Beam-ACO Based on Stochastic Sampling for Makespan Optimization Concerning the TSP with Time Windows

  • Manuel López-Ibáñez
  • Christian Blum
  • Dhananjay Thiruvady
  • Andreas T. Ernst
  • Bernd Meyer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5482)

Abstract

The travelling salesman problem with time windows is a difficult optimization problem that appears, for example, in logistics. Among the possible objective functions we chose the optimization of the makespan. For solving this problem we propose a so-called Beam-ACO algorithm, which is a hybrid method that combines ant colony optimization with beam search. In general, Beam-ACO algorithms heavily rely on accurate and computationally inexpensive bounding information for differentiating between partial solutions. In this work we use stochastic sampling as an alternative to bounding information. Our results clearly demonstrate that the proposed algorithm is currently a state-of-the-art method for the tackled problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ohlmann, J.W., Thomas, B.W.: A compressed-annealing heuristic for the traveling salesman problem with time windows. INFORMS J. Comput. 19(1), 80–90 (2007)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Savelsbergh, M.W.P.: Local search in routing problems with time windows. Annals of Operations Research 4(1), 285–305 (1985)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cheng, C.B., Mao, C.P.: A modified ant colony system for solving the travelling salesman problem with time windows. Mathematical and Computer Modelling 46, 1225–1235 (2007)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Gambardella, L., Taillard, E.D., Agazzi, G.: MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 63–76. McGraw Hill, London (1999)Google Scholar
  5. 5.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)MATHGoogle Scholar
  6. 6.
    Blum, C.: Beam-ACO–hybridizing ant colony optimization with beam search: an application to open shop scheduling. Comp. & Op. Res. 32, 1565–1591 (2005)CrossRefMATHGoogle Scholar
  7. 7.
    Blum, C.: Beam-ACO for simple assembly line balancing. INFORMS J. Comput. 20(4), 618–627 (2008)CrossRefMATHGoogle Scholar
  8. 8.
    Ow, P.S., Morton, T.E.: Filtered beam search in scheduling. Int. J. Prod. Res. 26, 297–307 (1988)CrossRefGoogle Scholar
  9. 9.
    López-Ibáñez, M., Blum, C.: Beam-ACO based on stochastic sampling: A case study on the TSP with time windows. In: Battiti, R., et al. (eds.) Proceedings of LION3. LNCS. Springer, Berlin (2009)Google Scholar
  10. 10.
    Juillé, H., Pollack, J.B.: A sampling-based heuristic for tree search applied to grammar induction. In: Proceedings of AAAI 1998, pp. 776–783. MIT press, Cambridge (1998)Google Scholar
  11. 11.
    Ruml, W.: Incomplete tree search using adaptive probing. In: Proceedings of IJCAI 2001, pp. 235–241. IEEE press, Los Alamitos (2001)Google Scholar
  12. 12.
    Blum, C., Dorigo, M.: The hyper-cube framework for ant colony optimization. IEEE T. Syst. Man Cyb. – Part B 34(2), 1161–1172 (2004)CrossRefGoogle Scholar
  13. 13.
    Potvin, J.Y., Bengio, S.: The vehicle routing problem with time windows part II: Genetic search. INFORMS J. Comput. 8, 165–172 (1996)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Manuel López-Ibáñez
    • 1
  • Christian Blum
    • 1
  • Dhananjay Thiruvady
    • 2
    • 3
  • Andreas T. Ernst
    • 3
  • Bernd Meyer
    • 2
  1. 1.ALBCOM Research GroupUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Calyton School of Information TechnologyMonash UniversityAustralia
  3. 3.CSIRO Mathematics and Information SciencesAustralia

Personalised recommendations