Distributed train timetable synchronization in metro network: An ADMM-based decomposition framework

The increasing spatial or temporal scales of metro networks generate an important research challenge in developing fast and efficient optimization methods for handling the train timetable synchronization problem (TTSP). This paper develops a distributed optimization algorithm for the TTSP of complex metro networks, with the objective of minimizing both the waiting time of inbound and transferring passengers in the whole network. We construct explicit dynamic equations of train passenger loads throughout the network and quantify the transferring passengers at transfer stations. These equations encapsulate the dynamic passenger transfer behavior within the metro system. To deal with the computationally expensive large-scale MINP problem, an alternating direction method of multipliers (ADMM) based decomposition approach is proposed to split the original TTSP into a set of single-line timetabling subproblems that can be solved in a decentralized manner. Furthermore, a novel heuristic two-level ADMM-based approach, where the upper level decides the connections among trains of different lines and the lower level applies standard ADMM with fixed binary variables to optimize the timetable, is designed to deal with the nonconvexity issue. We demonstrate its ability to conveniently obtain a high-quality solution to the network timetable synchronization problem numerically.