Advertisement

The Capacitated m Two-Node Survivable Star Problem: A Hybrid Metaheuristic Approach

  • Gabriel BayáEmail author
  • Antonio Mauttone
  • Franco Robledo
  • Pablo Romero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9668)

Abstract

In telecommunications, a traditional method to connect multiterminal systems is to use rings. The goal of the Capacitated m Ring Star Problem (CmRSP) is to connect terminals by m rings which meet at a distinguished node, and possibly by some pendant links, at minimum cost. In this paper, we introduce a relaxation for the CmRSP, called Capacitated m Two-Node Survivable Star Problem (CmTNSSP for short). The CmTNSSP belongs to the \(\mathcal {NP}\)-Hard class of computational problems. Therefore, we address a GRASP hybrid metaheuristic which alternates local searches that obtain incrementally better solutions, and exact resolution local searches based on Integer Linear Programming models. In consonance with predictions provided by Clyde Monma, the network can be equally robust but cheaper than in the original CmRSP.

Keywords

Network optimization CmRSP CmTSSP Hybrid metaheuristics GRASP VND ILP 

References

  1. 1.
    Baldacci, R., Dell’Amico, M., González, J.J.S.: The capacitated m-ring-star problem. Oper. Res. 55(6), 1147–1162 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Mantani, G.B.: Diseño Topológico de Redes. Caso de Estudio: Capacitated m Two-Node Survivable Star Problem. Master’s thesis, Universidad de la República. Pedeciba Informática, Montevideo, Uruguay (2014)Google Scholar
  3. 3.
    Bhandari, R.: Optimal physical diversity algorithms and survivable networks. In: 1997 Second IEEE Symposium on Computers and Communications, pp. 433–441 (1997)Google Scholar
  4. 4.
    Canale, E., Monzón, P., Robledo, F.: Global synchronization properties for different classes of underlying interconnection graphs for Kuramoto coupled oscillators. In: Lee, Y., Kim, T., Fang, W., Ślęzak, D. (eds.) FGIT 2009. LNCS, vol. 5899, pp. 104–111. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Hoshino, E.A., de Souza, C.C.: A branch-and-cut-and-price approach for the capacitated m-ring-star problem. Discrete Appl. Math. 160(18), 2728–2741 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)CrossRefGoogle Scholar
  7. 7.
    Labbé, M., Laporte, G., Martín, I.R., González, J.J.S.: The ring star problem: polyhedral analysis and exact algorithm. Networks 43(3), 177–189 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Mladenovic, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Monma, C., Munson, B.S., Pulleyblank, W.R.: Minimum-weight two-connected spanning networks. Math. Program. 46(1–3), 153–171 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Resende, M., Ribeiro, C.: Greedy randomized adaptive search procedures. In: Glover, F., Kochenberger, G. (eds.) Handbook of Methaheuristics. Kluwer Academic Publishers, Norwell (2003)Google Scholar
  11. 11.
    Resende, M., Ribeiro, C.: GRASP: Greedy randomized adaptive search procedures. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies, pp. 287–312. Springer, US (2014)CrossRefGoogle Scholar
  12. 12.
    Robledo, F.: GRASP heuristics for Wide Area Network design. Ph.D. thesis, INRIA/IRISA, Université de Rennes I, Rennes, France (2005)Google Scholar
  13. 13.
    Zizhen Zhang, H., Qin, A.L.: A memetic algorithm for the capacitated m-ring-star problem. Appl. Intell. 40(2), 305–321 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Gabriel Bayá
    • 1
    Email author
  • Antonio Mauttone
    • 1
  • Franco Robledo
    • 1
  • Pablo Romero
    • 1
  1. 1.Departamentp de Investigación OperativaUniversidad de la RepúblicaMontevideoUruguay

Personalised recommendations