Abstract
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 article 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.
Highlights
Public transportation is an important part of daily human life
When rescheduling trains during a disturbance, the goals of an infrastructure manager are focused on the operational feasibility of the rescheduled timetable, while railway operators aim at minimizing operation costs [1]
The main contributions of the research presented in this paper are: (i) findings from an experimental study showing the benefits of incorporating multiple objectives in train rescheduling, as well as identified challenges resulting from the expanded tree search, (ii) a proposed parallel algorithmic approach to address the abovementioned challenges, (iii) a systematic assessment of quality-related properties of the resulting rescheduling solutions
Summary
Consider a MOP with i objectives, where each objective function fi corresponding to the ith objective needs to be minimized. For every solution not in the pareto set, there exists at least one solution in the set that dominates it. The goal of multi-objective optimization [10] is two-fold: 1) to find a set of solutions as close as possible to the pareto front, 2) to find a set of solutions as diverse as possible. In our case, this set of solutions is presented to a human expert who selects one of these solutions based on the situation at hand and his/her experience. For a detailed introduction to multi-objective optimization, see [11, 12]
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