Solving the Static Design Routing and Wavelength Assignment Problem

  • Helmut Simonis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6384)


In this paper we present a hybrid model for the static design variant of the routing and wavelength assignment problem in directed networks, an important benchmark problem in optical network design. Our solution uses a decomposition into a MIP model for the routing aspect, combined with a graph coloring step modelled using either MIP (Coin-OR), SAT (minisat) or finite domain constraints (ECLiPSe). We consider two possible objective functions, one minimizing the maximal number of frequencies used on any of the links, the other minimizing the total number of frequencies used. We compare the models on a set of benchmark tests, results show that the constraint model is much more scalable than the alternatives considered, and is the only one producing proven optimal or near optimal results when minimizing the total number of wavelengths.


Optical Network Constraint Programming Wavelength Assignment Graph Coloring Problem Alldifferent Constraint 
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  1. 1.
    Banerjee, D., Mukherjee, B.: A practical approach for routing and wavelength assignment in large wavelength-routed optical networks. IEEE Journal on Selected Areas in Communications 14(5), 903–908 (1996)CrossRefGoogle Scholar
  2. 2.
    Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: Filtering algorithms for the nvalue constraint. Constraints 11(4), 271–293 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Jaumard, B., Meyer, C., Thiongane, B.: ILP formulations for the routing and wavelength assignment problem: Symmetric systems. In: Resende, M., Pardalos, P. (eds.) Handbook of Optimization in Telecommunications, pp. 637–677. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Jaumard, B., Meyer, C., Thiongane, B.: Comparison of ILP formulations for the RWA problem. Optical Switching and Networking 4(3-4), 157–172 (2007)CrossRefGoogle Scholar
  6. 6.
    Jaumard, B., Meyer, C., Thiongane, B.: On column generation formulations for the RWA problem. Discrete Applied Mathematics 157, 1291–1308 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Lever, J.: A local search/constraint propagation hybrid for a network routing problem. International Journal on Artificial Intelligence Tools 14(1-2), 43–60 (2005)CrossRefGoogle Scholar
  8. 8.
    Liatsos, V., Novello, S., El Sakkout, H.: A probe backtrack search algorithm for network routing. In: Proceedings of the Third International Workshop on Cooperative Solvers in Constraint Programming, CoSolv 2003, Kinsale, Ireland (September 2003)Google Scholar
  9. 9.
    Lougee-Heimer, R.: The common optimization interface for operations research. IBM Journal of Research and Development 47, 57–66 (2003)CrossRefGoogle Scholar
  10. 10.
    Ramaswami, R., Sivarajan, K.N.: Routing and wavelength assignment in all-optical networks. IEEE/ACM Trans. Netw. 3(5), 489–500 (1995)CrossRefGoogle Scholar
  11. 11.
    Shen, K., Schimpf, J.: Eplex: Harnessing mathematical programming solvers for constraint logic programming. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 622–636. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Simonis, H.: Constraint applications in networks. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming. Elsevier, Amsterdam (2006)Google Scholar
  13. 13.
    Simonis, H.: A hybrid constraint model for the routing and wavelength assignment problem. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 104–118. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    Smith, B.M.: Symmetry and search in a network design problem. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 336–350. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    van Hoeve, W.J.: The alldifferent constraint: A survey. CoRR, cs.PL/0105015 (2001)Google Scholar
  16. 16.
    Wallace, M., Novello, S., Schimpf, J.: ECLiPSe: A platform for constraint logic programming. ICL Systems Journal 12(1) (May 1997)Google Scholar
  17. 17.
    Zang, H., Jue, J.P., Mukherjee, B.: A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks. Optical Networks Magazine, 47–60 (January 2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Helmut Simonis
    • 1
  1. 1.Cork Constraint Computation Centre, Department of Computer ScienceUniversity College CorkIreland

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