Y. Wang, B. De Schutter, T.J.J. van den Boom, B. Ning, and T. Tang, "Efficient bi-level approach for urban rail transit operation with stop-skipping," IEEE Transactions on Intelligent Transportation Systems, vol. 15, no. 6, pp. 2658-2670, Dec. 2014.
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 bi-level 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 bi-level approach is compared with the existing bi-level 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 bi-level approach and the existing bi-level approach have a similar performance but the computation time of the efficient bi-level approach is around one magnitude smaller than that of the bi-level approach.