Integrated optimisation of train stop planning and timetabling in a railway network: a stochastic optimisation approach

This study investigates an integrated train stop planning and timetabling problem considering the uncertainty of passenger demand in a railway network. With the scenario-based representation of demand distribution, an integer linear programming (ILP) model is formulated to simultaneously optimise the train timetable and stop plan, in which the time-space network representation method is adopted to characterise the movements of trains and passengers. The objective is to jointly optimise the total travel time of trains and passengers, and the expected number of unsatisfied or over-satisfied passengers over all demand scenarios. By analyzing the characteristics of the model, we decompose it into two subproblems based on trains (timetabling) and passengers (assignment), respectively. Then, an iterative algorithm based on variable neighbourhood search (VNS) is designed to solve the two subproblems iteratively. Additionally, a series of numerical experiments based on the real-world instance in a high-speed railway (HSR) network are implemented to verify the effectiveness of the proposed stochastic programming (SP) model and the iterative algorithm. The results demonstrate that (i) the proposed SP model is easy to implement in practice, and (ii) the developed iterative algorithm exhibits much higher computational efficiency than the optimisation solver.