Lu Yang

High-speed railways (HSRs), with their advantages of safety, energy conservation, and convenience, are increasingly becoming the preferred mode of transportation. Railway operators schedule full-schedule timetables to operate as many trains and serve as many passengers as possible. However, due to the fluctuation in passenger demands, it is not necessary to operate all trains in full-schedule timetable, which results in high operation costs and too much energy consumption. Based on this, we propose an integrated approach to schedule passenger train plans and train timetables by selecting trains to operate from the full-schedule timetable, adjusting their stopping scheme and operation sequence to reduce operation costs and energy consumption and contribute to sustainable development. In the scheduling process, both operation costs and passenger service quality are considered, and a two-objective model is established. An algorithm is designed based on Non-dominated Sorting Genetic Algorithms-II (NSGA-II) to solve the model, containing techniques for acceleration that utilize overtaking patterns, in which overtaking chromosomes are used to illustrate the train operation sequence, and parallel computing, in which the decoding process is computed in parallel. A set of Pareto fronts are obtained to offer a diverse set of results with different operation costs and passenger service quality. The model and algorithm are verified by cases based on the Beijing–Shanghai HSR line. The results indicate that compared to the full-schedule timetable, the operation costs under three sets of passenger demands decreased by 35.4%, 27.7%, and 15.7% on average. Compared to the genetic algorithm with weighting multiple objectives and NSGA-II without acceleration techniques, the algorithm proposed in this paper with the two acceleration techniques of utilizing overtaking patterns and parallel computing can significantly accelerate the solution process, with an average reduction of 42.9% and 38.3% in calculation time, indicating that the approach can handle the integrated scheduling problem economically and efficiently.

This research paper proposes a Lagrangian method to address the passing capacity of the calculation problem (PCCP) for a hub station in a high-speed railway (HSR) system. The passing capacity of a hub station is critical for determining the train timetable and maximizing the number of trains that can operate on different lines. The objective of this study is to determine the maximum number of trains that can pass through, start at, or end at a hub station. To achieve this objective, a mathematical model was introduced to solve the PCCP. The model was decomposed into two parts using a Lagrangian relaxation algorithm. The first part of the model was a simple train arrival problem (TAP) that reflected the timing of trains at the hub station with simultaneous arrival and departure time constraints. The second part of the model was a train spatio-temporal routing problem (TSRP) that aimed to solve the shortest spatio-temporal path of trains with free conflict with the train’s trajectory. A real instance was provided to demonstrate the feasibility of the proposed approach and the effectiveness of the Lagrangian method. The results showed that the proposed method can efficiently solve the PCCP and maximize the passing capacity of a hub station in an HSR system.

Heavy-haul railway transport is a critical mode of regional bulk cargo transport. It dramatically improves the freight transport capacity of railway lines by combining several unit trains into one combined train. In order to improve the efficiency of the heavy-haul transport system and reduce the transportation cost, a critical problem involves arranging the combination scheme in the combination station (CBS) and scheduling the train timetable along the trains’ journey. With this consideration, this paper establishes two integer programming models in stages involving the train service plan problem (TSPP) model and train timetabling problem (TTP) model. The TSPP model aims to obtain a train service plan according to the freight demands by minimizing the operation cost. Based on the train service plan, the TTP model is to simultaneously schedule the combination scheme and train timetable, considering the utilization optimal for the CBS. Then, an effective hybrid genetic algorithm (HGA) is designed to solve the model and obtain the combination scheme and train timetable. Finally, some experiments are implemented to illustrate the feasibility of the proposed approaches and demonstrate the effectiveness of the HGA.