Train timetabling for a double-track urban rail transit line under dynamic passenger demand

Scheduling local and express trains in suburban rail transit lines: Mixed–integer nonlinear programming and adaptive genetic algorithm

Spatiotemporal synchronous coupling algorithm for urban rail transit timetables design under dynamic passenger demand

With many train operating companies sharing limited capacity on the UK rail network, the train timetabling problem is complex and difficult to solve. This paper reports on a cooperative coevolutionary approach for the automatic generation of planning train timetables at the early stages of the timetabling process, when the main objective is to try to accommodate the bids as much as possible and to identify the major conflicts that need resolving by negotiations with the train operating companies. Some test experiments based on artificial problem instances as well as a real network are discussed.

This paper aims to simultaneously optimise train timetabling and rolling stock scheduling in a bidirectional urban rail transit line. A novel variable train composition strategy is adopted to respond to time-dependent passenger demand by allowing modular train units to split and couple with each other at depots. We mathematically model this problem in an arrival time revision framework, simplifying the problem structure and rendering the model solved by a commercial solver. In particular, the proposed model considers two realistic first-in-first-out rules to capture passenger transportation accurately in the oversaturated urban rail transit system. The efficiency of the proposed strategy and model is validated on an illustrative example and a real-world instance in the Yizhuang Line of Beijing Subway. Results show that adopting the variable train composition strategy can save 63.6% and 44.6% of total passenger waiting time compared to the current fixed train composition strategy with eight and six units.

ABSTRACTThis study proposes a modelling framework for the demand-driven train timetable and stop pattern cooperative optimization problem on an urban rail transit line. By embedding the train stop pattern into the timetable optimization process, we consider the minimization of total passenger travel time. A binary variable determination (BVD) method, which can transform complicated linear constraints into simple logical constraints, is proposed to calculate the large number of binary variables easily, and a genetic algorithm (GA) based on the BVD method is designed to solve the proposed model. A case study of the Batong line in the Beijing subway network is conducted to test the proposed model and algorithm. This study can provide beneficial advice for the operator to improve the operational service of urban rail transit lines.

Modeling the first train timetabling problem with minimal missed trains and synchronization time differences in subway networks

The aim of the train timetabling problem is to find a conflict free timetable for a set of passenger and freight trains along their routes in an infrastructure network. Several constraints like station capacities and train dependent running and headway times have to be satisfied. In this work we deal with large scale instances of the aperiodic train timetabling problem for the German railway network. The problem is modelled in a classical way via time discretised networks, its Lagrange-dual is solved by a bundle method. In order to handle the enormous number of variables and constraints dynamic graph generation and dynamic rolling horizon techniques are employed.

A new method is proposed for single-track railway freight train timetable with two-stage solution of train scheduling problem. The method describes train scheduling problem in matrix with the "signaling block" concept. The matrix represents entire block occupancy of trains between inter-stations and internal-stations while decomposing individual train occupancy, making optimization method more flexible in design and use. The "two-stage solution" refers to that of train timetable with "conflict solution" and "timetable optimization." At the beginning, related data for trains are entered to build the initial timetable, which is then transferred and saved as the matrix format. All conflicts between interstations and internal-stations are located; solutions are made with manual scheduling to generate a feasible timetable. In the second stage, departure and stop time of freight trains, and passenger trains if necessary, are adjusted with Fuzzy system. Before optimization, storage is made in ascending amount of extra-time percent in freight train schedule. Execution is made subject to pre-ordered results during optimization for computer program acceleration of current manual spotting solution to find reasonable and feasible solution. The two-stage method also takes less time than the regular railway timetable design methods in cost saving of manual labor and providing higher operation performance and efficiency.

Service-oriented train timetabling problem with consideration of women-only passenger cars

In view of the conflict between the time-variation of urban rail transit passenger demand and the homogeneity of the train timetable, this paper takes into account the interests of both passengers and operators to build an urban rail transit scheduling model to acquire an optimized time-dependent train timetable. Based on the dynamic passenger volumes of origin-destination pairs from the automatic fare collection system, the model focuses on minimizing the total passenger waiting time with constraints on time interval between two consecutive trains, number and capacity of trains available, and load factor of trains. A hybrid algorithm which consists of the main algorithm based on genetic algorithm and the nested algorithm based on train traction calculation and safety distance requirement is designed to solve the model. To justify the effectiveness and the practical value of the proposed model and algorithm, a case of Nanjing Metro Line S1 is illustrated in this paper. The result shows that the optimized train timetable has advantage compared to the original one.

Passengers would like to choose the most suitable train based on their travel preferences, expenses, and train timetable in the high-speed railway corridor. Meanwhile, the railway department will constantly adjust the train timetable according to the distribution of passenger flows during a day to achieve the optimal operation cost and energy consumption saving plan. The question is how to meet the differential travel needs of passengers and achieve sustainable goals of service providers. Therefore, it is necessary to design a demand-oriented and environment-friendly high-speed railway timetable. This paper formulates the optimization of train timetable for a given high-speed railway corridor, which is based on the interests of both passengers and transportation department. In particular, a traveling time-space network with virtual departure arc is constructed to analyze generalized travel costs of passengers of each origin-destination (OD), and bilevel programming model is used to optimize the problem. The upper integer programming model regards the minimization of the operating cost, which is simplified to the minimum traveling time of total trains, as the goal. The lower level is a user equilibrium model which arranges each OD passenger flow to different trains. A general advanced metaheuristic algorithm embedded with the Frank–Wolfe method is designed to implement the bilevel programming model. Finally, a real-world numerical experiment is conducted to verify the effectiveness of both the model and the algorithm.

In recent years, with the global energy shortage and severe environmental deterioration, railway transport has begun to attract great interest as a green transportation mode. One of the vital means to realize social sustainable development is to improve railway transportation systems, in which providing a demand-oriented train timetable with a higher service level is the most viable method. A demand-oriented train timetable problem generally deals with passengers’ train-choice decisions according to the queue principle, but it is not adapted to rail systems, such as China’s, where passengers usually book tickets a few days in advance by telephone or online instead of going to stations. This paper is devoted to modeling and solving the demand-oriented train timetabling problem integrated with passengers’ train-booking decisions. Firstly, a bi-level programming model is formulated for their integrated optimization on a rail network. Its upper-level model is to optimize train arrival and departure times at each visited station with the aim of reducing passengers’ total travel cost, while its lower-level model aims to determine passengers’ train-booking behavior using the user equilibrium theory. Then, a priority-based heuristic algorithm is designed to solve this model. It has two main steps at each iteration: one is to determine the number of passengers booking each train with a given train timetable, and the other is to improve the current train timetable based on the valuable information of passenger train-booking decisions. The performance, convergence, and practicability of the proposed method were analyzed based on the Changsha–Zhuzhou–Xiangtan intercity rail in China. Experimental results show the proposed method can effectively reduce the travel cost for passengers, creating a greater passenger demand for railway travel, which is beneficial to the sustainable development of railway systems and even society.

In order to study the relationship between the accessibility along the urban rail transit line and the change in housing price, GA-BP model, which combining the genetic algorithm(GA) and back propagation neural network(BPNN), was used to predict the housing price along the urban rail transit line. The reliability of the model was verified by taking the price of residential areas along Nanjing Metro Line 10 as an example, and the performance between GA-BP model and the BP model was compared. It was found that the average absolute error rate of GA-BP model is 6.91%, which is 6.45% lower than that of BP model, and the mean square error of prediction results is significantly reduced. It can be seen that the price prediction algorithm based on GA-BP model for those residential areas along the urban rail transit line is reliable and can fully tap the potential relationship between the accessibility of urban transport network and the housing price.

Providing effective Through Train Services (TTSs) faces challenges due to complex infrastructure conditions, train performances and passenger demands. To enhance TTSs between two different classes of urban rail transit lines with variations in train speed and capacity, we propose a multi-objective Integer Non-Linear Programming (INLP) model. This model maximizes passenger travel time savings and average train load utilization, and develops an integrated approach to simultaneously optimize the frequencies of through express trains and local trains, as well as the operation zones, stopping patterns and type selection of through trains. Additionally, a Non-Dominated Sorting Genetic Algorithm II is designed to solve the INLP model based on a simple test network and a real-world case from the Nanjing Subway. The unique benefits of our proposed method are demonstrated by a comprehensive compared with the Single Line Operation Mode and the all-stop plans under Through Operation Mode.

Timetable Optimization for High-Speed Trains at Chinese Railways