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Regenerator location problem: Polyhedral study and effective branch-and-cut algorithms

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  • Li, Xiangyong
  • Aneja, Y.P.

Abstract

In this paper, we study the regenerator location problem (RLP). This problem arises in optical networks where an optical signal can only travel a certain maximum distance (called the optical reach) before its quality deteriorates, needing regenerations by regenerators deployed at network nodes. The RLP is to determine a minimal number of network nodes for regenerator placement, such that for each node pair, there exists a path of which no sub-path without internal regenerators has a length greater than the optical reach. Starting with a set covering formulation involving an exponential number of constraints, reported and studied in Rahman (2012) and Aneja (2012), we study the facial structure of the polytope arising from this formulation, significantly extending known results. Making use of these polyhedral results, we present a new branch-and-cut (B&C) solution approach to solve the RLP to optimality. We present a series of computational experiments to evaluate two versions of the proposed B&C approach. Over 400 benchmark RLP instances, we first compare them with an available exact method for the RLP in the literature. Because of the equivalence among the RLP, the minimum connected dominating set problem (MCDSP), and the maximum leaf spanning tree problem (MLSTP), we further compare our approaches with other available exact algorithms using 47 benchmark MCDSP/MLSTP instances.

Suggested Citation

  • Li, Xiangyong & Aneja, Y.P., 2017. "Regenerator location problem: Polyhedral study and effective branch-and-cut algorithms," European Journal of Operational Research, Elsevier, vol. 257(1), pages 25-40.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:1:p:25-40
    DOI: 10.1016/j.ejor.2016.07.032
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    References listed on IDEAS

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    1. Abilio Lucena & Nelson Maculan & Luidi Simonetti, 2010. "Reformulations and solution algorithms for the maximum leaf spanning tree problem," Computational Management Science, Springer, vol. 7(3), pages 289-311, July.
    2. Gendron, Bernard & Scutellà, Maria Grazia & Garroppo, Rosario G. & Nencioni, Gianfranco & Tavanti, Luca, 2016. "A branch-and-Benders-cut method for nonlinear power design in green wireless local area networks," European Journal of Operational Research, Elsevier, vol. 255(1), pages 151-162.
    3. Yogesh Agarwal & Yash Aneja, 2012. "Fixed-Charge Transportation Problem: Facets of the Projection Polyhedron," Operations Research, INFORMS, vol. 60(3), pages 638-654, June.
    4. Si Chen & Ivana Ljubić & S. Raghavan, 2015. "The Generalized Regenerator Location Problem," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 204-220, May.
    5. Bala G. Chandran & Dorit S. Hochbaum, 2009. "A Computational Study of the Pseudoflow and Push-Relabel Algorithms for the Maximum Flow Problem," Operations Research, INFORMS, vol. 57(2), pages 358-376, April.
    6. Pedrola, Oscar & Careglio, Davide & Klinkowski, Miroslaw & Velasco, Luis & Bergman, Keren & Solé-Pareta, Josep, 2013. "Metaheuristic hybridizations for the regenerator placement and dimensioning problem in sub-wavelength switching optical networks," European Journal of Operational Research, Elsevier, vol. 224(3), pages 614-624.
    7. Dorit S. Hochbaum, 2008. "The Pseudoflow Algorithm: A New Algorithm for the Maximum-Flow Problem," Operations Research, INFORMS, vol. 56(4), pages 992-1009, August.
    8. Bernard Gendron & Abilio Lucena & Alexandre Salles da Cunha & Luidi Simonetti, 2014. "Benders Decomposition, Branch-and-Cut, and Hybrid Algorithms for the Minimum Connected Dominating Set Problem," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 645-657, November.
    9. Buchanan, Austin & Sung, Je Sang & Boginski, Vladimir & Butenko, Sergiy, 2014. "On connected dominating sets of restricted diameter," European Journal of Operational Research, Elsevier, vol. 236(2), pages 410-418.
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    Cited by:

    1. Xiangyong Li & Y. P. Aneja, 2020. "A new branch-and-cut approach for the generalized regenerator location problem," Annals of Operations Research, Springer, vol. 295(1), pages 229-255, December.
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    3. Okan Arslan & Oya Ekin Karaşan & Ridha Mahjoub & Hande Yaman, 2019. "A Branch-and-Cut Algorithm for the Alternative Fuel Refueling Station Location Problem with Routing," Transportation Science, INFORMS, vol. 53(4), pages 1107-1125, July.

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