Rolling Stock Circulation Research Articles

Real-time train timetabling with virtual coupling operations on a Y-type metro line

The spatiotemporal imbalance of passenger flows is a prominent characteristic of urban rail transit systems. To match the provided transportation capacity with passenger distribution, this study considers an integer linear programming model to optimize train operation on a Y-type line, including the train timetable, rolling stock circulation plan and virtual coupling/uncoupling strategy that enables trains to switch between different compositions or configurations during operations. To enhance solution efficiency, certain integer decision variables in the model are relaxed to be continuous, and it is proved that this does not affect the optimal value of the model. To account for the dynamic nature of passenger flows, a “prediction + optimization” method with the rolling optimization framework, which utilizes real-time predicted passenger flow data to enable train operations to be performed and adjusted in response, is proposed. Three variants of the proposed model are embedded to meet the real-time requirements of operations. Numerical experiments verify the effectiveness and applicability of our proposed approach, with real-world data from Shanghai Metro Line 5. The computational results demonstrate that our method performs well under operation scenarios with both normal and abnormal passenger flows. Compared to fixed train composition, virtual coupling can perform much better in both peak and off-peak periods.

Integrated Optimization of Train Diagrams and Rolling Stock Circulation with Full-Length and Short-Turn Routes of Virtual Coupling Trains in Urban Rail Transit

The advancement of virtual coupling technology in urban rail transit has facilitated the online coupling and decoupling of trains, enabling a range of flexible transportation configurations, including various route types and adjustable formations. This study targets the fluctuating passenger demands on urban rail lines, aiming to minimize both passenger travel and operational costs. The model integrates constraints associated with virtual coupling, train operations, rolling stock circulation, and the interaction between virtually coupled trains and passenger arrivals. New decision variables are introduced to depict the train formation state under virtual coupling scenarios. An integrated optimization model for train diagrams and rolling stock circulation under virtual coupling conditions is developed, employing a genetic-simulated annealing algorithm informed by train operation simulations. A case study on an urban rail line during the morning peak examines the optimization of train diagrams for full-length and short-turn routes. Findings confirm that virtual coupling technology effectively adapts to lines with uneven passenger flow distribution, significantly enhancing the match between supply and demand, equalizing spatial and temporal traffic variations, and harmonizing the quality of passenger services with operational efficiency.

New Exact Algorithm for the integrated train timetabling and rolling stock circulation planning problem with stochastic demand

This paper studies an integrated train timetabling and rolling stock circulation planning problem with stochastic demand and flexible train composition (TRSF). A novel stochastic integer programming model, which is formulated on a space-time underlying network to simultaneously optimize the train timetable and rolling stock circulation plan with flexible train composition, is proposed by explicitly considering the random feature of passenger distribution on an urban rail transit line. To solve this problem efficiently, the proposed model is decomposed into a master problem and a series of sub-problems regarding different stochastic scenarios. We further prove that each sub-problem model is equivalent to its linear programming relaxation problem, by proving that the coefficient matrix of each linear programming relaxation model is totally unimodular. Then, the classical Benders decomposition algorithm is applied to the studied problem. Based on the model characteristics, both single-cut and multi-cut methods with some speed-up techniques are developed to solve the proposed model in a novel and effective way. Numerical experiments are conducted on small-scale cases and large-scale cases derived from Shanghai Metro Line 17, and the results show that solving the stochastic problem can extract gains in efficiency and the value of stochastic solution tends to be high.

Efficient asymmetric reposition strategy of rolling stock for urban rail transit systems

Balancing energy efficiency with high-quality service on urban rail lines with highly asymmetric passenger demand is a crucial yet challenging issue. This paper proposes an efficient asymmetric rolling stock reposition strategy to simultaneously optimize the train timetable, speed profiles and rolling stock circulation, given the passenger demand in the undersaturated direction and timetable in the oversaturated direction. By constructing space-time networks for passengers and rolling stocks, respectively, an integer linear programming model is formulated by considering the tradeoff between the passenger travel time and train energy cost. A rolling horizon scheme incorporating the Lagrangian relaxation decomposition technique is designed, which can be decomposed into two subproblems by relaxing the capacity constraints. The effectiveness of our proposed methodology is validated through numerical experiments on a test network and the Beijing Batong Line, demonstrating that the optimized train circulation plan significantly reduces energy consumption while incurring a minimal increase in travel time.

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.

Integrating stop planning, timetabling and rolling stock planning on high-speed railway lines: A multi-objective optimization approach

Designing railway operational planning is a complex and challenging task to cope with fluctuating passenger demand and satisfy actual operational requirements. Focusing on high-speed railway (HSR) lines, this paper proposes an integrated modeling framework for phase-oriented railway operational planning. The framework simultaneously optimizes the stop planning, train timetable problem (TTP) and rolling stock planning (RSP). A multi-objective optimization model, with macro passenger demand, two train speed levels, and overtaking operations taken into account, is formulated to minimize the total train running distance, train dwell time, and rolling stock resources. The constraints involve the train operation zones, train operation process, passenger demand, rolling stock circulation conditions, and actual operational requirements. The proposed model is addressed using a framework based on the ε-constraint method, from which an approximate Pareto-optimal solution set is obtained. A case study on the Beijing-Shanghai HSR corridor demonstrates the effectiveness of the proposed approach and reveals some trade-offs between the proposed objectives.

An Integrated Strategy for Rescheduling High-Speed Train Operation under Single-Direction Disruption

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.

Optimization of energy-efficiency train schedule considering passenger demand and rolling stock circulation plan of subway line

Optimization of energy-efficiency train schedule considering passenger demand and rolling stock circulation plan of subway line

Integrated rescheduling of train timetables and rolling stock circulation for metro line disturbance management: a Q-learning-based approach

Disturbance occurs inevitably on a metro line, resulting in train delays and low service quality. To improve the efficiency of disturbance management, this article investigates the integrated rescheduling problem of train timetable and rolling stock circulation. To balance service quality and operational cost, the considered problem is formulated as a multi-objective optimization model by capturing train operation processes as running arcs, dwell arcs and coming-out/back arcs based on the classical space–time network. For the purpose of improving computational efficiency, a Q-learning-based solution approach is proposed to derive a hierarchical policy for integrated rescheduling. The decisions on train timetable follow a lower-level policy that can be learned in the pre-training process, and the decisions on rolling stock circulation follow a higher-level policy that can be generated in the real-time planning process. Finally, two sets of numerical examples are carried out to evaluate the proposed method.

Integrated optimization of demand-driven timetable, train formation plan and rolling stock circulation with variable running times and dwell times

Timetable, train formation plan and rolling stock circulation are the key operational issues for efficient railway operation. The three issues are optimized sequentially based on the order of the operational plan. Sequential optimization manner cannot balance the costs of the three stages effectively and could create an infeasible solution for a later stage when the resources are limited. In addition, because of the computational complexity, multiple variable elements, such as the variable running times, variable dwell times and the coupling/decoupling operations, of a transportation system are ignored. This paper focuses on optimizing timetable, train formation plan and rolling stock circulation simultaneously to minimize costs and meet passenger demand. The key to solving the problem is to determine operation times (i.e., arrival times, departure times, running times and dwell times), the formation type of each train service and rolling stock connections (including the turnaround operations and the coupling/decoupling operations) between these train services. Considering the passenger costs and operator costs, a multi-objective mixed-integer nonlinear programming (MINLP) model is proposed to minimize the total passenger waiting time (TWT), the number of rolling stocks (NR), the number of formations (NF) and the number of coupling/decoupling operations (NC) based on a time–space network. The multi-objective MINLP model is further reformulated into a single-objective mixed-integer linear programming (MILP) model by logical linearizing, piecewise linearizing and fuzzy programming. A numerical example is used in which the exact solution of MINLP obtained by the BARON solver is compared with the approximate solution of MILP obtained by the CPLEX solver to verify the effectiveness of the piecewise linearization. Finally, the model is tested on a real-world case study of the Jinshan Line in Shanghai. The CPLEX solver can efficiently produce the approximate solution within a given computation time in acceptable gaps. The results demonstrate that the integrated model can reduce the number of rolling stocks and improve the utilization rate of rolling stocks. Furthermore, the integrated model can effectively resolve the shortage of rolling stocks when only one depot has rolling stocks or the number of available rolling stocks is limited. In addition, considering the multiple variable elements have a significant effect on the improvement of all the objectives and reduce both the passenger costs and the operator costs.

Modeling Real-time operations of Metro-based urban underground logistics system network: A discrete event simulation approach

Fast-growing logistics demand aggravates traffic congestion while posing great pressure on the urban ecology. A prospective solution is to split extensive goods movement from roads to underground, especially the metro systems. This paper proposes a simulation-based approach for supporting the operational decision-making of the metro-based urban underground logistics system (M−ULS). Based on a holistic concept of M−ULS network archetypes, two integration schemes of passengers and freight transport in metro network (i.e., collinear-detached metro and the collinear-trailer metro) are explicated. Next, mechanisms of metro freight service assignment, standardized packing, timetable coordination, and rolling stock circulation are proposed and formulated considering multiple criteria and travel patterns. A data-driven discrete-event simulation model with user interface is developed to acquire the real-time operating states of M−ULS in 36 tested scenarios. Experiments conducted on the Nanjing Metro case show that the proposed method can effectively capture the dynamic performance and bottlenecks of network operations in different operating periods and environments. The two considered system schemes show respective advantages in terms of freight demand backlog, capacity, traffic flow control, and efficiency, both of which have good compatibility with metro passenger services. The value of this paper is to provide a quantifiable design framework and assessment paradigm for M−ULS operations. It also offers new insights for solving “big-city diseases” and the potential innovations of urban underground space and metro systems.

Synchronous Optimization for Demand-Driven Train Operation Plan in Rail Transit Network Using Nondominated Sorting Coevolutionary Memetic Algorithm

In many cities and regions, decision makers independently develop Train Operation Plan (TOP) for each line in the rail transit network, resulting in a lack of TOP Synchronization (TOPS). Considering the entire network as a whole, researchers have realized that synchronous optimization is of great significance. In this paper, we formulate two Mixed-Integer Linear Programming (MILP) models to optimize demand-driven TOP in the network. The former is an Asynchronous TOP Optimization (ATOPO) model, while the latter is a Synchronous TOP Optimization (STOPO) model. The bi-objective models simultaneously determine train frequency, train timetable, and rolling stock circulation under small-granularity passenger demand to minimize trains’ total cost and passengers’ total time. Then, we propose the Nondominated Sorting Coevolutionary Memetic Algorithm (NSCMA) to solve the combinatorial optimization problems. The hybrid heuristic algorithm incorporates Coevolutionary Memetic Algorithm (CMA) into Advanced and Adaptive Nondominated Sorting Genetic Algorithm II (AANSGA-II) to ameliorate the evolution process for elite individuals. On this basis, we study the case of Shenyang Metro to verify the models and the algorithm. The results demonstrate that the STOPO model is better than the ATOPO model in reducing trains’ total cost and passengers’ total time. In addition, NSCMA is better than AANSGA-II in obtaining elite individuals.

Quadratic and higher-order unconstrained binary optimization of railway rescheduling for quantum computing

As consequences of disruptions in railway traffic affect passenger experience and satisfaction, appropriate rerouting and/or rescheduling is necessary. These problems are known to be NP-hard, given the numerous restrictions of traffic nature. With the recent advances in quantum technologies, quantum annealing has become an alternative method to solve such optimization problems. To use quantum annealing, the problem needs to be encoded in quadratic unconstrained binary optimization (QUBO) or higher-order binary optimization (HOBO) formulation that can be recast as a QUBO. This paper introduces QUBO and HOBO representations for rescheduling problems of railway traffic management; the latter is a new approach up to our knowledge. This new approach takes into account not only the single-track lines but also the double- and multi-track lines, as well as stations composed of tracks and switches. We consider the conditions of minimal headway between trains, minimal stay on stations, track occupation, and rolling stock circulation. Furthermore, a hybrid quantum-classical procedure is presented that includes rerouting. We demonstrate the proof of concept implementation on the D-Wave Quantum Processing Unit and D-Wave hybrid solver.

Joint optimization of train timetabling and rolling stock circulation planning: A novel flexible train composition mode

The tidal traffic phenomenon is one of the most prominent problems on some metro lines, where a large number of commuters during the peak hours might cause the non-equilibrium spatial–temporal distribution of passenger flow. In order to better match the passenger demand, this study proposes a mixed-integer linear programming (MILP) model to jointly optimize the train timetable and rolling stock circulation plan, in which the flexible train composition mode is particularly taken into account by allowing rolling stocks to change their compositions through uncoupling/coupling operations at the both ends of the focused metro line. To solve the model, a customized heuristic algorithm based on the variable neighborhood search (VNS) is developed to quickly generate high-quality solutions. Based on a small example and the real-world data from Beijing metro Batong line, two sets of numerical experiments are conducted to verify the effectiveness and applicability of the proposed methodology. The computation results show that in comparison to the fixed train composition mode, the proposed approaches can bring 17.1% reduction of operation costs in morning peak periods, with no increase of passenger waiting time.

Rolling Stock Allocation and Timetabling for Urban Rail Transit Network with Multiple Depots

Rolling stock management and train timetabling are two challenging but very related issues in urban rail systems. The former is to allocate a certain fleet of trains to each depot, and the latter determines the arrival and departure times of train services according to the available rolling stock at each depot. While most existing studies consider these two tasks for a single line, this study focuses on the integrated optimization of rolling stock allocation, train timetabling, and rolling stock circulation for a whole network, where each depot can serve multiple connected lines and the trains can change lines in one operational cycle (i.e., one day). A time-space network is constructed to model the rolling stock circulation among multiple lines and depots, and a novel integer linear programming model is proposed to jointly optimize the allocation of rolling stock and train timetables for the involved lines. The objective function maximizes the service quality provided to passengers with minimized rolling stock investment cost. Numerical experiments based on the real-world data of the Beijing rail transit network are conducted to validate the effectiveness of this approach. The results demonstrate that the proposed approach can reduce the fleet size of rolling stock by 5% while providing the same service quality to passengers.

Demand-oriented integration optimization of train timetabling and rolling stock circulation planning with flexible train compositions: A column-generation-based approach

Train timetabling and rolling stock circulation planning are two important optimization problems that arise in the daily operations of urban rail transit lines. This study proposes a novel approach to simultaneously optimize the train timetable and rolling stock circulation plan with flexible train compositions on an urban rail transit line in order to better match the passenger demand and supplied transport capacity, and further improve operation flexibility and extract gains in efficiency, in which the dynamic passenger demand is particularly considered in the formulation process. We first propose two integer linear programming models that are formulated on time-space networks by considering flexible coupling/splitting activities. The models consist of restricted master problems for optimizing the total generalized cost and subproblems that are used to generate different train composition routes. An effective column-generation-based diving heuristic algorithm is developed to solve the problem of interest, and it is able to simultaneously obtain the train timetable and rolling stock circulation plan. Several sets of experimental scenarios, involving relatively small-scale cases and a case derived from real-world Shanghai Metro data, are tested to verify the effectiveness of the proposed model and algorithm.

Joint optimization of train scheduling and rolling stock circulation planning with passenger flow control on tidal overcrowded metro lines

This study proposes a joint optimization method for train scheduling and rolling stock circulation planning with the consideration of passenger flow control strategy on a tidal oversaturated metro line, in which different types of rolling stocks with various loading capacities are put into operations to satisfy the uneven passenger demand in different periods (e.g., peak hours and off-peak hours). To characterize the problem mathematically, a mixed-integer nonlinear programming model is formulated to minimize the passenger waiting time and operating costs of the metro system simultaneously. This model is further reformulated equivalently into a mixed-integer linear programming model via the linearization method. An effective heuristic algorithm based on the tabu search and CPLEX solver is designed to find high-quality solutions for the proposed problem. Finally, two sets of numerical examples, including a small-scale example and a large-scale example based on the Beijing metro Batong line, are conducted to validate the performance of the proposed methods. The experimental results demonstrate that scheduling multiple types of rolling stocks can effectively reduce the transportation costs and satisfy passenger demand in different periods.

Optimization method of urban rail train operational plan based on O-D time-varying demand

PurposeUnder the constraints of given passenger service level and coupling travel demand with train departure time, this study optimizes the train operational plan in an urban rail corridor to minimize the numbers of train trips and rolling stocks considering the time-varying demand of urban rail passenger flow.Design/methodology/approachThe authors optimize the train operational plan in a special network layout, i.e. an urban rail corridor with dead-end terminal yard, by decomposing it into two sub-problems: train timetable optimization and rolling stock circulation optimization. As for train timetable optimization, the authors propose a schedule-based passenger flow assignment method, construct the corresponding timetabling optimization model and design the bi-directional coordinated sequential optimization algorithm. For the optimization of rolling stock circulation, the authors construct the corresponding optimization assignment model and adopt the Hungary algorithm for solving the model.FindingsThe case study shows that the train operational plan developed by the study's approach meets requirements on the passenger service quality and reduces the operational cost to the maximum by minimizing the numbers of train trips and rolling stocks.Originality/valueThe example verifies the efficiency of the model and algorithm.

Train timetabling with passenger data and heterogeneous rolling stocks circulation on urban rail transit line

AbstractThe planning process in urban rail transportation can be split into several stages, including line planning, timetabling, rolling stock scheduling and so on. The outcome of a stage provides inputs or constraints to the subsequent ones. However, while the output can be good or optimal at each stage, it rarely considers the global quality for the overall planning process. Furthermore, problems tackled at planning phase often use a more aggregate representation of reality, to achieve a more general overview. An integrated approach, while more complex to solve, may mitigate the gap between solution of different stages and a validation of a plan would still be required before its implementation in practice. In this paper, we focus on integrated optimization of train timetabling and rolling stock circulation for urban rail transit line with time-based origin-destination-dependent passenger travel demand and heterogeneous rolling stocks. The aim is to generate a comfortable timetable for passengers and an efficient timetable for operators. The objective is to minimize the total waiting time for passengers and the costs for operators, while constraints regarding train movements, passenger boarding and alighting, available rolling stocks and their capacity are considered. A mixed integer linear programming model is formulated and solved by an iterative programming approach. Computational experiments are performed on the Chongqing Rail Transit Line 2 to verify the efficiency and effectiveness of the proposed model and solving method. With respect to CPLEX, results show the proposed iterative programming approach has advantages both on computation time and solution quality.

Train Operational Plan Optimization for Urban Rail Transit Lines Considering Circulation Balance

The passenger demand of urban rail transit (URT) lines often present asymmetric tidal time-varying characteristics. To match the demand fluctuation, the train operational plan (TOP) generally has asymmetric bi-directional frequency/headway setting and imbalanced circulation, leading to high operation cost. This paper incorporates circulation balance into TOP optimization to balance the bi-directional arrival, departure, circulation, and resource utilization, and reduce the overall operation cost. Based on time-varying section demand and predetermined service level, bi-directional stepped maximum headway functions are collaboratively constructed, and then the circulation process is described by the trip flow circulation network that is formulated as a cost-oriented integer linear programming model. Using the optimized frequency setting, the final TOP is obtained by a two-stage approach to successively solve the schedule and rolling stock circulations at terminals. The case study based on an URT line in Shenzhen indicates that the proposed approach can not only ensure the required service level for travel demand, but also improve the efficiency of circulation and utilization, and effectively reduce the overall operation cost. The proposed approach provides an effective technique to keep balanced, stable and sustainable operation for URT lines.