Trajectory Optimization for High-Speed Trains via a Mixed Integer Linear Programming Approach

This paper proposes a trajectory optimization approach for high-speed trains to reduce traction energy consumption and increase riding comfort. Besides, the proposed approach can also achieve energy-saving effects by optimizing the operation time between stations. First, an optimization model is dev...

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Veröffentlicht in:	IEEE transactions on intelligent transportation systems Jg. 23; H. 10; S. 17666 - 17676
Hauptverfasser:	Cao, Yuan, Zhang, Zixuan, Cheng, Fanglin, Su, Shuai
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.10.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Comfort Control systems Energy conservation Energy consumption Energy efficiency High speed rail high-speed railway Integer programming Linear programming Mathematical models MILP Mixed integer Optimal control Optimization Optimization models Rail transportation riding comfort Switches Traction train control Trajectory optimization
ISSN:	1524-9050, 1558-0016
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Abstract	This paper proposes a trajectory optimization approach for high-speed trains to reduce traction energy consumption and increase riding comfort. Besides, the proposed approach can also achieve energy-saving effects by optimizing the operation time between stations. First, an optimization model is developed by defining the objective function as a trade-off function of the traction energy consumption and riding comfort. In addition to constraints in the classic optimal train control model, three new factors-the discrete throttle settings, neutral zones, and sectionalized tunnel resistance-are considered. Then, the model is discretized and turned into a multi-step decision optimization problem. All the nonlinear constraints are approximated using piecewise affine (PWA) functions, and the trajectory optimization problem is turned into a mixed integer linear programming (MILP) problem which can be solved by existing solvers CPLEX and YALMIP. Finally, some case studies with real-world data sets are conducted to present the effectiveness of the proposed approach. The simulation results are compared with the practical running data of trains, which shows that the proposed model and the optimization approach save energy and improve the riding comfort.
AbstractList	This paper proposes a trajectory optimization approach for high-speed trains to reduce traction energy consumption and increase riding comfort. Besides, the proposed approach can also achieve energy-saving effects by optimizing the operation time between stations. First, an optimization model is developed by defining the objective function as a trade-off function of the traction energy consumption and riding comfort. In addition to constraints in the classic optimal train control model, three new factors-the discrete throttle settings, neutral zones, and sectionalized tunnel resistance-are considered. Then, the model is discretized and turned into a multi-step decision optimization problem. All the nonlinear constraints are approximated using piecewise affine (PWA) functions, and the trajectory optimization problem is turned into a mixed integer linear programming (MILP) problem which can be solved by existing solvers CPLEX and YALMIP. Finally, some case studies with real-world data sets are conducted to present the effectiveness of the proposed approach. The simulation results are compared with the practical running data of trains, which shows that the proposed model and the optimization approach save energy and improve the riding comfort.
Author	Zhang, Zixuan Su, Shuai Cao, Yuan Cheng, Fanglin
Author_xml	– sequence: 1 givenname: Yuan orcidid: 0000-0001-6631-4908 surname: Cao fullname: Cao, Yuan organization: National Engineering Research Center of Rail Transportation Operation Control System and the School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, China – sequence: 2 givenname: Zixuan orcidid: 0000-0003-3353-4351 surname: Zhang fullname: Zhang, Zixuan organization: State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China – sequence: 3 givenname: Fanglin surname: Cheng fullname: Cheng, Fanglin organization: State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China – sequence: 4 givenname: Shuai orcidid: 0000-0001-8412-9853 surname: Su fullname: Su, Shuai email: shuaisu@bjtu.edu.cn organization: State Key Laboratory of Traffic Control and Safety, Beijing Jiaotong University, Beijing, China
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References	ref35 ref12 ref34 ref15 ref14 ref31 Atkinson (ref16) 1978 ref30 ref11 ref32 ref1 ref17 ref19 Howlett (ref2) 2000; 98 ref18 Howlett (ref10) 1995 ref24 ref23 ref26 ref25 ref20 ref22 ref21 ref27 ref29 ref8 ref7 Ko (ref13) 2004 ref9 ref4 ref3 ref6 ref5 Williams (ref33) 2013 Du (ref28) 2019
References_xml	– ident: ref8 doi: 10.1016/0005-1098(92)90017-A – volume-title: Energy-Efficient Train Control year: 1995 ident: ref10 doi: 10.1007/978-1-4471-3084-0 – ident: ref4 doi: 10.1016/j.tra.2003.07.001 – ident: ref14 doi: 10.1016/j.trc.2013.01.007 – ident: ref22 doi: 10.1049/ip-epa:19970797 – ident: ref5 doi: 10.1016/j.trc.2020.102886 – ident: ref24 doi: 10.1109/TITS.2009.2018324 – ident: ref9 doi: 10.1109/9.262051 – ident: ref31 doi: 10.1243/0954409001531306 – ident: ref35 doi: 10.1109/TTE.2020.2983855 – ident: ref23 doi: 10.1109/TITS.2019.2939358 – start-page: 103 volume-title: Computing Railways year: 2004 ident: ref13 article-title: Application of dynamic programming to optimization of running profile of a train – ident: ref18 doi: 10.1016/j.trc.2021.103249 – ident: ref26 doi: 10.1146/annurev.fluid.33.1.371 – ident: ref19 doi: 10.1177/0954409716671546 – ident: ref21 doi: 10.1177/0954409713515648 – ident: ref25 doi: 10.1016/j.tre.2021.102323 – volume-title: Research on the method of determining the key aerodynamic coefficient of high speed train passing through tunnel year: 2019 ident: ref28 – ident: ref17 doi: 10.1109/TITS.2013.2244885 – ident: ref30 doi: 10.1002/tee.20528 – ident: ref34 doi: 10.1016/j.jweia.2017.09.017 – ident: ref29 doi: 10.1002/tee.20479 – ident: ref32 doi: 10.1016/S0005-1098(98)00178-2 – ident: ref12 doi: 10.1093/imaman/10.2.89 – volume-title: Model Building in Mathematical Programming year: 2013 ident: ref33 – ident: ref7 doi: 10.1016/j.trb.2015.07.024 – ident: ref6 doi: 10.1016/j.trb.2015.07.023 – volume-title: An Introduction to Numerical Analysis year: 1978 ident: ref16 – ident: ref27 doi: 10.1016/j.isatra.2021.04.036 – ident: ref20 doi: 10.1109/MITS.2019.2907681 – ident: ref1 doi: 10.1299/jsme1958.11.857 – volume: 98 start-page: 65 issue: 1 year: 2000 ident: ref2 article-title: The optimal control of a train publication-title: Ann. Oper. Res. doi: 10.1023/A:1019235819716 – ident: ref11 doi: 10.1016/0005-1098(95)00184-0 – ident: ref3 doi: 10.1109/9.867018 – ident: ref15 doi: 10.1049/ip-epa:20000329
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SubjectTerms	Comfort Control systems Energy conservation Energy consumption Energy efficiency High speed rail high-speed railway Integer programming Linear programming Mathematical models MILP Mixed integer Optimal control Optimization Optimization models Rail transportation riding comfort Switches Traction train control Trajectory optimization
Title	Trajectory Optimization for High-Speed Trains via a Mixed Integer Linear Programming Approach
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