DOI QR코드

DOI QR Code

Multi Objective Vehicle and Drone Routing Problem with Time Window

  • Park, Tae Joon (Dept. of Yonsei School of Business, Yonsei University) ;
  • Chung, Yerim (Dept. of Yonsei School of Business, Yonsei University)
  • 투고 : 2018.10.02
  • 심사 : 2018.12.28
  • 발행 : 2019.01.31

초록

In this paper, we study the multi-objectives vehicle and drone routing problem with time windows, MOVDRPTW for short, which is defined in an urban delivery network. We consider the dual modal delivery system consisting of drones and vehicles. Drones are used as a complement to the vehicle and operate in a point to point manner between the depot and the customer. Customers make various requests. They prefer to receive delivery services within the predetermined time range and some customers require fast delivery. The purpose of this paper is to investigate the effectiveness of the delivery strategy of using drones and vehicles together with a multi-objective measures. As experiment datasets, we use the instances generated based on actual courier delivery data. We propose a hybrid multi-objective evolutionary algorithm for solving MOVDRPTW. Our results confirm that the vehicle-drone mixed strategy has 30% cost advantage over vehicle only strategy.

키워드

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Fig. 1. Network Model for MOVDRPTW

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Fig. 2. Structure of HMOEA

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Fig. 3. Random Generation of Initial Solutions

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Fig. 4. Variable Length Chromosome in the HMOEA

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Fig. 5. Route Exchange Crossover

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Fig. 6. Pseudo Code of Pareto Ranking and Elitism

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Fig. 7. Off-set Local Search Range

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Fig. 8. Desired Time Window and Arrival Time of the Two Customers in the Off-set Relationship

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Fig. 9. Customer Locations in Songpagu in Seoul

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Fig. 10. Average total cost

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Fig. 11. Total costs and the number of used vehicles and drones in each of four Scenarios

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Fig. 12. Average Service Cost

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Fig. 13. Time Cost and Operating Cost

Table 1. The operating cost and time cost per customer in drone and vehicle route in the drone mixed strategy./ () indicated the value of upper 20% of EA population

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참고문헌

  1. C. C. Murray and A. G. Chu, "The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery", Transportation Research Part C: Emerging Technologies, Vol. 54, pp. 86-109, 2015. https://doi.org/10.1016/j.trc.2015.03.005
  2. N. Agatz, P. Bouman, and M. Schmidt, "Optimization approaches for the traveling salesman problem with drone", 2016.
  3. Q. M. Ha, Q. Y. Deville, Q. D. Pham, and M. H. Ha, "Heuristic methods for the Traveling Salesman Problem with Drone", arXiv preprint arXiv:1509.08764, 2015.
  4. Q. M. Ha, Q. Y. Deville, Q. D. Pham, and M.H. Ha, "On the Min-cost Traveling Salesman Problem with Drone". arXiv preprint arXiv:1509.08764, 2015.
  5. Y. Chung, T. Park, and Y. Min, "Usefulness of Drones in the Urban Delivery System: Solving the Vehicle and Drone Routing Problem with Time Window", Journal of the Korean Operations Research and Management Science Society, Vol.41 No.3 ,pp. 75-96, 2016. https://doi.org/10.7737/JKORMS.2016.41.3.075
  6. T. Back, "Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithm.", Oxford university press, 1996.
  7. G. Laporte, M. Gendreau, J. Y. Potvin, and F. Semet, "Classical and modern heuristics for the vehicle routing problem", International transactions in operational research, Vol. 7, No. 4-5, pp. 285-300, 2000. https://doi.org/10.1111/j.1475-3995.2000.tb00200.x
  8. B. Ombuki, B. J. Ross, and F. Hanshar, "Multi-objective genetic algorithms for vehicle routing problem with time windows", Applied Intelligence, Vol. 24, No. 1, pp. 17-30, 2006. https://doi.org/10.1007/s10489-006-6926-z
  9. O. Braysy, W. Dullaert, and M. Gendreau, "Evolutionary algorithms for the vehicle routing problem with time windows", Journal of Heuristics, Vol. 10, No. 6, pp.587-611, 2004. https://doi.org/10.1007/s10732-005-5431-6
  10. S. C. Hong, and Y. B. Park, "A heuristic for bi-objective vehicle routing with time window constraints", International Journal of Production Economics, Vol. 62, No. 3, pp. 249-258, 1999. https://doi.org/10.1016/S0925-5273(98)00250-3
  11. K. Deb, "Multi-Objective Optimization Using Evolutionary Algorithms", John Wiley& Sons. Inc., New York, NY, 2001.
  12. E. Zitzler, M. Laumanns, and L. Thiele, SPEA2, "Improving the strength Pareto evolutionary algorithm", 2001.
  13. E. G. Talbi, "Metaheuristics: from design to implementation", Vol. 74, John Wiley & Sons, 2009.
  14. C. A. C. Coello, G. B. Lamont, and D. A. Van Veldhuizen, "Evolutionary algorithms for solving multi-objective problems", (Vol. 5, New York: Springer, 2007.
  15. J. Berger, and M. Barkaoui, "A hybrid genetic algorithm for the capacitated vehicle routing problem", In Genetic and evolutionary computation conference, pp. 646-656. Springer Berlin Heidelberg, July 2003.
  16. K. C. Tan, T. H. Lee, Y. H. Chew, and L. H. Lee, "A multiobjective evolutionary algorithm for solving vehicle routing problem with time windows", In Systems, Man and Cybernetics, 2003. IEEE International Conference, Vol. 1, pp. 361-366. IEEE, October, 2003.
  17. O. Braysy, "Fast local searches for the vehicle routing problem with time windows", INFOR: Information Systems and Operational Research, Vol. 40, No. 4, pp. 319-330, 2002. https://doi.org/10.1080/03155986.2002.11732660
  18. E. Zitzler, and L. Thiele, "An evolutionary algorithm for multiobjective optimization: The strength pareto approach", 1998.
  19. W. Chaovalitwongse, D. Kim, and P. M. Pardalos, "GRASP with a new local search scheme for vehicle routing problems with time windows", Journal of Combinatorial Optimization, Vol. 7, No. 2, pp. 179-207, 2003. https://doi.org/10.1023/A:1024427114516
  20. F. Glover, "New ejection chain and alternating path methods for traveling salesman problems", Computer science and operations research, Vol. 449, pp. 491-507, 1992.