Y. Wang, B. Ning, T. Tang, T.J.J. van den Boom, and B. De Schutter, "Efficient real-time train scheduling for urban rail transit systems using iterative convex programming," IEEE Transactions on Intelligent Transportation Systems, vol. 16, no. 6, pp. 3337-3352, Dec. 2015.
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 trade-off 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 trade-off between the control performance and the computational efficiency.