Advertisement

A Comparison Between ACO Algorithms for the Set Covering Problem

  • Lucas Lessing
  • Irina Dumitrescu
  • Thomas Stützle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3172)

Abstract

In this paper we present a study of several Ant Colony Optimization (ACO) algorithms for the Set Covering Problem. In our computational study we emphasize the influence of different ways of defining the heuristic information on the performance of the ACO algorithms. Finally, we show that the best performing ACO algorithms we implemented, when combined with a fine-tuned local search procedure, reach excellent performance on a set of well known benchmark instances.

Keywords

Local Search Lagrangean Relaxation Pheromone Trail Heuristic Information Cover Cost 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balas, E., Carrera, M.C.: A dynamic subgradient-based branch and bound procedure for set covering. Operations Research 44(6), 875–890 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Beasley, J.E., Chu, P.C.: A genetic algorithm for the set covering problem. European Journal of Operational Research 94(2), 392–404 (1996)zbMATHCrossRefGoogle Scholar
  3. 3.
    Dorigo, M., Gambardella, L.M.: Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)CrossRefGoogle Scholar
  4. 4.
    Dorigo, M., Stützle, T.: The ant colony optimization metaheuristic: Algorithms, applications and advances. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 251–285. Kluwer, Dordrecht (2002)Google Scholar
  5. 5.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, USA (2004)zbMATHCrossRefGoogle Scholar
  6. 6.
    Eremeev, V.: A genetic algorithm with a non-binary representation for the set covering problem. In: Kall, P., Lüthi, H.-J. (eds.) Operations Research Proceedings1998, pp. 175–181. Springer, Heidelberg (1999)Google Scholar
  7. 7.
    Fisher, M.L.: The Lagrangean relaxation method for solving integer programming problems. Management Science 27(1), 1–17 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Hadji, R., Rahoual, M., Talbi, E., Bachelet, V.: Ant colonies for the set covering problem. In: Dorigo, M., et al. (eds.) Proceedings of ANTS 2000, pp. 63–66 (2000)Google Scholar
  9. 9.
    Housos, E., Elmoth, T.: Automatic optimization of subproblems in scheduling airlines crews. Interfaces 27(5), 68–77 (1997)CrossRefGoogle Scholar
  10. 10.
    Leguizamón, G., Michalewicz, Z.: Ant Systems for subset problems (2000) (Unpublished manuscript)Google Scholar
  11. 11.
    Lessing, L.: Ant colony optimization for the set covering problem. Master’s thesis, Fachgebiet Intellektik, Fachbereich Informatik, TU Darmstadt, Germany (2004)Google Scholar
  12. 12.
    Lourenço, H.R., Portugal, R., Paixão, J.P.: Multiobjective metaheuristics for the bus-driver scheduling problem. Transportation Science 35(3), 331–343 (2001)zbMATHCrossRefGoogle Scholar
  13. 13.
    Lourenço, H.R., Serra, D.: Adaptive search heuristics for the generalized assignment problem. Mathware & Soft Computing 9(2-3), 209–234 (2002)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Maniezzo, V.: Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem. INFORMS Journal on Computing 11(4), 358–369 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Marchiori, E., Steenbeek, A.: An evolutionary algorithm for large scale set covering problems with application to airline crew scheduling. In: Oates, M.J., Lanzi, P.L., Li, Y., Cagnoni, S., Corne, D.W., Fogarty, T.C., Poli, R., Smith, G.D. (eds.) EvoIASP 2000, EvoWorkshops 2000, EvoFlight 2000, EvoSCONDI 2000, EvoSTIM 2000, EvoTEL 2000, and EvoROB/EvoRobot 2000. LNCS, vol. 1803, pp. 367–381. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  16. 16.
    Stützle, T., Hoos, H.H.: MAX–MIN Ant System. Future Generation Computer Systems 16(8), 889–914 (2000)CrossRefGoogle Scholar
  17. 17.
    Stützle, T., Hoos, H.H.: MAX–MIN Ant System and local search for combinatorial optimization problems. In: Voss, S., et al. (eds.) Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pp. 137–154. Kluwer, Dordrecht (1999)Google Scholar
  18. 18.
    Vasko, F.J., Wolf, F.E.: Optimal selection of ingot sizes via set covering. Operations Research 35, 115–121 (1987)CrossRefGoogle Scholar
  19. 19.
    Yagiura, M., Kishida, M., Ibaraki, T.: A 3-flip neighborhood local search for the set covering problem. Technical Report #2004-001, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Lucas Lessing
    • 1
  • Irina Dumitrescu
    • 2
  • Thomas Stützle
    • 1
  1. 1.Intellectics GroupDarmstadt University of Technology 
  2. 2.Canada Research Chair in Distribution Management, HEC Montreal 

Personalised recommendations