Integrated optimization of train routing and timetable of rail transit network with time-varying passenger demand
DOI:
https://doi.org/10.61089/aot2025.ym9m9956Keywords:
Rail transit network, Time-varying passenger demand, Train timetable, Train routing plan, Enumeration algorithm, Pareto optimalityAbstract
Urban rail transit is operated with network scenario mostly. Train routing determines spatial service range on the network, which will affect whether passengers transfer during the trip. Timetable determines arrival and departure time of each train at each station. To achieve balance between demand and supply and enhance service quality, simultaneous optimization of train routing and timetable is of significant importance for rail companies with the network. This will reduce the waiting time of passengers effectively, and the stations where train serve will be convenient for most passengers. However, existing studies in train operation planning with time-varying passenger demand haven’t addressed this aspect adequately. To bridge this gap, we develop an integrated optimization model for the Train Routing and Timetable Problem (TRTP) within a rail transit network, considering the dynamic of passenger demand and passenger path choice. Our objective is to minimize the operating costs for companies and to reduce the total waiting time experienced by passengers. The constrains of TRTP include time constraint, path constraint and train constraint. What’s more, the compatibility of headways on different routings is the focus when modeling. To verify the effectiveness of our proposed model, we conduct a numerical experiment with CPLEX. After that, the results of integrated optimization and staged optimization are compared to show the beneficial of integration with train routing and timetable. Moreover, we devise an algorithm tailored to this problem to solve the model, and a network case study is presented. As a case study, we apply the model to Guangzhou Metro Line 3 to validate its performance further, which is a Y-type line, the most common example of operation with network of urban rail transit in China. The results of our study demonstrate that the proposed integrated optimization model can achieve a reduction in operating costs and total waiting time for passengers effectively, providing convenience for passenger travel.
References
1. Cacchiani, V., Qi, J. & Yang, L. (2020). Robust optimization models for integrated train stop planning and timetabling with passenger demand uncertainty, Transportation Research Part B: Methodological, 136, 1-29. https://doi.org/10.1016/j.trb.2020.03.009
2. Canca, D., Barrena, E., De-Los-Santos, A. & Andrade-Pineda, J. (2016). Setting lines frequency and capacity in dense railway rapid transit networks with simultaneous passenger Assignment, Transportation Research Part B: Methodological, 93, 251-267. https://doi.org/10.1016/j.trb.2016.07.020
3. Cats, O. & Haverkamp, J. (2018). Optimal infrastructure capacity of automated on-demand rail-bound transit systems, Transportation Research Part B: Methodological, 117, 378-392. https://doi.org/10.1016/j.trb.2018.09.012
4. Ceder, A., Golany, B. & Tal, O. (2001). Creating bus timetables with maximal synchronization, Transportation Research Part A: Policy and Practice, 35(10), 913-928. https://doi.org/10.1016/S0965-8564(00)00032-X
5. Claessens, M., van Dijk, N. & Zwaneveld, P. (1998). Cost optimal allocation of rail passenger lines, European Journal of Operational Research, 110(3), 474-489. https://doi.org/10.1016/S0377-2217(97)00271-3
6. Dong, X., Li, D., Yin, Y., Ding, S. & Cao, Z. (2020). Integrated optimization of train stop planning and timetabling for commuter railways with an extended adaptive large neighborhood search metaheuristic approach, Transportation Research Part C: Emerging Technologies, 117, 102681. https://doi.org/10.1016/j.trc.2020.102681
7. Gao, Y., Schmidt, M., Yang, L. & Gao, Z. (2020). A branch-and-price approach for trip sequence planning of high-speed train units, Omega, 92, 102150. https://doi.org/10.1016/j.omega.2019.102150
8. Gong, C., Shi, J., Wang, Y., Zhou, H., Yang, L., Chen, D. & Pan, H. (2021). Train timetabling with dynamic and random passenger demand: A stochastic optimization method, Transportation Research Part C: Emerging Technologies, 123(1), 102963. https://doi.org/10.1016/j.trc.2021.102963
9. Goossens, J., van Hoesel, S. & Kroon, L. (2006). On solving multi-type railway line planning problems, European Journal of Operational Research, 168(2), 403-424. https://doi.org/10.1016/j.ejor.2004.04.036
10. Ibarra-Rojas, O. & Rios-Solis, Y. (2012). Synchronization of bus timetabling, Transportation Research Part B: Methodological, 46(5), 599-614. https://doi.org/10.1016/j.trb.2012.01.006
11. Kang, L., Zhu, X., Sun, H., Puchinger, J., Ruthmair, M. & Hu, B. (2016). Modeling the first train timetabling problem with minimal missed trains and synchronization time differences in subway networks, Transportation Research Part B: Methodological, 93, 17-36. https://doi.org/10.1016/j.trb.2016.07.006
12. Li, H., Chen, J. & He, S. (2021). The feeder-vehicle routing and high-speed-train assignment problem with time windows, Research in Transportation Business & Management, 38, 100521. https://doi.org/10.1016/j.rtbm.2020.100521
13. Lv, H., Zhang, Y., Huang, K., Yu, X. & Wu, J. (2019). An Energy-Efficient Timetable Optimization Approach in a Bi-Direction Urban Rail Transit Line: A Mixed-Integer Linear Programming Model, Energies, 12(14), 2686. https://doi.org/10.3390/en12142686
14. Meng, F., Yang, L., Wei, Y., Li, S., Gao, Z. & Shi, J. (2020). Collaborative passenger flow control on an oversaturated metro line: a path choice approach, Transportmetrica B: Transport Dynamics, 8(1), 376-404. https://doi.org/10.1080/21680566.2020.1777219
15. Mo, P., Yang, L., Wang, Y. & Qi, J. (2019). A flexible metro train scheduling approach to minimize energy cost and passenger waiting time, Computers & Industrial Engineering, 132, 412-432. https://doi.org/10.1016/j.cie.2019.04.031
16. Niu, H., Tian, X. & Zhou, X. (2015). Demand-driven train schedule synchronization for high-speed rail lines, IEEE Transactions on Intelligent Transportation Systems, 16(5), 2642-2652. https://doi.org/10.1109/TITS.2015.2415513
17. Polinder, G., Schmidt, M. & Huisman, D. (2021). Timetabling for strategic passenger railway planning, Transportation Research Part B: Methodological, 146, 111-135. https://doi.org/10.1016/j.trb.2021.02.006
18. Qi, J., Cacchiani, V., Yang, L., Zhang, C. & Di Z. (2021). An Integer Linear Programming model for integrated train stop planning and timetabling with time-dependent passenger demand, Computers & Operations Research, 136, 105484. https://doi.org/10.1016/j.cor.2021.105484
19. Robenek, T., Maknoon, Y., Azadeh, S., Chen, J. & Bierlaire, M. (2016). Passenger centric train timetabling problem, Transportation Research Part B: Methodological, 89, 107-126. https://doi.org/10.1016/j.trb.2016.04.003
20. Shakibayifar, M., Sheikholeslami, A. & Jamili, A. (2018). A multi-objective decision support system for real-time train rescheduling, IEEE Intelligent Transportation Systems Magazine, 10(3), 94-109. https://doi.org/10.1109/MITS.2018.2842037
21. Shang, P., Li, R., Liu, Z., Xian, K. & Guo, J. (2018). Timetable synchronization and optimization considering time-dependent passenger demand in an urban subway network, Transportation Research Record, 2672(8), 243-254. https://doi.org/10.1177/0361198118772958
22. Su, S., Tang, T., Xun, J., Cao, F. & Wang, Y. (2021). Design of running grades for energy-efficient train regulation: A case study for Beijing Yizhuang Line, IEEE Intelligent Transportation Systems Magazine, 13(2), 189-200. https://doi.org/10.1109/MITS.2019.2907681
23. Sun, Y., Cao, C. & Wu, C. (2014). Multi-objective optimization of train routing problem combined with train scheduling on a high-speed railway network, Transportation Research Part C: Emerging Technologies, 44, 1-20. https://doi.org/10.1016/j.trc.2014.02.023
24. Szeto, W. & Wu, Y. (2011). A simultaneous bus route design and frequency setting problem for Tin Shui Wai, Hong Kong, European Journal of Operational Research, 209(2), 141-155. https://doi.org/10.1016/j.ejor.2010.08.020
25. Tian, X. & Niu, H. (2020). Optimization of demand-oriented train timetables under overtaking operations: A surrogate-dual-variable column generation for eliminating indivisibility, Transportation Research Part B: Methodological, 142, 143-173. https://doi.org/10.1016/j.trb.2020.09.010
26. Wang, Y., D’Ariano, A., Yin, J., Meng, L., Tang, T. & Bin, N. (2018). Passenger demand oriented train scheduling and rolling stock circulation planning for an urban rail transit line, Transportation Research Part B: Methodological, 118, 193-227. https://doi.org/10.1016/j.trb.2018.10.006
27. Wang, Y., Li, D. & Cao, Z. (2020). Integrated timetable synchronization optimization with capacity constraint under time-dependent demand for a rail transit network, Computers & Industrial Engineering, 142, 106374. https://doi.org/10.1016/j.cie.2020.106374
28. Wong, R., Yuen, T., Fung, K. & Leung, J. (2008). Optimizing timetable synchronization for rail mass transit, Transportation Science, 42(1), 57-69. https://doi.org/10.1287/trsc.1070.0200
29. Wu, J., Liu, M., Sun, H., Li, T., Gao, Z. & Wang, D. (2015). Equity-based timetable synchronization optimization in urban subway network, Transportation Research Part C: Emerging Technologies, 51, 1-18. https://doi.org/10.1016/j.trc.2014.11.001
30. Wu, Y., Yang, H., Tang, J. & Yu, Y. (2016). Multi-objective re-synchronizing of bus timetable: model, complexity and solution, Transportation Research Part C: Emerging Technologies, 67, 149-168. https://doi.org/10.1016/j.trc.2016.02.007
31. Yin, J., D'Ariano, A., Wang, Y., Yang, L. & Tang, T. (2021). Timetable coordination in a rail transit network with time-dependent passenger demand, European Journal of Operational Research, 295(1), 183-202. https://doi.org/10.1016/j.ejor.2021.02.059
32. Yin, J., Yang, L., Tang, T., Gao, Z. & Ran, B. (2017). Dynamic passenger demand oriented metro train scheduling with energy-efficiency and waiting time minimization: Mixed-integer linear programming approaches, Transportation Research Part B: Methodological, 97(3), 182-213. https://doi.org/10.1016/j.trb.2017.01.001
33. Zhao, X., Sun, Q., Zhu, Y., Ding, Y., Ma, C. & Chen, Z. (2016). Multi-routing planning design of Y-type urban rail transit, Advances in Mechanical Engineering, 8(8): 1-12. https://doi.org/10.1177/1687814016667385
34. Zhou, W., Fan, W., You, X. & Deng, L. (2019). Demand-oriented train timetabling integrated with passenger train-booking decisions, Sustainability, 11(18), 4932. https://doi.org/10.3390/su11184932
35. Zhu, Y. & Goverde, R. (2019). Railway timetable rescheduling with flexible stopping and flexible short-turning during disruptions, Transportation Research Part B: Methodological, 123, 149-181. https://doi.org/10.1016/j.trb.2019.02.015
36. Zhu, Y. & Goverde, R. (2021). Dynamic railway timetable rescheduling for multiple connected disruptions, Transportation Research Part B: Methodological, 125, 103080. https://doi.org/10.1016/j.trc.2021.103080
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