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Decomposition Approach to Solve Dial-a-Ride Problems Using Ant Computing and Constraint Programming

  • Broderick Crawford
  • Carlos Castro
  • Eric Monfroy
  • Claudio Cubillos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4729)

Abstract

In this paper we solve the Dial-A-Ride Problem (DARP). The main objective of the DARP is to minimize operation costs for renting pieces of work from the transportation service providers. The resolution approach considered in this work, starting from a network formulation of the DARP, decomposes the problem in two phases: Clustering and Chaining. We model both phases like a Set Partitioning Problem (SPP) and solve them with an interesting sinergy between two different optimization methods: Ant Computing and Constraint Programming.

Keywords

Dial-A-Ride Problem Ant Colony Optimization Constraint Programming 

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References

  1. 1.
    Apt, K.R.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)Google Scholar
  2. 2.
    Balas, E., Padberg, M.: Set partitioning: A survey. SIAM Review 18, 710–760 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Balinski, M.L., Quandt, R.E.: On an integer program for a delivery problem. Operations Research 12(2), 300–304 (1964)Google Scholar
  4. 4.
    Beasley, J.E.: Or-library:distributing test problem by electronic mail. Journal of Operational Research Society 41(11), 1069–1072 (1990)CrossRefGoogle Scholar
  5. 5.
    Bessiere, C.: Constraint propagation. Technical Report 06020, LIRMM (March 2006), also in Rossi, F., van Beek, P., Walsh, T. (eds.) ch. 3 of the Handbook of Constraint Programming, Elsevier (2006)Google Scholar
  6. 6.
    Borndorfer, R., Grotschel, M., Klostermeier, F., Kuttner, C.: Telebus berlin: Vehicle scheduling in a dial-a-ride system. Technical Report SC 97-23, Konrad-Zuse-Zentrum fur Informationstechnik (1997)Google Scholar
  7. 7.
    Chu, P.C., Beasley, J.E.: Constraint handling in genetic algorithms: the set partitoning problem. Journal of Heuristics 4, 323–357 (1998)zbMATHCrossRefGoogle Scholar
  8. 8.
    Cordeau, J.-F.: A branch-and-cut algorithm for the dial-a-ride problem. Oper. Res. 54(3), 573–586 (2006)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Cordeau, J.-F., Laporte, G.: The dial-a-ride problem (darp): Variants, modeling issues and algorithms. Journal 4OR: A Quarterly Journal of Operations Research 1(2), 89–101 (2003)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Crawford, B., Castro, C., Monfroy, E.: A hybrid ant algorithm for the airline crew pairing problem. In: Gelbukh, A., Reyes-Garcia, C.A. (eds.) MICAI 2006. LNCS (LNAI), vol. 4293, pp. 381–391. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Dechter, R., Frost, D.: Backjump-based backtracking for constraint satisfaction problems. Artificial Intelligence 136, 147–188 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.): ANTS 2004. LNCS, vol. 3172. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    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
  14. 14.
    Dorigo, M., Stutzle, T.: Ant Colony Optimization. MIT Press, USA (2004)zbMATHGoogle Scholar
  15. 15.
    Focacci, F., Laburthe, F., Lodi, A.: Local search and constraint programming. In: Handbook of metaheuristics, Kluwer, Dordrecht (2002)Google Scholar
  16. 16.
    Gagne, C., Gravel, M., Price, W.: A look-ahead addition to the ant colony optimization metaheuristic and its application to an industrial scheduling problem. In: Sousa, J.P., et al. (eds.) MIC 2001. Proceedings of the fourth Metaheuristics International Conference, pp. 79–84 (July 2001)Google Scholar
  17. 17.
    Gandibleux, X., Delorme, X., T’Kindt, V.: An ant colony optimisation algorithm for the set packing problem. In: Dorigo, et al. [12], pp. 49–60Google Scholar
  18. 18.
    Gopal, R.D., Ramesh, R.: The query clustering problem: A set partitioning approach. IEEE Trans. Knowl. Data Eng. 7(6), 885–899 (1995)CrossRefGoogle Scholar
  19. 19.
    Hadji, R., Rahoual, M., Talbi, E., Bachelet, V.: Ant colonies for the set covering problem. In: Bosma, W. (ed.) Algorithmic Number Theory. LNCS, vol. 1838, pp. 63–66. Springer, Heidelberg (2000)Google Scholar
  20. 20.
    Kelly, J.P., Xu, J.: A set-partitioning-based heuristic for the vehicle routing problem. INFORMS J. on Computing 11(2), 161–172 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Kotecha, K., Sanghani, G., Gambhava, N.: Genetic algorithm for airline crew scheduling problem using cost-based uniform crossover. In: Manandhar, S., Austin, J., Desai, U., Oyanagi, Y., Talukder, A.K. (eds.) AACC 2004. LNCS, vol. 3285, pp. 84–91. Springer, Heidelberg (2004)Google Scholar
  22. 22.
    Leguizamón, G., Michalewicz, Z.: A new version of ant system for subset problems. In: CEC 1999. Congress on Evolutionary Computation, Piscataway, NJ, USA, pp. 1459–1464. IEEE Press, Los Alamitos (1999)Google Scholar
  23. 23.
    Lessing, L., Dumitrescu, I., Stützle, T.: A comparison between aco algorithms for the set covering problem. In: Dorigo, et al. [12], pp. 1–12Google Scholar
  24. 24.
    Levine, D.: A parallel genetic algorithm for the set partitioning problem. Technical Report ANL-94/23 Argonne National Laboratory (May 1994), available at http://citeseer.ist.psu.edu/levine94parallel.html
  25. 25.
    Maniezzo, V., Milandri, M.: An ant-based framework for very strongly constrained problems. In: Dorigo, M., Di Caro, G.A., Sampels, M. (eds.) Ant Algorithms. LNCS, vol. 2463, pp. 222–227. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  26. 26.
    Meyer, B., Ernst, A.: Integrating aco and constraint propagation. In: Dorigo, et al. [12], pp. 166–177Google Scholar
  27. 27.
    Michel, R., Middendorf, M.: An island model based ant system with lookahead for the shortest supersequence problem. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN V. LNCS, vol. 1498, pp. 692–701. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  28. 28.
    Savelsbergh, M.W.P.: The general pickup and delivery problem. Transportation Science 29(1), 17–29 (1995)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Broderick Crawford
    • 1
    • 2
  • Carlos Castro
    • 2
  • Eric Monfroy
    • 2
    • 3
  • Claudio Cubillos
    • 1
  1. 1.Pontificia Universidad Católica de ValparaísoChile
  2. 2.Universidad Técnica Federico Santa María, ValparaísoChile
  3. 3.LINA, Université de NantesFrance

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