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A general variable neighborhood search for the one-commodity pickup-and-delivery travelling salesman problem

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  • Mladenović, Nenad
  • Urošević, Dragan
  • Hanafi, Saı¨d
  • Ilić, Aleksandar
Abstract
We present a variable neighborhood search approach for solving the one-commodity pickup-and-delivery travelling salesman problem. It is characterized by a set of customers such that each of the customers either supplies (pickup customers) or demands (delivery customers) a given amount of a single product, and by a vehicle, whose given capacity must not be exceeded, that starts at the depot and must visit each customer only once. The objective is to minimize the total length of the tour. Thus, the considered problem includes checking the existence of a feasible travelling salesman’s tour and designing the optimal travelling salesman’s tour, which are both NP-hard problems. We adapt a collection of neighborhood structures, k-opt, double-bridge and insertion operators mainly used for solving the classical travelling salesman problem. A binary indexed tree data structure is used, which enables efficient feasibility checking and updating of solutions in these neighborhoods. Our extensive computational analysis shows that the proposed variable neighborhood search based heuristics outperforms the best-known algorithms in terms of both the solution quality and computational efforts. Moreover, we improve the best-known solutions of all benchmark instances from the literature (with 200 to 500 customers). We are also able to solve instances with up to 1000 customers.

Suggested Citation

  • Mladenović, Nenad & Urošević, Dragan & Hanafi, Saı¨d & Ilić, Aleksandar, 2012. "A general variable neighborhood search for the one-commodity pickup-and-delivery travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 220(1), pages 270-285.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:1:p:270-285
    DOI: 10.1016/j.ejor.2012.01.036
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    References listed on IDEAS

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    Cited by:

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    9. Masmoudi, Mohamed Amine & Hosny, Manar & Demir, Emrah & Genikomsakis, Konstantinos N. & Cheikhrouhou, Naoufel, 2018. "The dial-a-ride problem with electric vehicles and battery swapping stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 392-420.
    10. Dell’Amico, Mauro & Iori, Manuel & Novellani, Stefano & Subramanian, Anand, 2018. "The Bike sharing Rebalancing Problem with Stochastic Demands," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 362-380.
    11. Nair, D.J. & Grzybowska, H. & Fu, Y. & Dixit, V.V., 2018. "Scheduling and routing models for food rescue and delivery operations," Socio-Economic Planning Sciences, Elsevier, vol. 63(C), pages 18-32.
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    13. Baoyu Liao & Qingru Song & Jun Pei & Shanlin Yang & Panos M. Pardalos, 2020. "Parallel-machine group scheduling with inclusive processing set restrictions, outsourcing option and serial-batching under the effect of step-deterioration," Journal of Global Optimization, Springer, vol. 78(4), pages 717-742, December.
    14. Divya J. Nair & David Rey & Vinayak V. Dixit, 2017. "Fair allocation and cost-effective routing models for food rescue and redistribution," IISE Transactions, Taylor & Francis Journals, vol. 49(12), pages 1172-1188, December.
    15. Venkatesh Pandiri & Alok Singh, 2020. "Two multi-start heuristics for the k-traveling salesman problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1164-1204, December.
    16. Juan D. Palacio & Juan Carlos Rivera, 2022. "A multi-start evolutionary local search for the one-commodity pickup and delivery traveling salesman problem," Annals of Operations Research, Springer, vol. 316(2), pages 979-1011, September.
    17. Dell'Amico, Mauro & Hadjicostantinou, Eleni & Iori, Manuel & Novellani, Stefano, 2014. "The bike sharing rebalancing problem: Mathematical formulations and benchmark instances," Omega, Elsevier, vol. 45(C), pages 7-19.
    18. Bruno P. Bruck & Fábio Cruz & Manuel Iori & Anand Subramanian, 2019. "The Static Bike Sharing Rebalancing Problem with Forbidden Temporary Operations," Transportation Science, INFORMS, vol. 53(3), pages 882-896, May.
    19. Todosijević, Raca & Benmansour, Rachid & Hanafi, Saïd & Mladenović, Nenad & Artiba, Abdelhakim, 2016. "Nested general variable neighborhood search for the periodic maintenance problem," European Journal of Operational Research, Elsevier, vol. 252(2), pages 385-396.
    20. Xiao, Yiyong & Zhang, Renqian & Zhao, Qiuhong & Kaku, Ikou & Xu, Yuchun, 2014. "A variable neighborhood search with an effective local search for uncapacitated multilevel lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 102-114.
    21. Hernández-Pérez, Hipólito & Salazar-González, Juan-José, 2022. "A Branch-and-cut algorithm for the split-demand one-commodity pickup-and-delivery travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 297(2), pages 467-483.
    22. Lei, Chao & Ouyang, Yanfeng, 2018. "Continuous approximation for demand balancing in solving large-scale one-commodity pickup and delivery problems," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 90-109.
    23. Xiao, Yiyong & Konak, Abdullah, 2016. "The heterogeneous green vehicle routing and scheduling problem with time-varying traffic congestion," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 88(C), pages 146-166.
    24. Xu, Dongyang & Li, Kunpeng & Zou, Xuxia & Liu, Ling, 2017. "An unpaired pickup and delivery vehicle routing problem with multi-visit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 218-247.

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