Geographic decompositions in railway timetable planning: Modelling and computational assessment

Railway timetable planning is the core of railway operations, which aims to make efficient use of infrastructure capacity and provide fast, punctual, and reliable services for customers. A timetable consists of a feasible train schedule adhering to operational constraints and meeting certain quality objectives, and the complexity and scale of railway networks require advanced algorithms to address large-scale instances. For this, decomposition approaches have been developed, exploiting for instance the geographical structure of the problem by partitioning the problem into more manageable smaller areas or stations and junctions. Nevertheless, it remains an open question how these specific choices balance to a different extent the computation effort to solve decomposed subproblems versus coordinating them towards a global, optimal solution. In this paper, we carry out an extensive computational analysis to evaluate the effects of diverse decomposition scenarios in a real-life case study of the Swiss Federal Railways. For this, we model and implement automatic geographic decomposition architectures based on a systematic algorithmic approach, on an existing logic-based Benders decomposition framework for railway timetable planning. In particular, we explore a process based on aggregation of areas into larger areas to generate a set of decompositions. The results of the computational analysis by means of random forests show the potential to minimize runtimes in decompositions with small number of large-sized areas with a relatively small master problem, facilitating a simpler coordination mechanism between master problem and subproblems, which strongly influences the computational effort to solve problem instances. Nonetheless, despite finding explainability in the contributions of factors to the computational effort required to solve different decompositions of the timetabling problem, the analysis also reveals complex relationships between multiple factors.