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.

In railway traffic systems, it is essential to achieve a high punctuality to satisfy the goals of the involved stakeholders. Thus, whenever disturbances occur, it is important to effectively reschedule trains while considering the perspectives of various stakeholders. This typically involves solving a multi-objective train rescheduling problem, which is much more complex than its single-objective counterpart. Solving such a problem in real-time for practically relevant problem sizes is computationally challenging. The reason is that the rescheduling solution(s) of interest are dispersed across a large search tree. The tree needs to be navigated fast while pruning off branches leading to undesirable solutions and exploring branches leading to potentially desirable solutions. The use of parallel computing enables such a fast navigation of the tree. This paper presents a heuristic parallel algorithm to solve the multi-objective train rescheduling problem. The parallel algorithm combines a depth-first search with simultaneous breadth-wise tree exploration while searching the tree for solutions. An existing parallel algorithm for single-objective train rescheduling has been redesigned, primarily, by (i) pruning based on multiple metrics, and (ii) maintaining a set of upper bounds. The redesign improved the quality of the obtained rescheduling solutions and showed better speedups for several disturbance scenarios. CCBY

In railway traffic systems, whenever disturbances occur, it is important to effectively reschedule trains while optimizing the goals of various stakeholders. Algorithms can provide significant benefits to support the traffic controllers in train rescheduling, if well integrated into the overall traffic management process. In the railway research literature, many algorithms are proposed to tackle different versions of the train rescheduling problem. However, limited research has been performed to assess the capabilities and performance of alternative approaches, with the purpose of identifying their main strengths and weaknesses. Evaluation of train rescheduling algorithms enables practitioners and decision support systems to select a suitable algorithm based on the properties of the type of disturbance scenario in focus. It also guides researchers and algorithm designers in improving the algorithms. In this paper, we (1) propose an evaluation framework for train rescheduling algorithms, (2) present two train rescheduling algorithms: a heuristic and a MILP-based exact algorithm, and (3) conduct an experiment to compare the two multi-objective algorithms using the proposed framework (a proof-of-concept). It is found that the heuristic algorithm is suitable for solving simpler disturbance scenarios since it is quick in producing decent solutions. For complex disturbances wherein multiple trains experience a primary delay due to an infrastructure failure, the exact algorithm is found to be more appropriate. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.

Rescheduling train timetables is a hard optimization problem that often needs to be solved in real-time due to railway disturbances. The two main challenges faced by algorithmic approaches for train rescheduling are: (i) to efficiently search the vast solution spaces of real-world problems, (ii) to effectively reschedule trains and return a solution of practical relevance. We identify a few problem constraints of practical relevance by interviewing a rail domain expert and use a subset of the constraints to extend our basic problem model. This paper presents (i) an investigation on the effect of introducing three of the identified problem constraints on the search for rescheduling solutions, (ii) an improved parallel search algorithm for finding rescheduling solutions that adhere to the three additional constraints, called practical solutions in this paper. An experiment is conducted on a Swedish railway network with disturbances on single-tracked and double-tracked lines. It is found that apart from giving a practical solution, additional restrictions often improved the parallel search process by making the algorithm reach solutions sooner. The parallel search algorithm can quickly deliver practical solutions on an ordinary computer, even for significant disturbances.