Branch-and-cut-and-price algorithm for the constrained-routing and spectrum assignment problem

• Published in: Journal of combinatorial optimization Vol. 47; no. 4; p. 56
• Main Authors: Diarrassouba, Ibrahima, Hadhbi, Youssouf, Mahjoub, A. Ridha
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2024; Springer Nature B.V
• Subjects: Algorithms; Artificial intelligence; Combinatorics; Constraints; Convex and Discrete Geometry; Heuristic; Integer programming; Linear programming; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; S.I. : New Challenges in Combinatorial Optimization; Theory of Computation; Wave division multiplexing; Network design; Valid inequalities; Branch-and-Cut-and-Price; 5
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-024-01125-x

The Constrained-Routing and Spectrum Assignment (C-RSA) problem arises in the design of 5 G telecommunication optical networks. Given an undirected, loopless, and connected graph G , an optical spectrum of available contiguous frequency slots S , and a set of traffic demands K , the C-RSA consists of assigning, to each traffic demand k ∈ K , a path in G between its origin and destination, and a subset of contiguous frequency slots in S subject to certain technological constraints while optimizing some linear objective function. In this paper, we devise an exact algorithm to solve the C-RSA. We first introduce an extended integer programming formulation for the problem. Then we investigate the associated polytope and introduce several classes of valid inequalities. Based on these results, we devise a Branch-and-Cut-and-Price algorithm for the problem and present an extensive computational study. This is also be compared with a Branch-and-Cut algorithm of the state-of-the-art.