Optimal Trajectory Planning and Train Scheduling for Railway Systems

Abstract

Safe, fast, punctual, energy-efficient, and comfortable rail traffic systems are important for rail operators, passengers, and the environment. Due to the increasing energy prices and environmental concerns, the reduction of energy consumption has become one of the key objectives for railway systems. On the other hand, with the increase of passenger demands in urban rail transit systems of large cities, it is important to transport passengers safely and efficiently. The main focus of the research presented in this thesis is to determine and develop mathematical models and solution approaches to shorten the travel time of passengers and to reduce energy consumption in railway systems. More specifically, the travel time of passengers has been considered in train scheduling, where passenger demands of urban rail transit systems are included. The energy efficiency has been taken into account both in the train scheduling and in the operation of trains. The main topics investigated in the thesis can be summarized as: • Optimal trajectory planning for a single train. We have considered the optimal trajectory planning problem for a single train under various operational constraints, which include the varying line resistance, variable speed restrictions, and the varying maximum traction force. The objective function of the optimization problem is a trade-off between the energy consumption and the riding comfort. We have proposed two approaches to solve this optimal control problem, namely a mixed-integer linear programming (MILP) approach and the pseudospectral method. Simulation results comparing the MILP approach, the pseudospectral method, and a discrete dynamic programming approach have shown that the pseudospectralmethod results in the best control performance, but that if the required computation time is also take into consideration, the MILP approach yields the best overall performance. • Optimal trajectory planning for multiple trains. The optimal trajectory planning problem for multiple trains under fixed block signaling systems and moving block signaling systems has been investigated. Four solution approaches have been proposed: the greedy MILP approach, the simultaneous MILP approach, the greedy pseudospectral approach, the simultaneous pseudospectral method. Simulation results have shown that compared to the greedy approach, the simultaneous approach yields a better control performance but requires a higher computation time. In addition, the end time violations of the MILP approach are slightly larger than those of the pseudospectral method, but the computation time of the MILP approach is one to two orders of magnitude smaller than that of the pseudospectral method. • Train scheduling for a single line based on OD-independent passenger demands. The train scheduling problem for an urban rail transit line has been considered with the aim of minimizing the total travel time of passengers and the energy consumption of the operation of trains. The departure times, running times, and dwell times of the trains have been optimized based on origin-destination-independent (OD-independent) passenger demands. We have proposed a new iterative convex programming (ICP) approach to solve this train scheduling problem. The performance of the ICP approach has been comparedwith other alternative approaches, such as nonlinear programming approaches, a mixed integer nonlinear programming (MINLP) approach, and an MILP approach. The ICP approach has been shown, via a case study, to provide the best trade-off between performance and computational complexity for the train scheduling problem. • Train scheduling for a single line based on OD-dependent passenger demands. We have adopted a stop-skipping strategy to reduce the passenger travel time and the energy consumption further based on origin-destination dependent (OD-dependent) passenger demands in an urban rail transit line. The train scheduling problem with stop-skipping results in a mixed integer nonlinear programming problem and we have proposed a bi-level optimization approach and an efficient bi-level optimization approach to solve this problem. Simulation results show that the stop-skipping strategy outperforms the all-stop strategy. Moreover, the bi-level approach yields a better control performance than the efficient bi-level approach but at a cost of a higher computation time. • Train scheduling for networks with time-varying OD-dependent passenger demands. For the train scheduling for urban rail transit networks, we have developed an event-driven model, where the time varying OD-dependent passenger demands, the splitting of passenger flows, and the passenger transfer behavior at transfer stations is included. The resulting train scheduling problem is a real-valued nonlinear nonconvex problem, which can be solved by gradient-free nonlinear programming approaches (e.g., pattern search), gradient-based nonlinear programming approaches (e.g., sequential quadratic programming (SQP)), genetic algorithms, or an MILP approach. We have applied an SQP method and a genetic algorithm to solve the train scheduling problem for a case study, the results of which have shown that the SQP method provides a better trade-off between control performance and computational complexity with respect to the genetic algorithm.