Yihui Wang

A survey on optimal trajectory planning for train operations

Because of the rising energy prices and environmental concerns, the calculation of energy-optimal reference trajectories for trains is significant for energy saving. On the other hand, with the development automatic train operation (ATO), the optimal trajectory planning is significant to the performance of train operation. In this paper, we present an integrated survey of this field. First, a nonlinear continuous-time train model and a continuous-space model of train operations are described, after which the optimal trajectory planning problem is formulated based on these two models. The various approaches in the literature to calculate the reference trajectory are reviewed and categorized into two groups: analytical solutions and numerical optimization. Finally, a short discussion of some open topics in the field of optimal trajectory planning for train operations are given.

Efficient Bilevel Approach for Urban Rail Transit Operation With Stop-Skipping

The train scheduling problem for urban rail transit systems is considered with the aim of minimizing the total travel time of passengers and the energy consumption of the trains. We adopt a model-based approach, where the model includes the operation of trains at the terminus and at the stations. In order to adapt the train schedule to the origin-destination-dependent passenger demand in the urban rail transit system, a stop-skipping strategy is adopted to reduce the passenger travel time and the energy consumption. An efficient bilevel optimization approach is proposed to solve this train scheduling problem, which actually is a mixed-integer nonlinear programming problem. The performance of the new efficient bilevel approach is compared with the existing bilevel approach. In addition, we also compare the stop-skipping strategy with the all-stop strategy. The comparison is performed through a case study inspired by real data from the Beijing Yizhuang line. The simulation results show that the efficient bilevel approach and the existing bilevel approach have a similar performance but the computation time of the efficient bilevel approach is around one magnitude smaller than that of the bilevel approach.

Optimal trajectory planning for trains using mixed integer linear programming

The optimal trajectory planning for trains under constraints and fixed maximal arrival time is considered. The variable line resistance (including variable grade profile, tunnels, and curves) and arbitrary speed restrictions are included in this approach. The objective function is a trade-off between the energy consumption and the riding comfort. First, the nonlinear train model is approximated by a piece-wise affine model. Next, the optimal control problem is formulated as a mixed integer linear programming (MILP) problem, which can be solved efficiently by existing solvers. The good performance of this approach is demonstrated via a case study.

Efficient Real-Time Train Scheduling for Urban Rail Transit Systems Using Iterative Convex Programming

The real-time train scheduling problem for urban rail transit systems is considered with the aim of minimizing the total travel time of passengers and the energy consumption of the operation of trains. Based on the passenger demand in the urban rail transit system, the optimal departure times, running times, and dwell times are obtained by solving the scheduling problem. A new iterative convex programming (ICP) approach is proposed to solve the train scheduling problem. The performance of the ICP approach is compared with other alternative approaches, i.e., nonlinear programming approaches, a mixed-integer nonlinear programming (MINLP) approach, and a mixed-integer linear programming (MILP) approach. In addition, this paper formulates the real-time train scheduling problem with stop-skipping and shows how to solve it using an MINLP approach and an MILP approach. The ICP approach is shown, via a case study, to provide a better tradeoff between performance and computational complexity for the real-time train scheduling problem. Furthermore, for the train scheduling problem with stop-skipping, the MINLP approach turns out to have a good tradeoff between the control performance and the computational efficiency.

Real-time scheduling for single lines in urban rail transit systems

The real-time scheduling problem for urban rail transit systems is considered with the aim of minimizing the total passenger travel time, i.e. the sum of passenger waiting time at stations and passenger on-board time. The operation of trains and passenger demand characteristics are formulated in the real-time scheduling model. The minimum headway constraints are also taken into account to ensure the running safety of trains in urban rail transit. The resulting real-time scheduling problem is a nonlinear non-convex programming problem, which can be solved using state-of-the art algorithms to obtain the optimal departure times, running times, and dwell times of trains. A case study based on the data of Beijing Yizhuang line is used to demonstrate the performance of the proposed approach.

Energy-Efficient Operation of Single Train Based on the Control Strategy of ATO

Energy efficiency is paid more and more attention in urban rail transit systems. Optimization on Automatic Train Operation (ATO) is important to energy-efficient operation of trains. ATO generates the recommended speed curve based on the railway line parameters, the scheduled time table, and the vehicle conditions. The control strategy of ATO makes the train running along the recommended speed curve to meet the requirements on precision of train stopping, punctuality, energy-saving and riding comfort. The optimization of recommended speed curve in traditional research does not consider the influence of the control strategy of ATO. The energy consumption calculated by such a recommended speed curve and the practical curve of the train operation have a significant deviation. In this paper, a more accurate model of the train energy consumption is presented by considering the control strategy of ATO. Two modifications of Tabu Search (TS) algorithm, which are named as Acceleration Rate Decided Modification (ARDM) and Distance Decided Modification (DDM), are proposed to optimize train recommended speed curve based on the presented model. Case studies have been conducted based on Beijing Subway to illustrate that the proposed algorithm results in good performance with regards to energy saving. In addition, the computation time is within 1 s, which is short enough to be applied in the online control of trains.

Real-time scheduling for trains in urban rail transit systems using nonlinear optimization

The real-time train scheduling problem for urban rail transit systems is considered with the aim of minimizing the total travel time of passengers and the energy consumption of trains. Based on the passenger demand in urban rail transit systems, the optimal departure times, running times, and dwell times are obtained by solving the scheduling problem. Three solution approaches are proposed to solve the real-time scheduling problem for trains: a pattern search method, a mixed integer nonlinear programming (MINLP) approach, and a mixed integer linear programming (MILP) approach. The performance of these three approaches is compared via a case study based on the data of the Beijing Yizhuang line. The results show that the pattern search method provides a good trade-off between the control performance and the computational efficiency.

Ultraviolet Photodetectors With Narrow-Band Spectral Response Using TAPC Donor

Organic ultraviolet photodetectors (PDs) with a narrow-band spectral response are fabricated. TAPC and PBD were utilized as the electron donor and acceptor, respectively. Glass/indium tin oxide (ITO) was employed as the anode contact and the incident light window. The PDs reveal a narrow response width of 30 nm at 316-346 nm. A peak response of 0.12 A/W at 330 nm and a photo-to-dark ratio of about 1.1 ×102 under 330-nm light illumination with an intensity of 0.95 mW/cm2 were achieved. The realization of the narrow-band response should be ascribed to the steep absorption of organic materials at the long wavelength and the blocking role of glass/ITO contact at the short wavelength.

Optimal Trajectory Planning for Trains under Operational Constraints Using Mixed Integer Linear Programming

Abstract The optimal trajectory planning problem for trains under operational constraints is considered, which is essential for the success of the real-time operation and the rescheduling process for railway networks. The operational constraints caused by the timetable, real-time operation, or rescheduling often include target points and target window constraints. The approach proposed in this paper can take such constraints into account. In addition, the varying maximum traction force is approximated using a piecewise affine function and included in the trajectory planning problem. The optimal control problem is recast as a mixed integer linear programming problem, which can be solved efficiently by existing solvers. A case study is used to demonstrate the performance of the proposed approach.

Optimal Trajectory Planning and Train Scheduling for Urban Rail Transit Systems

Urban rail traffic plays a key role in public transportation since it combines high transport capacity and high efficiency. More specifically, a safe, fast, punctual, energy-efficient, and comfortable railway system is important for the economic, environmental, and social objectives of a country or a city. The main focus of this book is on saving energy in railway operations and on enhancing the passenger satisfaction, which can be achieved via optimal trajectory planning for trains and passenger demand-oriented train scheduling by utilizing several mathematical tools and programming methods like MILP, SQP, etc. In this chapter, we provide a brief introduction to railway operations and then present the structure of this book. 1.1 A Brief Introduction on Railway Operations A railway system consists of three essential elements: infrastructure (like tracks, stations, signaling equipment, etc.), rolling stock with locomotives and cars or electric multiple units (EMUs), and customers (like passenger and/or goods demands) [1–3]. The design, construction, and operation of the infrastructure and rolling stock are affected by the customers. Passenger railway systems could be classified into interurban railway systems (or standard railway systems) and urban rail transit systems (such as metros and subways). Rail infrastructure is a limited resource in interurban rail transit systems, where lines overlap or cross with each other and trains usually overtake or meet each other. On the other hand, in urban rail transit systems, the lines are separated from each other and each direction of the line has a dedicated infrastructure. Moreover, in principle trains do not overtake and meet each other in urban rail transit systems. The optimal trajectory planning (i.e., speed profile calculation) methods for the operation of trains proposed in this book can be applied both for interurban railway systems and urban rail transit systems. However, train scheduling approaches we present here are focused on urban rail transit systems. In railway systems, the operation of trains is in general controlled through a hierarchical control framework with five levels, i.e., scheduling, real-time (re)scheduling, remote traffic control, interlocking and signaling, and train and infrastructure control