Bi-objective optimization of timetable and rolling stock schedule for an urban rail passenger and freight line

The urban rail transit system, traditionally focused on passenger transport, is now also emerging as a potential solution to the increasing demands of urban freight transport on the road, by using its surplus capacity for freight transport. The collaboration between passenger and freight transport has become a key issue for ensuring service quality and efficiency. In this context, this paper addresses the train scheduling problem with integrated passenger and freight transportation, which involves determining the optimal train timetable and rolling stock circulation plan to accommodate both passenger and freight demands. We formulate the problem as a bi-objective mixed integer programming model, which focuses on (1) minimizing the total passenger waiting time and (2) reducing operating costs. We also propose a linearization technique to handle the nonlinear objective function. To solve large-scale instances more efficiently, we develop an Alternating Direction-based NSGA-II (AD-NSGA-II) solution framework with a two-block structure and compared it with the benchmarks obtained by the commercial solver Gurobi. Several groups of experiments, including small-case instances and real-world instances based on the Beijing Daxing Airport line, are investigated to verify the effectiveness of the proposed model and algorithm. The numerical results show that adding freight services will not have a significant impact on passenger service quality. We also analyze the impacts of freight demand quantity, freight transport time budget, and freight train type on passenger service quality and operating costs, to provide valuable insights and inspiration for tactical decision-making.