Scheduling local and express trains in suburban rail transit lines: Mixed–integer nonlinear programming and adaptive genetic algorithm

We investigate the train timetabling problem in suburban rail transit lines by considering (1) the traditional stopping mode (TSM), in which all trains stop at each station, and (2) the express/local stopping mode (ELM), in which express trains can skip certain low–demand stations. We first propose...

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Veröffentlicht in:	Computers & operations research Jg. 135; S. 105436
Hauptverfasser:	Tang, Lianhua, D’Ariano, Andrea, Xu, Xingfang, Li, Yantong, Ding, Xiaobing, Samà, Marcella
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Elsevier Ltd 01.11.2021 Pergamon Press Inc
Schlagworte:	Adaptive algorithms Adaptive genetic algorithm (A–GA) Case studies Express/local stopping mode (ELM) Genetic algorithms Integer programming Linear programming Mathematical models Mixed–integer nonlinear programming (MINLP) Nonlinear programming Operations research Optimization Parameter sensitivity Passenger travel time (PTT) Rail transportation Railway stations Sensitivity analysis Suburban rail transit (SRT) Traditional (all) stopping mode (TSM) Train overtaking Train timetabling Trains Travel time Train overtaking Adaptive genetic algorithm (A–GA) Traditional (all) stopping mode (TSM) Express/local stopping mode (ELM) Suburban rail transit (SRT) Mixed–integer nonlinear programming (MINLP) Passenger travel time (PTT) Train timetabling
ISSN:	0305-0548, 0305-0548
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Abstract	We investigate the train timetabling problem in suburban rail transit lines by considering (1) the traditional stopping mode (TSM), in which all trains stop at each station, and (2) the express/local stopping mode (ELM), in which express trains can skip certain low–demand stations. We first propose two mixed–integer linear programming models for the train timetabling problem under the TSM with and without capacity constraints. Next, we develop two mixed–integer nonlinear programming models under the ELM with and without “overtaking”; thus, a total of four optimization models are proposed. The objective is to minimize the passenger travel time (PTT). Owing to the NP–hardness of the studied problem, we propose an adaptive genetic algorithm (A–GA) that can efficiently solve the four proposed models. The A–GA is customized to solve the train timetabling problem with train capacity, overtaking, and other operational constraints, reducing the PTT. To evaluate the performance of the proposed algorithm, we conduct numerical experiments on 60 randomly generated realistic instances and a real–world case study based on Shanghai Metro Line 16. The computational results for the realistic instances indicate that our A–GA can obtain near–optimal solutions with significantly less computation time than an established commercial solver. The computational results from the real-world case study quantify the benefits of considering the combination of the ELM and overtaking strategies in train timetabling. Furthermore, we perform a sensitivity analysis on key parameters of our mathematical formulations. The results provide insights to railway managers on how to set key parameters when applying the proposed formulations and solution methodology in practice. •We propose mixed–integer programming formulations for train timetabling in suburban transit lines.•We consider passengers being left behind under limited train capacity and express/local stopping mode.•We accurately calculate passenger waiting times under oversaturated traffic conditions.•We present an adaptive genetic algorithm for optimizing train timetables with overtaking possibility.•The proposed algorithm yields good quality solutions in a short computation time.
AbstractList	We investigate the train timetabling problem in suburban rail transit lines by considering (1) the traditional stopping mode (TSM), in which all trains stop at each station, and (2) the express/local stopping mode (ELM), in which express trains can skip certain low–demand stations. We first propose two mixed–integer linear programming models for the train timetabling problem under the TSM with and without capacity constraints. Next, we develop two mixed–integer nonlinear programming models under the ELM with and without "overtaking"; thus, a total of four optimization models are proposed. The objective is to minimize the passenger travel time (PTT). Owing to the NP–hardness of the studied problem, we propose an adaptive genetic algorithm (A–GA) that can efficiently solve the four proposed models. The A–GA is customized to solve the train timetabling problem with train capacity, overtaking, and other operational constraints, reducing the PTT. To evaluate the performance of the proposed algorithm, we conduct numerical experiments on 60 randomly generated realistic instances and a real–world case study based on Shanghai Metro Line 16. The computational results for the realistic instances indicate that our A–GA can obtain near–optimal solutions with significantly less computation time than an established commercial solver. The computational results from the real-world case study quantify the benefits of considering the combination of the ELM and overtaking strategies in train timetabling. Furthermore, we perform a sensitivity analysis on key parameters of our mathematical formulations. The results provide insights to railway managers on how to set key parameters when applying the proposed formulations and solution methodology in practice. We investigate the train timetabling problem in suburban rail transit lines by considering (1) the traditional stopping mode (TSM), in which all trains stop at each station, and (2) the express/local stopping mode (ELM), in which express trains can skip certain low–demand stations. We first propose two mixed–integer linear programming models for the train timetabling problem under the TSM with and without capacity constraints. Next, we develop two mixed–integer nonlinear programming models under the ELM with and without “overtaking”; thus, a total of four optimization models are proposed. The objective is to minimize the passenger travel time (PTT). Owing to the NP–hardness of the studied problem, we propose an adaptive genetic algorithm (A–GA) that can efficiently solve the four proposed models. The A–GA is customized to solve the train timetabling problem with train capacity, overtaking, and other operational constraints, reducing the PTT. To evaluate the performance of the proposed algorithm, we conduct numerical experiments on 60 randomly generated realistic instances and a real–world case study based on Shanghai Metro Line 16. The computational results for the realistic instances indicate that our A–GA can obtain near–optimal solutions with significantly less computation time than an established commercial solver. The computational results from the real-world case study quantify the benefits of considering the combination of the ELM and overtaking strategies in train timetabling. Furthermore, we perform a sensitivity analysis on key parameters of our mathematical formulations. The results provide insights to railway managers on how to set key parameters when applying the proposed formulations and solution methodology in practice. •We propose mixed–integer programming formulations for train timetabling in suburban transit lines.•We consider passengers being left behind under limited train capacity and express/local stopping mode.•We accurately calculate passenger waiting times under oversaturated traffic conditions.•We present an adaptive genetic algorithm for optimizing train timetables with overtaking possibility.•The proposed algorithm yields good quality solutions in a short computation time.
ArticleNumber	105436
Author	Tang, Lianhua Ding, Xiaobing D’Ariano, Andrea Li, Yantong Samà, Marcella Xu, Xingfang
Author_xml	– sequence: 1 givenname: Lianhua surname: Tang fullname: Tang, Lianhua organization: The Key Laboratory of Road and Traffic Engineering, Ministry of Education, Tongji University, 201804 Shanghai, China – sequence: 2 givenname: Andrea surname: D’Ariano fullname: D’Ariano, Andrea organization: Department of Engineering, Roma Tre University, Via della Vasca Navale, 79, 00146 Roma, Italy – sequence: 3 givenname: Xingfang surname: Xu fullname: Xu, Xingfang email: xfx@tongji.edu.cn organization: The Key Laboratory of Road and Traffic Engineering, Ministry of Education, Tongji University, 201804 Shanghai, China – sequence: 4 givenname: Yantong orcidid: 0000-0002-9703-3882 surname: Li fullname: Li, Yantong organization: School of Maritime Economics and Management, Dalian Maritime University, 116026 Dalian, China – sequence: 5 givenname: Xiaobing surname: Ding fullname: Ding, Xiaobing organization: School of Urban Rail Transportation, Shanghai University of Engineering Science, 201620 Shanghai, China – sequence: 6 givenname: Marcella surname: Samà fullname: Samà, Marcella organization: Department of Engineering, Roma Tre University, Via della Vasca Navale, 79, 00146 Roma, Italy
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Keywords	Train overtaking Adaptive genetic algorithm (A–GA) Traditional (all) stopping mode (TSM) Express/local stopping mode (ELM) Suburban rail transit (SRT) Mixed–integer nonlinear programming (MINLP) Passenger travel time (PTT) Train timetabling
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Snippet	We investigate the train timetabling problem in suburban rail transit lines by considering (1) the traditional stopping mode (TSM), in which all trains stop at...
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SubjectTerms	Adaptive algorithms Adaptive genetic algorithm (A–GA) Case studies Express/local stopping mode (ELM) Genetic algorithms Integer programming Linear programming Mathematical models Mixed–integer nonlinear programming (MINLP) Nonlinear programming Operations research Optimization Parameter sensitivity Passenger travel time (PTT) Rail transportation Railway stations Sensitivity analysis Suburban rail transit (SRT) Traditional (all) stopping mode (TSM) Train overtaking Train timetabling Trains Travel time
Title	Scheduling local and express trains in suburban rail transit lines: Mixed–integer nonlinear programming and adaptive genetic algorithm
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