The integrated optimization of robust train timetabling and electric multiple unit circulation and maintenance scheduling problem

Train timetables provide trains’ departure and arrival times at each space node, and electric multiple unit circulation and maintenance schedules assign the tasks of trips and maintenance to electric multiple units. Forming two schedules independently could bring infeasible solutions in both phases of forming and practice, so the purpose of this study is to avoid infeasibilities and generate a better integrated solution. To illustrate the two problems in one mathematical model, we introduce a space–time–state framework, which can show not only electric multiple units’ trajectories, but also their accumulative running distance (the core factor in maintenance) as the state dimension simultaneously. Due to the occurrence of the disruptions, delays might be caused in both trains’ traveling and maintenance. Therefore, the buffer time should be inserted into the activities such as running in sections, electric multiple unit circulation and maintenance in order to guarantee robustness. A 0-1 nonlinear integer programming model is built, which integrates the formulations of both robust train timetabling and electric multiple unit circulation and maintenance scheduling problems. It is verified by GAMS solver within small-scale instance. However, due to the large scale of the real-world cases, the GAMS solver cannot deal with that in a receivable computational time. In order to solve this integrated model effectively, we propose an improved ant colony algorithm. This algorithm provides solutions not only as good as GAMS in small-scale cases, but also of high quality in large-scale cases. We obtain the robust train timetables and electric multiple unit assignment and maintenance schedules of Beijing–Shanghai high-speed railway in a relatively short time using the proposed ant colony algorithm.