Abstract
A branch-and-price based heuristic algorithm (B&P_HA) is presented to solve the vehicle routing problem with soft time window (VRPSTW), whose objective is to minimize the total cost. In the B&P_HA, the linear problem (LP) relaxation of the set partitioning reformulation of the VRPSTW is solved by column generation. Specifically, a heuristic algorithm with greedy rules is firstly developed to construct initial columns, and then feasible columns are generated by using the special designed label correcting algorithm to solve the pricing subproblem (i.e., the single vehicle pricing subproblem). Furthermore, the branching scheme introduced is implemented when the LP's solution is fractional. Experimental results show that the B&P_HA algorithm outperforms the traditional branch-and-price algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
He, M., Wei, Z., Wu, X., et al.: An adaptive variable neighborhood search ant colony algorithm for vehicle routing problem with soft time windows. IEEE Access 9, 21258–21266 (2021)
Salehi Sarbijan, M., Behnamian, J.: Emerging research fields in vehicle routing problem: a short review. Archives Comput. Methods Eng. 30(4), 2473–2491 (2023)
Sexton, T.R., Choi, Y.M.: Pickup and delivery of partial loads with “soft” time windows. Am. J. Math. Manag. Sci. 6(3–4), 369–398 (1986)
Liberatore, F., Righini, G., Salani, M.: A column generation algorithm for the vehicle routing problem with soft time windows. 4OR 9, 49–82 (2011)
Bettinelli, A., Ceselli, A., Righini, G.: A branch-and-price algorithm for the multi-depot heterogeneous-fleet pickup and delivery problem with soft time windows. Math. Program. Comput. 6, 171–197 (2014)
Abdallah, K.S., Jang, J.: An exact solution for vehicle routing problems with semi-hard resource constraints[J]. Comput. Ind. Eng. 76, 366–377 (2014)
Taş, D., Gendreau, M., Dellaert, N., et al.: Vehicle routing with soft time windows and stochastic travel times: A column generation and branch-and-price solution approach. Eur. J. Oper. Res. 236(3), 789–799 (2014)
Wang, Z., Zeng, Q., Li, X., et al.: A branch-and-price heuristic algorithm for the ART and external truck scheduling problem in an automated container terminal with a parallel layout. Trans. Res. Part E: Logist. Trans. Rev. 184, 103464 (2024)
Yuan, Y., Cattaruzza, D., Ogier, M., et al.: A column generation based heuristic for the generalized vehicle routing problem with time windows. Trans. Res. Part E: Logist. Trans. Rev. 152, 102391 (2021)
Hosoda, J., Maher, S.J., Shinano, Y., et al.: A parallel branch-and-bound heuristic for the integrated long-haul and local vehicle routing problem on an adaptive transportation network. Comput. Operat. Res., 106570 (2024)
Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35(2), 254–265 (1987)
Han, Y.J., Peng, Y.F., Wei, H., et al.: Hyper-heuristic genetic algorithm for vehicle routing problem with soft time windows. Comput. Integr. Manuf. Syst. 25(10), 2571–2579 (2019)
Dror, M.: Note on the complexity of the shortest path models for column generation in VRPTW. Oper. Res. 42(5), 977–978 (1994)
Feillet, D., Dejax, P., Gendreau, M., et al.: An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems. Netw. Inter. J. 44(3), 216–229
Desrochers, M.: An algorithm for the shortest path problem with resource constraints. École des hautes études commerciales, Groupe d'études et de recherche en analyse des décisions (1988)
Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res.. Res. 8(1), 101–111 (1960)
Acknowledgement
This research was supported by the National Natural Science Foundation of China (62173169, 72362026) and the Basic Research Key Project of Yunnan Province (202201AS0700 30).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Li, H., Qian, B., Yu, Nk., Hu, R., Li, Zc. (2024). A Branch-and-Price Heuristic Algorithm for Vehicle Routing Problem with Soft Time Windows. In: Huang, DS., Zhang, X., Chen, W. (eds) Advanced Intelligent Computing Technology and Applications. ICIC 2024. Lecture Notes in Computer Science, vol 14862. Springer, Singapore. https://doi.org/10.1007/978-981-97-5578-3_36
Download citation
DOI: https://doi.org/10.1007/978-981-97-5578-3_36
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-97-5577-6
Online ISBN: 978-981-97-5578-3
eBook Packages: Computer ScienceComputer Science (R0)