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Optimal Placement of Add/Drop Multiplexers: Heuristic and Exact Algorithms

Author

Listed:
  • Alain S. Sutter

    (CNET, France Telecom, France)

  • François Vanderbeck

    (Cambridge University, England)

  • Laurence Wolsey

    (Université Catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

We study a problem that has arisen recently in the design of telecommunications transmission networks at France Telecom. Given a set of centers in a city or conglomeration linked together on a ring architecture, given the expected demands between the centers and an essentially unlimited availability of rings of fixed capacity on the network, assign demand pairs and corresponding add/drop multiplexers to the rings so as to satisfy the demands and minimize the number of “costly” multiplexers installed.Heuristics based on simulated annealing have been developed for the basic problem and several variants. France Telecom is particularly interested in validating the effectiveness of the heuristics. An exact algorithm based on integer column generation is shown to provide tight performance guarantees, and in most cases to give provable minimum cost solutions. Column generation is used even though the subproblems are strongly NP -hard and are solved by standard mixed integer programming software. In addition, the Master Problems involve both integer columns and integer variables, whereas these are 0–1 in most reported applications.

Suggested Citation

  • Alain S. Sutter & François Vanderbeck & Laurence Wolsey, 1998. "Optimal Placement of Add/Drop Multiplexers: Heuristic and Exact Algorithms," Operations Research, INFORMS, vol. 46(5), pages 719-728, October.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:5:p:719-728
    DOI: 10.1287/opre.46.5.719
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    References listed on IDEAS

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    Cited by:

    1. Polinder, G.-J. & Schmidt, M.E. & Huisman, D., 2020. "Timetabling for strategic passenger railway planning," ERIM Report Series Research in Management ERS-2020-001-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. François Vanderbeck, 2000. "On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm," Operations Research, INFORMS, vol. 48(1), pages 111-128, February.
    3. Fortz, Bernard & Soriano, Patrick & Wynants, Christelle, 2003. "A tabu search algorithm for self-healing ring network design," European Journal of Operational Research, Elsevier, vol. 151(2), pages 280-295, December.
    4. Hanif D. Sherali & J. Cole Smith, 2001. "Improving Discrete Model Representations via Symmetry Considerations," Management Science, INFORMS, vol. 47(10), pages 1396-1407, October.
    5. Cole Smith, J., 2004. "Algorithms for distributing telecommunication traffic on a multiple-ring SONET-based network," European Journal of Operational Research, Elsevier, vol. 154(3), pages 659-672, May.
    6. Polinder, Gert-Jaap & Schmidt, Marie & Huisman, Dennis, 2021. "Timetabling for strategic passenger railway planning," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 111-135.
    7. Hanif D. Sherali & J. Cole Smith & Youngho Lee, 2000. "Enhanced Model Representations for an Intra-Ring Synchronous Optical Network Design Problem Allowing Demand Splitting," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 284-298, November.
    8. Garg, Manish & Smith, J. Cole, 2008. "Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios," Omega, Elsevier, vol. 36(6), pages 1057-1071, December.
    9. Polinder, G.-J. & Cacchiani, V. & Schmidt, M.E. & Huisman, D., 2020. "An iterative heuristic for passenger-centric train timetabling with integrated adaption times," ERIM Report Series Research in Management ERS-2020-006-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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