Skip to main content

Advertisement

SpringerLink
Log in

A biased random-key genetic algorithm for the tree of hubs location problem

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

Abstract

Hubs are facilities used to treat and dispatch resources in a transportation network. The objective of Hub Location Problems (HLP) is to locate a set of hubs in a network and route resources from origins to destinations such that the total cost of attending all demands is minimized. In this paper, we investigate a particular HLP, called the Tree of Hubs Location Problem in which hubs are connected by means of a tree and the overall network infrastructure relies on a spanning tree. This problem is particularly interesting when the total cost of building the hub backbone is high. We propose a biased random key genetic algorithm for solving the tree of hubs location problem. Computational results show that the proposed heuristic is robust and effective to this problem. The method was able to improve best known solutions of two benchmark instances used in the experiments.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Abreu Júnior, J. C., Noronha, T. F., Santos, A. C.: O problema de localização de concentradores em árvores: um procedimento para acelerar um algoritmo baseado em decomposição de Benders. In XLVII Simpósio Brasileiro de Pesquisa Operacional (SBPO), page 9p., Porto de Galinhas, Brazil (2015)

  2. Adler, N., Hashai, N.: Effect of open skies in the Middle East region. Trans. Res. Part A Policy Pract. 39(10), 878–894 (2005)

  3. Alumur, S., Kara, B.Y.: Network hub location problems: The state of the art. Euro. J. Operat. Res. 190, 1–21 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Beasley, J. E.: Population heuristics. In P. M. Pardalos and M. G. C. Resende, editors, Handbook of Applied Optimization, pages 168–183. Oxford University Press (2002)

  5. Berman, O., Drezner, Z., Wesolowsky, G.O.: The transfer point location problem. Euro. J. Operat. Res. 179(3), 978–989 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, H., Campbell, A.M., Thomas, B.W.: Network design for time-constrained delivery. Naval Res. Logist. 55, 493–515 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Coco, A. A., Noronha, T. F., Santos, A. C.: Algoritmo baseado em BRKGA para o problema de árvore geradora mínima robusta. In Proceedings of the XLV Simpósio Brasileiro de Pesquisa Operacional (SBPO), Natal, Brazil, pp 3658–3669 (2013)

  8. Contreras, I., Fernández, E., Marín, A.: Tight bounds from a path based formulation for the tree of hub location problem. Comp. Operat. Res. 36(12), 3117–3127 (2009)

    Article  MATH  Google Scholar 

  9. Contreras, I., Fernández, E., Marín, A.: The tree of hubs location problem. Euro. J. Operat. Res. 2, 390–400 (2010)

    Article  MATH  Google Scholar 

  10. Costa, T. F. G., Lohmann, G., Oliveira, A. V. M.: A model to identify airport hubs and their importance to tourism in Brazil. Res. Trans. Econ., 26(1):3–11. ISSN 0739-8859. Economics of Transport for Tourism (2010)

  11. Cunha, C.B., Silva, M.R.: A genetic algorithm for the problem of configuring a hub-and-spoke network for a LTL trucking company in Brazil. Euro. J. Operat. Res. 179(3), 747–758 (2007)

    Article  MATH  Google Scholar 

  12. Farahani, R.Z., Hekmatfar, M., Arabani, A.B., Nikbakhsh, E.: Hub location problems: a review of models, classification, solution techniques, and applications. Comp. Indust. Eng. 64(4), 1096–1109 (2013)

    Article  Google Scholar 

  13. D. B. M. M. Fontes and J. F. Gonçalves. A multi-population hybrid biased random key genetic algorithm for hop-constrained trees in nonlinear cost flow networks. Optimization Letters, 7(6):1303–1324. ISSN 1862-4472 (2013)

  14. Gelareh, S., Nickel, S.: A Benders decomposition for hub location problems arising in public transport. In: Kalcsics, Jörg, Nickel, Stefan (eds.) Oper. Re. Procee. 2007. Operations research proceedings, vol. 2007, pp. 129–134. Springer, Berlin Heidelberg (2008)

    Chapter  Google Scholar 

  15. Gonçalves, J.F., Resende, M.G.C.: Biased random-key genetic algorithms for combinatorial optimization. J. Heuristics 17, 487–525 (2011)

    Article  Google Scholar 

  16. Hakimi, S.L.: Optimum locations of switching centers and the absolute centers and medians of a graph. Oper. Res. 12(3), 450–459 (1964)

    Article  MATH  Google Scholar 

  17. Ishfaq, R., Sox, C.R.: Design of intermodal logistics networks with hub delays. Euro. J. Operat. Res. 220(3), 629–641 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Limbourg, S., Jourquin, B.: Optimal rail-road container terminal locations on the European network. Trans. Res. Part E Logist. Trans. Rev. 45(4), 551–563 (2009)

    Article  Google Scholar 

  19. O’Kelly, M.E.: A quadratic integer program for the location of interacting hub facilities. Euro. J. Operat. Res. 32, 393–404 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  20. Resende, M.G.C.: Biased random-key genetic algorithms with applications in telecommunications. TOP 20, 120–153 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Resende, M.G.C., Martí, R., Gallego, M., Duarte, A.: GRASP and path-relinking for the max-min diversity problem. Comp. Operat. Res. 37, 498–508 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ribeiro, C.C., Uchoa, E., Werneck, R.F.: A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS J. Comp. 14, 228–246 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. Ruiz, E., Albareda-Sambola, M., Fernández, E., Resende, M.G.C.: A biased random-key genetic algorithm for the capacitated minimum spanning tree problem. Comp. Operat. Res. 57, 95–108 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sá, E.M., Camargo, R.S., Miranda, G.: An improved Benders decomposition algorithm for the tree of hubs location problem. Euro. J. Operat. Res. 226(2), 185–202 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  25. Sá, E.M., Contreras, I., Cordeau, J.F.: Exact and heuristic algorithms for the design of hub networks with multiple lines. Euro. J. Operat. Res. 246(1), 186–198 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  26. Spears, W. M., DeJong, K. A.: On the virtues of parameterized uniform crossover. In Proceedings of the Fourth International Conference on Genetic Algorithms, pp 230–236 (1991)

  27. Wang, J.J., Cheng, M.C.: From a hub port city to a global supply chain management center: A case study of Hong Kong. J. Trans. Geograph 18(1), 104–115 (2010)

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, PUC-Rio, Rua Marquês de São Vicente, 225, Gávea, 22453-900, Rio de Janeiro, RJ, Brazil

    Luciana S. Pessoa

  2. ICD-LOSI, UMR CNRS 6281, Université de Technologie de Troyes, 12, rue Marie Curie, CS 42060, 10004, Troyes CEDEX, France

    Andréa C. Santos

  3. Mathematical Optimization and Planning (MOP), Amazon.com, Seattle, WA, 98109, USA

    Mauricio G. C. Resende

Authors
  1. Luciana S. Pessoa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andréa C. Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mauricio G. C. Resende
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luciana S. Pessoa.

Additional information

The research of Luciana S. Pessoa was partially supported by PNPD/Capes and PUC-Rio. The work of Mauricio G. C. Resende was done while he was employed by AT&T Labs Research.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pessoa, L.S., Santos, A.C. & Resende, M.G.C. A biased random-key genetic algorithm for the tree of hubs location problem. Optim Lett 11, 1371–1384 (2017). https://doi.org/10.1007/s11590-016-1082-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-016-1082-9

Keywords

Search

Navigation