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A cross entropy multiagent learning algorithm for solving vehicle routing problems with time windows

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  • Tai-Yu Ma

    (LET - Laboratoire d'économie des transports - UL2 - Université Lumière - Lyon 2 - ENTPE - École Nationale des Travaux Publics de l'État - CNRS - Centre National de la Recherche Scientifique)

Abstract

The vehicle routing problem with time windows (VRPTW) has been the subject of intensive study because of its importance in real applications. In this paper, we propose a cross entropy multiagent learning algorithm, which considers an optimum solution as a rare event to be learned. The routing policy is node-distributed, controlled by a set of parameterized probability distribution functions. Based on the performance of experienced tours of vehicle agents, these parameters are updated iteratively by minimizing Kullback-Leibler cross entropy in order to generate better solutions in next iterations. When applying the proposed algorithm on Solomon's 100-customer problem set, it shows outperforming results in comparison with the classical CE approach. Moreover, this method needs only very small number of parameter settings. Its implementation is also relatively simple and flexible to solve other vehicle routing problems under various dynamic scenarios.

Suggested Citation

  • Tai-Yu Ma, 2011. "A cross entropy multiagent learning algorithm for solving vehicle routing problems with time windows," Post-Print halshs-00592118, HAL.
    • Handle: RePEc:hal:journl:halshs-00592118
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00592118v2
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    References listed on IDEAS

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    1. T. Ibaraki & S. Imahori & M. Kubo & T. Masuda & T. Uno & M. Yagiura, 2005. "Effective Local Search Algorithms for Routing and Scheduling Problems with General Time-Window Constraints," Transportation Science, INFORMS, vol. 39(2), pages 206-232, May.
    2. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms," Transportation Science, INFORMS, vol. 39(1), pages 104-118, February.
    3. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part II: Metaheuristics," Transportation Science, INFORMS, vol. 39(1), pages 119-139, February.
    4. Marius M. Solomon, 1987. "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints," Operations Research, INFORMS, vol. 35(2), pages 254-265, April.
    5. Reuven Rubinstein, 1999. "The Cross-Entropy Method for Combinatorial and Continuous Optimization," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 127-190, September.
    6. Braysy, Olli & Hasle, Geir & Dullaert, Wout, 2004. "A multi-start local search algorithm for the vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 159(3), pages 586-605, December.
    7. G. A. Croes, 1958. "A Method for Solving Traveling-Salesman Problems," Operations Research, INFORMS, vol. 6(6), pages 791-812, December.
    8. Mads Jepsen & Bjørn Petersen & Simon Spoorendonk & David Pisinger, 2008. "Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows," Operations Research, INFORMS, vol. 56(2), pages 497-511, April.
    9. Homberger, Jorg & Gehring, Hermann, 2005. "A two-phase hybrid metaheuristic for the vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 162(1), pages 220-238, April.
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    Cited by:

    1. Liam Graham, 2011. "Individual rationality, model-consistent expectations and learning," CDMA Working Paper Series 201112, Centre for Dynamic Macroeconomic Analysis.

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