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Heavy-haul railway transport is a critical mode of regional bulk cargo transport. It dramatically improves the freight transport capacity of railway lines by combining several unit trains into one combined train. In order to improve the efficiency of the heavy-haul transport system and reduce the transportation cost, a critical problem involves arranging the combination scheme in the combination station (CBS) and scheduling the train timetable along the trains’ journey. With this consideration, this paper establishes two integer programming models in stages involving the train service plan problem (TSPP) model and train timetabling problem (TTP) model. The TSPP model aims to obtain a train service plan according to the freight demands by minimizing the operation cost. Based on the train service plan, the TTP model is to simultaneously schedule the combination scheme and train timetable, considering the utilization optimal for the CBS. Then, an effective hybrid genetic algorithm (HGA) is designed to solve the model and obtain the combination scheme and train timetable. Finally, some experiments are implemented to illustrate the feasibility of the proposed approaches and demonstrate the effectiveness of the HGA.

The “left-behind” phenomenon occurs frequently in Urban Rail Transit (URT) networks with booming travel demand, especially during peak hours in a complex URT network, which makes passenger travel patterns more complicated. This paper proposes a methodology to mine passenger travel patterns based on fare transaction records from automatic fare collection (AFC) systems and Automatic Vehicle Location (AVL) data from Communication Based Train Control (CBTC) Systems or tracking systems. By introducing the concept of a sequence, a space-time-sequence trajectory model is proposed to simulate a passenger’s travel activities, including when they are left-behind. The paper analyzes passenger travel trajectory links and estimates the weight of each feasible trajectory under tap-in/tap-out constraints. The station time parameters, including access/egress and transfer walking-time parameters, are important inputs for the model. The paper also presents a maximum-likelihood approach to estimate these parameters from AFC transaction data and AVL data. The methodology is applied to a case study using AFC and AVL data from the Beijing URT network during peak hours to test the proposed model and algorithm. The estimation results are consistent with the results obtained from the authorities, and this finding verifies the feasibility of our approach.

Compared with other modes of transportation, a high-speed railway has energy saving advantages, it is environmentally friendly, safe, and convenient for large capacity transportation between cities. With the expansion of the high-speed railway network, the operation of high-speed railways needs to be improved urgently. In this paper, a hybrid approach for quickly solving the timetable of high-speed railways, inspired by the periodic model and the aperiodic model, is proposed. A space–time decomposition method is proposed to convert the complex passenger travel demands into service plans and decompose the original problem into several sub-problems, to reduce the solving complexity. An integer programming model is proposed for the sub-problems, and then solved in parallel with CPLEX. After that, a local search algorithm is designed to combine the timetables of different periods, considering the safety operation constraints. The hybrid approach is tested on a real-world case study, based on the Beijing–Shanghai high-speed railway (HSR), and the results show that the train timetable calculated by the approach is superior to the real-world timetable in many indexes. The hybrid approach combines the advantages of the periodic model and the aperiodic model, it can deal with the travel demands of passengers well and the solving speed is fast. It provides the possibility for flexible adjustment of a timetable and timely response to the change of passenger travel demands, to avoid the waste of transportation resources and achieve sustainable development.

Emerging transportation network services, such as customized buses, hold the promise of expanding overall traveler accessibility in congested metropolitan areas. A number of internet-based customized bus services have been planned and deployed for major origin-destination (OD) pairs to/from inner cities with limited physical road infrastructure. In this research, we aim to develop a joint optimization model for addressing a number of practical challenges for providing flexible public transportation services. First, how to maintain minimum loading rate requirements and increase the number of customers per bus for the bus operators to reach long-term profitability. Second, how to optimize detailed bus routing and timetabling plans to satisfy a wide range of specific user constraints, such as passengers’ pickup and delivery locations with preferred time windows, through flexible decision for matching passengers to bus routes. From a space-time network modeling perspective, this paper develops a multi-commodity network flow-based optimization model to formulate a customized bus service network design problem so as to optimize the utilization of the vehicle capacity while satisfying individual demand requests defined through space-time windows. We further develop a solution algorithm based on the Lagrangian decomposition for the primal problem and a space-time prism based method to reduce the solution search space. Case studies using both the illustrative and real-world large-scale transportation networks are conducted to demonstrate the effectiveness of the proposed algorithm and its sensitivity under different practical operating conditions.

To improve the service quality of the railway system (e.g., punctuality and travel times) and to enhance the robust timetabling methods further, this paper proposes an integrated two-stage approach to consider the recovery-to-optimality robustness into the optimized timetable design without predefined structure information (defined as flexible structure) such as initial departure times, overtaking stations, train order and buffer time. The first-stage timetabling model performs an iterative adjustment of all departure and arrival times to generate an optimal timetable with balanced efficiency and recovery-to-optimality robustness. The second-stage dispatching model evaluates the recovery-to-optimality robustness by simulating how each timetable generated from the first-stage could recover under a set of restricted scenarios of disturbances using the proposed dispatching algorithm. The concept of recovery-to-optimality is examined carefully for each timetable by selecting a set of optimally refined dispatching schedules with minimum recovery cost under each scenario of disturbance. The robustness evaluation process enables an updating of the timetable by using the generated dispatching schedules. Case studies were conducted in a railway corridor as a special case of a simple railway network to verify the effectiveness of the proposed approach. The results show that the proposed approach can effectively attain a good trade-off between the timetable efficiency and obtainable robustness for practical applications.

This paper considers a high-speed rail corridor that requires high fidelity scheduling of train speed for a large number of trains with both tight power supply and temporal capacity constraints. This research aims to systematically integrate problems of macroscopic train timetabling and microscopic train trajectory calculations. We develop a unified modeling framework using three-dimensional space-time-speed grid networks to characterize both second-by-second train trajectory and segment-based timetables at different space and time resolutions. The discretized time lattices can approximately track the train position, speed, and acceleration solution through properly defined spacing and modeling time intervals. Within a Lagrangian relaxation-based solution framework, we propose a dynamic programming solution algorithm to find the speed/acceleration profile solutions with dualized train headway and power supply constraints. The proposed numerically tractable approach can better handle the non-linearity in solving the differential equations of motion, and systematically describe the complex connections between two problems that have been traditionally handled in a sequential way. We further use a real-world case study in the Beijing-Shanghai high-speed rail corridor to demonstrate the effectiveness and computational efficiency of our proposed methods and algorithms.

With the rapid development of high-speed railway (HSR) systems, the increasing demand for passenger traffic has put forward higher requirements for HSR train timetabling problems (HSRTTPs). This paper establishes two mathematical optimisation models with different optimisation objectives for an HSRTTP and solves these models through a column generation-based algorithm. However, the column generation-based algorithm has the disadvantage of a slow convergence rate, thus we put forward corresponding acceleration strategies for five stages of the algorithm: preprocessing, restricted master problem, pricing problem, branch-and-bound and postprocessing from a symmetry point between the computation efficiency and the accuracy. The effectiveness of the acceleration strategies was validated by a case study of the Beijing&ndash, Shanghai HSR. The results show that the proposed optimal acceleration strategies can increase the computation efficiency of the algorithm by 11.8&times, on average while ensuring the accuracy.

High-speed railway (HSR) systems have been developing rapidly in China and various other countries throughout the past decade; as a result, the question of how to efficiently operate such large-scale systems is posing a new challenge to the railway industry. A high-quality train timetable should take full advantage of the system’s capacity to meet transportation demands. This paper presents a mathematical model for optimizing a train timetable for an HSR system. We propose an innovative methodology using a column-generation-based heuristic algorithm to simultaneously account for both passenger service demands and train scheduling. First, we transform a mathematical model into a simple linear programming problem using a Lagrangian relaxation method. Second, we search for the optimal solution by updating the restricted master problem (RMP) and the sub-problems in an iterative process using the column-generation-based algorithm. Finally, we consider the Beijing–Shanghai HSR line as a real-world application of the methodology; the results show that the optimization model and algorithm can improve the defined profit function by approximately 30% and increase the line capacity by approximately 27%. This methodology has the potential to improve the service level and capacity of HSR lines with no additional high-cost capital investment (e.g., the addition of new tracks, bridges and tunnels on the mainline and/or at stations).

It is a multiobjective mixed integer programming problem that calculates the carrying capacity of high speed railway based on mathematical programming method. The model is complex and difficult to solve, and it is difficult to comprehensively consider the various influencing factors on the train operation. The multiagent theory is employed to calculate high speed railway carrying capacity. In accordance with real operations of high speed railway, a three-layer agent model is developed to simulate the operating process of high speed railway. In the proposed model, railway network agent, line agent, station agent, and train agent are designed, respectively. To validate the proposed model, a case study is performed for Beijing–Shanghai high speed railway by using NetLogo software. The results are consistent with the actual data, which implies that the proposed multiagent method is feasible to calculate the carrying capacity of high speed railway.

This paper is concerned with the scheduling of Electrical Multiple Units (EMUs) under the condition of their utilization on one sector or within several interacting sectors. Based on the introduction of the train connection graph which describes the possible connection relationship between trains, the integer programming model of EMU circulation planning is constructed. In order to analyzing the resolution of the model, a heuristic which shares the characteristics with the existing methods is introduced first. This method consists of two stages: one is a greedy strategy to construct a feasible circulation plan fragment, and another is to apply a stochastic disturbance to it to generate a whole feasible solution or get a new feasible solution. Then, an exact branch and bound method which is based on graph designing is proposed. Due to the complexity, the lower bound is computed through a polynomial approximation algorithm which is a modification from the one solving the degree constraint minimum 1-tree problem. Then, a branching strategy is designed to cope with the maintenance constraints. Finally, we report extensive computational results on a railway corridor in which the sectors possess the basic feature of railway networks.

Methods for solving the carrying capacity problem for High-Speed Railways (HSRs) have received increasing attention in the literature in the last few years. As important nodes in the High-Speed Railway (HSR) network, large stations are usually the carrying capacity bottlenecks of the entire network due to the presence of multiple connections in different directions and the complexity of train operations at these stations. This paper focuses on solving the station carrying capacity problem and considers train set utilization constraints, which are important influencing factors that have rarely been studied by previous researchers. An integer linear programming model is built, and the CPLEX v12.2 software is used to solve the model. The proposed approach is tested on a real-world case study of the Beijing South Railway Station (BS), which is one of the busiest and most complex stations in China. Studies of the impacts of different train set utilization constraints on the practical station carrying capacity are carried out, and some suggestions are then presented for enhancing the practical carrying capacity. Contrast tests indicate that both the efficiency of the solving process and the quality of the solution show huge breakthroughs compared with the heuristic approach.

The Urban Rail Transit (URT) passenger travel space–time trajectory reflects a passenger’s path-choice and the components of URT network passenger flow. This paper proposes a model to estimate a passenger’s maximum-likelihood space–time trajectory using Automatic Fare Collection (AFC) transaction data, which contain the passenger’s entry and exit information. First, a method is presented to construct a space–time trajectory within a tap in/out constraint. Then, a maximum likelihood space–time trajectory estimation model is developed to achieve two goals: (1) to minimize the variance in a passenger’s walk time, including the access walk time, egress walk time and transfer walk time when a transfer is included; and (2) to minimize the variance between a passenger’s actual walk time and the expected value obtained by manual survey observation. Considering the computational efficiency and the characteristics of the model, we decompose the passenger’s travel links and convert the maximum likelihood space–time trajectory estimation problem into a single-quadratic programming problem. Real-world AFC transaction data and train timetable data from the Beijing URT network are used to test the proposed model and algorithm. The estimation results are consistent with the clearing results obtained from the authorities, and this finding verifies the feasibility of our approach.

This paper aims to optimize high-speed railroad timetables for a corridor. We propose an integer programming model using a time-space network-based approach to consider passenger service demands, train scheduling, and station service demands simultaneously. A modified branch-and-price algorithm is used for the computation. This algorithm solves the linear relaxation of all nodes in a branch-and-bound tree using a column generation algorithm to derive a lower-bound value (LB) and derive an upper-bound value (UB) using a rapid branching strategy. The optimal solution is derived by iteratively updating the upper- and lower-bound values. Three acceleration strategies, namely, initial solution iteration, delayed constraints, and column removal, were designed to accelerate the computation. The effectiveness and efficiency of the proposed model and algorithm were tested using Wuhan-Guangzhou high-speed railroad data. The results show that the proposed model and algorithm can quickly reduce the defined cost function by 38.2% and improve the average travel speed by 10.7 km/h, which indicates that our proposed model and algorithm can effectively improve the quality of a constructed train timetable and the travel efficiency for passengers.

The main difference between locomotive schedule of heavy haul railways and that of regular rail transportation is the number of locomotives utilized for one train. One heavy-loaded train usually has more than one locomotive, but a regular train only has one. This paper develops an optimization model for the multilocomotive scheduling problem (MLSP) through analyzing the current locomotive schedule of Da-qin Railway. The objective function of our paper is to minimize the total number of utilized locomotives. The MLSP is nondeterministic polynomial (NP) hard. Therefore, we convert the multilocomotive traction problem into a single-locomotive traction problem. Then, the single-locomotive traction problem (SLTP) can be converted into an assignment problem. The Hungarian algorithm is applied to solve the model and obtain the optimal locomotive schedule. We use the variance of detention time of locomotives at stations to evaluate the stability of locomotive schedule. In order to evaluate the effectiveness of the proposed optimization model, case studies for 20 kt and 30 kt heavy-loaded combined trains on Da-qin Railway are both conducted. Compared to the current schedules, the optimal schedules from the proposed models can save 62 and 47 locomotives for 20 kt and 30 kt heavy-loaded combined trains, respectively. Therefore, the effectiveness of the proposed model and its solution algorithm are both valid.

The train-set circulation plan problem (TCPP) belongs to the rolling stock scheduling (RSS) problem and is similar to the aircraft routing problem (ARP) in airline operations and the vehicle routing problem (VRP) in the logistics field. However, TCPP involves additional complexity due to the maintenance constraint of train-sets: train-sets must conduct maintenance tasks after running for a certain time and distance. The TCPP is nondeterministic polynomial hard (NP-hard). There is no available algorithm that can obtain the optimal global solution, and many factors such as the utilization mode and the maintenance mode impact the solution of the TCPP. This paper proposes a train-set circulation optimization model to minimize the total connection time and maintenance costs and describes the design of an efficient multiple-population genetic algorithm (MPGA) to solve this model. A realistic high-speed railway (HSR) case is selected to verify our model and algorithm, and, then, a comparison of different algorithms is carried out. Furthermore, a new maintenance mode is proposed, and related implementation requirements are discussed.

With the urban rail transit becoming more and more networked, determining the departure time of last trains has been an important part for the urban rail transit network operations organization. First analyze two aspects of passengers and vehicles to determine reasonable time intervals of last trains, then analyze last train departure time optimization, minimizing the total loss in the transfer station as the objective to build the mathematical model, by adding and shifting line at the transfer station to reduce the connection direction loss, an auxiliary line being added or not according to the operating time so as to determine the final operation result. Finally, use the Beijing subway to verify and the result shows that the method has practical significance for the improvement of urban rail transit operation organization.

This paper defines a new method of modeling the running line by describing a station with the station plan, which originally is just a point of the line. It analyzes the problems of using the original method to calculate the brake point. Then this paper provide an algorithm of forward prediction based on clock-step method to calculate the brake point, the result is proved more accurate and more feasible.

We discussed the crew scheduling rules for High-speed railway in China. These rules are mainly relates to crew members and railway operators. One of the aims to establish the rules is to protect the legitimate rights and interests of crew members, and the other is to reduce the operating cost as possible. The idea of biological evolution for engineering optimization problems has been developed for years, the applicability of different algorithms were compared to solve this problem. It shows that simulated evolution method is more applicable and then discussed the main steps of using method SE method to deal with this problem. Finally, based on the computer technology, we designed a prototype system.

This paper analyzes the command mode of high speed railway (HSR) train dispatching based on control system CTCS-3.In order to draw up the optimum allocation plan of time and space resources for HSR, a basic concept of management and control integration was proposed in this paper, including the HSR train coordination scheduling, the structure of hardware and software, and the theory of train operation. Furthermore, the basic framework of train operation dispatching command system based on the integration of management and control was designed to optimize the HSR operation and organization.

Urban rail transit is occupying assume an increasingly important role in urban traffic areas as a means of urban public transport. This paper will analyze the various factors impacting the subway fares, and research the relationship between all the factors based on system dynamics, ultimately some suggestions formulated.

Chinese high-speed railway is in a boom and making train diagram with high-density trains to relieve capacity intense and improve operational efficiency has become the research focus. Different kinds of station intervals between adjacent trains are the basis for the train diagram. According to the situation in which trains with different speed run on the same line and the proportion of high-speed trains is much larger than that of middle-speed trains, this paper raises principles and methods to determine the minimum departure interval between trains with same speed at the relatively initial station. The minimum departure interval between trains with same speed at the relatively initial station is a necessary and sufficient condition for making train diagram since there is no overtaking between same-speed trains.

This paper deals with the optimization problem of motor train-set in dedicated passenger line, a motor train-set operational model was proposed and maintenance constraint was considered . To solve this model and utilize the motor train-set efficiently, we described a two-step method and the problem was divided into two sub-problems: one is to make sub-routings and another is to combine these sub-routings to new circulations. First step the Hungarian algorithm was used to get circulations of the motor train-set without considering maintenance constraint and the circulations will be divided into several sub-routings by the constraint of maintenance. In order to utilize the motor train-set more balanced, the second step is to combine these sub-routing to new circulations by path exchange rules. This approach was evaluated on the Jing-Hu Passenger Dedicated Line, the computational results show that this new method is feasible and we provide a new idea to solve such problems.

Timetable is the core technical plan of the railway transportation organization, and it is the basis for the daily work. However, at present, China’s timetable management technology is relatively backward, which cannot meet the safety and efficiency of actual transportation. This paper analyzes the problems in the current situation of tiemetable management. Starting from the problem, the application research of big data platform is proposed. Firstly, the data is collected and normalized, then the safety analysis and index analysis are carried out, and finally the intelligent optimization is carried out.

Under the background of the urban mass transit becoming network increasingly, time coordination of the first and last trains becomes the important part of urban mass transit network operation, and has special significance. This paper firstly ascertains the time range of first and last running of trains and analyzes from two aspects. Then find the time quantum that the passengers and companies all accept. The paper analyzes the departed principle of networked first and last running time of trains, the target is the minimum of the passengers total loss of time at the transfer stations, setting up a multiple-direction trains transfer mathematical model that achieves attainability and rationality for transferring among different lines and getting a local optimal solution by using the method of iteration, and the optimal solution is within the feasible region and fits actual situations. Lastly a specific urban rail network is taken as an example to check the model and algorithm.

With the rapid development of China’s social economy and the improvement of people’s living standards, people’s travel demand grows rapidly. As high-speed rail provides fast and comfortable services, the number of high-speed railway passengers is increasing exponentially. During the holidays, huge numbers of railway passengers always bring great pressure and challenge to the transport companies, particularly at large railway stations. Accurately forecasting passengers’ travel demand during holidays is of practical significance to efficiently develop train schedules, formulate effective emergency plans and early warning schemes and guarantee the operating safety. With historical passenger flow data of Beijing West Railway Station during the Spring Festival, we analyse and forecast the future passenger flow using a trend analysis method. The result provides suggestions on organization optimization and improvement for Beijing West Railway Station, which can be used by other railway passenger stations as references.

As one of the most basic transport plan, urban railway transit vehicle use plan has important influence on operating costs and transportation service quality. It is urgent demand to find practical and effective mathematical models and solving method. Based on the development reality of urban railway transit and the advanced experience, this paper make research on optimization model of urban railway transit vehicle use plan and propose rolling time and space assignment model. An example of Shenzhen Metro Line 8 was presented to show the feasibility of the proposed model and algorithm

This paper introduces a microscopic simulation based method to analyze and calculate carrying capacity of railway stations. Due to the random disturbance of train operations in station area, an analytical stochastic model of train delay and operation time is proposed, which considers the stochastic variations of train operations and resources occupations. In addition, we implement a computer-aided tool to analyze and evaluate the carrying capacity of railway stations. Finally, taking Beijing South railway station as a real world example, we use the method to calculate the capacity of this station.

In rail freight transportation, general merchandise freight cars may pass through many classification stations on their route from origin to destination. The Railroad Blocking Problem (RBP) is to reclassify inbound traffic from various origins in the classification stations and put them on outbound trains with the same or close destinations, the objective of the RBP is to minimize the total operating costs of delivering all traffic on the railway network while satisfying the resource and capacity constraints at the stations and the priority constraints for shipments. In this paper, we introduce a new mathematic model which can comprehensively describe the blocking strategy and various combinations of multi-route O-D pairs in large scale railway network. Furthermore, we propose an improved Ant Colony (AC) algorithm for RPB, and a computational experiment derived from the real life instances of coal heavy haul rail network in north China is given. Experimental results verified the validation of the model and effectiveness of the algorithm.

This paper focuses on solving the problem of abnormal flight recovery, which is a hot topic of airline. In the background of an exception occurring at an airport under multi-airport conditions, this paper analyses multi-type flight recovery problem, taking multi-type aircraft capacity, passenger seat allocation, interline flights of passengers and airport capacity into account. And a multi-type flight recovery model is constructed with the objective of minimizing the total delay time of passengers. The improved GRASP algorithm based on the path relinking algorithm is designed to solve the model. Finally, the correctness of the model and the effectiveness of the algorithm are verified by the case.

This paper has carried out some researches on organization method of wagon flow of coal transportation corridor to meet the demand of heavy-haul railway. To improve the capacity of a collecting and distributing system, the optimal problem is described as: coordination of loading capacity and unloading capacity to determine the wagon flow. Based on the analysis of the capacity of loading end and unloading end of Daqin Railway, the model with the minimization of the transportation price and the idle cost of the equipment and the maximization of the total loading and unloading wagons of the system is constructed. Then t he paper transformed this multi-objective programming into a transportation problem by using main objective method, so that the model can be solved easily. Finally, by solving of the problem respectively on Daqin Railway, the model is proved to use on capacity coordination of loading and unloading stations on heavy-haul r ailway.