A parallel algorithm for train rescheduling

Document Type

Journal Article

Publication Date


Subject Area

mode - rail, planning - methods, place - europe, operations - performance, operations - scheduling


Railway traffic, Rescheduling, Parallel depth-first search, Optimization


One of the crucial factors in achieving a high punctuality in railway traffic systems, is the ability to effectively reschedule the trains when disturbances occur. The railway traffic rescheduling problem is a complex task to solve both from a practical and a computational perspective. Problems of practically relevant sizes have typically a very large search space, making them time-consuming to solve even for state-of-the-art optimization solvers. Though competitive algorithmic approaches are a widespread topic of research, not much research has been done to explore the opportunities and challenges in parallelizing them. This paper presents a parallel algorithm to efficiently solve the real-time railway rescheduling problem on a multi-core parallel architecture. We devised (1) an effective way to represent the solution space as a binary tree and (2) a novel sequential heuristic algorithm based on a depth-first search (DFS) strategy that quickly traverses the tree. Based on that, we designed a parallel algorithm for a multi-core architecture, which proved to be 10.5 times faster than the sequential algorithm even when run on a single processing core. When executed on a parallel machine with 8 cores, the speed further increased by a factor of 4.68 and every disturbance scenario in the considered case study was solved within 6 s. We conclude that for the problem under consideration, though a sequential DFS approach is fast in several disturbance scenarios, it is notably slower in many other disturbance scenarios. The parallel DFS approach that combines a DFS with simultaneous breadth-wise tree exploration, while being much faster on an average, is also consistently fast across all scenarios.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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