Multi-train trajectory optimization for energy-efficient timetabling

This paper proposes a novel approach for energy-efficient timetabling by adjusting the running time allocation of given timetables using train trajectory optimization. The approach first converts the arrival and departure times to time window constraints in order to relax the given timetable. Then a train trajectory optimization method is developed to find optimal arrival/departure times and optimal energy-efficient speed profiles within the relaxed time windows. The proposed train trajectory optimization method includes two types, a single-train trajectory optimization (STTO), which focuses on optimizing individual train movements within the relaxed arrival and departure time windows, and a multi-train trajectory optimization (MTTO), which computes multi-train trajectories simultaneously with a shared objective of minimizing multi-train energy consumption and an additional target of eliminating conflicts between trains. The STTO and MTTO are re-formulated as a multiple-phase optimal control problem, which has the advantage of accurately incorporating varying gradients, curves and speed limits and different train routes. The multiple-phase optimal control problem is then solved by a pseudospectral method. The proposed approach is applied in case studies to fine-tune two timetables, for a single-track railway corridor and a double-track corridor of the Dutch railway. The results suggest that the proposed approach is able to improve the energy efficiency of a timetable.