4OR

, Volume 14, Issue 2, pp 201–220 | Cite as

Model-hierarchical column generation and heuristic for the routing and wavelength assignment problem

  • Christophe Duhamel
  • Philippe Mahey
  • Alexandre X. Martins
  • Rodney R. Saldanha
  • Mauricio C. de Souza
Research paper

Abstract

The routing and wavelength assignment (RWA) problem typically occurs in wavelength division multiplexing optical networks. Given a number of available wavelengths, we consider here the problem of maximising the number of accepted connections with respect to the clash and continuity constraints. We first propose a new strategy which combines two existing models. This leads to an improved column generation scheme. We also present two heuristics to compute feasible solutions: a hybrid heuristic and the integer solution at the root node of the column generation. Our approaches are compared with the best existing results on a set of classic RWA instances.

Keywords

Routing and wavelength assignment Optical networks   Column generation Heuristics 

Mathematics Subject Classification

90 Operations research, Mathematical programming 

References

  1. Banerjee D, Mukherjee B (1996) A practical approach for routing and wavelength assignment in large wavelength-routed optical networks. IEEE J Sel Areas Commun 14:903–908CrossRefGoogle Scholar
  2. Chlamtac I, Ganz A, Karmi G (1992) Lightpath communications: an approach to high-bandwidth optical WANs. IEEE Trans Commun 40:1171–1182CrossRefGoogle Scholar
  3. Corteel S, Gardy D, Valencia-Pabon M, Bath D, Denise A (2003) The permutation-path coloring problem on trees. Theoret Comput Sci 297:119–143CrossRefGoogle Scholar
  4. Erlebach T, Jansen K (2001) The complexity of path coloring and call scheduling. Theoret Comput Sci 255:33–50CrossRefGoogle Scholar
  5. Jaumard B, Meyer C, Thiongane B (2007) Comparison of ILP formulations for the RWA problem. Opt Switch Netw 4:157–172CrossRefGoogle Scholar
  6. Jaumard B, Meyer C, Thiongane B (2009) On column generation formulations for the RWA problem. Discrete Appl Math 157:1291–1308CrossRefGoogle Scholar
  7. Jaumard B, Meyer C, Thiongane B, Yu X (2004) ILP formulations and optimal solutions for the RWA problem. Proc IEEE GLOBECOM 3:1918–1924Google Scholar
  8. Krishnaswamy RM, Sivarajan KN (2001) Design of logical topologies: a linear formulation for wavelength-routed optical networks with no wavelength changers. IEEE/ACM Trans Netw 9:186–198CrossRefGoogle Scholar
  9. Lee T, Lee K, Park S (2000) Optimal routing and wavelength assignment in WDM ring networks. IEEE J Sel Areas Commun 18:2146–2154CrossRefGoogle Scholar
  10. Li G, Simha R (2000) The partition coloring problem and its application to wavelength routing and assignment. In: Proceedings of the First Workshop on Optical NetworksGoogle Scholar
  11. Manohar P, Manjunath D, Shevgaonkar RK (2002) Routing and wavelength assignment in optical networks from edge disjoint path algorithms. IEEE Commun Lett 6:211–213CrossRefGoogle Scholar
  12. Martins AX, Duhamel C, Mahey P, Saldanha RR, de Souza MC (2012) Variable neighborhood descent with iterated local search for routing and wavelength assignment. Comput Oper Res 39:2133–2141CrossRefGoogle Scholar
  13. Noronha TF, Ribeiro CC (2006) Routing and wavelength assignment by partition colouring. Eur J Oper Res 171:797–810CrossRefGoogle Scholar
  14. Noronha TF, Resende MGC, Ribeiro CC (2008) Efficient implementations of heuristics for routing and wavelength assignment. Lect Notes Comput Sci 5038:169–180CrossRefGoogle Scholar
  15. Noronha TF, Resende MGC, Ribeiro CC (2011) A biased random-key genetic algorithm for routing and wavelength assignment. J Global Optim 50:503–518CrossRefGoogle Scholar
  16. Ramaswami R, Sivarajan KN (1995) Routing and wavelength assignment in all-optical networks. IEEE/ACM Trans Netw 3:489–500CrossRefGoogle Scholar
  17. Skorin-Kapov N (2007) Routing and wavelength assignment in optical networks using bin packing based algorithms. Eur J Oper Res 177:1167–1179CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Christophe Duhamel
    • 1
  • Philippe Mahey
    • 1
  • Alexandre X. Martins
    • 2
  • Rodney R. Saldanha
    • 3
  • Mauricio C. de Souza
    • 4
  1. 1.LIMOSUniversité Blaise PascalClermont-FerrandFrance
  2. 2.Departamento de Ciências Exatas e AplicadasUniversidade Federal de Ouro PretoJoão MonlevadeBrazil
  3. 3.Departamento de Engenharia ElétricaUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  4. 4.Departamento de Engenharia de ProduçãoUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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