An integrated micro-macro approach for high-speed railway energy-efficient timetabling problem

Abstract

Energy efficiency of train operations is influenced largely by the speed control and the scheduled running time in the train timetable. In practice, the running time of a train is often determined in the train timetabling process at the macroscopic level while the energy-efficient speed control of a train on a segment is often determined at the microscopic level with the given timetable. They are usually optimized separately due to limited computational resources, which however may result in sub-optimal solutions. To address this issue, this paper proposes a novel integrated micro-macro approach for better incorporating train energy-efficient speed control into the railway timetabling process. Firstly, we formulated the integrated train timetabling and speed control optimization problem as a nonlinear mixed-integer programming model. Due to its complexity, we reformulate it on the basis of flow conservation theory in a space–time-speed (STS) network and solve the problem in two steps. In the first step, a set of pre-solved energy-efficient train trajectory templates is generated by a segment-level optimization approach with consideration of train travel time, entry speed and exit speed to save computation time. In the second step, a near-optimum train energy-efficient timetable solution is found by a fast algorithm, which consists of the shortest generalized cost path algorithm, conflict detection and resolution algorithm, and calculation of dynamic headways between two successive trains. The numerical experiments demonstrate that the developed approach provides better outcomes than the benchmark case in terms of both train journey time and energy consumption.