Variable Neighborhood Search and Alternating Direction Method of Multipliers for Integrated Optimization of Maintenance Windows and Train Timetables

Train timetables play an important role in improving passenger services and transportation efficiency. The arrangement of maintenance windows directly affects the maintenance quality, which in turn interacts with the train timetable. In this study, we investigated the integrated optimization of maintenance windows and train timetables. We creatively abstracted the occupation of track capacity for maintenance activities as arcs and constructed an integrated space-time network for maintenance activities and trains. The initial model was converted into a multicommodity network flow model containing multiple types of arcs. Furthermore, we divided the problem into two subproblems: (1) the arrangement of major maintenance activities. (2) the integrated optimization of maintenance windows and train timetables for fixed maintenance activities. Heuristic algorithms based on the customized variable neighborhood search and the alternation direction method of multipliers framework were designed respectively to solve the aforementioned subproblems. The effectiveness and efficiency of the proposed model and algorithm are demonstrated through a series of practical case studies using data from the Wuchang-Zhuzhou Conventional railway.