Railway train working diagram compiling method, computer system and computer storage medium

Abstract

The invention discloses a railway train working diagram compilation method based on a differentiated arc weight system. The method comprises the following steps: S1, constructing a time-space network of train operation; s2, generating a runtime space sub-network; s3, constructing a train working diagram optimization model; s4, establishing an arc weight system based on train difference; s5, initializing penalty weights of all arcs to be 0, and searching paths column by column based on the current penalty weight; s6, updating the penalty right; s7, a conflict train path is adjusted; and S8, determining arrival and departure moments of the trains passing through the stations according to the current paths of the trains, and outputting a train working diagram. According to the method, the train sub-network is designed, and the differentiated arc weight system is constructed according to different urgencies of different trains on the same arc, so that the train working diagram compiling efficiency is improved, the transportation resource waste can be reduced, and technical guidance is provided for a railway department to compile the train working diagram.

Description

Technical Field

[0001] The present invention belongs to the field of prediction or optimization methods, and in particular relates to a method for optimizing railway train operation, a computer system, and a computer storage medium. Background Art

[0002] High-speed railways provide safe, fast, convenient and high-quality travel services for the vast number of passengers in my country, and have become the first choice for passengers. With the improvement of the service quality of my country's high-speed railways and the effective implementation of flexible fare strategies, the number of passengers choosing to travel by rail continues to increase, which requires the railway department to compile train operation diagrams with increasing density to organize more trains to meet the travel needs of passengers. At the same time, due to the influence of social and economic activities, the distribution of high-speed railway passenger travel demand in each quarter and month of the year is significantly different. The railway department needs to frequently adjust the running trains to adapt to the changes in passenger travel demand. In order to cope with the problem of high-speed railway operation diagram compilation with increasing frequency and increasing density of trains, designing a more efficient train operation diagram compilation method is of great practical significance to the railway department.

[0003] The train operation diagram is the basis of railway transportation organization. Through the compilation of the train operation diagram, the arrival and departure times of trains running on the railway line can be obtained, and the number of trains running to meet the driving requirements can be determined. Mathematical programming method is a common method for the compilation of train operation diagrams. This method mainly describes the timetable optimization problem as a linear programming problem, and then uses methods such as branch and bound, or directly uses commercial solvers such as Cplex to solve it. However, for large-scale diagram compilation problems, its solution efficiency is low and the solution time is too long. In particular, when the number of trains to be mapped exceeds the line capacity, it will directly lead to an unsolvable problem, and it will not be possible to generate a feasible operation diagram by canceling some train operations.

[0004] In addition to mathematical programming methods, modern heuristic algorithms that have developed rapidly in recent years, such as genetic algorithms and Lagrangian relaxation algorithms, are also widely used to solve train operation diagram problems. The basic idea of ​​this method is to generate new solutions through continuous iterations on the basis of generating the initial solution, and to update and optimize the current solution until the final solution is obtained. For large-scale problems, modern heuristic methods can obtain a solution in a relatively short time compared to mathematical programming methods. However, as the number of trains increases, the constraints between trains increase, which makes it easy to generate infeasible solutions during iterations, making it very limited to search for feasible solutions, and the algorithm is prone to fall into local optimality. In particular, when the train lines are very dense, the correlation between trains will become stronger. When resolving conflicts, a conflict resolution is likely to cause the generation of new conflicts. The nested constraints between conflicts will result in the final conflict being unable to be resolved and some trains being unable to be laid out.

[0005] Therefore, in order to address the large-scale diagram compilation problem, a new train operation diagram compilation method is urgently needed. Summary of the invention

[0006] The technical problem to be solved by the present invention is to overcome the deficiencies and defects mentioned in the above background technology and provide a railway train operation diagram compilation method based on a differentiated arc right system with high compilation efficiency and quality, as well as a computer system and a computer storage medium.

[0007] In order to solve the above technical problems, the technical solution proposed by the present invention is:

[0008] A method for compiling a railway train operation diagram based on a differentiated arc right system comprises the following steps:

[0009] S1: Construct a spatiotemporal network of train operation based on a given railway line and operating time range;

[0010] S2: Generate the running time-space sub-network for each specific train;

[0011] S3: Based on the constructed space-time network, a train operation diagram optimization model is constructed with the goal of minimizing the total train travel time. The model considers the constraints related to a single train path and the constraints related to multiple train paths.

[0012] S4: According to the constructed space-time network and the train operation diagram optimization model, an arc weight system based on train differences is established. For each directed arc in any train space-time subnetwork, two types of weights, time weight and penalty weight, are set;

[0013] S5: Initialize the penalty weights of all arcs to 0, and search for paths column by column based on the current penalty weights;

[0014] S6: Update the penalty weight. Based on the current path of any train, take the train as the main train and other trains as the dominant trains, and update the penalty weight of each arc in the space-time subnetwork of each main train.

[0015] S7: Adjust the conflicting train paths. For any two trains, determine whether there is a conflict based on the established train operation diagram optimization model. If there is a conflict, select the train with a larger penalty weight, and re-search the path for it based on the sum of the updated penalty weight and time weight. For any train whose path is adjusted, update the penalty weight for other trains, and repeat the above process until there is no conflicting train.

[0016] S8: Determine the arrival and departure times of the trains passing through each station according to the current routes of the trains, and output the train operation diagram.

[0017] In the above-mentioned railway train operation diagram compilation method, preferably, the step S1 comprises the following steps:

[0018] S101: Discretize the railway operation time range for the whole day into multiple discrete moments t in units of minutes, half minutes or seconds, denoted as t=T start ,T start +1,…,T end , where T start ,T end are the start and end times of line operation respectively;

[0019] S102: for each discrete time t, a passing point and two arrival and departure points are generated for each railway station, and the two arrival and departure points correspond to the throats at both ends of the station respectively;

[0020] S103: For any railway section direction, four types of operation arcs that meet the section operation time requirements are generated between the corresponding arrival and departure points or passing points of the preceding and following stations, namely, stop-stop, stop-go, go-stop, and go-go;

[0021] S104: construct slow-moving arcs between adjacent discrete-time passing points at the same station and between two adjacent discrete-time arrival and departure points at the same throat to describe the slow movement of trains in the section; the slow-moving arcs between adjacent passing points are used by both up and down direction trains, and the slow-moving arcs between adjacent arrival and departure points at both ends of the throat are used by both up and down direction trains;

[0022] S105: First, an entry arc is constructed between different entry choke points and departure points at the same time to describe the train stopping and entering the station; at the same time, a stay arc is constructed between each choke point at adjacent discrete times to the departure point to describe the train stopping at the station after entering the station.

[0023] In the above-mentioned method for compiling a railway train operation diagram, preferably, the step S2 comprises the following steps:

[0024] S201: The earliest departure time of the train Departure: Determine the earliest arrival, departure or passing time of the train at each station according to the fastest running mode, which is called the left boundary of the sub-network;

[0025] S202: For train i, the fastest running mode is the mode that runs through all sections with the minimum running time, stops at required stations with the minimum stopping time, and passes through non-required stations. The corresponding required travel time is recorded as Γ i fastest , based on the latest departure time of the train The train starts and runs in the slowest mode to get a running line, considering the maximum travel time Γ actually allowed by the train i allowed , further with time Start the train and run it in the fastest running mode to get another running line. The running lines will inevitably intersect, and the first running line segment before the intersection and the second running line segment after the intersection will form the right boundary of the sub-network;

[0026] S203: Based on the left and right boundaries of the train operation, determine the earliest and latest arrival and departure or passing time of each station, and use the arrival and departure points and passing points distributed between the two at discrete times as the train operation sub-network node set; if the station is a must-stop station for the train, only add the departure point; if it is a must-pass station for the train, only add the passing point; otherwise, both types of nodes are added;

[0027] S204: Correspondingly, the running arc, the station entry arc, the station stop arc, and the slow-moving arc between any two nodes in the sub-network node set corresponding to the speed level of the train are added to the sub-network directed arc set to form a sub-network for the operation of train i.

[0028] In the above-mentioned railway train operation diagram compilation method, preferably, the step S3 comprises the following steps:

[0029] S301: Define a railway line consisting of K stations and K-1 double-track one-way sections. The line runs V types of speed grade trains. Trains of different speed grades have different start-stop additional time minutes and pure running time minutes when running in the same section direction. For the σ-th, 2-th, …, V-th speed grade trains, their pure running time minutes and start-stop additional time minutes in the section direction [k, k′] (k′ is another station different from k, and the subsequent similar cases where the same character is added with ' are all such cases) are recorded as For stations k = 1, 2, …, K, any two trains entering the station from the interval direction [k′, k] must meet the minimum entry safety interval. According to whether the two trains stop at the station, the entry safety interval can be divided into four types: through-to, through-through, to-to, and to-through. These four intervals have different minimum safety values, which are respectively denoted as Similarly, the exit safety intervals from station k to the interval direction [k, k′] are divided into four types: pass-to-post, pass-to-pass, post-post, and post-to-pass, which are denoted as

[0030] S302: It is known that a total of N trains need to be deployed on the above railway line, where the speed level of the i-th = 1, 2, ..., N trains is denoted by σ i , the starting station and the terminal station are denoted as r i ,s i , the starting time range is recorded as The maximum allowed travel time is denoted as Γ i allowed , whether it is necessary to stop at station k for boarding or disembarking is recorded as when If it is on, it means stop; otherwise, Indicates no parking;

[0031] S303: Define u, v, u′, v′ as nodes of any type at any station, (u, v) as a directed arc between nodes of any type u to v in the network (the combination of any two nodes has the same meaning, indicating a directed arc between the two nodes), and define a decision variable p i represents the running path of train i in its running subnetwork, which can uniquely determine its arrival and departure time, stop time, and interval running time at each station. Define the decision variable x i (u,v) represents the path p i The inclusion relationship between the arc (u,v) is that if the path p i Contains the arc (u,v), then x i (u,v)=1, otherwise, x i (u,v)=0, minimizing the total train travel time minz is selected as the model optimization objective, that is:

[0032]

[0033] Among them, T(p i ) is the path p taken by train i i The total travel time of , t(u,v) represents the time consumed by any directed arc (u,v);

[0034] S304: Determine the single path constraints of the train, including path flow balance constraints, departure time range constraints, interval minimum running time and maximum slow-moving time constraints, station minimum and maximum stop time constraints, and full-trip maximum travel time constraints;

[0035] The path flow balance constraints are as follows:

[0036]

[0037] Among them, V i origin is the set of originating nodes in the train i running sub-network, are the incoming arc set and outgoing arc set of node v in the running subnetwork of train i, respectively. are the running arc set and the station entry arc set of the running subnetwork of train i, respectively. i terminal is the set of terminal nodes in the running sub-network of train i;

[0038] The departure time range constraints are as follows:

[0039] The departure time corresponding to the starting point of each train i falls within the starting time range. Inside;

[0040] The maximum slow-moving time and the minimum running time of the interval are constrained as follows:

[0041]

[0042] in, is the interval direction [k,k′]∈E in the train i subnetwork i Added slow arc set, is the maximum slow-moving time allowed for train i in the section direction [k, k′], E i is a set of intervals;

[0043] The minimum running time required for trains of different speed levels to run in different entry and exit modes in the interval is different. Considering that when constructing the interval running arc in the network, four types of interval running arcs are designed for the interval running of trains of the same speed level with different entry and exit modes: pass-pass, stop-pass, pass-stop, and stop-stop. The duration of each interval running arc is the minimum running time of the corresponding entry and exit mode. Therefore, no matter which interval running arc is selected, the corresponding interval minimum running time requirement is met.

[0044] The minimum and maximum stop time constraints at the station are as follows:

[0045] The number of stopover arcs of train i in its subnetwork path including station k satisfies:

[0046]

[0047]

[0048] in, is the set of stay arcs about station k in the train i subnetwork, are the minimum and maximum stopping times allowed for train i to stop at station k without being overtaken, is the maximum allowed stop time when a train is overtaken. Indicates whether train i is passed at station k, Indicates whether train i is overtaken by train j at station k. If so, the arrival time and departure time of train j must be between the arrival time and departure time of train i, that is, it satisfies:

[0049]

[0050] Among them, S i and S j is the set of stations for trains i and j, t u is the time of node u, M is an integer constant, For trains i and j, they run arcs between the interval [k, k′], are the entry arcs of trains i and j at station k, respectively. The former makes it so that when train j passes train i at station k, that is, The arrival time of train i at station k is It is required to be less than the arrival or passing time of train j at the station Otherwise, there is no limit between the arrival times of the two buses, which further makes the When , train i will leave the station later than train j, that is, Otherwise, there is no constraint between the two departure times;

[0051] The maximum travel time constraints for the entire journey are as follows:

[0052]

[0053] Among them, Γ i max is the maximum travel time that can be achieved by train i by increasing the interval slow travel time, the number of station stops, and the station stop time;

[0054] S305: determining related constraints between multiple train paths, expressed in the form of incompatible arc sets, including a safety interval occupancy arc set related to departure operations, a safety interval occupancy arc set related to arrival operations, and a safety interval occupancy arc set related to passing operations;

[0055] The set of safety interval occupancy arcs associated with the departure operation is as follows:

[0056] Define u k For any node of station k, define is the arrival and departure point of the throat connecting station k to station k′ at discrete time t, u k,t is the passing point of station k at discrete time t (other changes in node u (such as node v), station k, and discrete time t, etc., all represent the same meaning). The safety intervals related to the departure operation of train stations include the safety interval between passing and dispatching, the safety interval between dispatching and passing, and the safety interval between dispatching and dispatching. When train i is in its subnetwork on path p i Via stop-go arcs on the interval [k, k′] or stop-stop operation arc When, it means that the train stops at station k and departs from the station to station k' at discrete time t. At this time, in order to meet the safety interval requirements of passing-departing and departing-passing, the starting time belongs to the time range The stop-stop and go-go arcs in the interval [k, k′] cannot be used by other trains; at the same time, in order to meet the departure-departure safety interval requirements, the starting time belongs to the time range The stop-stop and stop-go arcs in the interval [k, k′] cannot be used by other trains.

[0057] remember is the set of arcs that can no longer be used by other trains when train i leaves station k at discrete time t and enters interval [k, k′] in order to meet the relevant safety interval requirements, which can be expressed as:

[0058]

[0059] in, is the running arc between the interval [k, k′], t′ is the time when the train departure safety interval is not met, (u k,t′ ,v) is the point u connected to station k at time t′ k,t′ Any arc of To connect the station to the departure point Any arc of (other changes in nodes, stations, discrete moments, etc. represent the same meaning);

[0060] The set of safe interval occupancy arcs associated with the arrival operation is as follows:

[0061] The safety intervals related to the train station arrival operation include the through-to safety interval, the to-through safety interval, and the to-to safety interval. i Via the pit stop arc , which means that the train stops at station k from station k′ at time t. At this time, in order to meet the arrival-to-arrival safety interval requirement, the node time belongs to the time range All the entry arcs about station k can no longer be used by other trains; in order to pass-to safety interval and to-to safety interval, the starting time belongs to the time range All stop-go and go-go arcs in the interval [k′, k] will no longer be used by other trains;

[0062] remember is the set of arcs that train i needs to occupy when it stops at station k from station k′ to station k at time t to meet the requirements of through-to, to-through, and to-to safety intervals. It can be expressed as:

[0063]

[0064] in, is the arc running between the interval [k′,k], is the train’s entry arc at station k;

[0065] The set of safe interval occupancy arcs associated with through operations is as follows:

[0066] The safety intervals related to the train station passing operation include five types of safety intervals: through-through, departure-through, through-departure, through-arrival, and arrival-through. When train i is in its sub-network path p i Via the on-off arc , which means that the train passes through station k at time t. At this time, in order to meet the pass-to-pass safety interval requirements, the starting time belongs to the time range The start-stop and start-stop arcs within the time range cannot be used anymore; in order to meet the start-stop and start-start safety interval requirements, the start time belongs to the time range The stop-go and stop-stop arcs within the time range cannot be used; in order to meet the requirements of the safety interval between go-go and go-go, the starting time belongs to the time range The pit stop arc inside can no longer be used;

[0067] remember is the set of arcs that need to be occupied due to the train passing operation, which can be expressed as:

[0068]

[0069] Train i uses path p i By summarizing the occupied arc sets of the corresponding operations passing through the stations, the train path p can be obtained. i The occupied arc set for:

[0070]

[0071] in, It is represented as the entry arc of station k at time t;

[0072] In order to meet various safety interval requirements related to train station arrival, passing, and departure operations, when train i uses path p i After that, any other train j can no longer use path p i Occupancy Arc Set Any arc in satisfies:

[0073]

[0074] In the above-mentioned railway train operation diagram compilation method, preferably, the step S4 comprises the following steps:

[0075] For each directed arc in any train space-time subnetwork, two types of rights are set: time right and penalty right. The time right reflects the travel time that the train needs to bear when passing through the arc, and the penalty right reflects the urgency of the train's use of the arc, and also reflects the severity of the operational conflict between the train's use of the arc and other train paths. Specifically:

[0076] (1) Directed arc time weight: For any directed arc in the train space-time subnetwork, its time weight is the difference between the corresponding time of the arc end point and the corresponding time of the arc start point. The time weight of the stop arc and the slow arc is 1, and the time weight of the entry arc is 0. The time weight of the running arc is the travel time of the train of the corresponding speed level in the section. The time weight of the same directed arc in all train space-time subnetworks is the same and will remain unchanged during the mapping process.

[0077] (2) Directed arc penalty weight: If a directed arc is not used by any train, the penalty weight of the arc in the train subnetwork is 0. The train that uses the arc penalty weight to search for paths is the main train, and the train that determines the size of the arc penalty weight is the dominant train. Each directed arc in the main train subnetwork has multiple different penalty weights because it can be used by multiple dominant trains.

[0078] For any directed arc (u,v), let T(u,v) be its time weight. is the penalty weight added to the directed arc (u, v) in the main train i subnetwork due to the occupied path of the dominant train j. For the directed arc (u, v) in the main train i subnetwork, the total penalty weight of the arc can be obtained by summing the penalty weights added by each dominant train. Right now:

[0079]

[0080] For train i, the time weight and total penalty weight of each directed arc in its space-time subnetwork are linearly weighted and summed to obtain the total weight of the directed arc, which will serve as the basis for the path search of the main train i.

[0081] In the above-mentioned railway train operation diagram compilation method, preferably, the step S5 comprises the following steps:

[0082] Initialize the penalty weights of all arcs to 0, sort the trains according to the speed level from high to low and the mileage from large to small, and randomly select a time as the train departure time in the departure time domain of each train based on the current penalty weight in this order, and then calculate the arrival and departure time of the train at each passing station according to the sequence of stations passed by the train, with the minimum travel time and minimum stop time requirements, and determine an initial path in the train subnetwork accordingly based on the obtained train running line.

[0083] In the above-mentioned railway train operation diagram compilation method, preferably, the step S6 comprises the following steps:

[0084] For the main train i, record its sub-network Arc set and train j initial path p j The intersection of the occupied arc sets is The main train i will conflict with the train j in the operation safety interval when using any directed arc in the intersection, denoted by ρ i,j (u,v) indicates when train i uses directed arc When it is the same as the path p of train j j The difference between the actual time interval and the minimum safety interval, the penalty weight of the arc (u, v) in the main train i sub-network due to the dominant train j is initialized as follows:

[0085]

[0086] in, When train i is the main train and train j is the dominant train (when replacing the order of i and j, train j is the main train), the initial total penalty weight allocated to the main train i will be calculated according to arc ρ i,j (u,v) value size is allocated to There are arcs in each of them, and:

[0087]

[0088] Among them, the parameters As a reference to the penalty right, it directly controls the change range of the algorithm penalty right; i ,w j are the departure time domain widths of trains i and j respectively; i ,Ψ j are the rank quantization values ​​of trains i and j respectively;

[0089] For any directed arc (u, v) in the main train i subnetwork, the total penalty weight of the arc is obtained by summing up the penalty weights generated by all the dominant trains j, that is,

[0090]

[0091] in, is the initial total penalty weight of the directed arc (u, v) in the train i subnetwork.

[0092] In the above-mentioned railway train operation diagram compilation method, preferably, the step S7 comprises the following steps:

[0093] S701: For any train, according to the current penalty weights of each directed arc in its subnetwork, check the penalty weights of the directed arcs in its current path. If all of them are 0, it means that there is no operation conflict between the path and other train paths; otherwise, it means that there is an operation conflict with at least one other train path, and its path needs to be adjusted;

[0094] S702: Two trains with conflicting paths are called conflicting train pairs. By train The conflicting train pairs, is the set of conflicting train pairs determined based on the current train paths In order of conflict occurrence from smallest to largest Select the conflicting train pairs one by one in the above example, and record the currently selected conflicting train pair as Two trains The maximum penalty weights of the directed arcs contained in the current path are By comparison The size of the train is used to determine the train that needs to change its route. When selecting a train Re-search the route, otherwise, select the train Re-search the path;

[0095] S703: When it is a conflict train or After re-searching the new path, the penalty weights on other train j≠i sub-networks will change accordingly. The arc set occupied by the path re-searched by train i is The original path occupied arc set before this is For each directed arc (u, v) in the train j subnetwork, the penalty weight update for train i can be divided into the following three cases:

[0096] (1) If the directed arc (u, v) belongs to the set of arcs occupied by the new path But it does not belong to the old path occupied arc set Then the arc penalty weight is initialized;

[0097] (2) If the directed arc (u, v) does not belong to the set of arcs occupied by the new path But it belongs to the old path occupied arc set Then directly set the penalty weight for train i to 0;

[0098] (3) If the directed arc (u, v) belongs to the set of arcs occupied by the new path Also belongs to the old path occupied arc set This means that the current penalty weight of the arc is not enough to make the train change its path, so the penalty weight needs to be increased. The specific update method is as follows:

[0099]

[0100] in, represents the penalty weight of the nth iteration of arc (u,v), Indicates that train i and train j jointly occupy the arc set, the parameter α is greater than 1.00, α is the number of consecutive iterations that train i searches for a path containing arc (u, v), and m is the number of times the power function is set;

[0101] S704: Determine whether one of the following termination conditions is met. If so, stop conflict resolution; otherwise, repeat the above steps:

[0102] (1) There is no conflict between all train paths, that is, the set of conflicting train pairs determined is an empty set;

[0103] (2) The total number of iterations reaches a given upper limit;

[0104] (3) The number of times any train's route is adjusted reaches the upper limit.

[0105] As a general technical concept, the present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps in the above method when executing the computer program.

[0106] As a general technical concept, the present invention also provides a computer storage medium on which a computer program is stored, and when the program is executed by a processor, the steps in the above method are implemented.

[0107] Regarding the algorithm for compiling train operation diagrams, the mathematical programming methods used in existing studies have low efficiency and long solution time for large-scale problems, while heuristic algorithms are prone to produce infeasible solutions during the iteration process, and are very likely to fall into local optimality as the scale of the problem increases. In order to improve the efficiency and quality of the compilation of railway train operation diagrams, the present invention establishes a spatiotemporal network, builds a model and designs a solution algorithm based on the spatiotemporal network, and conducts case analysis. The railway train operation diagram compilation method based on the differentiated arc weight system established by the present invention has the following characteristics: First, each arc contains two types of arc weights, time weight and penalty weight, to ensure that in the process of train path search, both the goal of minimizing train travel time and the requirements for resolving safety conflicts between paths are taken into account; second, the penalty weight of the directed arc varies not only from train to train and from the dominant train path to the dominant train path, but also reflects the influence of all dominant train paths on the main train path search, which is conducive to the global search of the main train path.

[0108] The present invention constructs a method based on directed graph arc weight optimization, so that the conflict resolution process has higher adaptability. The method is based on the initial path of each train on the space-time network, considers the urgency of different trains occupying incompatible arcs, and guides the train to choose a path without conflict or with the least conflict by setting the arc weight of the directed arc of the conflict train, so as to achieve the goal of conflict resolution. This method can not only fully consider the adjustment difficulty of the conflict train, but also integrate the influence of other trains on conflict resolution in the conflict environment, and can quickly and effectively resolve the conflict according to the conflict situation. When the number of trains is large, even if some conflicts cannot be resolved in the end, the mutual influence between trains is better considered during the conflict resolution, so that the final conflict only occurs in a small number of trains. When the number of algorithm iterations reaches a preset upper limit or the number of train adjustments reaches a preset upper limit, the train will be selected to be deleted so that a satisfactory operation diagram can be obtained.

[0109] Compared with the prior art, the advantages of the present invention are:

[0110] The method for compiling a railway train operation diagram based on a differentiated arc right system of the present invention first designs a train space-time network, and constructs a space-time subnetwork for each train to improve the effectiveness of path search, and then based on the constructed space-time network, takes minimizing the total travel time of the train as the goal, considers the constraints related to a single train path and the constraints related to multiple train paths to establish a train operation diagram compilation model, and designs an arc penalty right design algorithm by establishing an arc right system based on train differences. The present invention constructs a differentiated arc right system according to the different urgency of different trains occupying the same arc by designing a train subnetwork, which not only improves the efficiency of train operation diagram compilation, but also reduces the waste of transportation resources, and provides technical guidance for the railway department to compile train operation diagrams. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0112] Figure 1 The present invention is a framework diagram of a method for compiling a railway train operation diagram based on a differentiated arc right system.

[0113] Figure 2 Schematic diagram of the interval running arc structure in the embodiment.

[0114] Figure 3 It is a schematic diagram of the interval slow-moving arc structure in the embodiment.

[0115] Figure 4 It is a schematic diagram of the station entry arc and the stay arc in the embodiment.

[0116] Figure 5 It is the left and right boundary of the train operation sub-network in the embodiment.

[0117] Figure 6 The currently selected paths for the four trains in the embodiment.

[0118] Figure 7 based on Figure 6 The penalty weights for the arcs in the G2 subnetwork determined by the train path shown. DETAILED DESCRIPTION

[0119] In order to facilitate the understanding of the present invention, the present invention will be described more comprehensively and meticulously below in conjunction with the accompanying drawings and preferred embodiments of the present invention, but the protection scope of the present invention is not limited to the following specific embodiments.

[0120] It should be noted that when an element is described as being "fixed, fixed, connected or connected to" another element, it can be directly fixed, fixed, connected or connected to the other element, or it can be indirectly fixed, fixed, connected or connected to the other element through other intermediate connectors.

[0121] Unless otherwise defined, all the professional terms used below have the same meanings as those generally understood by those skilled in the art. The professional terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the scope of protection of the present invention.

[0122] Example:

[0123] like Figure 1 As shown, a method for compiling a railway train operation diagram based on a differentiated arc right system comprises the following steps:

[0124] S1: Based on the given railway line and operating time range, construct a spatiotemporal network of train operation, effectively describing the operation process of trains in the interval, slow running, stopping, arriving, staying, departing, and passing without stopping in four entry and exit modes of the interval: stop-stop, stop-pass, pass-stop, and pass-pass. The specific steps include:

[0125] S101: Discretize the railway operation time range for the whole day into multiple discrete moments t in units of minutes, half minutes or seconds, denoted as t=T start ,T start +1,…,T end , where T start ,T end are the start and end times of line operation respectively;

[0126] S102: for each discrete time t, a passing point and two arrival and departure points are generated for each railway station, and the two arrival and departure points correspond to the throats at both ends of the station respectively;

[0127] S103: For any railway section direction, four types of operation arcs that meet the section operation time requirements are generated between the corresponding arrival and departure points or passing points of the preceding and following stations, namely, stop-stop, stop-go, go-stop, go-go; Figure 2 Obviously, the time difference between the front and rear nodes of each type of operation arc, that is, the duration of the operation arc is exactly equal to the minimum running time of the train in the section under the corresponding entry and exit mode. Since the running time of trains of different speed levels is different in the section, the above four types of section operation arcs need to be constructed for different speed levels respectively;

[0128] S104: Considering the possibility of slow movement of trains in the section, slow movement arcs are constructed between the passing points at adjacent discrete times at the same station and between the departure points at two adjacent discrete times at the same throat to describe the slow movement of trains in the section, such as Figure 3 As shown; the slow arcs between adjacent passing points are used by trains in both the up and down directions, and the slow arcs between adjacent arrival and departure points at both ends of the throat are used by trains in both the up and down directions respectively;

[0129] S105: In order to describe the arrival, departure, stay, and passing of trains at the station, firstly, an arrival arc is constructed between the arrival and departure points of different entry throats at the same time to describe the train stopping and entering the station; at the same time, a stay arc is constructed between the arrival and departure points of each throat at adjacent discrete times of the station to describe the train stopping at the station after entering the station. Figure 4 As shown. A train visiting the station's departure point does not mean entering the station. Since the train may pass through the slow-moving arc, it is stipulated that only visiting the station entry arc means that the train enters the station, such as train 4 in the figure. In summary, according to whether the train stops at the station, the possible running paths of the train when passing through the station are divided into 4 types as shown in the figure: 1) Train 1 passes through station B without slowing down, and directly leaves the station through a passing point of station B; 2) Train 2 passes through station B after slowing down, and leaves the station after passing through multiple adjacent slow-moving arcs (the number depends on the length of slow-moving); 3) Train 3 does not stop at the station at slowing down, first passes through an station entry arc, and then passes through several adjacent stay arcs (the number depends on the length of stay) to leave the station; 4) Train 4 stops at the station after slowing down, and passes through several adjacent slow-moving arcs, one station entry arc, and several adjacent stay arcs in sequence to leave the station. It is worth noting that the arrival time of a train at a station depends on the discrete moment corresponding to the arc through which the train enters the station, and the passing time and departure time depend on the discrete moment corresponding to the starting point of the arc through which the train passes. For example, in the figure, the arrival times of trains 3 and 4 are moments 5 and 7 respectively, and their departure times are moments 6 and 8 respectively; the passing times of trains 1 and 2 are moments 2 and 4 respectively.

[0130] S2: Generate the running time-space sub-network for each specific train; specifically, it includes the following steps:

[0131] S201: The earliest departure time of the train Departure: Determine the earliest arrival, departure or passing time of the train at each station according to the fastest running mode, such as Figure 5 The running line on the left side of the middle is called the left boundary of the subnetwork;

[0132] S202: For train i, the fastest running mode is the mode that runs through all sections with the minimum running time, stops at required stations with the minimum stopping time, and passes through non-required stations. The corresponding required travel time is recorded as Γ i fastest , based on the latest departure time of the train Start the train and run it in the slowest mode to get a running line ( Figure 5 The black running line in the middle) takes into account the maximum travel time Γ actually allowed by the train i allowed , further with time Start the train and run it in the fastest running mode to get another running line ( Figure 5 The running lines will inevitably intersect, and the first running line segment before the intersection and the second running line segment after the intersection form the right boundary of the subnetwork;

[0133] S203: Based on the left and right boundaries of the train operation, determine the earliest and latest arrival and departure or passing time of each station, and use the arrival and departure points and passing points distributed between the two at discrete times as the train operation sub-network node set; if the station is a must-stop station for the train, only add the departure point; if it is a must-pass station for the train, only add the passing point; otherwise, both types of nodes are added;

[0134] S204: Correspondingly, the running arc, the station entry arc, the station stop arc, and the slow-moving arc between any two nodes in the sub-network node set corresponding to the speed level of the train are added to the sub-network directed arc set to form a sub-network for the operation of train i.

[0135] S3: Based on the constructed space-time network, a train operation diagram optimization model is constructed with the goal of minimizing the total train travel time; the model considers the constraints related to a single train path and the constraints related to multiple train paths; it includes the following steps:

[0136] S301: Define a railway line consisting of K stations and K-1 double-track one-way sections. The line runs V types of speed grade trains. Trains of different speed grades have different start-stop additional time minutes and pure running time minutes when running in the same section direction. For the σ=1, 2, …, V speed grade trains, their pure running time minutes and start-stop additional time minutes in the section direction [k, k′] are recorded as For stations k = 1, 2, …, K, any two trains entering the station from the interval direction [k′, k] must meet the minimum entry safety interval. According to whether the two trains stop at the station, the entry safety interval can be divided into four types: through-to, through-through, to-to, and to-through. These four intervals have different minimum safety values, which are respectively denoted as Similarly, the exit safety intervals from station k to the interval direction [k, k′] are divided into four types: pass-to-post, pass-to-pass, post-post, and post-to-pass, which are denoted as

[0137] S302: It is known that a total of N trains need to be deployed on the above railway line, where the speed level of the i-th = 1, 2, ..., N trains is denoted by σ i , the starting station and the terminal station are denoted as r i ,s i , the starting time range is recorded as The maximum allowed travel time is denoted as Γ i allowed , whether it is necessary to stop at station k for boarding or disembarking is recorded as when If it is on, it means stop; otherwise, Indicates no parking;

[0138] S303: Define u, v, u′, v′ as nodes of any type at any station, (v, v) as a directed arc between nodes u and p of any type in the network, and define decision variable p i represents the running path of train i in its running subnetwork, which can uniquely determine its arrival and departure time, stop time, and interval running time at each station. Define the decision variable x i (u,v) represents the path p i The inclusion relationship between the arc (u,v) is that if the path p i Contains the arc (u,v), then x i (u,v)=1, otherwise, x i (u,v)=0, minimizing the total train travel time minz is selected as the model optimization objective, that is:

[0139]

[0140] Among them, T(p i ) is the path p taken by train i i The total travel time of , t(u,v) represents the time consumed by any directed arc (u,v);

[0141] S304: Determine the single path constraints of the train, including path flow balance constraints, departure time range constraints, interval minimum running time and maximum slow-moving time constraints, station minimum and maximum stop time constraints, and full-trip maximum travel time constraints;

[0142] The path flow balance constraints are as follows:

[0143]

[0144] Among them, V i origin is the set of originating nodes in the train i running sub-network, are the incoming arc set and outgoing arc set of node v in the running subnetwork of train i, respectively. are the running arc set and the station entry arc set of the running subnetwork of train i, respectively. i terminal is the set of terminal nodes in the running sub-network of train i;

[0145] The departure time range constraints are as follows:

[0146] The departure time corresponding to the starting point of each train i falls within the starting time range. Inside;

[0147] The maximum slow-moving time and the minimum running time of the interval are constrained as follows:

[0148]

[0149] in, is the interval direction [k,k′]∈E in the train i subnetwork i Added slow arc set, is the maximum slow-moving time allowed for train i in the section direction [k, k′], E i is a set of intervals;

[0150] The minimum running time required for trains of different speed levels to run in different entry and exit modes in the interval is different. Considering that when constructing the interval running arc in the network, four types of interval running arcs are designed for the interval running of trains of the same speed level with different entry and exit modes: pass-pass, stop-pass, pass-stop, and stop-stop. The duration of each interval running arc is the minimum running time of the corresponding entry and exit mode. Therefore, no matter which interval running arc is selected, the corresponding interval minimum running time requirement is met.

[0151] The minimum and maximum stop time constraints at the station are as follows:

[0152] The number of stopover arcs of train i in its subnetwork path including station k satisfies:

[0153]

[0154] in, is the set of stay arcs about station k in the train i subnetwork, are the minimum and maximum stopping times allowed for train i to stop at station k without being overtaken, is the maximum allowed stop time when a train is overtaken. Indicates whether train i is passed at station k, Indicates whether train i is overtaken by train j at station k. If so, the arrival time and departure time of train j must be between the arrival time and departure time of train i, that is, it satisfies:

[0155]

[0156] Among them, S i and S j is the set of stations for trains i and j, t u is the time of node u, M is an integer constant, For trains i and j, they run arcs between the interval [k, k′], are the entry arcs of trains i and j at station k, respectively. The former makes it so that when train j passes train i at station k, that is, The arrival time of train i at station k is It is required to be less than the arrival or passing time of train j at the station Otherwise, there is no limit between the arrival times of the two buses, which further makes the When , train i will leave the station later than train j, that is, Otherwise, there is no constraint between the two departure times;

[0157] The maximum travel time constraints for the entire journey are as follows:

[0158]

[0159] Among them, Γ i max is the maximum travel time that can be achieved by train i by increasing the interval slow travel time, the number of station stops, and the station stop time;

[0160] S305: determining related constraints between multiple train paths, expressed in the form of incompatible arc sets, including a safety interval occupancy arc set related to departure operations, a safety interval occupancy arc set related to arrival operations, and a safety interval occupancy arc set related to passing operations;

[0161] The set of safety interval occupancy arcs associated with the departure operation is as follows:

[0162] Define u k For any node of station k, define is the arrival and departure point of the throat connecting station k to station k′ at discrete time t, u k,t is the passing point of station k at discrete time t. The safety intervals related to the departure operation of trains at stations include the safety interval between passing and dispatching, the safety interval between dispatching and passing, and the safety interval between dispatching and dispatching. i Via stop-go arcs on the interval [k, k′] or stop-stop operation arc When, it means that the train stops at station k and departs from the station to station k' at discrete time t. At this time, in order to meet the safety interval requirements of passing-departing and departing-passing, the starting time belongs to the time range The stop-stop and go-go arcs in the interval [k, k′] cannot be used by other trains; at the same time, in order to meet the departure-departure safety interval requirements, the starting time belongs to the time range The stop-stop and stop-go arcs in the interval [k, k′] cannot be used by other trains.

[0163] remember is the set of arcs that can no longer be used by other trains when train i leaves station k at discrete time t and enters interval [k, k′] in order to meet the relevant safety interval requirements, which can be expressed as:

[0164]

[0165] in, is the running arc between the interval [k, k′], t′ is the time when the train departure safety interval is not met, (u k,t′ ,v) is the point u connected to station k at time t′ k,t′ Any arc of To connect the station to the departure point Any arc of

[0166] The set of safe interval occupancy arcs associated with the arrival operation is as follows:

[0167] The safety intervals related to the train station arrival operation include the through-to safety interval, the to-through safety interval, and the to-to safety interval. i Via the pit stop arc , which means that the train stops at station k from station k′ at time t. At this time, in order to meet the arrival-to-arrival safety interval requirement, the node time belongs to the time range All the entry arcs about station k can no longer be used by other trains; in order to pass-to safety interval and to-to safety interval, the starting time belongs to the time range All stop-go and go-go arcs in the interval [k′, k] will no longer be used by other trains;

[0168] remember is the set of arcs that train i needs to occupy when it stops at station k from station k′ to station k at time t to meet the requirements of through-to, to-through, and to-to safety intervals. It can be expressed as:

[0169]

[0170] in, is the arc running between the interval [k′,k], is the train’s entry arc at station k;

[0171] The set of safe interval occupancy arcs associated with through operations is as follows:

[0172] The safety intervals related to the train station passing operation include five types of safety intervals: through-through, departure-through, through-departure, through-arrival, and arrival-through. When train i is in its sub-network path p i Via the on-off arc , which means that the train passes through station k at time t. At this time, in order to meet the pass-to-pass safety interval requirements, the starting time belongs to the time range The start-stop and start-stop arcs within the time range cannot be used anymore; in order to meet the start-stop and start-start safety interval requirements, the start time belongs to the time range The stop-go and stop-stop arcs within the time range cannot be used; in order to meet the requirements of the safety interval between go-go and go-go, the starting time belongs to the time range The pit stop arc inside can no longer be used;

[0173] remember is the set of arcs that need to be occupied due to the train passing operation, which can be expressed as:

[0174]

[0175] Train i uses path p i By summarizing the occupied arc sets of the corresponding operations passing through the stations, the train path p can be obtained. i The occupied arc set for:

[0176]

[0177] in, It is represented as the entry arc of station k at time t;

[0178] In summary, in order to meet various safety interval requirements related to train station arrival, passing, and departure operations, when train i uses path p iAfter that, any other train j can no longer use path p i Occupancy Arc Set Any arc in satisfies:

[0179]

[0180] S4: According to the constructed space-time network and the train operation diagram optimization model, an arc weight system based on train differences is established. For each directed arc in any train space-time subnetwork, two types of weights, time weight and penalty weight, are set; including the following steps:

[0181] For each directed arc in any train space-time subnetwork, two types of rights are set: time right and penalty right. The time right reflects the travel time that the train needs to bear when passing through the arc, and the penalty right reflects the urgency of the train's use of the arc, and also reflects the severity of the operational conflict between the train's use of the arc and other train paths. Specifically:

[0182] (1) Directed arc time weight: For any directed arc in the train space-time subnetwork, its time weight is the difference between the time corresponding to the arc end point and the time corresponding to the arc start point. The time weight of the stop arc and the slow arc is 1, and the time weight of the entry arc is 0. The time weight of the running arc is the travel time of the train of the corresponding speed level in the section. The time weight of the same directed arc in all train space-time subnetworks is the same and will remain unchanged during the mapping process, which means that any train visiting the arc will always have the same travel time.

[0183] (2) Directed arc penalty weight: The penalty weight of a directed arc can be understood as the weight set when a train occupies a directed arc to prevent other trains from using the arc again and causing path conflicts. Obviously, if a directed arc is not used by any train, the penalty weight of the arc in the train subnetwork is 0. The train that uses the arc penalty weight to search for paths is the main train, and the train that determines the size of the arc penalty weight is the dominant train. Each directed arc in the main train subnetwork has multiple different penalty weights because it can be used by multiple dominant trains; Figure 6 The G2 train subgraph is shown. There are 4 trains in total. Since the minimum safety interval is 2, trains G1 and G3 have path conflicts with train G2, but have no conflict with train G4. Figure 7 The penalty weights of each arc in the train G2 subnetwork with respect to trains G1, G3, and G4 are given (the three numbers in brackets next to the arcs in the figure correspond to the penalty weights of the three trains respectively);

[0184] For any directed arc (u,v), let T(u,v) be its time weight. is the penalty weight added to the directed arc (u, v) in the main train i subnetwork due to the occupied path of the dominant train j. For the directed arc (u, v) in the main train i subnetwork, the total penalty weight of the arc can be obtained by summing the penalty weights added by each dominant train. Right now:

[0185]

[0186] For train i, the time weight and total penalty weight of each directed arc in its space-time subnetwork are linearly weighted and summed to obtain the total weight of the directed arc, which will be used as the basis for the path search of the main train i. Figure 7 The arc penalty weight distribution in the G2 subnetwork of train G2 is shown in Figure 1. By searching for a new path for this train, a new path that does not conflict with trains G1, G3, and G4 can be obtained (see Figure 6 dotted line train path).

[0187] S5: Initialize the penalty weights of all arcs to 0, and search for paths column by column based on the current penalty weights; including the following steps:

[0188] Initialize the penalty weights of all arcs to 0, sort the trains according to the speed level from high to low and the mileage from large to small, and randomly select a time as the train departure time in the departure time domain of each train based on the current penalty weight in this order, and then calculate the arrival and departure time of the train at each passing station according to the sequence of stations passed by the train, with the minimum travel time and minimum stop time requirements, and determine an initial path in the train subnetwork accordingly based on the obtained train running line.

[0189] S6: Update the penalty weight, based on the current path of any train, take the train as the main train and other trains as the dominant trains, and update the penalty weight of each arc in the space-time subnetwork of each main train; including the following steps:

[0190] Based on the obtained initial train path, each train is used as the main train and other trains are used as the dominant trains to update the penalty weight of each arc in each main train subnetwork. Specifically, for main train i, its subnetwork is recorded as Arc set and train j initial path p j The intersection of the occupied arc sets is The main train i will conflict with the train j in the operation safety interval when using any directed arc in the intersection. i,j (u,v) indicates when train i uses directed arc When it is the same as the path p of train j j The difference between the actual time interval and the minimum safety interval. For example, when arc (u, v) is an entry arc and the corresponding train arrival time is 9:00, path p jIf the train's arrival time at the station is 9:02 and the minimum safety interval is 5 minutes, then ρ i,j (u,v)=5-(9:02-9:00)=3. Obviously, the larger the difference, the closer the arc (u,v) used by train i will be to path p. j The more serious the safety interval conflict is, the larger the penalty weight should be. The penalty weight of arc (u, v) in the main train i subnetwork due to the dominant train j is initialized as follows:

[0191]

[0192] Among them, (u′,v′) is the directed arc occupied by train i, When train i is the main train and train j is the dominant train, the initial total penalty weight allocated to main train i will be calculated according to arc ρ i,j (u,v) value size is allocated to On each directed arc in , usually due to the different levels of trains i and j, the initial total penalty weights allocated to the two trains are not the same. Generally, the train with higher level and narrower departure time range will get smaller initial total penalty weight than the other train, which tends to make the other train change its path to resolve the train path conflict. Therefore:

[0193]

[0194] Among them, the parameters As a reference to the penalty right, it directly controls the change range of the algorithm penalty right; i ,w j are the departure time domain widths of trains i and j respectively; i ,Ψ j are the grade quantization values ​​of trains i and j respectively; in this embodiment, the train grades are divided into 1, 2, ... grade values. The smaller the grade value, the higher the corresponding train grade. The specific grade classification of the train can be determined comprehensively based on factors such as its speed grade and whether it is a benchmark train;

[0195] For any directed arc (u, v) in the main train i subnetwork, the total penalty weight of the arc is obtained by summing up the penalty weights generated by all the dominant trains j, that is,

[0196]

[0197] in, is the initial total penalty weight of the directed arc (u, v) in the train i subnetwork.

[0198] S7: adjusting the conflicting train paths. For any two trains, judging whether there is a conflict between them based on the established train operation diagram optimization model. If there is a conflict, selecting the train with a larger penalty weight, re-searching the path for it based on the sum of the updated penalty weight and time weight. For any train whose path is adjusted, updating the penalty weight for other trains, repeating the above process until there is no conflicting train. The steps include:

[0199] S701: For any train, according to the current penalty weights of each directed arc in its subnetwork, check the penalty weights of the directed arcs in its current path. If all of them are 0, it means that there is no operation conflict between the path and other train paths; otherwise, it means that there is an operation conflict with at least one other train path, and its path needs to be adjusted;

[0200] S702: Two trains with conflicting paths are called conflicting train pairs. By train The conflicting train pairs, is the set of conflicting train pairs determined based on the current train paths In order of conflict occurrence from smallest to largest Select the conflicting train pairs one by one in the above example, and record the currently selected conflicting train pair as Two trains The maximum penalty weights of the directed arcs contained in the current path are By comparison The size of the train is used to determine the train that needs to change its route. When selecting a train Re-search the route, otherwise, select the train Re-search the path;

[0201] S703: When it is a conflict train or After re-searching the new path, the penalty weights on other train j≠i sub-networks will change accordingly. The arc set occupied by the path re-searched by train i is The original path occupied arc set before this is For each directed arc (u, v) in the train j subnetwork, the penalty weight update for train i can be divided into the following three cases:

[0202] (1) If the directed arc (u, v) belongs to the set of arcs occupied by the new path But it does not belong to the old path occupied arc set Then the arc penalty weight is initialized;

[0203] (2) If the directed arc (u, v) does not belong to the set of arcs occupied by the new path But it belongs to the old path occupied arc set Then directly set the penalty weight for train i to 0;

[0204] (3) If the directed arc (u, v) belongs to the set of arcs occupied by the new path It also belongs to the old path occupied arc set This means that the current penalty weight of the arc is not enough to make the train change its path, so the penalty weight needs to be increased. The specific update method is as follows:

[0205]

[0206] in, represents the penalty weight of the nth iteration of arc (u,v), Indicates that train i and train j jointly occupy the arc set, the parameter α is greater than 1.00, α is the number of consecutive iterations that train i searches for a path containing arc (u, v), and m is the number of times the power function is set;

[0207] S704: Determine whether one of the following termination conditions is met. If so, stop conflict resolution; otherwise, repeat the above steps:

[0208] (1) There is no conflict between all train paths, that is, the set of conflicting train pairs determined is an empty set;

[0209] (2) The total number of iterations reaches a given upper limit;

[0210] (3) The number of times any train's route is adjusted reaches the upper limit.

[0211] S8: Determine the arrival and departure times of the trains passing through each station according to the current routes of the trains, and output the train operation diagram.

[0212] The embodiment further provides a computer system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the steps in the above method are implemented when the processor executes the computer program.

[0213] The embodiment further provides a computer storage medium having a computer program stored thereon, and the program implements the steps in the above method when executed by a processor.

Claims

1. A method for compiling a railway train operation diagram based on a differentiated arc weight system, characterized in that: The following steps are involved: S1: Construct a spatiotemporal network of train operation based on a given railway line and operating time range; S2: Generate the running time-space sub-network for each specific train; S3: Based on the constructed space-time network, a train operation diagram optimization model is constructed with the goal of minimizing the total train travel time. The model considers the constraints related to a single train path and the constraints related to multiple train paths. S4: According to the constructed space-time network and the train operation diagram optimization model, an arc weight system based on train differences is established. For each directed arc in any train space-time subnetwork, two types of weights, time weight and penalty weight, are set; S5: Initialize the penalty weights of all arcs to 0, and search for paths column by column based on the current penalty weights; S6: Update the penalty weight. Based on the current path of any train, take the train as the main train and other trains as the dominant trains, and update the penalty weight of each arc in the space-time subnetwork of each main train. S7: Adjust the conflicting train paths. For any two trains, determine whether there is a conflict based on the established train operation diagram optimization model. If there is a conflict, select the train with a larger penalty weight, and re-search the path for it based on the sum of the updated penalty weight and time weight. For any train whose path is adjusted, update the penalty weight for other trains, and repeat the above process until there is no conflicting train. S8: Determine the arrival and departure times of the trains passing through each station according to the current routes of the trains, and output the train operation diagram.

2. The method for compiling a railway train operation diagram according to claim 1, characterized in that: The step S1 comprises the following steps: S101: Discretize the railway operation time range for the whole day into multiple discrete moments t in units of minutes, half minutes or seconds, denoted as t=T start ,T start +1,…,T end , where T start ,T end are the start and end times of line operation respectively; S102: for each discrete time t, a passing point and two arrival and departure points are generated for each railway station, and the two arrival and departure points correspond to the throats at both ends of the station respectively; S103: For any railway section direction, four types of operation arcs that meet the section operation time requirements are generated between the corresponding arrival and departure points or passing points of the preceding and following stations, namely, stop-stop, stop-go, go-stop, and go-go; S104: construct slow-moving arcs between adjacent discrete-time passing points at the same station and between two adjacent discrete-time arrival and departure points at the same throat to describe the slow movement of trains in the section; the slow-moving arcs between adjacent passing points are used by both up and down direction trains, and the slow-moving arcs between adjacent arrival and departure points at both ends of the throat are used by both up and down direction trains; S105: First, an entry arc is constructed between different entry choke points and departure points at the same time to describe the train stopping and entering the station; at the same time, a stay arc is constructed between each choke point at adjacent discrete times to the departure point to describe the train stopping at the station after entering the station.

3. The method for compiling a railway train operation diagram according to claim 1, characterized in that: The step S2 comprises the following steps: S201: The earliest departure time of the train Departure: Determine the earliest arrival, departure or passing time of the train at each station according to the fastest running mode, which is called the left boundary of the sub-network; S202: For train i, the fastest running mode is the mode that runs through all sections with the minimum running time, stops at required stations with the minimum stopping time, and passes through non-required stations. The corresponding required travel time is recorded as Γ i fastest , based on the latest departure time of the train The train starts and runs in the slowest mode to get a running line, considering the maximum travel time Γ actually allowed by the train i allowed , further with time Start the train and run it in the fastest running mode to get another running line. The running lines will inevitably intersect, and the first running line segment before the intersection and the second running line segment after the intersection will form the right boundary of the sub-network; S203: Based on the left and right boundaries of the train operation, determine the earliest and latest arrival and departure or passing time of each station, and use the arrival and departure points and passing points distributed between the two at discrete times as the train operation sub-network node set; if the station is a must-stop station for the train, only add the departure point; if it is a must-pass station for the train, only add the passing point; otherwise, both types of nodes are added; S204: Correspondingly, the running arc, the station entry arc, the station stop arc, and the slow-moving arc between any two nodes in the sub-network node set corresponding to the speed level of the train are added to the sub-network directed arc set to form a sub-network for the operation of train i.

4. The method for compiling a railway train operation diagram according to claim 1, characterized in that: The step S3 comprises the following steps: S301: Define a railway line consisting of K stations and K-1 double-track one-way sections. The line runs V types of speed grade trains. Trains of different speed grades have different start-stop additional time minutes and pure running time minutes when running in the same section direction. For the σ=1, 2, …, V speed grade trains, their pure running time minutes and start-stop additional time minutes in the section direction [k, k′] are recorded as For stations k = 1, 2, …, K, any two trains entering the station from the interval direction [k′, k] must meet the minimum entry safety interval. According to whether the two trains stop at the station, the entry safety interval can be divided into four types: through-to, through-through, to-to, and to-through. These four intervals have different minimum safety values, which are respectively denoted as Similarly, the exit safety intervals from station k to the interval direction [k, k′] are divided into four types: pass-to-post, pass-to-pass, post-post, and post-to-pass, which are denoted as S302: It is known that a total of N trains need to be deployed on the above railway line, where the speed level of the i-th = 1, 2, ..., N trains is denoted by σ i The starting station and the terminal station are denoted as r i ,s i , the starting time range is recorded as The maximum allowed travel time is denoted as Γ i allowed , whether it is necessary to stop at station k for boarding or disembarking is recorded as when If it is on, it means stop; otherwise, Indicates no parking; S303: Define u, v, v′, v′ as nodes of any type at any station, (u, v) as a directed arc between nodes u and v of any type in the network, and define decision variables p i represents the running path of train i in its running subnetwork, which can uniquely determine its arrival and departure time, stop time, and interval running time at each station. Define the decision variable x i (u,v) represents the path p i The inclusion relationship between the arc (u,v) is that if the path p i Contains the arc (u,v), then x i (u,v)=1, otherwise, x i (u,v)=0, minimizing the total train travel time minz is selected as the model optimization objective, that is: Among them, T(p i ) is the path p taken by train i i The total travel time of , t(u,v) represents the time consumed by any directed arc (u,v); S304: Determine the single path constraints of the train, including path flow balance constraints, departure time range constraints, interval minimum running time and maximum slow-moving time constraints, station minimum and maximum stop time constraints, and full-trip maximum travel time constraints; The path flow balance constraints are as follows: Among them, V i origin is the set of originating nodes in the train i running sub-network, are the incoming arc set and outgoing arc set of node v in the running subnetwork of train i, respectively. are the running arc set and the station entry arc set of the running subnetwork of train i, respectively. i terminal is the set of terminal nodes in the running sub-network of train i; The departure time range constraints are as follows: The departure time corresponding to the starting point of each train i falls within the starting time range. Inside; The maximum slow-moving time and the minimum running time of the interval are constrained as follows: in, is the interval direction [k,k′]∈E in the train i subnetwork i Added slow arc set, is the maximum slow-moving time allowed for train i in the section direction [k, k′], E i is a set of intervals; The minimum running time required for trains of different speed levels to run in different entry and exit modes in the interval is different. Considering that when constructing the interval running arc in the network, four types of interval running arcs are designed for the interval running of trains of the same speed level with different entry and exit modes: pass-pass, stop-pass, pass-stop, and stop-stop. The duration of each interval running arc is the minimum running time of the corresponding entry and exit mode. Therefore, no matter which interval running arc is selected, the corresponding interval minimum running time requirement is met. The minimum and maximum stop time constraints at the station are as follows: The number of stopover arcs of train i in its subnetwork path including station k satisfies: in, is the set of stay arcs about station k in the train i subnetwork, are the minimum and maximum stopping times allowed for train i to stop at station k without being overtaken, is the maximum allowed stop time when a train is overtaken. Indicates whether train i is passed at station k, Indicates whether train i is overtaken by train j at station k. If so, the arrival time and departure time of train j must be between the arrival time and departure time of train i, that is, it satisfies: Among them, S i and S j is the set of stations for trains i and j, t u is the time of node u, M is an integer constant, For trains i and j, they run arcs between the interval [k, k′], are the entry arcs of trains i and j at station k, respectively. The former makes it so that when train j passes train i at station k, that is, The arrival time of train i at station k is It is required to be less than the arrival or passing time of train j at the station Otherwise, there is no limit between the arrival times of the two buses, which further makes the When , train i will leave the station later than train j, that is, Otherwise, there is no constraint between the two departure times; The maximum travel time constraints for the entire journey are as follows: Among them, Γ i max is the maximum travel time that can be achieved by train i by increasing the interval slow travel time, the number of station stops, and the station stop time; S305: determining related constraints between multiple train paths, expressed in the form of incompatible arc sets, including a safety interval occupancy arc set related to departure operations, a safety interval occupancy arc set related to arrival operations, and a safety interval occupancy arc set related to passing operations; The set of safety interval occupancy arcs associated with the departure operation is as follows: Define u k For any node of station k, define is the arrival and departure point of the throat connecting station k to station k′ at discrete time t, u k,t is the passing point of station k at discrete time t. The safety intervals related to the departure operation of trains at stations include the safety interval between passing and dispatching, the safety interval between dispatching and passing, and the safety interval between dispatching and dispatching. i Via stop-go arcs on the interval [k, k′] or stop-stop operation arc When, it means that the train stops at station k and departs from the station to station k' at discrete time t. At this time, in order to meet the safety interval requirements of passing-departing and departing-passing, the starting time belongs to the time range The stop-stop and go-go arcs in the interval [k, k′] cannot be used by other trains; at the same time, in order to meet the departure-departure safety interval requirements, the starting time belongs to the time range The stop-stop and stop-go arcs in the interval [k, k′] cannot be used by other trains. remember is the set of arcs that can no longer be used by other trains when train i leaves station k at discrete time t and enters interval [k, k′] in order to meet the relevant safety interval requirements, which can be expressed as: in, is the running arc between the interval [k, k′], t′ is the time when the train departure safety interval is not met, (u k,t′ ,v) is the point u connected to station k at time t′ k,t′ Any arc of To connect the station to the departure point Any arc of The set of safe interval occupancy arcs associated with the arrival operation is as follows: The safety intervals related to the train station arrival operation include the through-to safety interval, the to-through safety interval, and the to-to safety interval. i Via the pit stop arc , which means that the train stops at station k from station k′ at time t. At this time, in order to meet the arrival-to-arrival safety interval requirement, the node time belongs to the time range All the entry arcs about station k can no longer be used by other trains; in order to pass-to safety interval and to-to safety interval, the starting time belongs to the time range All stop-go and go-go arcs in the interval [k′, k] will no longer be used by other trains; remember is the set of arcs that train i needs to occupy to meet the through-to, to-through, and to-to safety interval requirements when it stops at station k from station k′ at time t. It can be expressed as: in, is the arc running between the interval [k′,k], is the train’s entry arc at station k; The set of safe interval occupancy arcs associated with through operations is as follows: The safety intervals related to the train station passing operation include five types of safety intervals: through-through, departure-through, through-departure, through-arrival, and arrival-through. When train i is in its sub-network path p i Via the on-off arc , which means that the train passes through station k at time t. At this time, in order to meet the pass-to-pass safety interval requirements, the starting time belongs to the time range The start-stop and start-stop arcs within the time range cannot be used anymore; in order to meet the start-stop and start-start safety interval requirements, the start time belongs to the time range The stop-go and stop-stop arcs within the time range cannot be used; in order to meet the requirements of the safety interval between go-go and go-go, the starting time belongs to the time range The pit stop arc inside can no longer be used; remember is the set of arcs that need to be occupied due to the train passing operation, which can be expressed as: Train i uses path p i By summarizing the occupied arc sets of the corresponding operations passing through the stations, the train path p can be obtained. i The occupied arc set for: in, It is represented as the entry arc of station k at time t; In order to meet various safety interval requirements related to train station arrival, passing, and departure operations, when train i uses path p i After that, any other train j can no longer use path p i Occupancy Arc Set Any arc in satisfies:

5. The method for compiling a railway train operation diagram according to claim 1, characterized in that: The step S4 comprises the following steps: For each directed arc in any train space-time subnetwork, two types of rights are set: time right and penalty right. The time right reflects the travel time that the train needs to bear when passing through the arc, and the penalty right reflects the urgency of the train's use of the arc, and also reflects the severity of the operational conflict between the train's use of the arc and other train paths. Specifically: (1) Directed arc time weight: For any directed arc in the train space-time subnetwork, its time weight is the difference between the corresponding time of the arc end point and the corresponding time of the arc start point. The time weight of the stop arc and the slow arc is 1, and the time weight of the entry arc is 0. The time weight of the running arc is the travel time of the train of the corresponding speed level in the section. The time weight of the same directed arc in all train space-time subnetworks is the same and will remain unchanged during the mapping process. (2) Directed arc penalty weight: If a directed arc is not used by any train, the penalty weight of the arc in the train subnetwork is 0. The train that uses the arc penalty weight to search for paths is the main train, and the train that determines the size of the arc penalty weight is the dominant train. Each directed arc in the main train subnetwork has multiple different penalty weights because it can be used by multiple dominant trains. For any directed arc (u,v), let T(u,v) be its time weight. is the penalty weight added to the directed arc (u, v) in the main train i subnetwork due to the occupied path of the dominant train j. For the directed arc (u, v) in the main train i subnetwork, the total penalty weight of the arc can be obtained by summing the penalty weights added by each dominant train. Right now: For train i, the time weight and total penalty weight of each directed arc in its space-time subnetwork are linearly weighted and summed to obtain the total weight of the directed arc, which will serve as the basis for the path search of the main train i.

6. The method for compiling a railway train operation diagram according to claim 1, characterized in that: The step S5 comprises the following steps: Initialize the penalty weights of all arcs to 0, sort the trains according to the speed level from high to low and the mileage from large to small, and randomly select a time as the train departure time in the departure time domain of each train based on the current penalty weight in this order, and then calculate the arrival and departure time of the train at each passing station according to the sequence of stations passed by the train, with the minimum travel time and minimum stop time requirements, and determine an initial path in the train subnetwork accordingly based on the obtained train running line.

7. The method for compiling a railway train operation diagram according to claim 1, characterized in that: The step S6 comprises the following steps: For the main train i, record its sub-network Arc set and train j initial path p j The intersection of the occupied arc sets is The main train i will conflict with the train j in the operation safety interval when using any directed arc in the intersection, denoted by ρ i,j (u,v) indicates when train i uses directed arc When it is the same as the path p of train j j The difference between the actual time interval and the minimum safety interval, the penalty weight of the arc (u, v) in the main train i sub-network due to the dominant train j is initialized as follows: in, When train i is the main train and train j is the dominant train, the initial total penalty weight allocated to main train i will be calculated according to arc ρ i,j (u,v) value size is allocated to There are arcs in each of them, and: Among them, the parameters As a reference to the penalty right, it directly controls the change range of the algorithm penalty right; i ,w j are the departure time domain widths of trains i and j respectively; i ,Ψ j are the rank quantization values ​​of trains i and j respectively; For any directed arc (u, v) in the main train i subnetwork, the total penalty weight of the arc is obtained by summing up the penalty weights generated by all the dominant trains j, that is, in, is the initial total penalty weight of the directed arc (u, v) in the train i subnetwork.

8. The method for compiling a railway train operation diagram according to claim 1, characterized in that: The step S7 comprises the following steps: S701: For any train, according to the current penalty weights of each directed arc in its subnetwork, check the penalty weights of the directed arcs in its current path. If all of them are 0, it means that there is no operation conflict between the path and other train paths; otherwise, it means that there is an operation conflict with at least one other train path, and its path needs to be adjusted; S702: Two trains with conflicting paths are called conflicting train pairs. By train The conflicting train pairs, is the set of conflicting train pairs determined based on the current train paths In order of conflict occurrence from smallest to largest Select the conflicting train pairs one by one in the above example, and record the currently selected conflicting train pair as Two trains The maximum penalty weights of the directed arcs contained in the current path are By comparison The size of the train is used to determine the train that needs to change its route. When selecting a train Re-search the route, otherwise, select the train Re-search the path; S703: When it is a conflict train or After re-searching the new path, the penalty weights on other train j≠i sub-networks will change accordingly. The arc set occupied by the path re-searched by train i is The original path occupied arc set before this is For each directed arc (u, v) in the train j subnetwork, the penalty weight update for train i can be divided into the following three cases: (1) If the directed arc (u, v) belongs to the set of arcs occupied by the new path But it does not belong to the old path occupied arc set Then the arc penalty weight is initialized; (2) If the directed arc (u, v) does not belong to the set of arcs occupied by the new path But it belongs to the old path occupied arc set Then directly set the penalty weight for train i to 0; (3) If the directed arc (u, v) belongs to the set of arcs occupied by the new path It also belongs to the old path occupied arc set This means that the current penalty weight of the arc is not enough to make the train change its path, so the penalty weight needs to be increased. The specific update method is as follows: in, represents the penalty weight of the nth iteration of arc (u,v), Indicates that train i and train j jointly occupy the arc set, the parameter α is greater than 1.00, α is the number of consecutive iterations that train i searches for a path containing arc (u, v), and m is the number of times the power function is set; S704: Determine whether one of the following termination conditions is met. If so, stop conflict resolution; otherwise, repeat the above steps: (1) There is no conflict between all train paths, that is, the set of conflicting train pairs determined is an empty set; (2) The total number of iterations reaches a given upper limit; (3) The number of times any train's route is adjusted reaches the upper limit.

9. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps in the method of any one of claims 1 to 8 are implemented.

10. A computer storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in any one of the methods of claims 1 to 8 are implemented.

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