Energy-efficient high-speed train rescheduling during a major disruption

Disruptions are inevitable in daily train operations, and can cause high-speed trains to deviate from their official schedules. Therefore, the efficient rescheduling of disrupted trains is critical for ensuring smooth daily operations. We sought to determine the appropriate arrival and departure times and orders of trains at each station during a disruption, and the speed profile of each train, to reduce the delay costs and energy consumption. To embed the train speed profile corresponding to energy saving into the train rescheduling problem, a space-time-speed network is applied for problem formulation. Thus, the energy-efficient train speed profile is embedded in the speed dimension in the space-time-speed hypernetwork. The detailed train speed profile between two stations is formulated as a multiple-phase optimal control model, which is solved using a pseudospectral method. Then, an integer linear programming model based on multicommodity flow is built to solve the train rescheduling problem. We decompose it via the alternating direction method of multipliers into a series of easy-to-solve shortest path subproblems. Each subproblem is then efficiently solved using a dynamic programming algorithm. Finally, the Xi'an-Chengdu high-speed railway line is used to test our model and algorithms, thereby demonstrating the trade-off between passenger-service quality and energy efficiency