Abstract
The Constrained-Routing and Spectrum Assignment (C-RSA) problem arises in the design of 5G telecommunication optical networks. Given an undirected, loopless, and connected graph G, an optical spectrum of available contiguous frequency slots \({\mathbb {S}}\), and a set of traffic demands K, the C-RSA consists of assigning, to each traffic demand \(k\in K\), a path in G between its origin and destination, and a subset of contiguous frequency slots in \({\mathbb {S}}\) 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
Enquiries about data availability should be directed to the authors.
References
Amar D (2016) Performance assessment and modeling of flexible optical networks. Thesis, Institut National des Télécommunications
Bertero F, Bianchetti M, Marenco J (2018) Integer programming models for the routing and spectrum allocation problem. In: Official Journal of the Spanish Society of Statistics and Operations Research, pp 465–488
Brun B, Baraketi S (2014) Routing and wavelength assignment in optical networks, pp 1–41. https://hal.archives-ouvertes.fr/hal-01062321
Cai A, Shen G, Peng L, Zukerman M (2013) Novel node-arc model and multiiteration heuristics for static routing and spectrum assignment in elastic optical networks. J Lightw Technol 3402–3413
Chen X, Guo J, Zhu Z, Proietti R, Castro A, Yoo SJB (2018) Deep-RMSA: a deep-reinforcement-learning routing, modulation and spectrum assignment agent for elastic optical networks. In: Optical fiber communications conference and exposition (OFC), pp 1–3
Chlamtac I, Ganz A, Karmi G (1992) Lightpath communications: an approach to high bandwidth optical WAN’s. IEEE Trans Commun 1171–1182
Chouman H, Gravey A, Gravey P, Hadhbi Y, Kerivin H, Morvan M, Wagler A (2021) Impact of RSA optimization objectives on optical network state, pp 1–7. https://hal.uca.fr/hal-03155966
Chouman H, Luay A, Colares R, Gravey A Gravey P, Kerivin H, Morvan M, Wagler A (2021) Assessing the health of flexgrid optical networks, pp 1–7. https://hal.archives-ouvertes.fr/hal-03123302
Christodoulopoulos K, Manousakis K, Varvarigos E (2010) Offline routing and wavelength assignment in transparent wdm networks. In: Networking, IEEE/ACM transactions, pp 1557–1570
Christodoulopoulos K, Tomkos I, Varvarigos EA (2011) Elastic bandwidth allocation in flexible OFDM-based optical networks. In: Lightwave technology, pp 1354–1366
Colares R, Kerivin H, Wagler A (2021) An extended formulation for the Constraint Routing and Spectrum Assignment Problem in Elastic Optical Networks, pp 1–16. https://hal.uca.fr/hal-03156189
Cplex II (2020) V12. 9: User’s manual for CPLEX. Int Bus Mach Corp 46(53):157
Crowder H, Johnson EL, Padberg MW (1983) Solving large scale zero-one linear programming problems. Oper Res 31:803–834
Diarrassouba I, Hadhbi Y (2022) The constrained-routing and spectrum assignment problem: valid inequalities and branch-and-cut algorithm. In: Ljubić I, Barahona F, Dey SS, Mahjoub AR (eds) Combinatorial optimization, ISCO, Lecture Notes in Computer Science, vol 13526
Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1(1):269–271
Ding Z, Xu Z, Zeng X, Ma T, Yang F (2014) Hybrid routing and spectrum assignment algorithms based on distance-adaptation combined coevolution and heuristics in elastic optical networks. J Opt Eng 1–10
Dror M (1994) Note on the complexity of the shortest path models for column generation in VRPTW. J Oper Res 977–978
Dumitrescu I, Boland N (2001) Algorithms for the weight constrained shortest path problem. Int Trans Oper Res 15–29
Gamrath G, Anderson D, Bestuzheva K, Chen WK, Eifler L, Gasse M, Gemander P, Gleixner A, Gottwald L, Halbig K, Hendel G, Hojny C, Koch T, Bodic L, Maher PJ, Matter F, Miltenberger M, Mühmer E, Müller B, Pfetsch ME, Schlösser F, Serrano F, Shinano Y, Tawfik C, Vigerske S, Wegscheider F, Weninger D, Witzig J (March 2020) The SCIP Optimization Suite 7.0. http://www.optimization-online.org/DB_HTML/2020/03/7705.html
Goldberg AV, Tarjan RE (1986) A new approach to the maximum flow problem. In: Proceedings of the Eighteenth Annual Association for Computing Machinery Symposium on Theory of Computing, pp 136–146
Gong L, Zhou X, Lu W, Zhu Z (2012) A two-population based evolutionary approach for optimizing routing, modulation and spectrum assignments (RMSA) in O-OFDM networks. IEEE Commun Lett 1520–1523
Goscien R, Walkowiak K, Klinkowski M (2015) Tabu search algorithm, routing, modulation and spectrum allocation, anycast traffic, elastic optical networks. J Comput Netw 148–165
Grötschel M, Lovász L, Schrijver A (1988) Stable sets in graphs. In: Geometric algorithms and combinatorial optimization. algorithms and combinatorics, vol 2. Springer, Berlin, Heidelberg
Gurobi Optimization LLC (2021) Gurobi optimizer reference manual. https://www.gurobi.com
Gu R, Yang Z, Ji Y (2020) Machine learning for intelligent optical networks: a comprehensive survey. J CoRR 1–42
Hadhbi Y (2022) The constrained-routing and spectrum assignment problem: polyhedral analysis and algorithms. PhD thesis at Clermont Auvergne University
Hadhbi Y, Kerivin H, Wagler A (2019) A novel integer linear programming model for routing and spectrum assignment in optical networks. In: Federated conference on computer science and information systems (FedCSIS) , pp 127–134
Hai DH, Hoang KM (2017) An efficient genetic algorithm approach for solving routing and spectrum assignment problem. J Recent Adv Signal Process 187–192
Hai DH, Morvan M, Gravey P (2017) Combining heuristic and exact approaches for solving the routing and spectrum assignment problem. J Iet Optoelectron 65–72
Hai DT, Morvan M, Gravey P (2017) Combining heuristic and exact approaches for solving the routing and spectrum assignment problem. IET Optoelectron 12:65–72
He S, Qiu Y, Xu J (2020) Invalid-resource-aware spectrum assignment for advanced-reservation traffic in elastic optical network. In: Sensors
Jaumard B, Daryalal M (2016) Scalable elastic optical path networking models. In: 18th international conference transparent optical networks (ICTON), pp 1–4
Jiang R, Feng M, Shen J (2017) An defragmentation scheme for extending the maximal unoccupied spectrum block in elastic optical networks. In: 16th international conference on optical communications and networks (ICOCN), pp 1–3
Karp RM (1972) Reducibility among combinatorial problems. In: Complexity of computer computations: proceedings of a symposium on the complexity of computer computations, held March 20–22, 1972, at the IBM Thomas J. Watson Research Center, pp 85–94
Klabjan D, Nemhauser GL, Tovey C (1998) The complexity of cover inequality separation. Oper Res Lett 35–40
Klinkowski M, Pedro J, Careglio D, Pioro M, Pires J, Monteiro P, Sole-Pareta J (2010) An overview of routing methods in optical burst switching networks. Opt Switch Network 41–53
Klinkowski M, Pioro M, Zotkiewicz M, Ruiz M, Velasco L (2014) Valid inequalities for the routing and spectrum allocation problem in elastic optical networks. In: 16th international conference on transparent optical networks (ICTON), pp 1–5
Klinkowski M, Pioro M, Zotkiewicz M, Ruiz M, Velasco L (2015) A simulated annealing heuristic for a branch and price-based routing and spectrum allocation algorithm in elastic optical networks. In: Intelligent data engineering and automated learning – IDEAL, Springer International Publishing, pp 290–299
Klinkowski M, Pióro M, Żotkiewicz M, Walkowiak K, Ruiz M, Velasco L (2015) Spectrum allocation problem in elastic optical networks - A branch-and-price approach. In: 17th international conference on transparent optical networks (ICTON), pp 1–5
Klinkowski M, Walkowiak K (2011) Routing and spectrum assignment in spectrum sliced elastic optical path network. IEEE Commun Lett 884–886
Lezama F, Martinez-Herrera AF, Castanon G, Del-Valle-Soto C, Sarmiento AM, Munoz de Cote A (2021) Solving routing and spectrum allocation problems in flexgrid optical networks using pre-computing strategies. J Photon Netw Commun 41:17–35
Liu Z, Rouskas GN (2013) Link selection algorithms for link-based ilps and applications to rwa in mesh networks. In: Optical network design and modeling (ONDM), 17th international conference. IEEE, pp 59–64
Liu L, Yin S, Zhang Z, Chu Y, Huang S (2019) A Monte Carlo based routing and spectrum assignment agent for elastic optical networks. In: Asia communications and photonics conference (ACP), pp 1–3
Lohani V, Sharma A, Singh YN (2019) Routing, modulation and spectrum assignment using an AI based algorithm. In: 11th international conference on communication systems & networks (COMSNETS), pp 266–271
Lopez V, Velasco L (2016) Elastic optical networks: architectures, technologies, and control. Springer Publishing Company, Incorporated
Mesquita LAJ, Assis K, Santos AF, Alencar M, Almeida RC (2018) A routing and spectrum assignment heuristic for elastic optical networks under incremental traffic. In: SBFoton international optics and photonics conference (SBFoton IOPC), pp 1–5
Nemhauser GL, Sigismondi G (1992) A strong cutting plane/branch-and-bound algorithm for node packing. J Oper Res Soc 443–457
Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, Hoboken
Nguyen DM, Ngoc LA, Huong PTV, Son NH, Hai DT (2019) An efficient column generation approach for solving the routing and spectrum assignment problem in elastic optical networks. In: the 6th NAFOSTED conference on information and computer science (NICS), Hanoi, Vietnam, pp 130–135
Orlowski S, Pióro M, Tomaszewski A, Wessäly R (2007) SNDlib 1.0-survivable network design library. In: Proceedings of the 3rd international network optimization conference (INOC 2007), Spa, Belgium
Padberg MW (1973) On the facial structure of set packing polyhedra. Math Program 5:199–215
Pedro H, Fernandes da Silva, Kerivin H, Nant JP, Wagler A (2022) A framework for routing and spectrum assignment in optical networks, driven by combinatorial properties. In: The international network optimization conference (INOC), pp 1–6
Ramaswami R (2009) Optical networks: a practical perspective, 3rd edn. Morgan Kaufmann Publishers Inc
Ramaswami R, Sivarajan K, Sasaki G (1993) Multiwavelength lightwave networks for computer communication. In: IEEE communications magazine, pp 78–88
Rebennack S, Reinelt G, Pardalos PM (2012) A tutorial on branch and cut algorithms for the maximum stable set problem. J Int Trans Oper Res 161–199
Ruiz M, Pioro M, Zotkiewicz M, Klinkowski M, Velasco L (2013) Column generation algorithm for RSA problems in flexgrid optical networks. Photon Netw Commun 53–64
Ruiz M, Pioro M, Zotkiewicz M, Klinkowski M, Velasco L (2020) A hybrid meta-heuristic approach for optimization of routing and spectrum assignment in Elastic Optical Network (EON). J Enterprise Inform Syst 11–24
Salani M, Rottondi C, Tornatore M (2019) Routing and spectrum assignment integrating machine-learning-based QoT estimation in elastic optical networks. In: IEEE INFOCOM - IEEE Conference on Computer Communications, p 173846
Shirazipourazad S, Zhou C, Derakhshandeh Z, Sen A (2013) On routing and spectrum allocation in spectrum-sliced optical networks. In: Proceedings IEEE INFOCOM, pp 385–389
Shiva-Kumar M, Sreenivasa-Kumar P (2002) Static lightpath establishment in wdm networksnew ilp formulations and heuristic algorithms. Comput Commun 109–114
Simonis H (2011) Solving the static design routing and wavelength assignment problem. In: Recent advances in constraints. Springer, pp 59–75
Siregar H, Takagi H, Zhang Y (2003) Efficient routing and wavelength assignment in wavelength-routed optical networks. In: Proceedings of 7th Asia-Pacific Network Operations and Mgmt Symposium, pp 116–127
Skorin-Kapov N (2007) Routing and wavelength assignment in optical networks using bin packing based algorithms. Eur J Oper Res 1167–1179
Talebi S, Alam F , Katib I, Khamis M, Salama R, Rouskas GN (2014) Spectrum management techniques for elastic optical networks: a survey. In: Optical switching and networking, pp 34–48
Velasco L, Klinkowski M, Ruiz M, Comellas J (2012) Modeling the routing and spectrum allocation problem for flexgrid optical networks. Photon Network Commun 177–186
Zang H, Jue JP, Mukherjee B et al (2000) A review of routing and wavelength assignment approaches for wavelength-routed optical wdm networks. In: Optical networks magazine, pp 47–60
Zhang Y, Xin J, Li X, Huang S (2020) Overview on routing and resource allocation based machine learning in optical networks. J Opt Fiber Technol 1–21
Zotkiewicz M, Pioro M, Ruiz M, Klinkowski M, Velasco L (2013) Optimization models for flexgrid elastic optical networks. In: 15th international conference on transparent optical networks (ICTON), pp 1–4
Funding
The authors have not disclosed any funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The authors have not disclosed any competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work was supported by the French National Research Agency grant ANR-17-CE25-0006, project FLEXOPTIM.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Diarrassouba, I., Hadhbi, Y. & Mahjoub, A.R. Branch-and-cut-and-price algorithm for the constrained-routing and spectrum assignment problem. J Comb Optim 47, 56 (2024). https://doi.org/10.1007/s10878-024-01125-x
Accepted:
Published:
DOI: https://doi.org/10.1007/s10878-024-01125-x