Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Heuristics for the multi-level capacitated minimum spanning tree problem

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

The capacitated minimum spanning tree (CMST) problem is fundamental to the design of centralized communication networks. In this paper we consider the multi-level capacitated minimum spanning tree problem, a generalization of the well-known CMST problem. Based on work previously done in the field, three heuristics are presented, addressing unit and non-unit demand cases. The proposed heuristics have been also integrated into a mixed integer programming solver. Evaluation results are presented, for an extensive set of experiments, indicating the improvements that the heuristics bring to the particular problem.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Ahuja, R.K., Orlin, J.B., Sharma, D.: Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem. Math. Progr. 91, 71–97 (2001)

    MATH  MathSciNet  Google Scholar 

  2. Breslau, L., Cao, P., Fan, L., Phillips, G., Shenker, S.: Web caching and zipf-like distributions: evidence and implications. In: INFOCOM9, vol. 1, pp. 126–134 (1999)

  3. Esau, L.R., Williams, K.C.: On teleprocessing system design: part ii a method for approximating the optimal network. IBM Syst. J. 5, 142–147 (1966)

    Article  Google Scholar 

  4. Falkenauer, E.: A hybrid grouping genetic algorithm for bin packing. J. Heuristics 2, 5–30 (1996)

    Article  Google Scholar 

  5. Gamvros, I., Golden, B., Raghavan, S.: The multilevel capacitated minimum spanning tree problem. INFORMS J. Comput. 18(3), 348–365 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gamvros, I., Raghavan, S., Golden, B.: An evolutionary approach for the multi-level capacitated minimum spanning tree. Institute for Systems Research, University of Maryland, Technical Report (2002)

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

    Google Scholar 

  8. Gavish, B.: Formulations and algorithms for the capacitated minimal directed tree problem. J. ACM 30, 118–132 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gouveia, L.: A comparison of directed formulations for the capacitated minimal spanning tree problem. Telecommun. Syst. 1, 51–76 (1993)

    Article  Google Scholar 

  10. Gouveia, L.: A 2n constraint formulation for the capacitated minimal spanning tree problem. Oper. Res. 43, 130–141 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  11. IBM Corp.: ILOG CPLEX V12.1-User’s Manual for CPLEX. url:ftp://public.dhe.ibm.com/software/websphere/ilog/docs/optimization/cplex/ps_usrmancplex.pdf

  12. Martins, A.X., Souza, M.C., Souza, M.J., Toffolo, T.A.: Grasp with hybrid heuristic-subproblem optimization for the multi-level capacitated minimum spanning tree problem. J. Heuristics 15, 133–151 (2009)

    Article  MATH  Google Scholar 

  13. Papadimitriou, C.: The complexity of the capacitated tree problem. Networks 8, 217–230 (1978)

    Article  MathSciNet  Google Scholar 

  14. Papagianni, C., Pappas, C., Lefkaditis, N., Venieris, I.: Particle swarm optimization for the multi level capacitated minimum spanning tree. In: IMCSIT, pp. 765–770 (2009)

  15. Uchoa, E., Toffolo, T.A.M., de Souza, M.C., Martins, A.X.: Branch-and-cut and grasp with hybrid local search for the multi-level capacitated minimum spanning tree problem. In: INOC 2009. Pisa, Italy (2009)

Download references

Acknowledgments

This work was financially supported by the National Technical University of Athens in the frame of “Basic Research Funding Program 2009” (PEVE 2009).

Author information

Authors and Affiliations

  1. Intelligent Communications and Broadband Networks Laboratory, National Technical University of Athens, Iroon Polytechneiou 9 Str., Zografou, 15773 , Athens, Greece

    Christos A. Pappas, Angelos-Christos G. Anadiotis & Iakovos S. Venieris

  2. Network Management and Optimal Design Laboratory, National Technical University of Athens, Iroon Polytechneiou 9 Str., Zografou, 15773 , Athens, Greece

    Chrysa A. Papagianni

Authors
  1. Christos A. Pappas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Angelos-Christos G. Anadiotis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chrysa A. Papagianni
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Iakovos S. Venieris
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christos A. Pappas.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pappas, C.A., Anadiotis, AC.G., Papagianni, C.A. et al. Heuristics for the multi-level capacitated minimum spanning tree problem. Optim Lett 8, 435–446 (2014). https://doi.org/10.1007/s11590-013-0607-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-013-0607-8

Keywords

Search

Navigation