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Telecommunication Systems

, Volume 21, Issue 2–4, pp 301–318 | Cite as

Ring Network Design by Lagrangean Based Column Generation

  • M. Henningsson
  • K. Holmberg
  • M. Rönnqvist
  • P. Värbrand
Article

Abstract

We discuss the problem of designing a telecommunication network with the survivability requirement that the network should be composed of connected rings of links. The network design problem is then to choose links from a given network, and compose them into a number of rings. Furthermore, the rings should be connected at certain transit nodes. The traffic between rings may pass through other rings. Each ring is associated with a certain fixed cost depending on the length of the ring. We describe the problem, modeled as a linear integer programming problem, and a heuristic solution method, based on column generation and Lagrangean relaxation.

network design rings column generation Lagrangean relaxation heuristic 

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References

  1. [1]
    M. DellAmico, F. Maffioli and P. Värbrand, On prize-collecting tours and the asymmetric traveling salesman problem, International Transactions in Operational Research 2 (1995) 297–308.Google Scholar
  2. [2]
    M. Fischetti and P. Toth, An additive approach for the optimal solution of the prize-collecting travelling salesman problem, Vehicle Routing: Methods and Studies (1988) 319–343.Google Scholar
  3. [3]
    M. Gendreau, M. Labbé and G. Laporte, Efficient heuristics for the design of ring networks, Technical Report, Institut de Statistique, Université Libre De Bruxelles (1994).Google Scholar
  4. [4]
    D. Gensch, An industrial application of the traveling salesmans subtour problem, AIIE Transactions 10(4) (1978) 362–370.Google Scholar
  5. [5]
    M. Henningsson, K. Holmberg, M. Rönnqvist and P. Värbrand, A ring network design problem, Working paper, LiTH-MAT-OPT-WP-98-03, Department of Mathematics, Linköping Institute of Technology, Sweden (1998).Google Scholar
  6. [6]
    R.V. Kulkarni and P.R. Bhave, Integer programming formulations of vehicle routing problems, European Journal of Operational Research 20 (1985) 58–67.Google Scholar
  7. [7]
    M. Laguna, Clustering for the design of SONET rings in interoffice telecommunications, Management Science 40 (1994) 1533–1541.Google Scholar
  8. [8]
    V. Sridhar, J.S. Park and B. Gavish, Optimal interconnection of token ring networks using source routing bridges, Research Report, Ohio University, USA (1994).Google Scholar
  9. [9]
    O.J. Wasem, An algorithm for designing rings for survivable fiber networks, IEEE Transactions on Reliability 40 (1991) 428–432.Google Scholar
  10. [10]
    J. Xu, S.Y. Chiu and F. Glover, Optimizing a ring-based private line telecommunication network using tabu search, Working paper (1998).Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M. Henningsson
    • 1
  • K. Holmberg
    • 1
  • M. Rönnqvist
    • 1
  • P. Värbrand
    • 1
  1. 1.Department of MathematicsLinköping UniversityLinköpingSweden

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