Energy-efficient and demand-driven train timetable optimization with a flexible train composition mode

Given the dynamic and unevenly distributed metro or urban rail passenger demand, this paper investigates the train timetabling optimization that is responsive to demand fluctuations while also improving energy efficiency with a flexible train composition mode. For the studied problem, a mixed-integer nonlinear programming (MINLP) model is first developed to simultaneously optimize the number of train compositions (e.g., train carriages), the train headways, and the optimal speed profile selection decisions over the planning time horizon to minimize passenger waiting time and energy consumption. The nonlinear model is then reconstructed through a series of linearization techniques into an equivalent mixed-integer linear programming (MILP) model that can be solved by commercial MILP solvers. Furthermore, a customized heuristic algorithm employing Variable Neighborhood Search (VNS) is developed to produce high-quality solutions for large-scale problems. To demonstrate the effectiveness of the proposed model and algorithm, two numerical examples are presented, i.e., a small example and a real-world example based on the Yizhuang metro line. Computational findings demonstrate that our method significantly reduces energy consumption while maintaining service quality, thus contributing to the advancement of sustainable urban transportation systems, in contrast to existing methods reliant on fixed train compositions.