This study discusses the issue of train rescheduling in high-speed railways (HSR) when unexpected interruptions occur. These interruptions can lead to delays, cancellations, and disruptions to passenger travel. An optimization model for train rescheduling under uncertain-duration interruptions is proposed. The model aims to minimize both the decline in passenger service quality and the total operating cost, thereby achieving sustainable rescheduling. Then, a hybrid optimization algorithm combining rolling horizon optimization with a deep-learning-embedded NSGA-II algorithm is introduced to solve this multi-objective problem. This hybrid algorithm combines the advantages of each single algorithm, significantly improving computational efficiency and solution quality, particularly in large-scale scenarios. Furthermore, a case study on the Beijing–Shanghai high-speed railway shows the effectiveness of the model and algorithm. The optimization rates are 16.27% for service quality and 15.58% for operational costs in the small-scale experiment. Compared to other single algorithms or algorithm combinations, the hybrid algorithm enhances computational efficiency by 26.21%, 15.73%, and 25.13%. Comparative analysis shows that the hybrid algorithm outperforms traditional methods in both optimization quality and computational efficiency, contributing to enhanced overall operational efficiency of the railway system and optimized resource utilization. The Pareto front analysis provides decision makers with a range of scheduling alternatives, offering flexibility in balancing service quality and cost. In conclusion, the proposed approach is highly applicable in real-world railway operations, especially under complex and uncertain conditions, as it not only reduces operational costs but also aligns railway operations with broader sustainability goals.

Comparing to other modes of transportation, high-speed railway has the advantages of energy saving, environment friendly, safety and convenience for passengers, and has been more and more popular. However, unforeseen emergencies may disrupt the normal train operation. In this paper, an integrated dispatch strategy (IDS) is proposed to synergistically reschedule the train timetable and rolling stock circulation plan under single-direction disruptions. A two-objective model is formulated, aiming at minimizing both the delay time of passengers and the operation costs of railway companies, to reschedule the train operation efficiently and economically. An algorithm based on Non-dominated Sorting Genetic Algorithms-II (NSGA-II) is designed to solve the model. To accelerate the solving process, we propose a quick method to generate an assignment plan to serve disrupted passengers, and based on the practical experiences, the algorithm acceleration strategy (AAS) is proposed to improve the quality of initial solutions. The model and algorithm are tested on real-world instances of the Beijing-Shanghai high-speed railway line. The results indicate that the average minimized delay time of passengers is 6,012,386 min and the average minimized additional operation costs (operation mileage of standby rolling stocks) are 1623 km, with a decrease of 28.5% and 18.3%, respectively, indicating the model and algorithm are adaptable to handle single-direction disruptions on the railway line, and AAS can further accelerate the computing speed and improve the solutions quality. Finally, the characteristics of disrupted sections of railway lines are well studied and analyzed.

For high-speed railway operations at the network level, unforeseen events that lead to operation interruptions are inevitable, which should be handled within a short period of time to reduce the influence of the events as much as possible. This paper introduces an integrated optimization method to deal with rescheduling problems at the railway network level under emergencies, rescheduling the train timetable, and utilizing the train sets. train set A three-objective optimization model is proposed with the aim of minimizing additional operation costs, total delay, and the number of transfer passengers. Then, an algorithm based on NSGA-III is proposed to solve the model. Computational experiments on real data are conducted to show the adaptability of the model and algorithm. The average optimization rate of the three objectives is 12.12%, 14.12%, and 10.57%, indicating the effectiveness of the method. Moreover, more experiments on a railway network in China are being conducted to analyze which section and which time have the greatest impact on the railway network when emergencies occur. According to the experiment, the bottleneck section is section 15, and the bottleneck time is 11:00 am. In addition, the importance of all the depots is discussed, and depot II is selected as the most important depot.

Nowadays, high-speed railway (HSR) has become one of the main choices for passengers. As the number of passengers increases, their travel demands become diverse and the fluctuation range of passenger travel demands will also increase. In order to adapt to the change of passenger travel demands, the switching frequency of timetables needs to be increased. When switching the timetable, the train-set circulation plan also needs to be considered. In this paper, a scheduling approach for quickly solving the timetable and the train-set circulation plan in the transition time is proposed. A section sequence is constructed in the integer programming model, and the primary train-set circulation plan is obtained. Then a stop plan is obtained on the basis of passenger travel demands. To obtain the final train-set circulation plan and the timetable, a genetic algorithm (GA) is designed, and a method that can ensure that the timetable meets the safety operation requirements is proposed. The scheduling approach is tested on the Beijing-Shanghai HSR. The results show that by extending the transition time, the scheduling approach can switch the train-set position from the old state to new state, without additional consumption of resources, on the premise of meeting the travel demands of passengers.

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.

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.