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An Adaptive Tabu Search Algorithm for the Open Vehicle Routing Problem with Split Deliveries by Order

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Abstract

In order to reduce the cost of logistics distribution, a capacitated open vehicle routing problem with split deliveries by order is studied. According to the actual situation of split deliveries by order in the practice of logistics distribution, the condition of non-split in the traditional open vehicle routing problem is relaxed, and a new form of discrete split deliveries by order is designed. Based on the classical model of open vehicle routing problem, a corresponding double objective mathematical model with split deliveries by order is established, and an adaptive tabu search algorithm is designed to solve the problem. In order to improve the optimization performance, an adaptive penalty mechanism is designed, a multiple neighborhood structure is constructed, and the tabu list is reinitialized. The comparison with other methods in the literature shows the effectiveness of the algorithm.

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References

  1. Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80–91.

    Article  MathSciNet  Google Scholar 

  2. Pu, E., Wang, F., Yang, Z. L., et al. (2017). Hybrid differential evolution optimization for the vehicle routing problem with time windows and driver-specific times. Wireless Personal Communications, 95(3), 2345–2357.

    Article  Google Scholar 

  3. Han, F. W., & Chu, Y. C. (2016). A multi-start heuristic approach for the split-delivery vehicle routing problem with minimum delivery amounts. Transportation Research Part E Logistics & Transportation Review., 88, 11–31.

    Article  Google Scholar 

  4. Fu, Z., Eglese, R., & Li, L. Y. O. (2005). A new tabu search heuristic for the open vehicle routing problem. Journal of the Operational Research Society, 56(3), 267–274.

    Article  Google Scholar 

  5. Xia, Y. K., Fu, Z., & Xie, J. Y. (2017). Material distribution route planning for multiple automated guided vehicles with split deliveries by order. Computer Integrated Manufacturing Systems, 23(7), 1520–1528. https://doi.org/10.13196/j.cims.2017.07.017. (in Chinese).

    Article  Google Scholar 

  6. Dror, M., & Trudeau, P. (2006). Savings by split delivery routing. Transportation Science, 23(2), 141–145.

    Article  Google Scholar 

  7. Archetti, C., Hertz, A., & Speranza, M. G. (2006). A tabu search algorithm for the split delivery vehicle routing problem. Transportation Science, 40(1), 64–73.

    Article  Google Scholar 

  8. Fu, Z., Eglese, R., & Li, L. Y. O. (2008). A unified tabu search algorithm for vehicle routing problems with soft time windows. Journal of the Operational Research Society, 59(5), 663–673.

    Article  Google Scholar 

  9. Archetti, C., Bianchessi, N., & Speranza, M. G. (2014). Branch-and-cut algorithms for the split delivery vehicle routing problem. European Journal of Operational Research, 238(3), 685–698.

    Article  MathSciNet  Google Scholar 

  10. Sariklis, D., & Powell, S. A. (2000). A heuristic method for the open vehicle routing problem. Journal of the Operational Research Society, 51(5), 564–573.

    Article  Google Scholar 

  11. Tarantilis, C. D., Diakoulaki, D., & Kiranoudis, C. T. (2004). Combination of geographical information system and efficient routing algorithms for real life distribution operations. European Journal of Operational Research, 152(2), 437–453.

    Article  Google Scholar 

  12. Tarantilis, C. D., Ioannou, G., Kiranoudis, C. T., et al. (2004). A threshold accepting approach to the open vehicle routing problem. Rairo Operations Research., 38(4), 345–360.

    Article  MathSciNet  Google Scholar 

  13. Tarantilis, C. D., Ioannou, G., Kiranoudis, C. T., et al. (2005). Solving the open vehicle routing problem via a single parameter metaheuristic algorithm. The Journal of Operational Research Society, 56(5), 588–596.

    Article  Google Scholar 

  14. Joseph, I. V., & Cavalier, T. M. (2012). A Genetic algorithm for the split delivery vehicle routing problem. American Journal of Operations Research, 2(2), 207–216.

    Article  Google Scholar 

  15. Berbotto, L., Garcia, S., & Nogales, F. J. (2014). A randomized granular tabu search heuristic for the split delivery vehicle routing problem. Annals of Operations Research, 222(1), 153–173.

    Article  MathSciNet  Google Scholar 

  16. Li, S. B., Chai, Y. M., & Wang, L. M. (2011). Research on split delivery open vehicle routing problem. Computer Engineering, 37(6), 168–171. https://doi.org/10.3969/j.issn.1000-3428.2011.06.064. (in Chinese).

    Article  Google Scholar 

  17. Sun, G. H. (2012). Modeling and algorithm for open vehicle routing problem with full-truckloads and time windows. Systems Engineering-Theory & Practice, 32(8), 1801–1807. https://doi.org/10.12011/1000-6788(2012)8-1801. (in Chinese).

    Article  Google Scholar 

  18. Salani, M., & Vacca, I. (2011). Branch and price for the vehicle routing problem with discrete split deliveries and time windows. European Journal of Operational Research, 213(3), 470–477.

    Article  MathSciNet  Google Scholar 

  19. Syslo, M., Deo, N., & Kowalski, J. S. (1983). Discrete optimization algorithms with pascal programs. New Jersey: Prentice Hall Inc.

    MATH  Google Scholar 

  20. Btandao, J. (2004). A tabu search algorithm for the open vehicle routing problem. European Journal of Operational Research, 157(3), 552–564.

    Article  MathSciNet  Google Scholar 

  21. Wang, X., Golden, B., & Gulczynski, D. (2014). A worst-case analysis for the split delivery capacitated team orienteering problem with minimum delivery amounts. Optimization Letters, 8(8), 2349–2356.

    Article  MathSciNet  Google Scholar 

  22. Lai, M., Battarra, M., Francesco, M. D., et al. (2015). An adaptive guidance meta-heuristic for vehicle routing problem with splits and clustered backhauls. Journal of the Operational Research Society, 66(7), 1222–1236.

    Article  Google Scholar 

  23. Yao, B., Yu, B., Hu, P., et al. (2016). An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot. Annals of Operations Research, 242(2), 1–18.

    Article  MathSciNet  Google Scholar 

  24. Fu, Z., Liu, W., & Qiu, M. (2017). A tabu search algorithm for the vehicle routing problem with soft time windows and split deliveries by order. Chinese Journal of Management Science, 25(5), 78–86. https://doi.org/10.16381/j.cnki.issn1003-207x.2017.05.010. (in Chinese).

    Article  Google Scholar 

  25. Brito, J., Martinez, F. J., Moreno, J. A., et al. (2015). An ACO hybrid metaheuristic for close-open vehicle routing problems with time windows and fuzzy constraints. Applied Soft Computing, 32, 154–163.

    Article  Google Scholar 

  26. Wang, Y., Ma, X. L., Lao, Y. T., et al. (2014). A fuzzy-based customer clustering approach with hierarchical structure for logistics network optimization. Expert Systems with Applications, 41(2), 521–534.

    Article  Google Scholar 

  27. Wang, Y., Ma, X. L., Xu, M. Z., et al. (2015). Two-echelon logistics distribution region partitioning problem based on a hybrid particle swarm optimization-genetic algorithm. Expert Systems with Applications, 42(12), 5019–5031.

    Article  Google Scholar 

  28. Alemayehu, T. S., & Kim, J. H. (2017). Efficient nearest neighbor heuristic TSP algorithms for reducing data acquisition latency of UAV relay WSN. Wireless Personal Communications, 95(3), 3271–3285.

    Article  Google Scholar 

  29. Rabik, M. M., & Balasubada, K. (2017). Distributive aware probabilistic back propagation (DAPBP) routing scheme for vehicular networks. Wireless Personal Communications, 97(1), 483–493.

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge the China Society of Logistics (Grant 2016CSLKT3-077), the Fundamental Research Funds for the Central Universities (Grant 2017zzts198).

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Authors and Affiliations

  1. School of Traffic and Transportation Engineering, Central South University, Changsha, 410075, Hunan, China

    Yangkun Xia & Zhuo Fu

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  1. Yangkun Xia
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  2. Zhuo Fu
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Correspondence to Yangkun Xia.

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Xia, Y., Fu, Z. An Adaptive Tabu Search Algorithm for the Open Vehicle Routing Problem with Split Deliveries by Order. Wireless Pers Commun 103, 595–609 (2018). https://doi.org/10.1007/s11277-018-5464-4

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