Batong Line Research Articles

Estimation of schedule preference and crowding perception in urban rail corridor commuting: An inverse optimization method

This paper introduces an inverse optimization method to uncover commuters’ schedule preference and crowding perception based on aggregated observations from smart card data for an urban rail corridor system. The assessment of time-of-use preferences typically involves the use of econometric models of discrete choice based on detailed travel survey data. However, discrete choice models often struggle with potential endogeneity issues in behavioral observations when estimating individual samples from massive transit data with limited exogenous identifying information. This motivates us to employ an equilibrium modeling approach to capture the dynamism hidden in commuters’ departure time decision-making from aggregations. Assuming user optimality in observed choices, an inverse optimization method is proposed to find a set of preference parameters in the stochastic user equilibrium-based morning commuting model with heterogeneous commuters so that the resulting equilibrium pattern best approximates the observed departure rate distribution over time. The proposed inverse optimization problem can be formulated by a bi-level programming model and a sensitivity analysis-based solution framework is further designed for model estimation. Lastly, the smart card data and train timetable data from the rail corridor along the Beijing Subway Batong Line are synthesized for a case study to estimate commuters’ departure time choice preferences during morning peak periods, as well as to validate the robustness and practicality of the proposed method.

Coordinated Control of the Onboard and Wayside Energy Storage System of an Urban Rail Train Based on Rule Mining

There are three major challenges to the broad implementation of energy storage systems (ESSs) in urban rail transit: maximizing the absorption of regenerative braking power, enabling online global optimal control, and ensuring algorithm portability. To address these problems, a coordinated control framework between onboard and wayside ESSs is proposed in this study, and the related control strategy is obtained by transforming the global optimization problem into a combination of rule-based and local optimization problems. The design process of the strategy is divided into three parts: offline optimization, rule extraction, and local optimization. First, a genetic algorithm is used to optimize the charge/discharge threshold curves under typical operational conditions. Then, the rules of offline optimization results are obtained from an expert system, and the nonlinear rules are mined with local optimization methods. Finally, a coordinated strategy is presented based on the outcomes of the three parts. A power hardware-in-the-loop (PHIL) experimental platform based on RTLAB is built, and the above coordination strategy is verified based on data for the Beijing Metro Batong Line. The experimental results show that the strategy can effectively improve the energy-saving rate and reduce the regeneration failure rate substantially, with the effect being close to the offline global optimal solution. The algorithm proposed in this paper achieves near global optimal energy-saving optimization results with lower computational costs, and has strong portability, providing a good solution for the large-scale application of onboard and wayside energy storage coordination control.

Collaborative optimization of passenger flow control and bus-bridging services in commuting metro lines

With the advantages of high speed and punctuality, urban rail transit has become the preferred choice for many commuters. However, overcrowding of urban rail transit lines during peak hours is a common problem in megacities owing to the excessive passenger demand. To address this problem, this study proposes an integrated optimization method that combines passenger flow control and bus-bridging services. An integer nonlinear optimization model is developed to minimize the weighted passenger waiting time and operating cost of bus-bridging services by considering the coupling relationships between passenger movements on both the metro and buses. Then, the proposed model is equivalently transformed into a linear form with better mathematical properties, and variants of this model are further formulated to extend the usability. Finally, real-world case studies based on the operational data of the Beijing Metro Batong line are conducted to verify the effectiveness of the proposed methods. The computational results indicate that the proposed approach can effectively alleviate overcrowding and reduce passengers' waiting time, thereby improving the operational efficiency and safety of the urban rail transit system.

Improving passenger travel efficiency through a dynamic autonomous non-stop rail transit system

This study proposes a dynamic autonomous non-stop rail transit (DANRT) system to improve the travel efficiency of passengers in urban rail transit (URT) systems and solves a pertinent carriage scheduling problem derived from the DANRT system using a mathematical programming model. In the DANRT system, passengers traveling to the same destination are allocated to the same carriage(s), and each carriage can be attached to and detached from trains using the modular autonomous vehicle (MAV) technology effortlessly, which enables all trains to run non-stop throughout the focused operation period. We offer a cost-effective design for the DANRT system. To ensure safe and efficient operations, a mathematical model is proposed for the carriage scheduling problem in the DANRT system, where the number and destinations of carriages required by each station are determined. A linearization and segmentation method for the model is proposed. To examine the effectiveness of the DANRT system, we compare the travel efficiency of passengers in the DANRT system with that in the traditional system by using the origin-destination distribution of passengers on the Batong Line of Beijing Subway. The results demonstrate that passengers in DANRT can save about 2.9 % to 8.6 % of travel time compared with the traditional system. Finally, we conclude several observations and operational characteristics of the DANRT system by numerical experiments.

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.

Research on the contribution of metro-based freight to reducing urban transportation exhaust emissions

Most carbon emissions come from cities, including mainly human activities in the fields of the urban economy, urban construction, and urban transportation. In terms of urban transportation, a truck produces far more carbon emissions than does a car. From the perspective of reducing the freight amount of urban road transport, underground logistics systems are a feasible solution in the future. Currently, metro-based freight is easier to implement, and the redundant transport capacity of the urban metro during off-peak hours can be put to good use. In addition, the pressure of the ground freight can be alleviated. Against the background of the coordinated operation mode of metro-based freight and ground freight, this study aims to measure the contribution of metro-based freight to reducing urban transportation carbon emissions by using the optimization method of metro passenger–freight coordinated transportation and traffic flow theory. Taking the Beijing Metro Batong Line as an example, the results of experiments show that the coordinated operation mode can significantly reduce urban transportation exhaust emissions.

Train schedule optimization for commuter-metro networks

The interconnection and synchronization among different transport modes have been more and more attractive as the modern transportation system is moving towards Mobility-as-a-Service. In this study, we address the train scheduling problem for “commuter rail-metro” systems, where the trains from commuter rail lines can go directly into metro systems to provide seamless services for passengers. To optimize the schedule of trains for both commuter rail lines and metro lines, we propose a job shop scheduling model where precedence constraints from commuter-metro networks are taken into account and develop a mixed-integer programming (MIP) model with quadratic constraints. Our model considers the orders of different types of trains and the safety constraints, due to different types of signalling equipment in commuter and metro systems. Since these constraints involve a set of IF-THEN rules, we prove that these constraints can be equivalently reformulated as linear inequalities, without adding new variables. To solve the proposed model efficiently, we design an iterative solution framework, which generates a feasible solution using dynamic programming, next solves a MIP model, then calculates the train speed profiles, and if train speed profiles violate the safety constraints, re-optimizes the MIP model with modified alternative constraints. To verify the effectiveness of the proposed approaches, numerical experiments are performed on small and real-world instances based on the Beijing metro Line 1 and the Batong Line operational data.

Timetable optimization for maximization of regenerative braking energy utilization in traction network of urban rail transit

Timetable optimization is one of the effective solution methods for urban rail transit to achieve energy-saving. Previous studies on timetable optimization only focused on the transfer and utilization of mechanical energy, which did not consider the exchange of energy and line losses in the traction network. Therefore, this paper constructs a cross-substation energy transmission and utilization model taking into account the characteristics of the actual traction power supply systems. An overlap current method is presented to increase the utilization of regenerative braking energy (RBE) of trains and reduce the energy supply of the traction substation by considering the line loss, which is achieved by compensating the current generated by accelerating and braking trains in the substation. The compensation current can be maximized by adjusting the dwell time to achieve energy-saving. The traction power supply systems with highly nonlinear dynamic characteristics are linearized to construct a mixed-integer linear programming (MILP) model, which utilizes the utilization of RBE as the objection and dwell time as the variable. The method of maximum compensation current is verified by numerical examples based on Beijing Batong Line. The results show that the energy-efficient of the method is greatly improved compared with the method of maximizing the overlap time between the accelerating train and the braking train.

Novel empty train return strategy and passenger control strategy to satisfy asymmetric passenger demand: A joint optimization with train timetabling

Big cities’ bi-directional metro lines often have unbalanced passenger demand, i.e., up-directional passenger demand is oversaturated but down-directional passenger demand is unsaturated. In recent years, the method to relieve congestion in oversaturated direction has attracted much attention, but many problems in the unsaturated direction have not gotten as much attention, e.g., the waste of transportation resources caused by low loading rate, and the insufficient utilization of platform space resources caused by less waiting passengers. To address these problems, this paper introduces a new collaborative optimization model for the train timetable, passenger control and rolling stock schedule on a bi-directional metro line with unbalanced passenger demand. With consider the real-time state of bi-directional platform passengers, a platform passenger control strategy is designed to promote the utilization of platform resources, and an empty train return strategy is proposed to transfer transportation resources to oversaturated direction. To characterize the problem mathematically, a multi-objective mixed-integer nonlinear programming model (MINLP) is formulated to minimize the passengers’ waiting time, the difference of bi-directional platform passenger density and the use cost of trains. An effective heuristic algorithm based on the non-dominated sorting genetic algorithm (NSGA-II) and the adaptive large neighborhood search (ALNS) is designed to find high-quality solutions for the proposed model. Finally, five sets of numerical examples based on the Beijing metro Batong line, are conducted to validate the performance of the proposed method in this paper. The experimental results demonstrate the method can fully utilize the transportation and platform resources of the unsaturated direction, to improve transport efficiency and relieve platform congestion of oversaturated direction.

Robust collaborative passenger flow control on a congested metro line: A joint optimization with train timetabling

With the rapid increase in residents in megacities, the passenger demand of metro systems is rising sharply and steadily, bringing immense pressure to train operations. To improve the service quality, this paper discusses systematically investigating a joint optimization of the robust passenger flow control strategy and train timetable on a congested metro line. A deterministic model for train timetabling and passenger flow control at each station is first developed to make a trade-off between operation efficiency and service fairness. Then, the uncertain passenger demand is further considered at each station, and three integer linear programming models are formulated to derive the robust passenger flow control strategies. The first two models are related to the technique of Light Robustness, in which the uncertainty is handled by inserting expected protection levels at stations or on trains. In addition, with a stochastic scenario set that characterizes the uncertain passenger information, the last model aims to find a solution that is feasible for all involved scenarios, and thus, reduces the impact of the uncertainty in metro systems. To improve the computational efficiency of large-scale instances, a customized decomposition-based algorithm is developed. Finally, some real-world case studies based on the operation data of the Beijing metro Batong line are conducted to verify the performance and effectiveness of the proposed approaches.

Time-dependent pricing strategies for metro lines considering peak avoidance behaviour of commuters

With growing concerns about travel demand management practices in overcrowded metro systems, it is considered that time-dependent pricing strategies are effective for dealing with the crowding occurring during peak commuting hours. In this study, a bi-level optimisation framework is used to consider the peak avoidance behaviour of commuters in the development of time-dependent pricing strategies. The behavioural sensitivity of commuters to pricing factors is investigated in terms of departure time and mode shift decisions based on a stated preference survey conducted in Beijing, China. The proposed bi-level programming model comprises a multi-objective optimisation model at the upper level and a nested logit-based stochastic user equilibrium model at the lower level. Based on an empirical case study of the Batong line in Beijing metro, nine optimal time-dependent pricing strategies are tailored by representative decision preferences, yielding up to 13.97% decrease in the peak ridership during rush hours.

Integrated optimization of train formation plan and rolling stock scheduling under Time-dependent demand

Both train formation plan (TFP) and rolling stock scheduling (RSS) have significant impacts on train operation. However, traditional sequential optimization could lead to infeasible RSS for the predetermined TFP, especially when the number of available rolling stocks is limited. This paper focuses on integrally optimizing TFP and RSS, where each train service can utilize different train formations and multiple turnaround operations occur in the depot. The key to solving the problem is to determine how many formations are needed for each train service and how train services are connected by rolling stocks. The multiple turnaround operations include immediate turnaround, turnaround with entering/exiting depot operations, and turnaround with coupling/decoupling operations. Considering the fixed costs and operating costs, we propose a multi-objective mixed-integer nonlinear programming (MINLP) model to minimize the number of rolling stocks (NR), the number of formations (NF), and the number of coupling/decoupling operations (NC) based on the time–space network. The model is further reformulated into a single-objective mixed-integer linear programming (MILP) model by the linearization method and fuzzy programming, and the reformulated model can be effectively solved by the MILP solver CPLEX. We test the model on realistic instances of the Batong Line in Beijing Subway Network to verify its effectiveness. The results demonstrate that the integrated model effectively solves the shortage of rolling stocks when the number of available rolling stocks is limited. Furthermore, in the integrated model, the decrease in the number of the rolling stocks and coupling/decoupling operations are at the cost of more formations used to balance the conflicts among objectives.

Joint optimization of modular vehicle schedule and fair passenger flow control under heterogeneous passenger demand in a rail transit system

With the rapid development of intelligent rail transit, fully automatic operation is progressively being achieved, and more approaches have appeared to enable operators to solve the supply–demand matching problem. Allowing advance reservations is one of the most efficient approaches under the novel “reservation and customization” operational logic. Passengers send trip requests via a reservation platform in real time, and operators plan the operational schedule based on the collected demand. To realize the operational pattern, we propose a trip reservation system (TRS) and introduce its architecture. To solve the trip reservation problem (TRP), a vehicle scheduling and passenger flow control (VSPFC) model is proposed. Using this model, the total cost of the system based on time and space capacity constraints is minimized, and the heterogeneity of passengers, fairness of passenger flow control and modular vehicle schedules are taken into consideration. A nested heuristic algorithm is applied to optimize the timetable and vehicle formation and obtain the passenger flow control plan, including feedback for reserved passengers. The Batong Line of the Beijing Subway is taken as a real-world case study to test the feasibility of the proposed model and algorithms. The results show that passenger travel efficiency can be improved as the number of reserved passengers increases. The passenger waiting time can be reduced and passenger flow can be controlled in a fair manner using the TRS proposed in this study, demonstrating its benefits over the flow control policies in a previous study.

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.

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.

Flexible train capacity allocation for an overcrowded metro line: A new passenger flow control approach

Metro lines of some mega cities usually suffer from extreme congestions in peak hours, leading to serious operation risks. To relieve the extreme saturation for overcrowded metro lines, this study explores a novel train operation strategy, i.e., flexibly allocating the capacities through reserving carriages at different stations according to the time-variant passenger demand. With this strategy, the train capacities are reasonably distributed to each station, especially for stations with large passenger flows, so as to balance the passenger accumulation over the whole line. A nonlinear integer programming model is developed by considering the passenger dynamics, and an efficient variable neighborhood search (VNS) algorithm is developed to solve the problem of interest. Finally, a set of numerical experiments with real-world data from Beijing metro Batong line are conducted to verify the performance and effectiveness of the proposed model and algorithm. The experimental results show that our proposed approach can effectively obtain high-quality carriage reservation plans in a short computing time, and the generated plans can well balance the passenger accumulation at all involved stations.

Joint optimization of carriage arrangement and flow control in a metro-based underground logistics system

Under the background of developing sustainable urban freight transportation on the operation level, this study investigates a joint optimization problem of carriage arrangement and flow control in a metro-based underground logistics system, in which passengers and freights are allowable to share each service train. By introducing the carriage arrangement variable and flow assignment variables related to passengers and freights, the problem of interest is formulated as an integer linear programming model with the objective of minimizing the weighted sum of the operation cost and the total delay penalty. To handle the solution challenges posed by a large number of integer decision variables, it is proved that the proposed model can be transformed into an equivalent mixed-integer linear programming model. Then, for solving the proposed model, an improved Benders decomposition algorithm is designed based on the model characteristics. Finally, a set of numerical examples on the Beijing metro Batong line are conducted to verify the performance and effectiveness of the proposed approaches.

Adaptive Threshold Adjustment Strategy Based on Fuzzy Logic Control for Ground Energy Storage System in Urban Rail Transit

The installation of a ground energy storage system (ESS) in the substation can improve the recovery and utilization of regenerative braking energy. This paper proposes an energy management strategy (EMS) of adaptive threshold adjustment for ground ESS. In this regard, this paper analyzes the energy flow in traction power supply system (TPSS) with different headways and no-load voltage. According to the influence of charge and discharge threshold on the energy flow in TPSS, the laws of energy flow are formulated. Subsequently, an EMS based on fuzzy logic control (FLC) is designed. The proposed EMS is adaptive to the variation of headway and no-load voltage. By monitoring the charge-discharge effect of ESS and the variation of substation output energy within two adjacent periods, the charge-discharge threshold is adjusted adaptively to guarantee the recovery effect of regenerative braking energy. Finally, the simulation and field experiment of proposed EMS are carried out with ground energy storage device and actual line conditions of Beijing Batong line. The experiment results indicate the good performance of proposed EMS in terms of energy saving.

Two-Stage Synthetic Optimization of Supercapacitor-Based Energy Storage Systems, Traction Power Parameters and Train Operation in Urban Rail Transit

The stationary supercapacitor energy storage system (SCESS) is one of effective approaches for the utilization of train's regenerative braking energy in urban rail systems. In this paper, the capacity configuration of SCESSs, the no-load voltage of substation, the control of onboard braking resistors and train operation diagrams are considered comprehensively. Based on the equivalent circuit model, the effects of traction power system parameters on the energy transmission between powering trains, braking trains and SCESSs are analyzed, and the relationships between the train operating parameters and system energy consumptions are revealed. A multi-variable synthetic optimization method is proposed to optimize the SCESS capacity, train operation diagrams and traction power system parameters collaboratively. In order to reduce the search space and improve the efficiency of the optimization algorithm, a hierarchical multi-objective optimization model is established, based on which the design variables and the control variables are optimized iteratively. And as the traffic density has a great impact on the regenerative braking energy distribution of the system, the optimization objective function fully considers the frequency distribution of headways throughout the day. Combined the Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) with the traction power flow simulator, the flowchart of the two-stage optimization algorithm is designed, and the pareto set of the multi-objective problem is obtained. The advantages of reducing system energy consumptions and configuration cost under the proposed algorithm are verified based on case studies of Beijing Batong Line.

Mitigating unfairness in urban rail transit operation: A mixed-integer linear programming approach

In oversaturated urban rail transit systems, passengers departing from downstream stations often experience long waiting times due to unbalanced space-time demand and limited transit capacity. This is often prevalent during morning and evening peak periods in transit systems. This paper aims to mitigate the unfairness of waiting time among a time-varying number of passengers through train timetable's adjustment by optimizing the train skip-stopping pattern. We develop an approximate general model by clustering passengers into groups and introducing an aggregation granularity parameter. To characterize feasible passenger travel patterns, both rigid first-in-first-out rule and capacity constraints are incorporated in the proposed model. Preprocessing is proposed to reduce the space of solutions. Some small-scale case studies show that the proposed method outperforms the original timetable and the preprocessing is effective to reduce computation time. Case studies based on the Batong line of Beijing rail transit network are conducted, in which a variable neighborhood search algorithm is applied to obtain high-quality solutions in short computing times. The results show that the proposed approach not only mitigates the unfairness of waiting time among passengers but also improves other efficiency evaluation indexes, including the average waiting time and the maximum number of missed trains. We also investigate the impact of the aggregation granularity parameter on the computational effort and solution accuracy.