Simultaneously re-optimizing timetables and platform schedules under planned track maintenance for a high-speed railway network

Abstract

Train timetabling and train platforming are problems of crucial importance when scheduling high-speed trains. Often, these problems are solved separately and in sequence. It is also not uncommon for the problems to be further decomposed by direction since the use of tracks is usually direction specific in a high-speed network. In this paper, we consider the optimization problem of integrating re-timetabling and re-routing decisions within station areas for multiple stations when scheduled maintenance renders the existing, optimized schedules infeasible. We model the underlying problems using a space–time network on a mesoscopic level and propose a 0–1 binary integer programming model that can simultaneously modify the timings and routes of trains from different directions. Two different solution approaches are described. The first is a commonly used Lagrangian Relaxation (LR) approach, while the second utilizes the Alternating Direction Method of Multipliers (ADMM) concept. For both methods, a time-dependent dynamic programming approach is used to solve the resulting subproblems. A comparison of the two approaches on instances provided by the Chinese high-speed railway indicates that the ADMM-based approach provides tighter upper bounds and typically requires fewer iterations than the Lagrangian Relaxation approach. Furthermore, the results show that a flexible track utilization policy provides better timetables, with fewer cancellations and less total delay, than a fixed, dedicated direction, track policy.