IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v91y2016icp424-445.html
   My bibliography  Save this article

A stochastic model for the integrated optimization on metro timetable and speed profile with uncertain train mass

Author

Listed:
  • Yang, Xin
  • Chen, Anthony
  • Ning, Bin
  • Tang, Tao

Abstract

The integrated timetable and speed profile optimization model has recently attracted more attention because of its good achievements on energy conservation in metro systems. However, most previous studies often ignore the spatial and temporal uncertainties of train mass, and the variabilities of tractive force, braking force and basic running resistance on energy consumption in order to simplify the model formulation and solution algorithm. In this paper, we develop an integrated metro timetable and speed profile optimization model to minimize the total tractive energy consumption, where these real-world operating conditions are explicitly considered in the model formulation and solution algorithm. Firstly, we formulate a two-phase stochastic programming model to determine the timetable and speed profile. Given the speed profile, the first phase determines the timetable by scheduling the arrival and departure times for each station, and the second phase determines the speed profile for each inter-station with the scheduled arrival and departure times. Secondly, we design a simulation-based genetic algorithm procedure incorporated with the optimal train control algorithm to find the optimal solution. Finally, we present a simple example and a real-world example based on the operation data from the Beijing Metro Yizhuang Line in Beijing, China. The results of the real-world example show that, during peak hours, off-peak hours and night hours, the total tractive energy consumptions can be reduced by: (1) 10.66%, 9.94% and 9.13% in comparison with the current timetable and speed profile; and (2) 3.35%, 3.12% and 3.04% in comparison with the deterministic model.

Suggested Citation

  • Yang, Xin & Chen, Anthony & Ning, Bin & Tang, Tao, 2016. "A stochastic model for the integrated optimization on metro timetable and speed profile with uncertain train mass," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 424-445.
    • Handle: RePEc:eee:transb:v:91:y:2016:i:c:p:424-445
    DOI: 10.1016/j.trb.2016.06.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261516303745
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2016.06.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Niu, Huimin & Zhou, Xuesong & Gao, Ruhu, 2015. "Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 117-135.
    2. Alan J. King & R. Tyrrell Rockafellar, 1993. "Asymptotic Theory for Solutions in Statistical Estimation and Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 148-162, February.
    3. Cheng Gong & Shiwen Zhang & Feng Zhang & Jianguo Jiang & Xinheng Wang, 2014. "An Integrated Energy-Efficient Operation Methodology for Metro Systems Based on a Real Case of Shanghai Metro Line One," Energies, MDPI, vol. 7(11), pages 1-25, November.
    4. Xu, Xiaoming & Li, Keping & Yang, Lixing, 2015. "Scheduling heterogeneous train traffic on double tracks with efficient dispatching rules," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 364-384.
    5. Asadi Bagloee, Saeed & Ceder, Avishai (Avi), 2011. "Transit-network design methodology for actual-size road networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1787-1804.
    6. Li, Xiang & Lo, Hong K., 2014. "Energy minimization in dynamic train scheduling and control for metro rail operations," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 269-284.
    7. Zhou, Xuesong & Zhong, Ming, 2007. "Single-track train timetabling with guaranteed optimality: Branch-and-bound algorithms with enhanced lower bounds," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 320-341, March.
    8. Ghoseiri, Keivan & Szidarovszky, Ferenc & Asgharpour, Mohammad Jawad, 2004. "A multi-objective train scheduling model and solution," Transportation Research Part B: Methodological, Elsevier, vol. 38(10), pages 927-952, December.
    9. Bešinović, Nikola & Goverde, Rob M.P. & Quaglietta, Egidio & Roberti, Roberto, 2016. "An integrated micro–macro approach to robust railway timetabling," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 14-32.
    10. Kim, Myungseob (Edward) & Schonfeld, Paul, 2014. "Integration of conventional and flexible bus services with timed transfers," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 76-97.
    11. Cacchiani, Valentina & Caprara, Alberto & Toth, Paolo, 2010. "Scheduling extra freight trains on railway networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 215-231, February.
    12. Phil Howlett, 2000. "The Optimal Control of a Train," Annals of Operations Research, Springer, vol. 98(1), pages 65-87, December.
    13. Meng, Lingyun & Zhou, Xuesong, 2014. "Simultaneous train rerouting and rescheduling on an N-track network: A model reformulation with network-based cumulative flow variables," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 208-234.
    14. Chen, Anthony & Subprasom, Kitti, 2007. "Analysis of regulation and policy of private toll roads in a build-operate-transfer scheme under demand uncertainty," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(6), pages 537-558, July.
    15. L. Dai & C. H. Chen & J. R. Birge, 2000. "Convergence Properties of Two-Stage Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 489-509, September.
    16. Liu, Rongfang (Rachel) & Golovitcher, Iakov M., 2003. "Energy-efficient operation of rail vehicles," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(10), pages 917-932, December.
    17. Li, Xiang & Lo, Hong K., 2014. "An energy-efficient scheduling and speed control approach for metro rail operations," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 73-89.
    18. Yu, Chunhui & Ma, Wanjing & Lo, Hong K. & Yang, Xiaoguang, 2015. "Optimization of mid-block pedestrian crossing network with discrete demands," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 103-121.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yin, Jiateng & Wang, Miao & D’Ariano, Andrea & Zhang, Jinlei & Yang, Lixing, 2023. "Synchronization of train timetables in an urban rail network: A bi-objective optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 174(C).
    2. Guo, Xin & Sun, Huijun & Wu, Jianjun & Jin, Jiangang & Zhou, Jin & Gao, Ziyou, 2017. "Multiperiod-based timetable optimization for metro transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 46-67.
    3. Chen, Zhiwei & Li, Xiaopeng & Zhou, Xuesong, 2019. "Operational design for shuttle systems with modular vehicles under oversaturated traffic: Discrete modeling method," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 1-19.
    4. Huang, Hai-Jun & Xia, Tian & Tian, Qiong & Liu, Tian-Liang & Wang, Chenlan & Li, Daqing, 2020. "Transportation issues in developing China's urban agglomerations," Transport Policy, Elsevier, vol. 85(C), pages 1-22.
    5. Ye, Hongbo & Liu, Ronghui, 2016. "A multiphase optimal control method for multi-train control and scheduling on railway lines," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 377-393.
    6. Xiaowen Wang & Zhuang Xiao & Mo Chen & Pengfei Sun & Qingyuan Wang & Xiaoyun Feng, 2020. "Energy-Efficient Speed Profile Optimization and Sliding Mode Speed Tracking for Metros," Energies, MDPI, vol. 13(22), pages 1-29, November.
    7. Şafak, Özge & Çavuş, Özlem & Selim Aktürk, M., 2018. "Multi-stage airline scheduling problem with stochastic passenger demand and non-cruise times," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 39-67.
    8. Jianjun Fu & Junhua Chen, 2021. "A Green Transportation Planning Approach for Coal Heavy-Haul Railway System by Simultaneously Optimizing Energy Consumption and Capacity Utilization," Sustainability, MDPI, vol. 13(8), pages 1-25, April.
    9. Canca, David & Barrena, Eva, 2018. "The integrated rolling stock circulation and depot location problem in railway rapid transit systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 115-138.
    10. Huang, Kang & Wu, Jianjun & Sun, Huijun & Yang, Xin & Gao, Ziyou & Feng, Xujie, 2022. "Timetable synchronization optimization in a subway–bus network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    11. Zhaoxiang Tan & Shaofeng Lu & Kai Bao & Shaoning Zhang & Chaoxian Wu & Jie Yang & Fei Xue, 2018. "Adaptive Partial Train Speed Trajectory Optimization," Energies, MDPI, vol. 11(12), pages 1-33, November.
    12. Yang, Xin & Chen, Anthony & Ning, Bin & Tang, Tao, 2017. "Bi-objective programming approach for solving the metro timetable optimization problem with dwell time uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 22-37.
    13. Zhou, Li & Yang, Xin & Wang, Huan & Wu, Jianjun & Chen, Lei & Yin, Haodong & Qu, Yunchao, 2020. "A robust train timetable optimization approach for reducing the number of waiting passengers in metro systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    14. Jianqiang Liu & Nan Zhao, 2017. "Research on Energy-Saving Operation Strategy for Multiple Trains on the Urban Subway Line," Energies, MDPI, vol. 10(12), pages 1-19, December.
    15. Kang, Liujiang & Zhu, Xiaoning & Sun, Huijun & Puchinger, Jakob & Ruthmair, Mario & Hu, Bin, 2016. "Modeling the first train timetabling problem with minimal missed trains and synchronization time differences in subway networks," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 17-36.
    16. Chen, Zhiwei & Li, Xiaopeng & Zhou, Xuesong, 2020. "Operational design for shuttle systems with modular vehicles under oversaturated traffic: Continuous modeling method," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 76-100.
    17. Hu, Yuting & Li, Shukai & Dessouky, Maged M. & Yang, Lixing & Gao, Ziyou, 2022. "Computationally efficient train timetable generation of metro networks with uncertain transfer walking time to reduce passenger waiting time: A generalized Benders decomposition-based method," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 210-231.
    18. Franciszek Restel & Łukasz Wolniewicz & Matea Mikulčić, 2021. "Method for Designing Robust and Energy Efficient Railway Schedules," Energies, MDPI, vol. 14(24), pages 1-12, December.
    19. Canca, David & Zarzo, Alejandro, 2017. "Design of energy-Efficient timetables in two-way railway rapid transit lines," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 142-161.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhou, Wenliang & Tian, Junli & Xue, Lijuan & Jiang, Min & Deng, Lianbo & Qin, Jin, 2017. "Multi-periodic train timetabling using a period-type-based Lagrangian relaxation decomposition," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 144-173.
    2. Yin, Jiateng & Yang, Lixing & Tang, Tao & Gao, Ziyou & Ran, Bin, 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, Elsevier, vol. 97(C), pages 182-213.
    3. Albrecht, Amie & Howlett, Phil & Pudney, Peter & Vu, Xuan & Zhou, Peng, 2016. "The key principles of optimal train control—Part 1: Formulation of the model, strategies of optimal type, evolutionary lines, location of optimal switching points," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 482-508.
    4. Yin, Jiateng & Tang, Tao & Yang, Lixing & Gao, Ziyou & Ran, Bin, 2016. "Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 178-210.
    5. Zhang, Yongxiang & Peng, Qiyuan & Yao, Yu & Zhang, Xin & Zhou, Xuesong, 2019. "Solving cyclic train timetabling problem through model reformulation: Extended time-space network construct and Alternating Direction Method of Multipliers methods," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 344-379.
    6. Julia Lange & Frank Werner, 2018. "Approaches to modeling train scheduling problems as job-shop problems with blocking constraints," Journal of Scheduling, Springer, vol. 21(2), pages 191-207, April.
    7. Ye, Hongbo & Liu, Ronghui, 2016. "A multiphase optimal control method for multi-train control and scheduling on railway lines," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 377-393.
    8. Yang, Xin & Chen, Anthony & Ning, Bin & Tang, Tao, 2017. "Bi-objective programming approach for solving the metro timetable optimization problem with dwell time uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 22-37.
    9. Scheepmaker, Gerben M. & Goverde, Rob M.P. & Kroon, Leo G., 2017. "Review of energy-efficient train control and timetabling," European Journal of Operational Research, Elsevier, vol. 257(2), pages 355-376.
    10. Wang, Pengling & Goverde, Rob M.P., 2019. "Multi-train trajectory optimization for energy-efficient timetabling," European Journal of Operational Research, Elsevier, vol. 272(2), pages 621-635.
    11. Zhou, Leishan & Tong, Lu (Carol) & Chen, Junhua & Tang, Jinjin & Zhou, Xuesong, 2017. "Joint optimization of high-speed train timetables and speed profiles: A unified modeling approach using space-time-speed grid networks," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 157-181.
    12. Albrecht, Amie & Howlett, Phil & Pudney, Peter & Vu, Xuan & Zhou, Peng, 2018. "The two-train separation problem on non-level track—driving strategies that minimize total required tractive energy subject to prescribed section clearance times," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 135-167.
    13. Howlett, Phil, 2016. "A new look at the rate of change of energy consumption with respect to journey time on an optimal train journey," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 387-408.
    14. Luan, Xiaojie & Wang, Yihui & De Schutter, Bart & Meng, Lingyun & Lodewijks, Gabriel & Corman, Francesco, 2018. "Integration of real-time traffic management and train control for rail networks - Part 1: Optimization problems and solution approaches," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 41-71.
    15. Canca, David & Zarzo, Alejandro, 2017. "Design of energy-Efficient timetables in two-way railway rapid transit lines," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 142-161.
    16. Xiaoming Xu & Keping Li & Lixing Yang & Ziyou Gao, 2019. "An efficient train scheduling algorithm on a single-track railway system," Journal of Scheduling, Springer, vol. 22(1), pages 85-105, February.
    17. Gupta, Shuvomoy Das & Tobin, J. Kevin & Pavel, Lacra, 2016. "A two-step linear programming model for energy-efficient timetables in metro railway networks," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 57-74.
    18. Wang, Chao & Meng, Xin & Guo, Mingxue & Li, Hao & Hou, Zhiqiang, 2022. "An integrated energy-efficient and transfer-accessible model for the last train timetabling problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    19. Gonzalo Sánchez-Contreras & Adrián Fernández-Rodríguez & Antonio Fernández-Cardador & Asunción P. Cucala, 2023. "A Two-Level Fuzzy Multi-Objective Design of ATO Driving Commands for Energy-Efficient Operation of Metropolitan Railway Lines," Sustainability, MDPI, vol. 15(12), pages 1-24, June.
    20. Yang, Songpo & Liao, Feixiong & Wu, Jianjun & Timmermans, Harry J.P. & Sun, Huijun & Gao, Ziyou, 2020. "A bi-objective timetable optimization model incorporating energy allocation and passenger assignment in an energy-regenerative metro system," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 85-113.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:91:y:2016:i:c:p:424-445. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.