Railway trafficability bottleneck identification method and device, storage medium and product

Abstract

The invention discloses a railway trafficability bottleneck identification method and device, a storage medium and a product, and relates to the technical field of high-speed railway trafficability utilization. Obtaining a train running diagram of each section of the high-speed railway line, and constructing a new train running line alternative set of each section; encrypting the train running diagram of each section based on the newly added train running line alternative set of each section by taking the discrete space-time network as a framework; based on train operation constraints, establishing a train operation diagram encryption model by taking minimization of train operation cost as a target; solving a feasible solution of the train working diagram encryption model based on a Lagrange relaxation heuristic algorithm to obtain an encrypted saturated train working diagram; and determining a capability bottleneck identification result of each section based on the number of the corresponding train running routes of each section in the saturated train running diagram and the number of the train running routes of each section in the train running diagram. The invention provides an accurate and reliable method for identifying the passing capacity bottleneck of each section of the high-speed railway line.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-speed railway capacity utilization, and in particular relates to a railway capacity bottleneck identification method, device, storage medium and product. Background Art

[0002] As a vital component of the modern transportation system, high-speed rail's transportation efficiency and service quality are directly linked to national economic development and the convenience of public transportation. However, with the continuous improvement of the high-speed rail network and the continuous increase in passenger volume, high-speed rail capacity utilization has shown temporal and spatial imbalances. At the macro level, the number of high-speed rail trains operated is significantly influenced by passenger demand, which exhibits strong temporal and spatial characteristics. Furthermore, after the network is established, the number of trains in different sections is affected by cross-line trains. In some sections, cross-line trains converge, leading to relatively tight capacity utilization. This leads to significant imbalances in capacity utilization. In particular, in some sections, capacity saturation or configuration constraints make it difficult to add trains, creating a so-called "capacity bottleneck" phenomenon that significantly limits the overall capacity utilization of the line or network. Therefore, effectively identifying capacity bottlenecks is crucial for improving line capacity utilization and enhancing the overall efficiency and operational quality of the high-speed rail system.

[0003] Patent application number CN202311353282.9 proposes a method, device, and medium for calculating and identifying high-speed rail station capacity. This method first acquires historical CTC system data and extracts key information. Based on this key information, it calculates the capacity and actual utilization of bottleneck areas during peak hours, as well as the capacity and actual utilization of arrival and departure lines during peak hours. Capacity bottlenecks are identified by comparing the actual utilization of bottleneck areas during peak hours with the actual utilization of arrival and departure lines during peak hours. This technique uses capacity utilization as a metric to identify capacity bottlenecks, but this identification method has certain limitations. While capacity utilization can, to a certain extent, reflect the probability of a station or section becoming a capacity bottleneck, it cannot accurately determine whether a particular section is a capacity bottleneck. For example, when the number of trains operating is fixed, capacity utilization varies depending on factors such as train stops and transportation service quality requirements. The assessment of line capacity differs from the capacity of individual stations or sections, and a section's utilized capacity cannot be used to determine whether it is a bottleneck.

[0004] Therefore, how to provide an effective solution to accurately identify the capacity bottlenecks of various sections of high-speed railway lines has become a difficult problem that needs to be solved urgently in the existing technology. Summary of the Invention

[0005] The purpose of the present invention is to provide a railway capacity bottleneck identification method, device, storage medium and product to solve the above-mentioned problems existing in the prior art.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: In a first aspect, the present invention provides a method for identifying a railway capacity bottleneck, comprising: Obtain the train operation diagram of each section of the high-speed railway line and construct a new train operation line candidate set for each section; Using discrete space-time network as the framework, the train operation diagram of each section is encrypted based on the newly added train line candidate set of each section; Based on train operation constraints, a train operation diagram encryption model is established with the goal of minimizing train operation costs; The feasible solution of the train timetable encryption model is solved based on the Lagrangian relaxation heuristic algorithm, and the encrypted saturated train timetable is obtained. Based on the number of corresponding train routes of each section in the saturated train operation diagram and the number of train routes in the train operation diagram of each section, the capacity bottleneck identification result of each section is determined.

[0007] Based on the above-disclosed content, the present invention obtains the train operation diagram of each section of the high-speed railway line to construct a new train line alternative set for each section; uses a discrete space-time network as a framework, encrypts the train operation diagram of each section based on the new train line alternative set of each section; establishes a train operation diagram encryption model based on train operation constraints with the goal of minimizing train operation costs; solves the feasible solution of the train operation diagram encryption model based on the Lagrangian relaxation heuristic algorithm to obtain an encrypted saturated train operation diagram; determines the capacity bottleneck identification result of each section based on the number of corresponding train operation routes of each section in the saturated train operation diagram and the number of train operation routes in the train operation diagram of each section. In this way, by constructing a capacity bottleneck identification model with an encrypted operation diagram as the core based on a discrete space-time network, a precise and reliable method is provided for identifying capacity bottlenecks in various sections of high-speed railway lines, which provides more theoretical possibilities for the identification of capacity bottlenecks of high-speed railways. At the same time, it can locate sections with restricted capacity utilization and improve the network, provide decision-making references for the renewal of facilities and equipment, line reconstruction and the design of new lines, and provide references for the rational utilization and enhancement of line capacity. In addition, it is of great significance for giving full play to the network effect of the line, scientifically planning the high-speed railway network and the good development of high-speed railways.

[0008] In a possible design, constructing a new train route candidate set for each section includes: A new set of train route alternatives is added based on the existing train operation status in the train operation diagram of each section and the nature of the stations along the section.

[0009] In a possible design, the train operation diagram of each section is encrypted based on the newly added train line candidate set of each section using the discrete time space network as the framework, including: With the time axis as the horizontal coordinate and the space axis as the vertical coordinate, the train operation diagram of each section is converted into the initial discrete time-space network diagram; Adding a virtual departure site and a virtual arrival site to the initial discrete time-space network graph to obtain the discrete time-space network graph; Based on the newly added train running line candidate set of each section, a new running line is added to the discrete time-space network diagram.

[0010] In one possible design, establishing a train operation diagram encryption model based on train operation constraints with the goal of minimizing train operation costs includes: Based on the train departure and arrival constraints, train timetable feasibility constraints, and train operation conflict-free constraints, a train timetable encryption model is established with the goal of minimizing train operation costs. The train departure and arrival constraints include train departure station constraints, train arrival station constraints, and train operation path constraints; The feasibility constraints of the train operation diagram include the uniqueness constraint of the nodes occupied by the train in the operation path, the vehicle flow balance constraint of each node, the operation time constraint between nodes, and the node stop time constraint; The train operation non-conflict constraints include the train departure interval and arrival interval constraints of the nodes and the train non-overtaking constraints between adjacent nodes.

[0011] In a possible design, the Lagrangian relaxation heuristic algorithm is used to solve a feasible solution to the encrypted train diagram model to obtain an encrypted saturated train diagram, including: Performing Lagrangian relaxation transformation on the encrypted model of the train timetable to obtain a Lagrangian relaxation model corresponding to the encrypted model of the train timetable; Iteratively update the Lagrangian multiplier of the Lagrangian relaxation model, and solve the iteratively updated relaxation solution of the Lagrangian relaxation model based on the train operation constraints to obtain the optimal relaxation solution of the Lagrangian relaxation model; The train operation diagram of each section is updated based on the optimal relaxation solution to obtain the encrypted saturated train operation diagram.

[0012] In one possible design, determining the capacity bottleneck identification result of each section based on the number of corresponding train routes in each section in the saturated train operation diagram and the number of train routes in the train operation diagram of each section includes: Determine the number of newly added train routes for each section based on the number of corresponding train routes for each section in the saturated train operation diagram and the number of train routes in the train operation diagram for each section; Determine the throughput capacity utilization of each section based on the number of corresponding train routes in each section in the saturated train operation diagram and the number of train routes in the train operation diagram of each section; Based on the number of newly added train routes in each section and the throughput capacity utilization rate of each section, the throughput capacity bottleneck evaluation threshold of each section is determined; Based on the number of train routes in the train operation diagram of each section and the capacity bottleneck evaluation threshold of each section, it is determined whether each section is a capacity bottleneck.

[0013] In a second aspect, the present invention provides a railway capacity bottleneck identification device, comprising: An acquisition unit, used to obtain a train operation diagram for each section of the high-speed railway line; A construction unit, used to construct a new train line candidate set for each section; An encryption unit is used to encrypt the train operation diagram of each section based on the newly added train operation line candidate set of each section in a discrete space-time network framework; A modeling unit, configured to establish a train operation diagram encryption model based on train operation constraints with the goal of minimizing train operation costs; A solving unit, used for solving a feasible solution of the train timetable encryption model based on a Lagrangian relaxation heuristic algorithm to obtain an encrypted saturated train timetable; The determination unit is used to determine the capacity bottleneck identification result of each section based on the number of corresponding train running routes of each section in the saturated train operation diagram and the number of train running routes in the train operation diagram of each section.

[0014] In a third aspect, the present invention provides another railway capacity bottleneck identification device, comprising a memory, a processor and a transceiver that are communicatively connected in sequence, wherein the memory is used to store a computer program, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute the railway capacity bottleneck identification method as described in the first aspect or any possible design of the first aspect.

[0015] In a fourth aspect, the present invention provides a computer-readable storage medium having instructions stored thereon. When the instructions are executed on a computer, the method for identifying railway capacity bottlenecks according to the first aspect or any possible design of the first aspect is executed.

[0016] In a fifth aspect, the present invention provides a computer program product comprising instructions, which, when executed on a computer, causes the computer to execute the railway capacity bottleneck identification method as described in the first aspect or any possible design of the first aspect.

[0017] Beneficial effects: The railway capacity bottleneck identification method, device, storage medium and product provided by the present invention construct a capacity bottleneck identification model with an encrypted operation diagram as the core based on a discrete space-time network, providing an accurate and reliable method for identifying capacity bottlenecks in various sections of high-speed railway lines, providing more theoretical possibilities for the identification of high-speed railway capacity bottlenecks, and at the same time being able to locate sections where capacity utilization of the road network is restricted, providing decision-making references for the updating of facilities and equipment, line reconstruction and the design of new lines, and providing references for the rational utilization and enhancement of line capacity. In addition, it is of great significance for giving full play to the network effect of the line, scientifically planning the high-speed railway network and the good development of high-speed railways. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A flowchart of a method for identifying a railway capacity bottleneck provided in an embodiment of the present application; Figure 2 A train operation diagram for multiple sections of a high-speed railway line provided in an embodiment of the present application; Figure 3 A schematic diagram of a discrete space-time network provided in an embodiment of the present application; Figure 4 Flowchart of the Lagrangian relaxation heuristic algorithm provided in the embodiment of the present application; Figure 5 A schematic diagram showing the distribution of important stations along the Beijing-Guangzhou High-Speed ​​Railway provided in an embodiment of the present application; Figure 6 The train operation diagram of the Beijing-Guangzhou High-Speed ​​Railway provided in the embodiment of this application; Figure 7 The train operation diagram of the Beijing-Guangzhou High-Speed ​​Railway provided in the embodiment of the present application is encrypted; Figure 8 A schematic block diagram of a railway capacity bottleneck identification device provided in an embodiment of the present application; Figure 9 A block diagram of another railway capacity bottleneck identification device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the present invention will be briefly introduced below in conjunction with the drawings and the description of the embodiments or the prior art. Obviously, the following description of the structure of the drawings is only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. It should be noted that the description of these embodiments is used to help understand the present invention, but does not constitute a limitation of the present invention.

[0020] It should be understood that although the terms first, second, etc. may be used herein to describe various objects, these objects should not be limited by these terms. These terms are merely used to distinguish one object from another. For example, a first object can be referred to as a second object, and similarly, a second object can be referred to as a first object without departing from the scope of the exemplary embodiments of the present invention.

[0021] It should be understood that the term "and / or" that may appear in this document is merely a description of the association relationship between associated objects, indicating that there may be three relationships. For example, A and / or B can indicate three situations: A exists alone, B exists alone, or A and B exist at the same time. For another example, A, B and / or C can indicate the existence of any one of A, B and C or any combination of them. The term " / and" that may appear in this document describes another type of association object relationship, indicating that there may be two relationships. For example, A / and B can indicate two situations: A exists alone or A and B exist at the same time. In addition, the character " / " that may appear in this document generally indicates that the previous and next associated objects are in an "or" relationship.

[0022] Example: like Figure 1 As shown, the first aspect of this embodiment provides a method for identifying bottlenecks in railway throughput capacity. The method can be, but is not limited to, executed by a computer device with certain computing resources, such as a cloud server, a personal computer (PC, a multi-purpose computer with a size, price, and performance suitable for personal use; desktops, laptops, small laptops, tablets, and ultrabooks are all personal computers), a smartphone, a personal digital assistant (PDA), or a wearable device. Figure 1 As shown, the railway capacity bottleneck identification method may include, but is not limited to, the following steps S101 to S105.

[0023] Step S101: Obtain the train operation diagram of each section of the high-speed railway line and construct a new train operation line candidate set for each section.

[0024] In the embodiment of the present application, the train operation diagram of each section of the high-speed railway line can be obtained from the high-speed railway background management system. The train operation diagram can intuitively display the time and space relationship of the train running in the railway section through a two-dimensional line diagram. The train operation diagram records the order of each train occupying the section, the station arrival / departure time, the section running time, the stop time and other data. Figure 2 The following is a train operation diagram for multiple sections of a high-speed railway line. Figure 2It can be seen from the train schedule that there are multiple train lines with a total of 7 stations S1-S7 between 19:00-22:00.

[0025] In an embodiment of the present application, the problem of identifying bottlenecks in capacity can be converted into a timeline encryption problem, namely, how to add lines that satisfy train operation constraints to the original timeline to construct a saturated timeline. When constructing a candidate set of newly added train lines for each section, the candidate set of newly added train lines can be added based on the existing train operation status in the train timeline of each section and the nature of the stations along the way of each section. That is, under the condition that the train operation constraints are satisfied, additional train lines are added to the original train timeline until the train timeline reaches saturation. At this time, the set of newly added train lines for each section is the candidate set of newly added train lines for each section.

[0026] Step S102: Using the discrete space-time network as a framework, encrypt the train operation diagram of each section based on the newly added train operation line candidate set of each section.

[0027] Planning new train lines within the existing train timetable is known as encrypting the train timetable. To encrypt the train timetable for each section, the diagram can be converted into an initial discrete space-time network diagram, using the time axis as the horizontal coordinate and the space axis as the vertical coordinate. Virtual departure and arrival stations are then added to the initial discrete space-time network diagram to create a discrete space-time network diagram. Based on the candidate set of newly added train lines for each section, new routes are added to the discrete space-time network diagram.

[0028] The discrete time-space network replicates the physical network nodes (station sites) on the discrete time axis to generate two-dimensional time-space nodes. The discrete time-space network consists of the time axis and the space axis. The time-space nodes are represented as , any spatiotemporal node contains spatial attributes and time attributes , two space-time nodes 、 Connected to form directed arcs The train trajectory describes the specific time and space location of the train when it is running, which can be calculated using the nodes in the space-time network. It represents the space-time path of the train, and connects the space-time nodes occupied by the train in the order of occupancy to form the train's running track.

[0029] like Figure 3As shown, it is a schematic diagram of a discrete space-time network provided by an embodiment of the present application, in which the horizontal axis represents a discrete time point, and the vertical axis represents the position of each station. In order to better distinguish the running status of the train at the station, the embodiment of the present application decomposes each physical station into a train entering the station and a train leaving the station, and the line between the two nodes represents that the train passes through or stops at the station. In addition, a virtual starting point and a virtual terminal point are added to the discrete space-time network, and it is stipulated that all trains must depart from the virtual starting point and arrive at the virtual terminal point, thereby converting the layout of the train running line into a shortest path problem with a single source and a single sink in the network flow. When a train departs from a node (station site), it is said that the train departs and occupies the node, and when a train arrives at a node, it is said that the train arrives and occupies the node.

[0030] Figure 3 There are three stations, A, B, and C, each broken down into A1, A2, B1, B2, C1, and C2. The discrete space-time network contains four types of nodes: virtual departure nodes, virtual arrival nodes, entry nodes A1, B1, and C1, and exit nodes A2, B2, and C2. The discrete space-time network also contains five types of arcs: virtual departure arcs, virtual arrival arcs, virtual operation arcs, station operation arcs, and interval operation arcs. Virtual operation arcs are directed arcs from a virtual departure point to a virtual destination point. When a train cannot find a feasible path in the space-time network, it can choose to travel from the virtual departure point to the virtual destination point using a virtual operation arc.

[0031] Four trains run from station A to station C. All trains depart from a virtual departure node and arrive at a virtual destination node. The station operation arc occupancy time of each train at its origin and destination stations is 0 minutes. Trains 2 and 3 stop at station B, while trains 1 and 4 pass through station B without stopping, and train 3 is overtaken by train 4 at station B. The station operation arc occupancy time of trains 1 and 4 at station B is 0 minutes, while the station operation arc occupancy times of trains 2 and 3 at station B are 2 minutes and 6 minutes, respectively. Therefore, the station operation arc occupancy time can be used to flexibly indicate whether a train stops at an intermediate station and the duration of the stop.

[0032] The train trajectory in the discrete space-time network is composed of the above nodes and arcs. The train timetable encryption problem can be regarded as the problem of selecting appropriate space-time nodes for the newly added running lines when some nodes in the space-time network are occupied by existing running lines, and then deriving the shortest path from the specified source to the specified sink in the space-time network.

[0033] Step S103: Based on the train operation constraints, a train operation diagram encryption model is established with the goal of minimizing the train operation cost.

[0034] In an embodiment of the present application, a train operation diagram encryption model can be established based on train origin and destination constraints, train operation diagram feasibility constraints and train operation conflict-free constraints with the goal of minimizing train operation costs.

[0035] Among them, the train origin and destination constraints include train origin station constraints, train arrival station constraints and train operation path constraints; the train operation diagram feasibility constraints include train occupation node uniqueness constraints in the operation path, vehicle flow balance constraints at each node, operation time constraints between nodes and node stop time constraints; the train operation conflict-free constraints include node train departure interval and arrival interval constraints and train no-crossing constraints between adjacent nodes.

[0036] The train operation cost includes the fixed cost of train operation, the variable cost of train operation and the virtual operation cost of train. Among them, the fixed cost of train operation refers to the cost that is not related to the traffic volume. When the train enters the space-time network and does not use the virtual operation arc, the fixed cost is generated. The variable cost of train operation refers to the cost related to the traffic volume. In the embodiment of the present application, the travel time of the train in the operation diagram is multiplied by the unit time cost to represent the variable cost of train operation. Each train has a feasible path that runs directly from the virtual starting point to the virtual terminal point. The train operation cost of this path is the virtual operation cost. In order to avoid the train choosing this path, the virtual operation cost can be set to a larger value. The specific setting can be based on actual conditions.

[0037] For ease of understanding, various symbols such as sets, indexes, parameters, and decision variables required for encrypting the target train operation diagram model are defined in the embodiments of the present application. The detailed definitions are shown in Tables 1 to 4.

[0038] Table 1 Collection definition

[0039] Table 2 Index definition

[0040] Table 3 Parameter definition

[0041] Table 4 Variable definitions

[0042] The encrypted model of the train diagram can be expressed as ,in Indicates train l travel time, represents the variable cost of train operation, Indicates the judgment train lWhether to run along the virtual path. When the value is 0, the train does not run along the virtual path. When the value is 1, the train runs along the virtual path. represents the virtual cost of train operation, where is the virtual cost coefficient of train operation.

[0043] Train operation constraints include train departure and arrival constraints, train operation diagram feasibility constraints, and train operation conflict-free constraints. Among them, the train departure and arrival constraints include train departure station constraints, train arrival station constraints, and train operation path constraints. The train departure constraint can be expressed as , which means that all trains must start from the virtual departure node Departure means that the train must occupy the departure node. The train arrival constraint can be expressed as , which means that all trains must arrive at the virtual node Arrival, that is, the train needs to occupy the arrival node.

[0044] The train operation path constraint can be expressed as and , where the previous constraint indicates that the train starts from the virtual departure node After departure, its first time-space node must be the time-space node of the train's starting station or virtual arrival node The latter constraint indicates that the train arrives at the virtual terminal node The forward space-time node is the space-time node corresponding to the train's final arrival station. or virtual departure node .

[0045] The feasibility constraints of the train operation diagram include the uniqueness constraint of the nodes occupied by the train in the operation path, the traffic flow balance constraint of each node, the running time constraint between nodes, and the node stop time constraint.

[0046] The node uniqueness constraint in the vehicle occupation operation path can be expressed as and , where the previous constraint means that when the train departs, it occupies the decomposition station The total number of time and space nodes does not exceed 1. The latter constraint means that when a train arrives, it occupies the decomposed station The total number of space-time nodes does not exceed 1.

[0047] The traffic flow balance constraint at each node can be expressed as , this set of constraints represents the flow balance of each node in the discrete space-time network, except for the virtual starting point and virtual arrival points In addition, trains in discrete space-time networks l Arrival at occupied node The number of times is the same as the number of times the node is occupied by leaving.

[0048] The runtime constraints between nodes can be expressed as , the node stop time constraint can be expressed as , these two constraints represent the train l Any two consecutive decomposition stations in the running route and , the train arrives Station times and train departures The time difference between station departures is within a certain range .

[0049] The conflict-free constraints for train operation include the train departure interval and arrival interval constraints of the nodes and the train no-overtaking constraint between adjacent nodes. Among them, the train departure interval constraint of the node can be expressed as , where Representation node The starting conflict node set, the conflict node set The interval between any two nodes cannot meet the train departure interval This constraint represents the set of conflicting nodes At most one node is occupied by all train departures.

[0050] The train arrival interval constraint can be expressed as , where Representation node The set of arrival conflicting spatiotemporal nodes and conflicting node sets The interval time between nodes cannot meet the train arrival interval time This constraint represents the set of conflicting spatiotemporal nodes At most one node in the conflicting node can be occupied and arrived by a train. If any node in the conflicting node is occupied and arrived by a train, the remaining nodes in the conflicting node will be prohibited from being occupied and arrived by other trains.

[0051] Step S104: A feasible solution of the train timetable encryption model is obtained based on the Lagrangian relaxation heuristic algorithm to obtain an encrypted saturated train timetable.

[0052] Specifically, when solving a feasible solution to the encrypted train timetable model based on the Lagrangian relaxation heuristic algorithm, the encrypted train timetable model can be Lagrangian-relaxed transformed first to obtain a Lagrangian relaxation model corresponding to the encrypted train timetable model, and then the Lagrangian multipliers of the Lagrangian relaxation model can be iteratively updated, and the iteratively updated relaxation solution of the Lagrangian relaxation model can be solved based on the train operation constraints to obtain the optimal relaxation solution of the Lagrangian relaxation model. Finally, the train timetable of each section can be updated based on the optimal relaxation solution to obtain the encrypted saturated train timetable.

[0053] like Figure 4 The figure shows the flow chart of the Lagrangian relaxation heuristic algorithm. First, the train arrival and departure interval constraints are relaxed and a Lagrangian relaxation model is constructed. Secondly, the Lagrangian relaxation model is solved using the labeling method, the occupancy times of each space-time node are calculated, the Lagrangian multiplier is updated, and the lower bound solution of the original problem is obtained. Then, the Lagrangian profit value of each train is calculated, and the trains are sorted in descending order of profit value. A Lagrangian heuristic algorithm is designed to find a feasible solution to the original problem, i.e., the upper bound value. The difference between the upper and lower bounds is calculated and it is determined whether the algorithm termination condition is met. If the termination condition is met, the algorithm ends. If not, the upper and lower bound values ​​of the original problem are updated according to the above method until the termination condition is met.

[0054] More specifically, the Lagrangian relaxation heuristic algorithm may include, but is not limited to, the following steps S401 - S403 .

[0055] S401. Relax and decompose the encrypted model of the operation graph to obtain a Lagrangian relaxation model.

[0056] The train departure and arrival interval constraints represent the train departure and arrival interval time constraints, which lead to large-scale train combinations and affect the efficiency of the model solution. The above constraints are relaxed and added as penalty terms to the objective function. Specifically, for each departure node and arrival nodes Introducing non-negative Lagrange multipliers and , construct the Lagrangian relaxation model. The objective function of the Lagrangian relaxation model can be expressed as:

[0057] The expression for updating the Lagrange multiplier is shown below:

[0058] In the above formulas, Indicates the current iteration number, For the Iteration step size, is the step size factor.

[0059] S402. Design an optimization algorithm for solving the Lagrangian relaxation model based on the labeling method.

[0060] In the Lagrangian relaxation problem, the interdependencies between train routes are relaxed, and the remaining constraints define the spatiotemporal logical relationships within a single train. This decomposes the original problem into the problem of finding routes for multiple trains in a spatiotemporal network. The objective function of the relaxation problem is the sum of the objective functions corresponding to each train's spatiotemporal path. The problem of finding the optimal train route in a spatiotemporal network is essentially a time-varying shortest path problem. A minimum-varying-cost path search algorithm based on the labeling method is designed to solve train routes.

[0061] In the labeling method, first for any node Add distance labels , Indicates that from the source node To Node The length of a directed path. If and only if the following shortest path optimality conditions are met, Source node To Node The core idea of ​​the labeling method is to evaluate whether the distance labels of all nodes meet the optimal conditions. For distance labels that do not meet the optimal distance conditions, , update it to , while updating Forward Node This cycle is repeated until all distance labels meet the optimal condition. When all distance labels meet the optimality condition, the distance label of the node is the shortest path length from the source node to the node. The optimality condition of the shortest path can be expressed as .

[0062] S403. Obtain a heuristic algorithm for a feasible solution.

[0063] The solution to the Lagrangian relaxation model is often an infeasible solution to the original problem, necessitating the design of an efficient Lagrangian heuristic method. This method extracts information from the relaxed solution to derive a feasible solution to the original problem. Specifically, the solution to each train path subproblem serves as heuristic information. Based on the dual information of the Lagrangian multiplier values ​​at each node in the relaxed solution, the train paths are replanned and solved in a specific order, ultimately yielding a feasible solution to the original problem. Steps 1-3 below are the steps of the heuristic algorithm.

[0064] Step 1: Obtain the Lagrangian profit of each train in the relaxed solution of the Lagrangian problem and sort the trains according to the Lagrangian profit.

[0065] The labeling method is used to obtain the relaxed solution of the Lagrangian problem, and the running paths of each train and the Lagrangian profit are obtained. . Introducing symbols and The number of times a node in the arrival and departure conflict node set is occupied by a train is introduced. Indicates the station Stock market at all times The number of times a bus is occupied by a train.

[0066] Step 2: Use the labeling method to solve the train operation path in sequence according to the train sequence.

[0067] Step 2.1 When solving the train operation path, the objective function of the Lagrangian relaxation problem is used as the sub-problem objective function. Unlike solving the lower bound solution, when solving the feasible train operation path, the train arrival and departure interval constraints and station capacity restrictions must be considered. This process solves each train one by one, and after solving each train, 、 and The value is updated to determine whether the resources of each spatiotemporal node are idle.

[0068] Step 2.2 After the train is solved, update each 、 and Get the value.

[0069] Step 2.3 Repeat Step 2.1 and Step 2.2 until all train lines in the set are drawn.

[0070] Step 3: Determine whether all trains have found feasible paths, use the backtracking method to obtain the feasible paths for the trains and output them.

[0071] Step S105: Based on the number of corresponding train routes of each section in the saturated train operation diagram and the number of train routes in the train operation diagram of each section, determine the capacity bottleneck identification result of each section.

[0072] In the embodiment of the present application, determining the capacity bottleneck identification result of each segment may include, but is not limited to, the following steps S1051-S1054.

[0073] S1051. Based on the number of corresponding train routes in each section in the saturated train operation diagram and the number of train routes in the train operation diagram of each section, determine the number of newly added train operation routes in each section.

[0074] The number of new train routes in any section can be expressed as ,in Add the number of encrypted running lines to this section. The total number of train lines in the saturated operation diagram after encryption in this section. It is the total number of train lines in the original timetable of this section.

[0075] S1052. Determine the throughput capacity utilization rate of each section based on the number of corresponding train routes of each section in the saturated train operation diagram and the number of train routes in the train operation diagram of each section.

[0076] The throughput capacity utilization rate of a section can be expressed as .

[0077] S1053. Based on the number of newly added train routes in each section and the throughput capacity utilization rate of each section, determine the throughput capacity bottleneck evaluation threshold of each section.

[0078] The bottleneck evaluation threshold of the throughput capacity of a section can be determined, but is not limited to, based on the average value, median value, etc. of the throughput capacity utilization rate of each section, and is not specifically limited in the embodiments of the present application.

[0079] S1054. Determine whether each section is a capacity bottleneck based on the number of train routes in the train operation diagram of each section and the capacity bottleneck evaluation threshold of each section.

[0080] For any section, if the train running route of the section is less than the corresponding capacity bottleneck evaluation threshold, the section is determined to be a capacity bottleneck.

[0081] In the embodiment of this application, the Beijing-Guangzhou High-Speed ​​Railway is taken as an example for analysis. The important stations along the Beijing-Guangzhou High-Speed ​​Railway are distributed as follows: Figure 5 As shown, the operation diagram within a certain day is as follows Figure 6 As shown in Figure 2, this section identifies the capacity bottlenecks of the line by encrypting the operation diagram. Only the upward trains from Guangzhou South to Beijing West are considered when identifying the capacity bottlenecks.

[0082] The Beijing-Guangzhou High-Speed ​​Railway's section division nodes are Guangzhou South Station, Hengyang East Station, Changsha South Station, Wuhan Station, Zhengzhou East Station, Handan East Station, Shijiazhuang Station, and Xushui East Station. Table 5 shows the section divisions for each line and the number of train lines within each section.

[0083] Table 5 Section division of Beijing-Guangzhou High-Speed ​​Railway and number of operating lines within the section

[0084] When the Beijing-Guangzhou High-Speed ​​Railway timetable is refined, the operating sections, number, departure time domain, operating time range, and station stop time range of the newly added lines are shown in Table 6. When the line timetable is refined, the train arrival and departure interval is 4 minutes.

[0085] Table 6 Information on the new alternative lines for the Beijing-Guangzhou High-Speed ​​Railway

[0086] Table 7 lists the upper and lower bounds, optimal gap, and single-iteration computation time for the LR algorithm. The LR algorithm achieves high-quality upper and lower bounds in all cases, with the optimal gap being 9.6%. This demonstrates the LR algorithm's adaptability to cases of varying scales.

[0087] Table 7 Number of encrypted trains, lower bound value, upper bound value, optimal gap and calculation time for each example

[0088] Table 8 Number of intensified trains and capacity utilization rate in each line section (train arrival and departure interval: 4 minutes)

[0089] Note: Refers to the original number of trains in the section, The total number of encrypted trains, The number of newly added train lines is Add the median number of train running lines for each section of the line, To encrypt the operation diagram through capacity utilization, It is the median of the capacity utilization rate of each section of the line in the encrypted operation diagram. The encrypted Beijing-Guangzhou High-Speed ​​Railway operation diagram is as follows Figure 7 The saturated operation diagram is shown in the figure. The number of encrypted trains in each section and each line section in the saturated operation diagram and the capacity utilization rate are shown in Table 8.

[0090] According to the classification and identification criteria of capacity bottlenecks, a reasonable critical value can be established based on the distribution of the number of new train lines in each section of the line. , as the criterion for determining capacity bottlenecks. In this example, the capacity bottleneck determination rules are as follows. The capacity bottleneck determination rules are set as follows.

[0091] (1) The number of newly added train running lines in a certain section of the line is less than the median number of newly added train running lines in all sections of the line.

[0092] (2) The capacity utilization rate of a certain section of the line is greater than the median capacity utilization rate of the line. When a section meets the above two conditions, it may become the capacity bottleneck section of the line. However, whether it is a capacity bottleneck section needs to be comprehensively determined based on the number of newly added train operation lines on the entire line and the line capacity utilization rate.

[0093] Table 9 Bottleneck sections of road network capacity and their causes

[0094] Note: is the original number of trains in the section, The total number of trains after encryption, The number of newly added train lines is The median of the new train running lines in each section of the line where the section is located is added. Capacity utilization is passed for encrypted operation diagram.

[0095] Based on the above criteria and the number of encrypted trains in each line section in Table 8, the capacity bottlenecks in the road network are identified. The distribution of line capacity bottlenecks is shown in Table 9.

[0096] The median number of newly added lines in each section of the Guangzhou South-Beijing West line is 25.5, through capacity utilization The median is 78.19%. Among the sections of the line, the number of trains that can be added in the Guangzhou South-Hengyang East section and the Hengyang East-Changsha South section is 11, and the number of trains that can be added in the Xushui East-Beijing West and Shijiazhuang-Xushui East sections is 21. The above four sections have fewer added trains than the rest of the line, far below the median of 25.5 for the line. The number of trains that can be added in the rest of the line is greater than the median of 25.5, and the remaining capacity is relatively surplus. In addition, the capacity utilization rates of the Guangzhou South-Hengyang East, Hengyang East-Changsha South, Shijiazhuang-Xushui East, and Xushui East-Beijing West sections are 90.76%, 91.67%, 83.46%, and 80.56%, respectively. The capacity utilization rates of the above sections are relatively high, far higher than the median capacity utilization rate of 78.19%.

[0097] Based on the number of trains that can be increased and the level of capacity utilization, it can be determined that Guangzhou South-Hengyang East, Hengyang East-Changsha South, Shijiazhuang-Xushui East, and Xushui East-Beijing West are capacity bottlenecks for the Beijing-Guangzhou High-Speed ​​Railway. Guangzhou South and Shenzhen North are hub stations, and a large number of trains depart from these stations, resulting in a relatively dense train flow in the Guangzhou South-Hengyang East section. Hengyang East Station is on the Hengliu Line, and the Hengyang East-Changsha South section gathers trains from the Hengliu Line and the Beijing-Guangzhou Main Line running to Changsha South and beyond. This convergence of trains has made this section a capacity bottleneck. Shijiazhuang Station connects to the Shijiazhuang-Taiyuan Line and can originate trains. Trains originating from Shijiazhuang, other trains on the main line, and cross-line trains converge in the Shijiazhuang-Beijing West section, creating a capacity bottleneck.

[0098] In summary, the railway capacity bottleneck identification method provided by the present invention obtains the train operation diagram of each section of the high-speed railway line, constructs a new train line alternative set for each section; uses a discrete space-time network as a framework, encrypts the train operation diagram of each section based on the new train line alternative set of each section; based on the train operation constraints, establishes a train operation diagram encryption model with the goal of minimizing the train operation cost; solves the feasible solution of the train operation diagram encryption model based on the Lagrangian relaxation heuristic algorithm, and obtains the encrypted saturated train operation diagram; determines the capacity bottleneck identification result of each section based on the number of corresponding train operation routes of each section in the saturated train operation diagram and the number of train operation routes in the train operation diagram of each section. In this way, by constructing a capacity bottleneck identification model with an encrypted operation diagram as the core based on a discrete space-time network, a precise and reliable method is provided for identifying capacity bottlenecks in various sections of high-speed railway lines, which provides more theoretical possibilities for the identification of capacity bottlenecks of high-speed railways. At the same time, it can locate sections with restricted capacity utilization and improve the network, provide decision-making references for the renewal of facilities and equipment, line reconstruction and the design of new lines, and provide references for the rational utilization and enhancement of line capacity. In addition, it is of great significance for giving full play to the network effect of the line, scientifically planning the high-speed railway network and the good development of high-speed railways.

[0099] See also Figure 8 A second aspect of an embodiment of the present application provides a railway capacity bottleneck identification device, the railway capacity bottleneck identification device comprising: An acquisition unit, used to obtain a train operation diagram for each section of the high-speed railway line; A construction unit, used to construct a new train line candidate set for each section; An encryption unit is used to encrypt the train operation diagram of each section based on the newly added train operation line candidate set of each section in a discrete space-time network framework; A modeling unit, configured to establish a train operation diagram encryption model based on train operation constraints with the goal of minimizing train operation costs; A solving unit, used for solving a feasible solution of the train timetable encryption model based on a Lagrangian relaxation heuristic algorithm to obtain an encrypted saturated train timetable; The determination unit is used to determine the capacity bottleneck identification result of each section based on the number of corresponding train running routes of each section in the saturated train operation diagram and the number of train running routes in the train operation diagram of each section.

[0100] The working process, working details and technical effects of the railway capacity bottleneck identification device provided in the second aspect of this embodiment can be found in the first aspect of the embodiment and will not be repeated here.

[0101] like Figure 9As shown, the third aspect of an embodiment of the present application provides another railway capacity bottleneck identification device, including a memory, a processor and a transceiver that are communicatively connected in sequence, wherein the memory is used to store computer programs, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute the railway capacity bottleneck identification method as described in the first aspect of the embodiment.

[0102] For example, the memory may include, but is not limited to, random access memory (RAM), read-only memory (ROM), flash memory, first-in-first-out memory (FIFO) and / or first-in-last-out memory (FILO), etc.; the processor may include, but is not limited to, a microprocessor of the STM32F105 series, an ARM (Advanced RISC Machines), an X86 or other architecture processor, or a processor with an integrated NPU (neural-network processing units); the transceiver may include, but is not limited to, a WiFi (Wireless Fidelity) wireless transceiver, a Bluetooth wireless transceiver, a General Packet Radio Service (GPRS) wireless transceiver, a ZigBee protocol (a low-power local area network protocol based on the IEEE802.15.4 standard, ZigBee) wireless transceiver, a 3G transceiver, a 4G transceiver and / or a 5G transceiver, etc.

[0103] A fourth aspect of this embodiment provides a computer-readable storage medium storing instructions containing the method for identifying railway capacity bottlenecks described in the first aspect of the embodiment. Specifically, the computer-readable storage medium stores instructions that, when executed on a computer, execute the method for identifying railway capacity bottlenecks described in the first aspect. The computer-readable storage medium refers to a data storage medium and may include, but is not limited to, a floppy disk, a CD, a hard disk, a flash memory, a USB flash drive, and / or a memory stick. The computer may be a general-purpose computer, a dedicated computer, a computer network, or other programmable device.

[0104] A fifth aspect of this embodiment provides a computer program product comprising instructions, which, when executed on a computer, causes the computer to execute the railway capacity bottleneck identification method as described in the first aspect of the embodiment, wherein the computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device.

[0105] It should be understood that certain details are provided in the following description to facilitate a thorough understanding of the example embodiments. However, one of ordinary skill in the art will appreciate that the example embodiments can be practiced without these specific details. For example, a system may be shown in block diagrams to avoid obscuring the example with unnecessary detail. In other instances, well-known processes, structures, and techniques may be shown without unnecessary detail to avoid obscuring the example embodiments.

[0106] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A method for identifying railway capacity bottlenecks, characterized in that: include: Obtain the train operation diagram of each section of the high-speed railway line and construct a new train operation line candidate set for each section; Using discrete space-time network as the framework, the train operation diagram of each section is encrypted based on the newly added train line candidate set of each section; Based on train operation constraints, a train operation diagram encryption model is established with the goal of minimizing train operation costs; The feasible solution of the train timetable encryption model is solved based on the Lagrangian relaxation heuristic algorithm, and the encrypted saturated train timetable is obtained. Based on the number of corresponding train routes of each section in the saturated train operation diagram and the number of train routes in the train operation diagram of each section, the capacity bottleneck identification result of each section is determined.

2. The railway capacity bottleneck identification method according to claim 1, characterized in that: The constructing of the new train line candidate set for each section includes: A new set of train route alternatives is added based on the existing train operation status in the train operation diagram of each section and the nature of the stations along the section.

3. The railway capacity bottleneck identification method according to claim 1, characterized in that: The method of encrypting the train operation diagram of each section based on the newly added train operation line candidate set of each section using the discrete time-space network as the framework includes: With the time axis as the horizontal coordinate and the space axis as the vertical coordinate, the train operation diagram of each section is converted into the initial discrete time-space network diagram; Adding a virtual departure site and a virtual arrival site to the initial discrete time-space network graph to obtain the discrete time-space network graph; Based on the newly added train running line candidate set of each section, a new running line is added to the discrete time-space network diagram.

4. The railway capacity bottleneck identification method according to claim 3, characterized in that: The train operation diagram encryption model is established based on train operation constraints with the goal of minimizing train operation costs, including: Based on the train departure and arrival constraints, train timetable feasibility constraints, and train operation conflict-free constraints, a train timetable encryption model is established with the goal of minimizing train operation costs. The train departure and arrival constraints include train departure station constraints, train arrival station constraints, and train operation path constraints; The feasibility constraints of the train operation diagram include the uniqueness constraint of the nodes occupied by the train in the operation path, the vehicle flow balance constraint of each node, the operation time constraint between nodes, and the node stop time constraint; The train operation non-conflict constraints include the train departure interval and arrival interval constraints of the nodes and the train non-overtaking constraints between adjacent nodes.

5. The railway capacity bottleneck identification method according to claim 4, characterized in that: The Lagrangian relaxation heuristic algorithm is used to solve the feasible solution of the train timetable encryption model to obtain the encrypted saturated train timetable, including: Performing Lagrangian relaxation transformation on the encrypted model of the train timetable to obtain a Lagrangian relaxation model corresponding to the encrypted model of the train timetable; Iteratively update the Lagrangian multiplier of the Lagrangian relaxation model, and solve the iteratively updated relaxation solution of the Lagrangian relaxation model based on the train operation constraints to obtain the optimal relaxation solution of the Lagrangian relaxation model; The train operation diagram of each section is updated based on the optimal relaxation solution to obtain the encrypted saturated train operation diagram.

6. The railway capacity bottleneck identification method according to claim 1, characterized in that: The determining of the capacity bottleneck identification result of each section based on the number of corresponding train routes of each section in the saturated train operation diagram and the number of train routes in the train operation diagram of each section includes: Determine the number of newly added train routes for each section based on the number of corresponding train routes for each section in the saturated train operation diagram and the number of train routes in the train operation diagram for each section; Determine the throughput capacity utilization of each section based on the number of corresponding train routes in each section in the saturated train operation diagram and the number of train routes in the train operation diagram of each section; Based on the number of newly added train routes in each section and the throughput capacity utilization rate of each section, the throughput capacity bottleneck evaluation threshold of each section is determined; Based on the number of train routes in the train operation diagram of each section and the capacity bottleneck evaluation threshold of each section, it is determined whether each section is a capacity bottleneck.

7. A railway capacity bottleneck identification device, characterized in that: include: An acquisition unit, used to obtain a train operation diagram for each section of the high-speed railway line; A construction unit, used to construct a new train line candidate set for each section; An encryption unit is used to encrypt the train operation diagram of each section based on the newly added train operation line candidate set of each section in a discrete space-time network framework; A modeling unit, configured to establish a train operation diagram encryption model based on train operation constraints with the goal of minimizing train operation costs; A solving unit, used for solving a feasible solution of the train timetable encryption model based on a Lagrangian relaxation heuristic algorithm to obtain an encrypted saturated train timetable; The determination unit is used to determine the capacity bottleneck identification result of each section based on the number of corresponding train running routes of each section in the saturated train operation diagram and the number of train running routes in the train operation diagram of each section.

8. A railway capacity bottleneck identification device, characterized in that: The method comprises a memory, a processor and a transceiver which are communicatively connected in sequence, wherein the memory is used to store a computer program, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute the railway capacity bottleneck identification method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores instructions, and when the instructions are executed on a computer, the railway capacity bottleneck identification method according to any one of claims 1 to 6 is executed.

10. A computer program product comprising a computer program or instructions, characterized in that When the computer program or the instruction is executed by a computer, the method for identifying a railway capacity bottleneck according to any one of claims 1 to 6 is implemented.

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