Joint optimization of train scheduling and routing in a coupled multi-resolution space–time railway network

Train scheduling and routing are two critical and fundamental problems in the field of railway operations, especially under the large demand scenarios or complicated operation schemes. These problems are often solved separately and sequentially from the perspectives of different decision stages. To further make these two decision-making processes consistent, this paper develops a joint optimization model in a multi-resolution space–time network, by coupling the conflict-free routing constraints into the train scheduling process. To solve this model, a feedback iterative framework consisting of the Lagrangian relaxation and the branch-and-bound algorithm is developed, in which the Lagrangian relaxation aims to generate the train schedule and the branch-and-bound strategy with the constraint updating procedure resolves the potential micro conflicts. Compared with some existing approaches in the literature, the proposed model and solution algorithm have the merit of no requirement of optimization solvers. To test the performance of the proposed approach, we apply the algorithm to different small-scale operation scenarios and a real-life case with the INFORMS RAS 2016 (Railway Applications Section) dataset.