Train Timetabling Research Articles

Heuristic for Railway Crew Scheduling With Connectivity of Schedules

This paper addresses the crew scheduling for long-distance passenger train services. A heuristic with bin packing features is developed to generate repeatable crew schedules that satisfy the operational and crew allocation rules. By ensuring the connectivity of crew duties that can be repeated over periodic train schedules, a better estimate of the crew requirement in a region is also obtained. Further, the heuristic ensures a fair division of the total workload and creates long duty cycles, which also makes the process of cyclic rostering easier. The paper also presents an exact approach for crew scheduling using a combination of constraint programming and set covering formulations. The exact approach is not computationally viable for practical scale problem instances, but the heuristic generates good quality solutions (often very close to optimal) even on large data sets. We illustrate the approach on data from the Mumbai Division in Indian Railways and the computational results show that there is potential to reduce the total number of crew duties in the region by around 12%. The heuristic approach provides an efficient way to generate improved crew schedules every time there is a change in the train timetable.

Variable Neighborhood Search and Alternating Direction Method of Multipliers for Integrated Optimization of Maintenance Windows and Train Timetables

Variable Neighborhood Search and Alternating Direction Method of Multipliers for Integrated Optimization of Maintenance Windows and Train Timetables

A Customized Augmented Lagrangian Method for Block-Structured Integer Programming.

Integer programming with block structures has received considerable attention recently and is widely used in many practical applications such as train timetabling and vehicle routing problems. It is known to be NP-hard due to the presence of integer variables. We define a novel augmented Lagrangian function by directly penalizing the inequality constraints and establish the strong duality between the primal problem and the augmented Lagrangian dual problem. Then, a customized augmented Lagrangian method is proposed to address the block-structures. In particular, the minimization of the augmented Lagrangian function is decomposed into multiple subproblems by decoupling the linking constraints and these subproblems can be efficiently solved using the block coordinate descent method. We also establish the convergence property of the proposed method. To make the algorithm more practical, we further introduce several refinement techniques to identify high-quality feasible solutions. Numerical experiments on a few interesting scenarios show that our proposed algorithm often achieves a satisfactory solution and is quite effective.

Reinforcement Learning for Online Dispatching Policy in Real-Time Train Timetable Rescheduling

Reinforcement Learning for Online Dispatching Policy in Real-Time Train Timetable Rescheduling

Optimization of Train Timetables in High-Speed Railway Corridors Considering Passenger Departure Time and Price Preferences

Optimization of Train Timetables in High-Speed Railway Corridors Considering Passenger Departure Time and Price Preferences

Coordinated Maximum Power Demand Shaving of Multi-Traction Substations With Train Timetable Optimization

Coordinated Maximum Power Demand Shaving of Multi-Traction Substations With Train Timetable Optimization

Optimal management of full train load services in the shunting yard: A comprehensive study on Shunt-In Shunt-Out policies

A key aim of the European Union is to double freight rail traffic by 2050 in order to reduce pollution emissions and alleviate congestion by shifting traffic from roads to rail networks. To accomplish this objective, it is crucial to minimize emissions and high costs associated with shunting yard operations while maintaining an acceptable level of service. This research paper introduces a new MINLP model that optimizes the shunt-in and shunt-out (SISO) operations of wagons in a shunting yard that handles full train load services. Additionally, an efficient Multi-Objective Dijkstra Algorithm (MDA) is proposed to handle simultaneous shunt-out operations in a multi-train scenario. The MINLP model takes a mesoscopic approach, aiming to minimize the number of SISO operations while satisfying strategic and tactical objectives such as wagon fleet size, operational costs, and shunting locomotive emissions. Several versions of the mathematical model are described, each employing different Shunt-In (SI) policies with varying criteria for wagon selection and strong goal orientation. The Multi-Objective Dijkstra Algorithm determines the Multi-Objective Shortest Path between mandatory shunts, considering both the time required for shunting and clustering costs. It provides information on the clusters of wagons that need to be shunted out. To assess the effectiveness of the MINLP model, real train timetables for freight trains in the Bettembourg Eurohub Sud Terminal (Luxembourg) are used, and various KPIs related to tactical and strategic objectives are evaluated. Furthermore, the performance of the Multi-Objective Dijkstra Algorithm is compared to the Shunt-Out sub-model, considering average computation time and solution quality in relation to the MINLP model. The computational results demonstrate that the criteria for wagon selection have a significant impact on the analyzed KPIs.

Demand-driven flexible-periodicity train timetabling model and algorithm for a rail transit network

The optimization models for strict-cyclic and non-cyclic timetables are limited in their ability to be applied to different scenarios. This paper proposes a universal flexible-periodicity timetabling framework for rail transit networks under time-dependent demand, which can provide strict-cyclic, non-cyclic, and partial-cyclic timetables by adjusting the parameters. This approach reduces the complexity of scheduling for operators and allows them to choose the most appropriate timetable for a specific scenario. The demand-driven flexible-periodicity timetabling (DDFPT) model considers passenger waiting time, train operation cost, and timetable periodicity deviation as objectives. To fit the network scenario, the model also needs to take into account the feasibility of rolling stock connections at terminal stations and coordination of timetables on different lines. An adaptive large neighborhood search (ALNS) algorithm with eight destroy operators and a repair operator is proposed to solve the model. A numerical and a real-world network case are used to evaluate the performance of the model and the algorithm. Upon comparing the benefits of various types of timetables, it has been observed that the partial-cyclic timetable strikes a good balance between the passengers’ travel efficiency and the periodicity of the timetable. Additionally, the coordinated optimization of timetables between crossed lines at the network level greatly improves passengers’ travel efficiency at transfer stations.

Integrated optimization for passenger comfort-oriented train timetabling and passenger control strategy on an oversaturated metro line

The excessive travel demand in the metro system during peak hours may cause platform congestion and reduce the comfort of the passengers. Thus, this article proposes an approach for integrally optimizing the train timetable and passenger control on an oversaturated metro line, to improve the comfort of passengers on the platform. Specifically, taking the short-term impact of the boarding/alighting passengers into account, a novel quantitative assessment method of the perceived waiting time, considering the impact of the platform passengers’ density and passenger control strategy, named the generalized waiting time, is proposed. A mixed-integer nonlinear programming model is formulated to minimize the generalized waiting time, and a heuristic algorithm based on the adaptive simulated annealing genetic algorithm and the adaptive large neighbourhood search (ASAGA-ALNS) is designed to find high-quality solutions. The results of numerical experiments show that the method can alleviate platform congestion, while improving the comfort of waiting passengers.

High-speed train timetable optimization based on space–time network model and quantum simulator

Timetable scheduling is a combinatorial optimization problem that presents formidable challenges for classical computers. This paper introduces a pioneering methodology for addressing the high-speed train timetabling problem through quantum computing. Initially, a comprehensive binary integer programming model, grounded in the space–time network, is proposed (M1). To manage the intricacy of model M1, a knapsack problem reformulation is employed to establish a simplified binary integer programming model (M2). Both M1 and M2 are subsequently converted into quadratic unconstrained binary optimization (QUBO) models to harness the potential of quantum computing. Several techniques, including the Gurobi solver, simulated annealing, and the coherent Ising machine (CIM) quantum simulator, are deployed to solve the model across four distinct scenarios of varying complexity. The findings indicate that CIM quantum simulator outperforms the simulated annealing method in terms of solution quality for medium-scale problems.

Integrated train timetabling and rolling stock rescheduling for a disturbed metro system: A hybrid deep reinforcement learning and adaptive large neighborhood search approach

For a metro line with high density and short trip time, the original train timetable and rolling stock circulation face infeasible risks under unexpected disturbances. This paper focuses on integrated train timetabling and rolling stock rescheduling for a disturbed metro system to reduce the negative impact. The problem is formulated as a multi-objective master model, in which required operational constraints and dispatching strategies are taken into account. To satisfy the real-time requirement, an innovative solution framework consisting of an independent rescheduling process and a cooperative rescheduling process is proposed. In the independent rescheduling process, the master model is decomposed into a series of submodels in the unit of train service. The submodel can be transformed into a Markov Decision Process (MDP) with well-defined fundamental elements (i.e., state, action, and reward function). Based on the MDP, a hierarchical policy is developed by introducing deep reinforcement learning to generate the initial solution, including the lower-level policy for train timetable and the higher-level policy for flexible rolling stock circulation. In the cooperative rescheduling process, the selfishness of agents that appears after the model decomposition is overcome by an adaptive large neighborhood search algorithm, which can improve the solution quality. Finally, two sets of numerical experiments are conducted to demonstrate the performance of the proposed solution framework. The experimental results show that a near-optimal solution can be obtained in a short time, which is better than the currently used practical rules in the automatic train supervision system, especially during peak hours. Furthermore, the effects of different parameter settings are analyzed.

Approximate dynamic programming approach to efficient metro train timetabling and passenger flow control strategy with stop-skipping

Urban metro systems continuously face high travel demand during rush hours, which brings excessive energy waste and high risk to passengers. In order to alleviate passenger congestion, improve train service levels and reduce energy consumption, a nonlinear dynamic programming (DP) model of efficient metro train timetabling and passenger flow control strategy with stop-skipping is presented, which consists of state transition equations concerning train traffic and passenger load. To overcome the curse of dimensionality, the formulated nonlinear DP problem is transformed into a discrete Markov decision process, and a novel approximate dynamic programming (ADP) approach is designed based on the lookahead policy and linear parametric value function approximation. Finally, the effectiveness of this method is verified by three groups of numerical experiments. Compared with Particle Swarm Optimization (PSO) and Simulated Annealing (SA), the designed ADP approach could obtain high-quality solutions quickly, which makes it applicable to the practical implementation of metro operations.

Simulation-based optimization of timetables coordination in an urban rail transit network

Synchronous optimization of train timetables is to solve the problem of train service coordination among different lines in the urban rail transit network, which can reduce passenger waiting time and subsequently enhance passenger satisfaction. This paper develops an efficient simulation system to reproduce the train operation of an urban rail network. It takes into account the realistic characteristics of urban rail operations, including time-dependent demand, dynamic dwell time, and train capacity constraint. In the simulations, both the train trajectories and the passenger waiting time can be easily obtained. On this basis, a simulation-based algorithm (i.e., simultaneous perturbation stochastic approximation, SPSA) is designed to search an improved flexible-interval dispatch solution in the network. A case study of the Chengdu urban rail transit network is implemented to verify the effectiveness of the simulation system and the optimization algorithm. The simulation system is found to be time efficient since it takes less than 1 s to simulate the network with 4 h of operation and more than 200,000 passengers. The optimization algorithm is also effective as it can reduce the average passenger waiting time by 9.52 % compared to the equal-interval dispatch solution without increasing the train service frequency. It is also found that the reduction in waiting time is mainly due to the improved coordination of train services in the transfer station.

Pareto Optimization of Energy-Saving Timetables Considering the Non-Parallel Operation of Multiple Trains on a Metro Line

In light of reducing train operation energy consumption while maintaining the passenger service level for creating sustainable urban rail transit systems, we address a non-parallel train timetabling problem considering regenerative braking energy utilization and the non-parallel operation of multiple trains on a metro line via a newly proposed multi-objective timetable (MOT) optimization model and an evolutionary algorithm based on NSGA-II. The optimization objectives of the MOT model are to find satisfactory energy-saving timetables on the Pareto frontier by minimizing the total travel time of passengers and minimizing the net energy consumption of trains. An improved multi-objective evolutionary algorithm based on NSGA-II is constructed to generate the optimal arrival and departure times at each station for each train running in a non-parallel operation mode. This study tests the feasibility of the proposed optimization method via an empirical case using the data collected from the Yizhuang Line of the Beijing metro systems in China. The simulation results show that the proposed optimization method satisfies both the energy utilization and passenger service levels along a Pareto front. The MOT improves the overall effectiveness of regenerative braking energy utilization by 29.88% in comparison with the original timetable; it reduces the net operation energy consumption by 44.86% relative to the travel-oriented timetable (TOT); and it reduces the total passenger travel time by 27.18% compared with the energy-oriented timetable (EOT).

Decomposition and approximate dynamic programming approach to optimization of train timetable and skip-stop plan for metro networks

Carefully coordinating train timetables of different operating lines can help reduce transfer delays, which in turn reduces station crowding and improves overall service quality. This paper explores the optimization to train timetable and skip-stop plans that aims to minimize the total passenger waiting time and station crowding. The problem is formulated as a mixed-integer non-linear programming model. To effectively address the complexity of the model, a decomposition and approximate dynamic programming approach is designed to convert the original network-level problem into a series of small-scale subproblems, one for each operating line, to be solved quickly in a distributed manner. The effectiveness and practicability of the model and algorithm are demonstrated on two case networks: a small-scale synthetic network of three metro lines and a real-world network based on Beijing metro. The computational results illustrate that the proposed strategy to generate train timetables and skip-stop plans can effectively reduce passenger waiting time and station crowing. The proposed decomposition and approximate dynamic programming approach is also shown to perform more efficiently than traditional heuristic algorithms, such as genetic algorithm and simulated annealing algorithm for large-scale networks.

Optimization of train timetables and placement of charging facilities for battery‐powered LRT

AbstractThe energy consumption of a battery‐powered train in an interstation depends on the running time and state of energy (SOE) at departure. In this paper, we develop an optimization method of train timetables to minimize energy consumption in line with several stations. The variables in this proposed optimization model are running, dwell, and charging times as real numbers and places of charging facilities as binaries. Additionally, we conducted a case study using the real‐world light rail transit (LRT) route, vehicle, and onboard battery model to confirm the effectiveness. In the case study, the proposed method can optimize the timetable and placement of charging facilities by considering the track gradient and battery SOE.

Railway maintenance windows: Discrepancies between planning and practice in Sweden

Efficient and timely maintenance is essential for the robust operation of infrastructure across all types of transport. In the railway sector, track maintenance presents unique challenges. Specifically, some maintenance tasks require track closures, which can disrupt train schedules. Coordinating these closures with regular train operations makes the scheduling process complicated. To ensure sufficient time for maintenance and prevent conflicts with train operations, the Swedish Transport Administration introduced “maintenance windows.” Maintenance windows, ranging from two to six hours, are periods designated for maintenance, with the track free from train operations. They are set before finalizing the annual train timetable. In this study, we examined the practical application of maintenance windows on a railway line in Southern Sweden from 2019 to 2020. Our findings reveal that while 10% of the total line capacity was allocated for maintenance windows, 11% of the capacity was used for maintenance. Alarmingly, 68% of trackwork occurred outside maintenance windows, and only 34% of the reserved maintenance window capacity was utilized. There is a significant discrepancy between the time and location reserved for maintenance windows and their actual utilization. To address this, we propose aligning maintenance windows more closely with contractor needs by 1) incorporating maintenance windows on the weekends, 2) making maintenance windows available closer to the end of the planning horizon, 3) extending the duration of some maintenance windows, and 4) designing and integrating incentives to encourage contractors to operate within planned maintenance windows.

Joint optimization of energy conservation and transfer passenger service quality in rail transit system

ABSTRACT The complex electricity transmission process and transfer passenger demand in the rail transit system make it challenging to formulate optimal timetables and train speed profiles to meet the needs of the system. This study optimizes train timetable to meet energy conservation and passenger service quality of cross-mode rail transit system during different operation periods. Firstly, based on the spatiotemporal travel data of transfer passengers, the train-time matrix is proposed to construct a bi-objective optimization model (BOOM) that incorporates the total energy consumption optimization model (TECOM) and total waiting time optimization model of transfer passenger (TWTOM). It can better combine the passenger transport scheme and the train energy-saving operation strategy, thus improving energy-saving performance and passenger transport efficiency and simplifying the difficulty of mathematical modelling of such BOOM. Then, a method for determining the appropriate weight coefficient ratio and the improved non-dominated sorting genetic algorithm II (NSGA-II) are applied to obtain the efficient Pareto front solutions. Taking the numerical experiments as test cases, the improved NSGA-II can get a efficient solution faster than the traditional NSGA-II. Finally, two numerical experiments using real-world data are conducted to verify the practicability of the optimization model and the effectiveness of improved NSGA-II. The optimization results can reduce energy consumption by up to 11.02% and passenger waiting time by 137,320 s, respectively. This study helps to improve the energy efficiency and passenger service quality of cross-mode rail transit systems, and also provides a reference for dispatchers to optimize train timetable.

A train timetable rescheduling approach based on multi-train tracking optimization of high-speed railways

PurposeThis paper aims to propose a train timetable rescheduling (TTR) approach from the perspective of multi-train tracking optimization based on the mutual spatiotemporal information in the high-speed railway signaling system.Design/methodology/approachFirstly, a single-train trajectory optimization (STTO) model is constructed based on train dynamics and operating conditions. The train kinematics parameters, including acceleration, speed and time at each position, are calculated to predict the arrival times in the train timetable. A STTO algorithm is developed to optimize a single-train time-efficient driving strategy. Then, a TTR approach based on multi-train tracking optimization (TTR-MTTO) is proposed with mutual information. The constraints of temporary speed restriction (TSR) and end of authority are decoupled to calculate the tracking trajectory of the backward tracking train. The multi-train trajectories at each position are optimized to generate a time-efficient train timetable.FindingsThe numerical experiment is performed on the Beijing-Tianjin high-speed railway line and CR400AF. The STTO algorithm predicts the train’s planned arrival time to calculate the total train delay (TTD). As for the TSR scenario, the proposed TTR-MTTO can reduce TTD by 60.60% compared with the traditional TTR approach with dispatchers’ experience. Moreover, TTR-MTTO can optimize a time-efficient train timetable to help dispatchers reschedule trains more reasonably.Originality/valueWith the cooperative relationship and mutual information between train rescheduling and control, the proposed TTR-MTTO approach can automatically generate a time-efficient train timetable to reduce the total train delay and the work intensity of dispatchers.

Neural Network-Based Subway Regenerative Energy Optimization With Variable Headway Constraints

For subway regenerative energy optimization, the essential idea is to maximize the amount of regenerative energy absorption (AREA) between accelerating trains and braking trains by adjusting train timetable. The bottlenecks preventing the theoretical research from being used to industrial practice lie in the time-consuming simulation of AREA and the constant setting of headway threshold, which seriously reduces the computational efficiency and compresses the solution space. For addressing these issues, we formulate neural networks to speed up the AREA simulation, develop a bisection algorithm to dynamically adjust the headway threshold under moving block mechanism, and then establish a hybrid heuristic method integrating neural networks, genetic algorithm, variable neighborhood search and simulated annealing to determine the timetable, including dwell time distribution (DTD) at stations and headway time distribution (HTD) among consecutive trains. The effectiveness of the proposed method is confirmed by numerical experiments based on the real ATO data of Beijing Subway Changping Line. The results reveal that the neural networks could save 98.96% of the computational time at the expense of 1.76% of the accuracy loss, such that the hybrid heuristic algorithm could save 75.68% of the computational time. Benchmarked with the constant headway constraints used in literature, the variable headway constraints could achieve an average improvement of AREA by 8.94%. In addition, the joint optimization of DTD and HTD could increase the AREA by 15.28% on average, compared to the single optimization of HTD. This research is of great significance to improve the practicability of subway regenerative energy optimization algorithms.