This paper examines the integrated optimization of pricing, seat allocation, and overbooking strategies in high-speed railway (HSR) operations. Overbooking helps address inefficiencies arising from empty seats due to passenger no-shows or last-minute cancellations. The complexity of the problem stems from two main factors: (i) the interdependence of pricing, seat allocation, and overbooking decisions, which jointly influence railway system performance; and (ii) the uncertainties associated with passenger demand and no-show behavior. To tackle these complexities, we develop a two-stage stochastic programming model aimed at maximizing expected railway profit. In the first stage, the model determines HSR pricing and seat allocation, including overbooking, while the second stage addresses potential denied boarding due to overbooking, based on the first-stage decisions. To solve the model, we employ a sample average approximation method and introduce a tailored progressive hedging algorithm (PHA). Additionally, we adapt commonly used surrogate-based optimization methods, such as Kriging and radial basis function models, for comparative analysis. Numerical studies on both a small-scale example and a real-world HSR line reveal that the proposed joint optimization significantly boosts railway profit across various demand and no-show scenarios, with the PHA solution approach outperforming surrogate-based methods in terms of both solution quality and computational efficiency.

The spatiotemporal rules of passenger flow in urban rail transit (URT) hubs are complex, meaning that simulation modeling and analysis of passenger flow distributions in hubs are very important in terms of scientifically organizing passenger flow and improving travel efficiency. In this study, an analysis was conducted of passengers' travel processes and behaviors, and a simulation model combining cellular automata (CA) and agent-based modeling (ABM) was proposed. A CA grid environment was used to describe the spatial constraints and movement logic, whereas ABM was employed to construct passenger agents. This approach included a visual perception model, a behavior decision-making model that took into consideration the influence of multiple factors, a fuzzy logic-based multi-channel selection model, and a group-competition-based action execution model, in order to finely characterize the individual microscopic behaviors. Tiyu Xilu Station of Guangzhou Metro in China was taken as a case study, and the simulation results were used to verify the effectiveness of the model. The key findings were as follows: the simulation results for escalator passenger throughput were close to the design capacity, with a difference of -4.2%; the service level for the west platform of Line 3 was lower than for the east platform, with the lowest being Level E; during peak hours, for every 10% increase in the degree of bidirectional pedestrian flow, the average dwell time increased by approximately 6.8%. These research results provide decision support for optimizing passenger flow organization in URT hubs.

This paper proposes a hierarchical reinforcement learning framework, termed Learning-Enhanced Conflict-Free Optimization (LECFO), to address the Train Timetabling Problem (TTP) in high-speed rail systems operating multiple-type trains. A novel Conflict-Free Scheduling Environment (CFSE) based on a spatiotemporal network is firstly constructed to emulate dispatcher decision-making in resolving train conflicts for an initialized timetable. CFSE ensures timetable feasibility by adaptively adjusting arc occupancy costs, thereby generating conflict-free train paths under strict operational constraints. Within this hierarchical framework, the reinforcement learning layer develops forward-looking strategies, with CFSE embedded as prior domain knowledge that constrains and supports the learning process. By ensuring feasibility through CFSE, the framework improves timetable quality through the learning layer. Comprehensive experiments on two real-world railway networks confirm the effectiveness of the proposed framework: the architecture is scalable across different network sizes and consistently yields high-quality solutions. Even in large-scale and complex scenarios beyond the capability of commercial solvers, LECFO demonstrates strong adaptability and generalization, underscoring its potential for practical deployment in high-speed rail scheduling.

To address the energy-saving optimization problem of urban rail transit train operation, this paper proposes a collaborative optimization method for onboard energy storage device (OBESD) capacity configuration and train interstation operation strategies. Based on a train multi-interval operation model and a train energy flow model, a collaborative optimization framework is established with the objective of minimizing the total life-cycle cost, comprehensively considering both OBESD investment costs and train operational energy consumption costs. Constraints including multi-interval train operation, fixed interstation running times, OBESD charging/discharging power and capacity, and passenger riding comfort are incorporated into the model. With the number of OBESD modules and train speed profiles as decision variables, an energy-saving optimization model considering multi-interval train dynamics and time-varying energy flow is developed. To solve the model, a dual-layer optimization algorithm is proposed. The outer layer determines the optimal number of OBESD modules using a fixed-step search strategy, while the inner layer optimizes train operation strategies under a given storage configuration using a simulated annealing algorithm based on multiparameter speed combinations. This approach enables collaborative optimization between train operation strategies and onboard energy storage capacity. The proposed method is validated using real-world operational data from Guangzhou Metro Line 1. The results show that the proposed model can effectively reduce train net energy consumption while strictly satisfying interstation running time constraints, achieving an energy-saving rate of 13.90% for full-line operation. In addition, sensitivity analysis results indicate that the optimal OBESD configuration is significantly influenced by economic parameters such as electricity price, storage investment cost, and life-cycle years, highlighting the important role of economic conditions in practical engineering applications. The findings provide practical decision support for urban rail transit operators in configuring onboard energy storage systems to achieve cost-effective energy savings.

This study investigates the impact of passenger no-show uncertainty on railway profit and examines the integrated optimization of dynamic pricing, seat allocation and overbooking for high-speed trains. To mitigate empty seat loss due to passenger no-shows and denied boarding (DB) costs caused by overbooking, we impose limits on overbooking and denied boarding rates for each leg. A large-scale nonlinear optimization model is developed with the aim of maximizing expected railway profit subject to various constraints, including train capacity, demand, upper and lower price bounds, temporal and spatial price relationships, and DB rates. An iterative heuristic optimization method is proposed, which gradually adjusts the overbooking rate for each leg and updates train capacity constraints accordingly. The optimization problem is decomposed into two subproblems: (i) optimizing dynamic pricing and seat allocation under allowable overbooking conditions without involving passenger no-shows, which is solved using bi-level programming; and (ii) adjusting the number of allowable overbookings based on passenger no-shows and DB situations, where the Monte Carlo method is used to simulate no-show scenarios for profit calculation. The complex large-scale problem is solved by iterating between the two subproblems. The performance of the proposed approach is demonstrated using both large-scale and small-scale examples. The results show increases in expected railway profit of 6.48% and 5.88%, and in expected passenger kilometers of 10.22% and 13.08%, respectively. Overbooking is effective and generates higher profits under conditions of passenger no-show behaviors and high demand.

Urban rail transit trains consume a significant amount of energy; therefore, reducing the operational energy consumption is of great importance for train energy-saving efforts. To address this issue, and to avoid the limitations of solutions constrained by operational condition combination strategies and the combination explosion of schemes with interval-by-interval position searches under unrestricted operational strategies, an operation control scheme solution method based on curve splicing is proposed. This method involves selecting curve segments and continuously splicing and recombining them to efficiently generate new running curves without being restricted by the basic energy-saving curve framework. Based on this optimization concept, a splicing strategy is developed that includes four parameter variables: the splice point location, splice point speed, splice relationship type, and control force magnitude. On this basis, a curve splicing optimization model is established, with the objective function being the minimization of the train’s operational energy consumption while meeting interval running time requirements. A two-layer iterative optimization algorithm is designed based on the simulated annealing framework. Utilizing the data of Guangzhou Metro Line 2, the optimized scheme achieves energy savings of 11.713% in the Baiyun Cultural Square–Baiyun Park interval and 9.115% in the entire downward intervals.

Saving energy has both significant environmental benefits and economic advantages. As the urban rail transit network and its consumed energy continue to expand, it is crucial to optimize the energy-saving operation scheme of trains. Energy-saving train operation often requires longer section running times, which is obviously not conducive to the quality of passenger service. In order to ensure passenger service quality when pursuing the decrease of the train's energy consumption and rolling stocks' operation cost, this paper proposes an integrated optimization model of the demand-oriented and energy-efficiency train timetable and rolling stock circulation plan for urban rail transit. Its objective is to minimize train net energy consumption, rolling stock utilization cost, as well as passenger waiting time and travel time. Specifically, the net energy consumption is defined as the difference between train required traction energy consumption and regenerative braking energy utilization. To efficiently solve this large-scale mixed integer nonlinear model, we design a solution algorithm combining Variable Neighborhood Search (VNS) and CPLEX, in which seven different neighborhood structures are constructed. Based on the data of Guangzhou Metro Line 13, we have verified the effectiveness and performance of the model and algorithm through numerical experiments of various scales, as well as through comparisons with other algorithms and models. The results demonstrate that the timetable and rolling stock circulation plan obtained by VNS can reduce net energy consumption by 9.55 %, rolling stock utilization cost by 9 %, and passenger waiting time by 4.77 %, and their travel time by 0.87 % compared to the current timetable.

The accurate fitting of railway station track profiles is crucial for improving the quality of station-related engineering projects. However, in practice, there are still cases where straight lines are used to approximate vertical curve segments. To avoid the ‘straight-line approximation’ deviation in the gradient value of the profile’s straight segments, this paper establishes a mathematical programming model with the objective of minimising the total amount of track raising and lowering. To satisfy the model constraints, an optimal vertical curve fitting algorithm, utilising a bisector vector approach to unambiguously resolve the conjugacy issue in analytical circular curve calculations, and a genetic algorithm based on neighbourhood search, specifically designed to fine-tune initial least squares gradient estimates and avoid systematic deviations, are proposed. Finally, the effectiveness of the proposed model and algorithm is validated through a case study. With a total grade value adjustment of only 0.45‰ based on the least squares method, the proposed fitting algorithm achieves a 38.7% reduction in track raising and lowering compared to manual fitting. This demonstrates the effectiveness of the proposed method in achieving the integrated optimisation of straight-line segments and vertical curve segments within the longitudinal profile. The implementation of this algorithm through programming can significantly enhance both the efficiency and quality of railway station track profile fitting.

Focusing on the transportation organization characteristics of the high-speed maglev station, this article simulates the train operation process based on the train running calculation and the train operation scheme for multi-type trains, and analyzes the station capacity based on the simulation for multi-type trains and typical-layout stations. This study is carried out from the following three perspectives: (i) calculating train running in the train operation process, (ii) calculating the carrying capacity for single-type trains, and (iii) simulating the train operation scheme at the station. By analyzing the running process and working conditions of a high-speed maglev train during various operations, a kinematic model for the train running and a simulation method for the technical operation process based on the operation calculation are established. The simulation results for train running calculation are then used to determine the time required and the capacity for the station handing single-type trains, which is the basis of analyzing multi-type trains operations. In the simulation for operations of multi-type trains, three simulation strategies are designed: track selection strategy, route segment lock/unlock strategy, and operation method choosing strategy. The operational process of a high-speed maglev station under multi-train and multi-technology conditions is simulated based on the above strategies, and the capacity utilization of the station is calculated. The capacity utilization characteristics of typical-layout stations and the recommended layouts for stations under different scenarios are given for capacity analysis and optimization.

The spatial and temporal rules governing passenger flow in urban rail transit (URT) stations are complex, and simulation modeling and analysis of passenger flow distribution in stations are very important in regard to scientifically organizing and controlling passenger flow and improving passenger travel efficiency. With a focus on the multilevel three‐dimensional spatial structure of URT stations and the composition of multiclass passenger flow lines, the travel process and microbehavior of passengers are analyzed here. The goal‐driven behavior of passenger flow groups in the free area and the interaction between them are considered, and a static–dynamic field hybrid model describing the differences in speed between passengers, their walking, and avoidance behavior and a queue field model of queuing behavior are constructed. A selection behavior model for facility nodes such as gates, interlayer facilities, and waiting areas is constructed to represent heterogeneous passenger flow to multiservice channels. A passenger flow simulation method framework for URT stations that takes into account heterogeneous passenger flow, the 3D spatial structure, and multipotential energy field is also established. The effectiveness of the proposed model and method is verified via simulation of Changsha Metro Shumuling Station, and it is found that the proportion of escalators selected as interlayer facilities is significantly higher than that for stairs. After a train leaves the station, the passenger flow density on both sides of the platform reaches more than 1.5 person/m 2 , significantly higher than that in the central area of the platform. The average passing times for passengers at the exit gate and the ascending escalator are 16–18 and 13–14 s, respectively. The average queue length and passing times for passengers are higher than those at the entrance gate and the descending escalator. These results can provide support for decisions on the actual operation of URT stations.

To enhance the service scope and quality of urban public transport systems, this study investigates the optimal design problem of feeder-bus networks related to urban rail transit considering time windows (FBNDP-TW). To ensure an acceptable passenger travel time, we differentially set the travel time window for each origin-destination (OD) pair based on the ideal travel time. Considering logical constraints, capacity constraints and time window constraints, we construct an FBNDP-TW optimisation model to minimise passengers’ generalised travel cost and bus operators’ operating cost. To solve this model, a genetic algorithm is developed with a diverse multi-neighbourhood crossover operation that includes ‘direct’, ‘forward’ and ‘adjacent’ rules. This crossover operation mechanism can efficiently make the feeder-bus network quickly meet time window constraints to guarantee its quality. Finally, the proposed model and algorithm are evaluated using a standard example network. The results confirm that they can effectively ensure the travel time of each OD. Although integrating time window constraints slightly raises network cost, it significantly reduces the maximum OD detour ratio and ensures the travel time of all ODs within the acceptable range.

High-speed railways (HSR) and airlines can complement each other in long-distance journeys served by connecting flights through a hub. To encourage airline-HSR cooperation and promote intermodal transport services, we examine two capacity agreements under the capacity limitations of HSR and/or airlines and their effects on ticket pricing, passenger volume, travel time, frequency, consumer surplus, social welfare, and profitability. In a capacity sell agreement, HSR sells its capacity to airline (HSA), and airline provides the bundling service. In a capacity purchase agreement, HSR purchases airline capacity (HPA) and offers the bundled service. We first analytically compare two capacity agreements with no-cooperation cases, and find that the joint ticket price under the HSA agreement offers a price advantage over individual ticket purchases in non-cooperation scenarios only when HSR is capacity-constrained. Although the HPA agreement also exhibits a similar joint price advantage as the HSA agreement, it requires the stringent condition that both transport modes have limited capacities. Regarding consumer surplus, it tends to increase under the HSA agreement when both transport modes have capacity limitations or both do not have capacity limitations. However, the increasing trend can be relaxed to different capacity limitation conditions under the HPA agreement. We then directly compare the HSA and HPA agreements through simulations. The results indicate that the HSA agreement yields higher consumer surplus and profits than the HPA agreement, while the HPA agreement achieves greater social welfare.

For a given timetable in urban rail transit systems, this paper presents a practical energy efficiency optimization problem that carries out adjustments to the timetable, with the goal of energy saving. We propose two strategies to address this challenge, including adjusting the section running time by selecting a speed profile and improving the utilization of regenerative braking energy by adjusting the trains’ departure time. Constraints on the range of adjustment for energy-efficient time elements are constructed for maintaining the stability of elements of the given timetable. An energy efficiency optimization model is then established to minimize the total net energy consumption of the timetable, and a solution algorithm based on a genetic algorithm is proposed. We make small-scale adjustments to trains’ running trajectories to optimize the overlap time of braking and traction conditions among multiple trains. The case of the Guangzhou Metro Line 8 in China is presented to verify the effectiveness and practicality of our method. The results show that the consumption of traction energy is reduced by 0.95% and the use of regenerative braking energy is increased by 8.18%, with an improvement in energy efficiency of 6.78%. This method can achieve relatively significant energy efficiency results while ensuring the stable service quality of the train timetable and can provide support for an energy-efficient train timetable for urban rail transit operation enterprises.

To mitigate empty seat loss caused by random passenger no-show behavior, this study extends seat allocation to joint optimization of overbooking and seat allocation for high-speed railways (HSR). Assuming that stochastic passenger demand follows a specific distribution and considering various constraints, including train capacity, demand, and denied boarding rate constraints, a nonlinear stochastic programming model for joint optimization of overbooking and seat allocation for HSR is constructed with the aim of maximizing railway expected revenue. To solve this optimization model, a multi-level optimization algorithm is designed. Based on the sampling averaging approximation method, demand scenarios and passenger no-show scenarios are generated and the optimization problem is decomposed, including the joint optimization of overbooking and seat allocation under a single demand scenario, and the ticket adjustment under other demand scenarios. For the former, it is further divided into two sub-problems according to the stochastic nature of passenger no-show behavior, which is optimized iteratively. Finally, the effectiveness of the proposed model and algorithm is evaluated through numerical studies. The results demonstrate that the proposed joint optimization method effectively addresses the randomness of passenger demand and no-show behavior, thereby improving HSR expected revenue and making up for the empty seat loss resulting from passenger no-show behavior.

This paper investigates the optimization of multistage dynamic pricing for high-speed railway (HSR) considering flexible pre-sale period division scheme. To address the variability of daily demand during the booking horizon, an elastic demand function for each day is developed. Considering various constraints, including train capacity constraints, passenger demand constraints, price-related constraints, a non-linear mixed integer optimization model is formulated for the multistage dynamic pricing optimization problem to maximize railway revenue. The complicated capacity-sharing relationship for HSR and flexible pre-sale period division increase the problem’s scale. Thus, a comprehensive optimization approach is proposed based on decomposing the optimization problem into two subproblems. Subproblem 1 solves multistage dynamic pricing and ticket allocation based on a known period division scheme generated by subproblem 2, while subproblem 2 adjusts the boundaries between two consecutive periods to generate a period division neighborhood scheme. Subproblem 1 is solved by formulating as a bi-level programming problem. The numerical examples are conducted to evaluate the proposed model and solution methods, providing valuable decision support for railway operators.

According to the operation characteristics of urban rail transit in fast and slow train modes, this paper studies the energy-saving problem of the two train modes from the perspective of optimization of the train running curve. A method based on the control parameters including control force and speed is proposed. Under the constraint of the interval running time, considering the station speed limit and curve speed limit, and with the goal of minimizing the energy consumption during operation, an optimization model of an urban rail transit train running curve under fast and slow train modes is established, and a solution method based on the simulated annealing algorithm and multi-parameter control strategy is designed. Using the line and operation data of Guangzhou Metro Line 21, the interval energy-saving running curves under two modes are obtained, and the data of the energy consumption and interval running time are analyzed, verifying the effectiveness of the energy saving strategy. By comparing with the slow train, it is concluded that the energy consumption each kilometer of the fast train is reduced by 1.468 kW & sdot;h, saving 18.04%, and the energy consumption each hour is reduced by 36.213 kW & sdot;h, saving 6.76%, which provides support for energy-saving and cost reduction of the transportation sector under fast and slow train modes.

This paper studies the joint optimization problem of multistage pricing and seat allocation integrating pre-sale period division in high-speed railways (HSRs), taking the fluctuation of daily demand and the interaction between pricing and seat allocation into account. To maximize railway revenue, we establish an elastic demand function for each day, and then formulate a non-linear mixed integer optimization model, which considers real-life constraints, including price time and space relationships. The complex capacity sharing in HSRs and multistage pricing increase the scale of the optimization problem; the inclusion of pre-sale period division further complicates this. Therefore, we propose a multi-level comprehensive optimization method that decomposes the joint problem into two subproblems. The first subproblem optimizes multistage pricing and seat allocation under the given pre-sale period division scheme obtained from the second subproblem, while the second subproblem optimizes the pre-sale period division scheme by adjusting the period boundary between two adjacent periods to generate a new pre-sale period division scheme. Then, three algorithms are designed. Algorithm1 optimizes the first subproblem based on a divide-and-conquer strategy. Algorithm 2 optimizes the pre-sale period division scheme, with a high-quality initial solution given by Algorithm 3. Two numerical examples are presented to demonstrate the high quality and efficiency of the proposed model and algorithms, which could provide decision support for railway ticket pricing. When there are five periods, the total revenue increases by 3.11% and 2.59% for small and large-scale instances, respectively; the total passenger kilometers increase by 21.21% and 19.42%, respectively.

为缓解城市轨道交通线路客流时空分布不均衡问题,提高乘客服务水平和企业运营效益,本文提出多时段城轨控流方案与列车开行频率及票价一体化优化方法.构建双层规划模型,上层模型以社会福利最大化为优化目标,以多时段列车开行频率、票价率及控流方案为决策变量;下层模型描述一体化优化方案下乘客的出行选择行为,构建基于弹性需求的多时段随机客流分配模型.设计嵌套Logit随机用户客流分配方法的遗传算法求解模型,基于实际线路进行算例分析,验证模型与算法的有效性.算例结果表明:通过对各运营时段列车开行频率、票价率及控流方案进行一体化优化,能够降低高峰时段客流量,均衡不同运营时段内的出行需求,缓解线路客流时空分布不均衡现象;优化城轨票价能够吸引更多潜在客流需求,使企业票价收入提升11.81%,消费者剩余提高5.94%;优化列车开行频率可以提高列车运输能力利用水平,使企业运营成本降低8.11%;同时,实施控流方案可以进一步提升乘客服务水平和企业效益.因此,本文所提方法可为城轨列车开行方案与票价及控流方案的协同制定提供理论基础.

An energy-efficiency train schedule greatly contributes to alleviating some environmental issues such as carbon emissions. However, the pursuit of reducing train energy consumption often leads to passengers' longer travel time, and more operation cost of rolling stocks. Thus, it is necessary to consider costs of passengers and rolling stocks when optimizing the energy-efficiency schedule for better satisfying passenger demand and reducing trains' total operating cost. In this paper, a mixed integer nonlinear programming model of energy-efficiency train schedule considering passenger demand and rolling stock circulation plan is established for minimizing passengers' travel cost and trains' operating cost. More specifically, this model devotes to simultaneously optimizing: (1) passengers' travel choices to reduce passengers' waiting time and travel time, (2) the selection of train traction strategy in the section to reduce the traction energy consumption, and (3) the train connection scheme to ensure the economy of the rolling stock circulation plan. This paper designs a variable neighborhood search algorithm combined with CPLEX solver to solve the model efficiently. Based on the data of Guangzhou Metro Line 9, the optimization method proposed in this paper can reduce the train operation cost by 9.73% and the total passenger travel cost by 18.11%.

高速磁浮作为一种高速度、高舒适性的便捷公共交通方式已成为公共交通的重要组成部分.目前高速磁浮方式整体上处于技术研发为主,商业运营仍处于起步阶段,特别是针对车站能力的研究较为缺乏.基于高速磁浮列车的运输组织要求,对高速磁浮车站的列车作业优化和能力利用问题进行研究.通过将高速磁浮车站到发线与径路一体化考虑,从车站径路运用和车站径路分段解锁的层面着手,在时间-空间双重约束下建立给定时刻表下高速磁浮车站作业安排优化模型.根据问题特性,将遗传算法的全局搜索性能和模拟退火算法的局部搜索性能相结合,设计遗传模拟退火算法.通过高速磁浮车站算例得出总延误为0的车站作业安排优化方案,并对车站能力利用状况进行分析.设计基于列车作业紧凑安排的车站能力启发式算法,通过压缩给定时刻表下车站接发车作业的间隔时间,计算特定的车流构成类型和比例下的高速磁浮车站通过能力.对比分析不同运行图场景下的高速磁浮车站通过能力,探索其一般规律.分析得出不停站通过列车、始发终到列车、停站通过列车、立折列车对车站通过能力利用效率依次降低的规律.该研究从列车车站列车作业组织角度丰富了高速磁浮技术,可为高速磁浮车站的作业安排和能力利用提供借鉴.