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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.

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 realtime 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 singleobjective 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.

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