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 cross entropy 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.
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References
Cordeau, J.F., Desaulniers, G., Desrosiers, J., Solomon, M.M., Soumis, F.: The VRP with time windows. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. SIAM Monographs on Discrete Mathematics and Applications, pp. 157–194 (2002)
Braysy, O., Gendreau, M.: Vehicle routing problem with time windows. Part I: Route Construction and Local Search Algorithms. Transportation Science 39, 104–118 (2005)
Braysy, O., Gendreau, M.: Vehicle routing problem with time windows. Part II: Metaheuristics. Transportation Science 39, 119–139 (2005)
Golden, B., Raghavan, S., Wasil, E. (eds.): The vehicle routing problem, latest advances and new challenges. Operations Research/Computer Science Interfaces Series, vol. 43. Springer, Berlin (2008)
Ibaraki, T., Imahori, S., Kubo, M., Masuda, T., Uno, T., Yagiura, M.: Effective local search algorithms for routing and scheduling problems with general time window constraints. Transportation Science 39(2), 206–232 (2005)
Hashimoto, H., Ibaraki, T., Imahori, S., Yagiura, M.: The vehicle routing problem with exible time windows and traveling times. Discrete Applied Mathematics 154, 2271–2290 (2006)
Pisinger, D., Ropke, S.: A general heuristic for vehicle routing problems. Computers & Operations Research 34, 2403–2435 (2007)
Braysy, O., Dullaert, W., Gendreau, M.: Evolutionary algorithms for the vehicle routing problem with time windows. Journal of Heuristics 10, 587–611 (2004)
Homberger, J., Gehring, H.: A two-phase hybrid metaheuristic for the vehicle routing problem with time windows. European Journal of Operational Research 162, 220–238 (2005)
Martin, O., Otto, S.W., Felten, E.W.: Large-step Markov chains for the TSP incorporating local search heuristic. Operation Research Letters 11, 219–224 (1992)
Hashimoto, H., Yagiura, M., Ibaraki, T.: An iterated local search algorithm for the time-dependent vehicle routing problem with time windows. Discrete Optimization 5, 434–456 (2008)
Helsgaun, K.: An effective implementation of the Lin-Kernighan traveling salesman heuristic. Datalogiske skrifter, Writings on Computer Science, no. 81. Roskilde University (1999)
Braysy, O., Hasle, G., Dullaert, W.: A multi-start local search algorithm for the vehicle routing problem with time windows. European Journal of Operational Research 159, 586–605 (2004)
Rubinstein, R.Y.: The Cross-Entropy Method for Combinatorial and Continuous Optimization. Methodology and Computing in Applied Probability 2, 127–190 (1999)
Irnich, S., Funke, B., Grunert, T.: Sequential search and its application to vehicle-routing problems. Computers & Operations Research 33, 2405–2429 (2006)
Barbucha, D., Jedrzejowicz, P.: Multi-agent platform for solving the dynamic vehicle routing problem. In: Proc.of 11th Int. IEEE Conf. on Intelligent Transportation Systems, pp. 517–522 (2008)
Vokrinek, J., Komenda, A., Pechoucek, M.: Agents Towards Vehicle Routing Problems. In: Proc. of 9th Int. Conf. on Autonomous Agents and Multiagent Systems, pp. 773–780 (2010)
Davidson, P., Henesey, L., Ramstedt, L., Tornquist, J., Wernstedt, F.: An analysis of agent-based approaches to transport logistics. Trans. Res. Part C 13, 255–271 (2005)
De Boer, P.T., Kroese, D.P., Mannor, S., Rubinstein, R.Y.: A Tutorial on the Cross-Entropy Method. Annals of Operations Research 134(1), 19–67 (2005)
Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research 35, 254–265 (1987)
Rubinstein, R.Y., Kroese, D.K.: Simulation and the Monte Carlo Method. Wiley Series in Probability and Statistics (2008)
Croes, G.: A method for solving traveling-salesman problems. Operations Research 6, 791–812 (1958)
Jepsen, M., Petersen, B., Spoorendonk, S., Pisinger, D.: Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows. Operations Research 56(2), 497–511 (2008)
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Ma, TY. (2011). A Cross Entropy Multiagent Learning Algorithm for Solving Vehicle Routing Problems with Time Windows. In: Böse, J.W., Hu, H., Jahn, C., Shi, X., Stahlbock, R., Voß, S. (eds) Computational Logistics. ICCL 2011. Lecture Notes in Computer Science, vol 6971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24264-9_5
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DOI: https://doi.org/10.1007/978-3-642-24264-9_5
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