Collaborative optimization for train scheduling and train stop planning on high-speed railways

Focusing on providing a modelling framework for train operation problems, this paper proposes a new collaborative optimization method for both train stop planning and train scheduling problems on the tactic level. Specifically, through embedding the train stop planning constraints into train scheduling process, we particularly consider the minimization of the total dwelling time and total delay between the real and expected departure times from origin station for all trains on a single-track high-speed railway corridor. Using the stop planning indicators as important decision variables, this problem is formally formulated as a multi-objective mixed integer linear programming model, and effectively handled through linear weighted methods. The theoretical analyses indicate that the formulated model is in essence a large-scale optimization model for the real-life applications. The optimization software GAMS with CPLEX solver is used to code the proposed model and then generate approximate optimal solutions. Two sets of numerical examples are implemented to show the performance of the proposed approaches. The experimental results show that, even for the large-scale Beijing–Shanghai high-speed railway, the CPLEX solver can efficiently produce the approximate optimal collaborative operation strategies within the given gaps in acceptable computational times, demonstrating the effectiveness and efficiency of the proposed approaches.