A variable-splitting Lagrangian decomposition for train timetabling and skip-stopping with train-type decision

•Apply time-dependent and preference-grouped demand representation.•Construct a layered space–time network shared by multi-type trains.•Formulate the train timetabling and skip-stopping problem with train-type decisions.•Develop a variable-splitting Lagrangian decomposition for the proposed model. While designing the train timetabling and skip-stopping plan in a space–time network shared by multi-type trains, a prevailing approach is to predesignate a specific type for each train to simplify the problem. However, such a setting is unreasonable and inaccurate to a considerable extent. This paper focuses on how to jointly optimize the train timetabling and skip-stopping problem with train-type decision for a high-speed rail corridor. With the help of a time-dependent and preference-grouped demand representation, this problem is formulated as an integer linear programming model, in which the optimization objective is to minimize the total train- and passenger-related costs. Under the Lagrangian relaxation framework, we employ a variable-splitting technique to decompose the proposed model into several solvable subproblems. By further exploiting the dual solution information, a three-stage heuristic method is developed to generate the expected feasible solution to the problem under consideration. Finally, we conduct a series of numerical experiments to demonstrate the efficiency and effectiveness of the proposed approach.