A priority-based ADMM approach for flexible train scheduling problems

Abstract

In this study, we focus on how to optimize multi-type train scheduling problems in a practically available and computationally efficient manner. When solving the complicated train timetabling problem with overtaking operations for a congested high-speed rail corridor, a simplified approach is to predesignate a thin time interval from its origin station for each train. This setting is difficult and laborious in practice. What is more serious is that an imperfect setting may cause the expected solutions to be unreachable in many instances. To fundamentally get out of this thorny trouble, this study proposes a flexible scheduling framework that extends narrow time limitations to one-hour periods, which allows the trains to depart from any timestamp within the relaxed period. Further, a group of incompatibility constraints with a more compact form is formulated to mirror the coupling relation between train headway and regularity requirements. However, the relaxed time window increases the difficulty of obtaining the optimal or near-optimal solution under the standard Lagrangian-based decomposition framework. Therefore, an improved alternating direction method of multipliers (ADMM) approach is introduced for effectively eliminating the computational barriers that are due to its increased complexity. Specifically, a priority-based search sequence is employed by applying the associated dual costs during the solution of train-level path subproblems individually. Finally, a set of numerical experiments is conducted to demonstrate the effectiveness and availability of the proposed approach.