrained-routing; spectrum assignment; integer linear programming; polyhedron; dimension; valid inequality; facet; separation; branch-and-cut