Optimal Trajectory Planning for Trains under Operational Constraints Using Mixed Integer Linear Programming*

The optimal trajectory planning problem for trains under operational constraints is considered, which is essential for the success of the real-time operation and the rescheduling process for railway networks. The operational constraints caused by the timetable, real-time operation, or rescheduling often include target points and target window constraints. The approach proposed in this paper can take such constraints into account. In addition, the varying maximum traction force is approximated using a piecewise affine function and included in the trajectory planning problem. The optimal control problem is recast as a mixed integer linear programming problem, which can be solved efficiently by existing solvers. A case study is used to demonstrate the performance of the proposed approach.