A computational graph-based model and a back-propagation solution algorithm for a networked train rescheduling problem

Real-time train rescheduling is of more significant requirements on both the computation time and solution performance compared to offline scheduling. The motivation for this study is to develop an efficient and effective method to reschedule disrupted trains in the context of severe disruptions, e.g., a four-hour segment blockage. A novel computational graph (CG)-based model is proposed to provide a continuous representation of the problem, wherein the discrete “if-then” decision-making process is transformed into continuous numerical computations that can be efficiently addressed. A customized back-propagation (BP) algorithm is developed to refine the solutions through an iterative process that includes a forward calculation of the objective function and a backward derivation of the decision variables. Owing to these computationally efficient processes, our proposed methodology can effectively handle the increasing complexity arising from detailed mesoscopic-level formulations in large-scale instances. We conduct experiments on both a small hypothetical network and the real-world Chinese high-speed railway network to validate the effectiveness and efficiency of our method. We also perform experimental analysis to examine the appropriate parameter settings for improved system performance.