Skip to main content
SpringerLink
Log in

Model and heuristic for a generalized access network design problem

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

The generalized access network design problem consists of finding a topology, capacity assignment and routing that minimize the sum of costs to connect every pair of remote unit and its central node specified by the telecommunication company. We consider an integer programming formulation with a partial multicommodity structure. We analyze some aspects and extensions of the proposed model and we introduce a heuristic based on Lagrangian relaxation and the subgradient method. We report computational results for a set of randomly generated test problems. They include networks with up to 300 nodes and show that even problem instances defined in small networks can be extremely difficult problems. The heuristic generates effective and acceptable designs from the practical point of view. We compare our heuristic with a commercial code.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Agrawal, P.N. Klein and R. Ravi, When trees collide: An approximation algorithm for the generalized Steiner problem on networks, Technical Report CS-90-32, Department of Computer Science, Brown University, Providence, RI (1994).

    Google Scholar 

  2. A. Balakrishnan and K. Altinkemer, Using a hop-constrained model to generate alternative communication network design, ORSA Journal on Computing 4 (1992) 192–205.

    Google Scholar 

  3. A. Balakrishnan, T.L. Magnanti and P. Mirchandani, Modeling and heuristic worst-case performance analysis of two-level network design problem, Management Science 40 (1994) 846–867.

    Google Scholar 

  4. A. Balakrishnan, T.L. Magnanti, A. Shulman and R.T. Wong, Model for planning capacity expansion in local access telecommunication networks, Annals of Operations Research 33 (1991) 239–284.

    Article  Google Scholar 

  5. A. Balakrishnan, T.L. Magnanti and R.T. Wong, A dual-ascent procedure for large-scale uncapacitated network design, Operations Research 37 (1989) 716–740.

    Google Scholar 

  6. F. Barahona, Network design using cut inequalities, SIAM Journal on Optimization 6(3) (1996) 823–837.

    Article  Google Scholar 

  7. J.E. Beasley, An algorithm for solving large capacitated warehouse location problems, Journal of the Operational Research Society 33 (1988) 314–325.

    Article  Google Scholar 

  8. D. Bertsekas and R. Gallager, Data Networks (Prentice-Hall, Englewood Cliffs, NJ, 1987).

    Google Scholar 

  9. D. Bienstock and O. Günlük, Computational experience with a difficult mixed integer multicommodity flow problem, Mathematical Programming 68 (1995) 213–237.

    Google Scholar 

  10. D. Bienstock and O. Günlük, Capacitated network design – polyhedral structure and computation, Journal on Computing 8(3) (1996) 243–259.

    Google Scholar 

  11. R.R. Boorstyn and H. Frank, Large-scale network topological optimization, IEEE Transactions on Communications 25 (1977) 29–47.

    Article  Google Scholar 

  12. M.L. Fisher, The Lagrangean relaxation method for solving integer programming problems, Management Science 27 (1981) 1–18.

    Google Scholar 

  13. M.L. Fisher, An application oriented guide to Lagrangean relaxation, Interfaces 15 (1985) 10–21.

    Google Scholar 

  14. B. Gavish, Topological design of centralized computer networks – formulations and algorithms, Networks 12 (1982) 355–377.

    Google Scholar 

  15. B. Gavish, Formulations and algorithms for the capacitated minimal directed tree, Journal of the ACM 30 (1983) 118–132.

    Article  Google Scholar 

  16. B. Gavish, Topological design of telecommunication networks – Local access design methods, Annals of Operations Research 33 (1991) 17–71.

    Article  Google Scholar 

  17. A.M. Geoffrion, Lagrangean relaxation for integer programming, Mathematical Programming Study 2 (1974) 82–114.

    Google Scholar 

  18. L. Hall, Experience with a cutting plane algorithm for the capacitated spanning tree problem, Journal on Computing 8(3) (1996) 219–234.

    Google Scholar 

  19. D.S. Hochbaum and A. Segev, Analysis of a flow problem with fixed charges, Networks 19 (1989) 291–312.

    Google Scholar 

  20. K. Holmberg and J. Hellstrand, Solving the uncapacitated network design problem by a Lagrangean heuristic and branch-and-bound, Operations Research 46(2) (1998) 247–259.

    Article  Google Scholar 

  21. M.J. Lee and J.R. Yee, An algorithm for optimal minimax routing in ATM networks, Annals of Operations Research 49 (1994) 185–206.

    Article  Google Scholar 

  22. Y. Lee, S.Y. Chiu and J. Ryan, A branch and cut algorithm for a steiner tree-star problem, Journal on Computing 8(3) (1996) 194–201.

    Google Scholar 

  23. H.P.L. Luna, N. Ziviani and R.M.B. Cabral, The telephonic switching centre network problem: Formalization and computational experience, Discrete Applied Mathematics 18 (1987) 199–210.

    Article  Google Scholar 

  24. T.L. Magnanti and P. Mirchandani, Shortest paths, single origin–destination network design and associated polyhedra, Networks 23 (1993) 103–121.

    Google Scholar 

  25. T.L. Magnanti and R.T. Wong, Network design and transportation planning: Models and algorithms, Transportation Science 18 (1984) 1–55.

    Google Scholar 

  26. G.R. Mateus and C.T. Bornstein, Dominance criteria for the capacitated warehouse location problem, Journal of the Operational Research Society 42 (1991) 145–149.

    Article  Google Scholar 

  27. G.R. Mateus, F.R.B. Cruz and H.P.L. Luna, Algorithm for hierarchical network design, Location Science 2 (1994) 149–164.

    Google Scholar 

  28. G.R. Mateus and H.P.L. Luna, Decentralized decision-making and capacitated facility location, The Annals of Regional Science 26 (1992) 361–377.

    Article  Google Scholar 

  29. G.R. Mateus, H.P.L. Luna and L.C.M. Lage, Optimal planning of telecommunication networks with logical and physical aspects, in: SBT/IEEE Telecommunications Congress, Rio de Janeiro, Brasil, 1990, pp. 602–607.

  30. G.R. Mateus and J.M. Thizy, Exact sequential choice of locations in a network, Annals of Operations Research 86 (1999) 199–219.

    Article  Google Scholar 

  31. A. Mirzaian, Lagrangian relaxation for the star-star concentrator location problem: Approximation algorithm and bounds, Networks 15 (1985) 1–20.

    Google Scholar 

  32. A.S. Tanenbaum, Computer Networks (Prentice-Hall, New York, 1981).

    Google Scholar 

  33. R.E. Tarjan, Data Structures and Network Algorithms (SIAM, Philadelphia, PA, 1983).

    Google Scholar 

  34. Using the CPLEX Callable Library and CPLEX Mixed Integer Library, CPLEX Optimization (Incline Village, NV, 1993).

Download references

Authors
  1. Geraldo R. Mateus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raphaël Valéry L. Franqueira
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mateus, G.R., Franqueira, R.V.L. Model and heuristic for a generalized access network design problem. Telecommunication Systems 15, 257–271 (2000). https://doi.org/10.1023/A:1019147029476

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019147029476

Keywords

Search

Navigation