Periodic and aperiodic train timetabling and rolling stock circulation planning using an efficient Lagrangian relaxation decomposition

Abstract

Train timetabling and rolling stock circulation planning are problems of crucial importance for integrated planning. Often, these problems are separately solved in a sequential way without consideration of periodic train schedule. However, a notable drawback of this layered planning process is poor coordination and efficiency between train and rolling stock timetables, as well as lack of regularity. To this end, we explore the joint optimization problem of periodic and aperiodic train timetabling and rolling stock circulation planning in this paper. To address this comprehensive problem, an integer programming model is initially established by incorporating rolling stock circulation into optimizing periodic and aperiodic train timetabling. Due to the model-solving complexity, a three-dimensional space–time-state network is constructed to reformulate this model. Within this three-dimensional network, states are used to represent trains served by rolling stocks. Subsequently, the problem is transformed into a minimum-cost multi-commodity network flow problem with incompatible arcs based on the space–time-state network. And an efficient Lagrangian relaxation decomposition algorithm is proposed to solve this network flow problem. The effectiveness of the algorithm is verified through a series of case studies.