Skip to main content
SpringerLink
Log in

Solution approaches for the capacitated single allocation hub location problem using ant colony optimisation

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

Hub and spoke type networks are often designed to solve problems that require the transfer of large quantities of commodities. This can be an extremely difficult problem to solve for constructive approaches such as ant colony optimisation due to the multiple optimisation components and the fact that the quadratic nature of the objective function makes it difficult to determine the effect of adding a particular solution component. Additionally, the amount of traffic that can be routed through each hub is constrained and the number of hubs is not known a-priori. Four variations of the ant colony optimisation meta-heuristic that explore different construction modelling choices are developed. The effects of solution component assignment order and the form of local search heuristics are also investigated. The results reveal that each of the approaches can return optimal solution costs in a reasonable amount of computational time. This may be largely attributed to the combination of integer linear preprocessing, powerful multiple neighbourhood local search heuristic and the good starting solutions provided by the ant colonies.

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. Abdinnour-Helm, S., Venkataramanan, M.: Solution approaches to hub location problems. Ann. Oper. Res. 78, 31–50 (1998)

    Article  MATH  Google Scholar 

  2. Beasley, J.: OR-Library. Online at http://people.brunel.ac.uk/~mastjjb/jeb/info.html (2005)

  3. Blum, C., Dorigo, M.: The hyper-cube framework for ant colony optimization. Trans. Syst. Man Cybern. B 34, 1161–1172 (2004)

    Article  Google Scholar 

  4. Boland, N., Ebery, J., Ernst, A., Krishnamoorthy, M.: The capacitated multiple allocation hub location problem: Formulations and algorithms. J. Oper. Res. 120, 614–631 (2000)

    Article  MATH  Google Scholar 

  5. Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Sante Fe Institute Studies in the Science of Complexity, Oxford University Press, New York (1999)

    MATH  Google Scholar 

  6. Burkard, R.: Quadratic assignment problems. Eur. J. Oper. Res. 15, 283–289 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  7. Campbell, J.: Integer programming formulations of discrete hub location problems. Eur. J. Oper. Res. 72, 387–405 (1994)

    Article  MATH  Google Scholar 

  8. Campbell, J.: Hub location and the p-hub median problem. Oper. Res. 44, 923–935 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  9. Carello, G., Yaman, H.: Solving the hub location problem with integer links. Technical Report IEOR-2003-08, Department of Industrial Engineering, Bilkent University, Turkey (2003)

  10. Chamberland, S., Sanso, B., Marcotte, O.: Topological design of two-level telecommunication networks with modular switches. Oper. Res. 48, 745–760 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Cheung, B., Langevin, A., Villeneuve, B.: High performing evolutionary techniques for solving complex location problems in industrial system design. J. Intell. Manaf. 12, 455–466 (2001)

    Article  Google Scholar 

  12. Chu, P., Beasley, J.: A genetic algorithm for the generalised assignment problem. Comput. Oper. Res. 24, 17–23 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Costa, D., Hertz, A.: Ants can colour graphs. J. Oper. Res. Soc. 48, 295–305 (1997)

    Article  MATH  Google Scholar 

  14. Dorigo, M., Di Caro, G.: Ant colony optimization: a new meta-heuristic. In: Congress on Evolutionary Computation, vol. 2, pp. 1470–1477 (1999)

  15. Dorigo, M., Gambardella, L.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1(1), 53–66 (1997)

    Article  Google Scholar 

  16. Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: an autocatalytic optimizing process. Technical Report 91-016 Revised, Politecnico di Milano (1991)

  17. Dorigo, M., Maniezzo, V., Colorni, A.: The ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B 26(1), 1–13 (1996)

    Article  Google Scholar 

  18. Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Boston (2004)

    MATH  Google Scholar 

  19. Ernst, A., Krishnamoorthy, M.: Efficient algorithms for the uncapacitated single allocation p-hub problem. Locat. Sci. 4, 139–154 (1996)

    Article  MATH  Google Scholar 

  20. Ernst, A., Krishnamoorthy, M.: Efficient algorithms for the uncapacitated multiple allocation p-hub median problem. Eur. J. Oper. Res. 104, 100–112 (1998)

    Article  MATH  Google Scholar 

  21. Ernst, A., Krishnamoorthy, M.: Solution algorithms for the capacitated single allocation hub location problem. Ann. Oper. Res. 86, 141–159 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  22. Fotheringham, A.: A new set of spatial interaction models: the theory of competing distances. Environ. Plan. A 15, 15–36 (1983)

    Article  Google Scholar 

  23. Gambardella, L., Taillard, E., Dorigo, M.: Ant colonies for the quadratic assignment problem. J. Oper. Res. Soc. 50, 167–176 (1999)

    Article  MATH  Google Scholar 

  24. Glover, F., Laguna, M.: Tabu Search. Kluwer Academic, Boston (1997)

    MATH  Google Scholar 

  25. Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  26. Hansen, P., Mladenovic, N., Pierez-Brito, D.: Variable neighborhood decomposition search. J. Heuristics 7, 335–350 (2001)

    Article  MATH  Google Scholar 

  27. Hendtlass, T., Randall, M.: A survey of ant colony and particle swarm meta-heuristics and their application to discrete optimisation problems. In: Proceedings of the Inaugual Workshop on Artificial Life, Adelaide, Australia, pp. 15–25 (2001)

  28. Klincewicz, J.: Heuristics for the p-hub location problem. Eur. J. Oper. Res. 53, 25–37 (1991)

    Article  MATH  Google Scholar 

  29. Klincewicz, J.: Avoiding local optima in the p-hub location problem using tabu search and GRASP. Ann. Oper. Res. 40, 283–302 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  30. Lawler, E., Lenstra, J., Rinnoy, A., Shmoys, D.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley, Chichester (1990)

    Google Scholar 

  31. Love, R., Morris, J., Wesolowsky, G.: Facility Location: Models and Methods. Publications in Operations Research, vol. 7. North-Holland, New York (1988)

    Google Scholar 

  32. Montgomery, J., Randall, M., Hendtlass, T.: Search bias in constructive metaheuristics and implications for ant colony optimisation. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L., Mondada, F., Stützle, T. (eds.) Fourth International Workshop on Ant Algorithms. Lecture Notes in Computer Science, vol. 3172, pp. 390–397. Springer, New York (2004)

    Google Scholar 

  33. O’Kelly, M.: The location of interacting hub facilities. Transp. Sci. 20, 96–106 (1986)

    Google Scholar 

  34. O’Kelly, M.: A quadratic integer program for the location of interacting hub facilities. Eur. J. Oper. Res. 32, 393–404 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  35. Osman, I.: Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Ann. Oper. Res. 41, 421–451 (1993)

    Article  MATH  Google Scholar 

  36. Pamuk, F., Sepil, C.: A solution to the hub center problem via a single relocation algorithm with tabu search. IIE Trans. 33, 399–411 (2001)

    Google Scholar 

  37. Randall, M.: Scheduling aircraft landings using ant colony optimisation. In: Sixth IASTED International Conference Artificial Intelligence and Soft Computing, Banff, Canada, pp. 129–133 (2002)

  38. Randall, M.: Heuristics for ant colony optimisation using the generalised assignment problem. In: Proceedings of the Congress on Evolutionary Computing, Portland, Oregon, USA, pp. 1916–1923 (2004)

  39. Roli, A., Blum, C., Dorigo, M.: ACO for maximal constraint satisfaction problems. In: Fourth Metaheuristics International Conference (2001)

  40. Skorin-Kapov, D., Skorin-Kapov, J.: On tabu search for the location of interacting hub facilities. Eur. J. Oper. Res. 73, 502–509 (1994)

    Article  MATH  Google Scholar 

  41. Skorin-Kapov, D., Skorin-Kapov, J.: Tight linear programming relaxations of uncapacitated p-hub median problems. Eur. J. Oper. Res. 984, 582–593 (1994)

    Google Scholar 

  42. Smith, K., Krishnamoorthy, M., Palaniswami, M.: Neural versus traditional approaches to the location of interacting hub facilities. Locat. Sci. 4, 155–171 (1996)

    Article  MATH  Google Scholar 

  43. Solnon, C.: Ants can solve constraint satisfaction problems. IEEE Trans. Evol. Comput. 6, 347–357 (2002)

    Article  Google Scholar 

  44. Stützle, T., Hoos, H.: Improvements on the ant-system: introducing the \(\mathcal{MAX}{-}\mathcal{MIN}\) ant system. In: Proceedings of the Third International Conference on Artificial Neural Networks and Genetic Algorithms, pp. 245–249 (1997)

  45. Stützle, T., Hoos, H.: The \(\mathcal{MAX}{-}\mathcal{MIN}\) ant system and local search for combinatorial optimization problems. In: Voss, S., Martello, S., Osman, I., Roucairol, C. (eds.) Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pp. 313–329. Kluwer Academic, Boston (1998)

    Google Scholar 

  46. Stützle, T., Hoos, H.: \(\mathcal{MAX}{-}\mathcal{MIN}\) ant system. Futur. Gener. Comput. Syst. 16, 889–914 (2000)

    Article  Google Scholar 

  47. Taillard, E., Gambardella, L.: Adaptive memories for the quadratic assignment problem. Technical Report IDSIA-87-97, Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (1997)

Download references

Author information

Authors and Affiliations

  1. School of Information Technology, Bond University, Gold Coast, QLD, 4229, Australia

    Marcus Randall

Authors
  1. Marcus Randall
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcus Randall.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Randall, M. Solution approaches for the capacitated single allocation hub location problem using ant colony optimisation. Comput Optim Appl 39, 239–261 (2008). https://doi.org/10.1007/s10589-007-9069-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-007-9069-1

Keywords

Search

Navigation