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OD-Independent Train Scheduling for an Urban Rail Transit Line

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Optimal Trajectory Planning and Train Scheduling for Urban Rail Transit Systems

Part of the book series: Advances in Industrial Control ((AIC))

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Abstract

In the previous two chapters, we have discussed trajectory planning for trains in a railway network based on given train schedules. In this chapter, the train scheduling problem based on origin–destination-independent (OD-independent ) passenger demands for an urban rail transit line is considered with the aim of minimizing the total travel time of passengers and the energy consumption of trains. We propose a new iterative convex programming (ICP) approach to solve this train scheduling problem. Via a case study inspired by the Beijing Yizhuang line, the performance of the ICP approach is compared with other alternative approaches, such as nonlinear programming approaches, a mixed integer nonlinear programming (MINLP) approach, and a mixed integer linear programming (MILP) approach. The research discussed in this chapter is based on Wang et al. (Efficient real-time train scheduling for urban rail transit systems using iterative convex programming. IEEE Trans Intell Transp Syst 16:3337–3352, 2015) [1]; Wang et al. (Proceedings of the 1st IEEE international conference on intelligent rail transportation (2013 IEEE ICIRT), Beijing, China, 2013) [2]; Wang et al. (Proceedings of the 16th international IEEE conference on intelligent transportation systems (ITSC 2013), The Netherlands, The Hague,pp 1334–1339, 2013) [3].

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Notes

  1. 1.

    Here we use a deterministic model to describe the passenger arrival process.

  2. 2.

    When the SQP algorithm is applied to a nonlinear programming problem with a non-differentiable objective function, it might get stuck in a local solution. In the nonlinear programming problem proposed in this chapter, the minimum value of the objective function is usually not obtained at the points where the objective function is non-differentiable, so the SQP algorithm will jump over these points. Therefore, the SQP approach with multiple initial points works well in this case.

  3. 3.

    For more details about the MINLP BB solver, see [28].

  4. 4.

    More information about MATLAB software CVX, see [35].

References

  1. Wang Y, De Schutter B, van den Boom T, Ning B, Tang T (2015) Efficient real-time train scheduling for urban rail transit systems using iterative convex programming. IEEE Trans Intell Transp Syst 16:3337–3352

    Google Scholar 

  2. Wang Y, De Schutter B, van den Boom T, Ning B, Tang T (2013) Real-time scheduling in urban rail transit operations control. In: Proceedings of the 1st IEEE international conference on intelligent rail transportation (2013 IEEE ICIRT), Beijing, China. Paper 108

    Google Scholar 

  3. Wang Y, De Schutter B, van den Boom T, Ning B, Tang T (2013) Real-time scheduling for trains in urban rail transit systems using nonlinear optimization. In: Proceedings of the 16th international IEEE conference on intelligent transportation systems (ITSC 2013), The Netherlands, The Hague, pp 1334–1339

    Google Scholar 

  4. Vázquez-Abad F, Zubieta L (2005) Ghost simulation model for the optimization of an urban subway system. Discret Event Dyn Syst 15:207–235

    Article  MathSciNet  MATH  Google Scholar 

  5. Kwan C, Chang C (2005) Application of evolutionary algorithm on a transportation scheduling problem—the mass rapid transit. In: Proceedings of the IEEE congress on evolutionary computation, Edinburgh, UK, pp 987–994

    Google Scholar 

  6. Gassel C, Albrecht T (2009) The impact of request stops on railway operations. In: Proceedings of the 3rd international seminar on railway operations modeling and analysis, Zürich, Switzerland, pp 1–15

    Google Scholar 

  7. Higgins A, Kozan E, Ferreira L (1996) Optimal scheduling of trains on a single line track. Transp Res Part B 30:147–161

    Article  Google Scholar 

  8. Okrent M (1974) Effects of transit service characteristics on passenger waiting times. M.S. thesis, Northwestern University, Evanston, USA

    Google Scholar 

  9. Simon J, Furth P (1985) Generating a bus route O-D matrix from on-off data. J Transp Eng 111:583–593

    Article  Google Scholar 

  10. Hansen I, Pachl J (2008) Railway, timetable and traffic: analysis, modelling, simulation. Eurailpress, Hamburg, Germany

    Google Scholar 

  11. D’Ariano A, Pranzoand M, Hansen I (2007) Conflict resolution and train speed coordination for solving real-time timetable perturbations. IEEE Trans Intell Transp Syst 8:208–222

    Article  Google Scholar 

  12. Elberlein X, Wilson N, Bernstein D (2001) The holding problem with real-time information available. Transp Sci 35:1–18

    Article  MATH  Google Scholar 

  13. Li X, Wang D, Li K, Gao Z (2013) A green train scheduling model and fuzzy multi-objective optimization algorithm. Appl Math Model 37:617–629

    MathSciNet  Google Scholar 

  14. Goverde R (2005) Punctuality of railway operations and timetable stability analysis. PhD thesis, Delft University of Technology, Delft, Netherlands

    Google Scholar 

  15. van den Boom T, Kersbergen B, De Schutter B (2012) Structured modeling, analysis, and control of complex railway operations. In: Proceedings of the 51st IEEE conference on decision and control, Maui, Hawaii, pp 7366–7371

    Google Scholar 

  16. Kersbergen B, van den Boom T, De Schutter B (2013) Reducing the time needed to solve the global rescheduling problem for railway networks. In: Proceedings of the 16th international IEEE conference on intelligent transportation systems (ITSC 2013), The Hague, The Netherlands, pp 791–796

    Google Scholar 

  17. Pachl J (2009) Railway operation and control, 2nd edn. Gorham Printing, Centralia

    Google Scholar 

  18. Lin T, Wilson N (1992) Dwell time relationships for light rail systems. Transp Res Rec 1361:287–295

    Google Scholar 

  19. Vansteenwegen P, Oudheusden DV (2007) Decreasing the passenger waiting time for an intercity rail network. Transp Res Part B 41:478–492

    Article  Google Scholar 

  20. Ghoseiri K, Szidarovszky F, Asgharpour M (2004) A multi-objective train scheduling model and solution. Transp Res Part B 38:927–952

    Article  MATH  Google Scholar 

  21. Hooke R, Jeeves T (1961) Direct search solution of numerical and statistical problems. J Assoc Comput Mach 8:212–229

    Article  MATH  Google Scholar 

  22. Martí R (2010) Advaced multi-start methods. International series in operations research and management science: handbook of metaheuristics. Springer, New York, pp 265–281

    Google Scholar 

  23. The Mathworks Inc. (2004) Genetic algorithm and direct search toolbox for use with MATLAB: user’s guide. The Mathworks Inc., Natick, MA, USA

    Google Scholar 

  24. Boggs P, Tolle J (1995) Sequential quadratic programming. Acta Numerica 4:1–51

    Article  MathSciNet  MATH  Google Scholar 

  25. Gill P, Murray W, Saunders M (2002) SNOPT: an SQP algorithm for large-scale constrained optimization. Soc Ind Appl Math J Optim 12:979–1006

    MathSciNet  MATH  Google Scholar 

  26. The Mathworks Inc. (1999) Optimization toolbox for use with Matlab: user’s guide. The Mathworks Inc., Natick, MA, USA

    Google Scholar 

  27. Williams H (1999) Model building in mathematical programming, 4th edn. Wiley, Chichester

    MATH  Google Scholar 

  28. Holmström K, Göran AO, Edvall M (2007) User’s guide for tomlab/minlp. http://tomopt.com/docs/TOMLAB_MINLP.pdf

  29. Berthold T, Gamrath G, Gleixner A, Heinz S, Koch T, Shinano Y (2012) Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite. ZIB-Report 12–17. Zuse Institute Berlin. Berlin, Germany

    Google Scholar 

  30. Kvasnica M, Grieder P, Baotić M (2011) Automatic derivation of optimal piecewise affine approximations of nonlinear systems. In: Proceedings of the 18th IFAC world congress. Milano, Italy, pp 8675–8680

    Google Scholar 

  31. Williams H (1993) Model building in mathematical programming. Wiley, New York

    Google Scholar 

  32. Linderoth J, Ralphs T (2005) Noncommercial software for mixed-integer linear programming. In: Karlof J (ed) Integer programming: theory and practice., Operations research seriesCRC Press, Boca Raton, pp 253–303

    Google Scholar 

  33. Atamturk A, Savelsbergh M (2005) Integer-programming software systems. Annals of operations research 140:67–124

    Article  MathSciNet  MATH  Google Scholar 

  34. Byrd R, Hribar M, Nocedal J (1999) An interior point algorithm for large-scale nonlinear programming. SIAM J Optim 9:877–900

    Article  MathSciNet  MATH  Google Scholar 

  35. Grant M, Boyd S (2012) CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx

  36. Zhang B, Lu Y (2011) Research on dwelling time modeling of urban rail transit. Traffic Transp 27:48–52

    Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China

    Yihui Wang & Bin Ning

  2. Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands

    Ton van den Boom & Bart De Schutter

Authors
  1. Yihui Wang
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  2. Bin Ning
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  3. Ton van den Boom
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  4. Bart De Schutter
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Corresponding author

Correspondence to Yihui Wang .

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Wang, Y., Ning, B., van den Boom, T., De Schutter, B. (2016). OD-Independent Train Scheduling for an Urban Rail Transit Line. In: Optimal Trajectory Planning and Train Scheduling for Urban Rail Transit Systems. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-30889-0_5

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  • DOI: https://doi.org/10.1007/978-3-319-30889-0_5

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  • Online ISBN: 978-3-319-30889-0

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