Trajectory optimization for passenger and freight trains on a single track railway line

This paper focuses on the trajectory optimization problem for both passenger and freight trains traveling in opposite directions on a single-track railway line. Firstly, we formulate a trajectory optimization problem that aims to simultaneously minimize the traction energy consumption of passenger and freight trains, as well as the total travel time of freight trains. Both types of trains are subject to their respective operational constraints, such as safety, punctuality and static speed limits. Secondly, we transform this problem into a multi-phase optimal control problem that incorporates the timetable, track gradients, speed limits and signal positions. The multi-phase optimal control problem is then solved by GPOPS-II software. Our approach enables us to model the multi-tracks at stations, allowing trains to meet and overtake at stations. Finally, the proposed method is applied to case studies of passenger and freight trains in a single-track railway, and the numerical simulation results validate the effectiveness of the proposed method.