Train planning timetable compilation method and device based on distribution robust optimization model

Abstract

The embodiment of the application relates to the technical field of transportation planning and optimization, and particularly relates to a train plan timetable compiling method and device based on a distribution robust optimization model, aiming at how to compile a plan timetable which can better consider traffic efficiency and robustness under the condition of uncertain train driving time length by using limited historical running time length data. The method firstly constructs a data-driven 1-Wasserstein two-stage distribution robust train timetable optimization model with an experience distribution as a center for a diagram compilation and rescheduling decision process, the two-stage distribution robust train timetable optimization model taking minimizing total driving time length and total delay degree of trains as a target; historical data of train line planning and train operation are input into the two-stage distribution robust train timetable optimization model, the two-stage distribution robust train timetable optimization model is solved by designing a main problem and a sub-problem iterative solving algorithm, and a train plan timetable is obtained.

Description

Technical Field

[0001] This application relates to the field of transportation planning and optimization technology, and in particular to a method and apparatus for compiling train schedules based on a distributed bar optimization model. Background Technology

[0002] Railway transportation is one of the main modes of passenger transport, and railway transportation planning is crucial to both economic efficiency and passenger experience. The process of developing a railway transportation plan typically includes: railway network design, route planning, basic timetable development, station and platform allocation planning, route planning, and train crew scheduling planning. The basic timetable is the graphical representation of the planned train schedule, specifying the departure and arrival times of each train at each station. It is a key link in the entire train operation planning decision-making process, playing a crucial role in connecting the preceding and following stages. Furthermore, the train timetable is an important source of information for passengers when purchasing tickets and reflects the railway's service capacity and quality. On the one hand, passengers hope for the shortest possible travel time, meaning the travel time reflected in the timetable should be as small as possible; on the other hand, passengers also hope that trains will run on time according to the timetable.

[0003] However, during train operation, the actual travel time between stations fluctuates due to real-time factors such as weather conditions, posing a risk of delays. Because of the "delay propagation" effect, a delay in one train can potentially cause delays in multiple subsequent trains. Therefore, train timetables need to appropriately extend the planned travel time to absorb the impact of these disturbances. Thus, how to insert appropriate buffers into train timetables to balance train efficiency and robustness, thereby improving the service quality and competitiveness of railway transportation, is a problem of significant research value and practical importance. Summary of the Invention

[0004] In view of the above problems, this application provides a method and apparatus for compiling train schedules based on a split-bar optimization model, so as to overcome the above problems or at least partially solve the above problems.

[0005] A first aspect of this application discloses a method for compiling train timetables based on a split-bar optimization model, the method comprising:

[0006] For the timetable compilation and rescheduling decision-making process, a data-driven 1-Wasserstein two-stage sub-Brussels bar train timetable optimization model centered on experience distribution is constructed. The two-stage sub-Brussels bar train timetable optimization model aims to minimize the total travel time and total delay of trains.

[0007] The train route plan and historical train operation data are input into the two-stage sub-Blu-ray bar train timetable optimization model. The route plan includes: the set of trains to be scheduled, the route sections of each train, and the driving and stopping data of each train. The historical data is the actual driving data of each train in each driving section.

[0008] By designing iterative solutions for the main problem and sub-problems, the two-stage sub-Bruker train timetable optimization model is solved to obtain the train timetable plan.

[0009] Optionally, the two-stage sub-Blu-ray train timetable optimization model includes: a first-stage optimization model and a second-stage optimization model, and the two-stage sub-Blu-ray train timetable optimization model is expressed as:

[0010]

[0011] Where, min x∈x Q I (x) represents the model in the first optimization stage. For the second-stage optimization model, x represents the planned timetable, indicating the arrival and departure times of each train at each station in the timetable. χ is the feasible region of x as defined by operating regulations and safety constraints. Q I (x) represents the traffic efficiency loss function of the planned timetable x, ξ is a random vector representing the travel time of each train between adjacent stations, and Q II (x, ξ) represents the total degree of delay function given a planned timetable x and the known ξ. Let F represent a set of distribution functions, containing the empirical distribution F formed by N historical data points. N Centered on Ξ, with Ξ as the support set, and the Wasserstein distance not exceeding ε N The probability distribution function.

[0012] Optionally, the first-stage optimization model aims to minimize the travel time while ensuring driving safety, and includes the following components:

[0013] Construct a traffic efficiency loss function, wherein the decision vector of the traffic efficiency loss function is the time when each train enters each track section and the time when the train leaves the track section;

[0014] Determine the constraints for train operation, including:

[0015] Each train must not depart from the initial station earlier than the given time.

[0016] The travel time of each train in each section shall not be less than the shortest possible travel time, and the stop time at the station shall not be less than the required stop time.

[0017] Overtaking is only allowed within stations, and two adjacent trains on the same section must maintain a certain interval.

[0018] The total running time of each train shall not exceed the sum of the proportion of the shortest travel time and the proportion of the shortest stop time.

[0019] Optionally, the second-stage optimization model aims to minimize the deviation between the adjusted timetable and the planned timetable based on actual conditions. The second-stage optimization model includes:

[0020] Construct a total delay severity function, the decision vector of which is the time when each train enters each track section and the time when each train leaves the track section after the second stage adjustment;

[0021] Determine the actual operational constraints, including:

[0022] The actual departure time of each train from the station shall not be earlier than the scheduled time, and the actual arrival time at the station shall not be earlier than the scheduled time;

[0023] The actual travel time of each train in each section shall not be less than the shortest possible travel time, and the actual stop time at the station shall not be less than the required stop time.

[0024] Overtaking can only occur within a station, and two adjacent trains on the same section must maintain a certain headway.

[0025] Optionally, before solving the two-stage sub-Bruker train timetable optimization model, the following steps are also included:

[0026] The two-stage partial Brussels bar optimization model containing random variables is transformed into a semi-infinite programming two-stage partial Brussels bar optimization model without random variables. The semi-infinite programming two-stage partial Brussels bar optimization model without random variables is expressed as follows:

[0027]

[0028] st

[0029]

[0030] λ≥0

[0031] (b I , I )∈χ

[0032] in, Historical data set One of the samples, (b) I e I ) represents the planned timetable, bI and e I Q represents the time when each train enters and leaves its respective track section. I (b I e I ) is the planned timetable (b I e I The efficiency loss function of s n and As intermediate variables in the model transformation process, For a given planned timetable (b) I e I ) and known The total delay severity function, χ, is defined by operating regulations and safety constraints (b) I e I The feasible region of ).

[0033] Optionally, the iterative solution algorithm for the main design problem and subproblems includes:

[0034] Design a subproblem-solving model and obtain multiple vertices of the constraint parameters of the semi-infinite programming two-stage sub-Bruker optimization model through a hybrid programming solver;

[0035] The two-stage partial Brussels bar optimization model of the semi-infinite programming is transformed into a two-stage partial Brussels bar optimization model with finite constraints, and the main problem solution model is obtained.

[0036] The main problem is solved using the multiple vertices.

[0037] Optionally, the main problem-solving model includes a first type of constraint and a second type of constraint;

[0038] The first type of constraint is based on the Benders decomposition framework, with each pair of vertices corresponding to one constraint, and does not introduce new decision variables;

[0039] The second type of constraint is based on a row-column generation decomposition framework, with each vertex corresponding to a constraint, and introduces new decision variables that satisfy the constraints corresponding to the second-stage optimization model.

[0040] Optionally, solving the two-stage sub-Blu-ray train timetable optimization model includes the following steps:

[0041] Step S1: Determine the train departure sequence and initial arrival and departure timetable. Establish a sample mean approximation model based on historical train operation data. Solve the sample mean approximation model using mixed integer linear programming to obtain the initial train operation timetable.

[0042] Step S2: Set the solver initialization parameters by inputting the train departure sequence, initial arrival and departure timetable, and historical train operation data into the solver;

[0043] Step S3: Call the mixed integer programming solver to solve the subproblem solving model, obtain multiple vertices of the constraint parameters of the semi-infinite programming two-stage sub-Bruker optimization model, update the parameters of the mixed integer programming solver, and determine whether the iteration has terminated. If the iteration termination condition is met, execute step S5; otherwise, execute step S4.

[0044] Step S4: Input the multiple vertices into the linear programming solver to solve the main problem model, obtain a new train timetable, update the solver parameters, determine whether the iteration has terminated, and if the iteration termination condition is met, proceed to step S5; otherwise, return to step S3.

[0045] Step S5: Output the current train timetable.

[0046] A second aspect of this application discloses a train timetable compilation device based on a split-bar optimization model, the device comprising:

[0047] The model building module is used to build a data-driven two-stage sub-Browsing bar train timetable optimization model for the process of creating operation diagrams and rescheduling decisions.

[0048] The parameter input module is used to input the train route plan and historical train operation data into the two-stage sub-Blu-ray bar train timetable optimization model. The route plan includes: the set of trains to be scheduled, the route sections of each train, and the driving and stopping data of each train. The historical data is the actual driving data of each train in each driving section.

[0049] The model solving module is used to solve the two-stage sub-Bruker train timetable optimization model by designing iterative solving algorithms for the main problem and sub-problems, and obtain the train timetable plan.

[0050] Optionally, the model building module includes:

[0051] The first function construction module is used to construct the traffic efficiency loss function, wherein the decision vector of the traffic efficiency loss function is the time when each train enters each track section and the time when the train leaves the track section;

[0052] The first constraint determination module is used to determine the train operation constraints, including: the departure time of each train from the starting station must not be earlier than a given time; the travel time of each train in each section must not be less than the shortest possible travel time, and the stop time at the station must not be less than the required stopping time; overtaking can only occur within the station, and two adjacent trains in the same section must maintain a certain headway; the total running time of each train must not exceed the sum of the proportion of the shortest travel time and the proportion of the shortest stop time.

[0053] The embodiments of this application have the following advantages:

[0054] In this embodiment, a robust timetable is developed using limited historical travel time data when train travel time is uncertain. First, a data-driven, experience-distribution-centered 1-Wasserstein two-stage sub-Bruker train timetable optimization model is constructed for the timetable development and rescheduling decision-making process. This model aims to minimize the total train travel time and the total delay level. Then, iterative algorithms for solving the main problem and sub-problems are designed to solve the model, resulting in the planned train timetable. Because the model is a two-stage sub-Bruker optimization model based on the 1-Wasserstein distribution set, compared to models that use the experience distribution of historical data as the true probability distribution of travel time, this model maintains robustness in scenarios beyond historical data even with limited historical data. Compared to robust optimization models that do not use probability distribution information, this model achieves stronger robustness by extending the planned train travel time by less. Furthermore, by designing iterative algorithms for sub-problems and the main problem to solve the two-stage bibliometric optimization model, the infinite constraint programming problem that cannot be solved by general solvers can be solved, thus improving the solution efficiency. Attached Figure Description

[0055] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart of the steps of a train timetable compilation method based on a split-bar optimization model provided in this application embodiment;

[0057] Figure 2This application provides a flowchart of the steps for solving a two-stage split-Brow bar train timetable optimization model.

[0058] Figure 3 This is a schematic diagram of a train timetable compilation device based on a split-bar optimization model provided in an embodiment of this application. Detailed Implementation

[0059] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0060] In related technologies, methods for handling uncertain train running times fall into two main categories: one is stochastic programming methods. These methods assume the probability distribution of running times is known and then solve the optimization problem based on this. If the distribution function is complex, a sample mean approximation method is often used to approximate the original problem model. However, the probability distribution of running times is difficult to know; only limited historical data can be observed. If the model is approximated using the sample mean of historical data, the results may not perform well in scenarios outside of historical samples. The other category does not consider the probability distribution of running times, assuming that the probability distribution of running times is completely unknown. Robust optimization methods belong to this category. They assume that the values ​​of random parameters are in a given set and make optimization decisions based on the worst possible scenarios. Lightly robust methods belong to another category. These methods increase the robustness of the model by adding slack variables to the constraints. The model is simple, so it is relatively fast to solve. However, because these methods do not fully utilize probability distribution information, their results may require sacrificing significant traffic efficiency to improve timetable robustness.

[0061] The Partial Brutal Optimization method combines the ideas of stochastic programming and robust optimization. It assumes that the true distribution of the random parameters is unknown, but it is known that they belong to a set of distributions. Robust results are obtained by optimizing the performance under the worst distribution. Therefore, to overcome the limitations of existing technologies, the applicant proposes the following technical concept: Based on the Partial Brutal Optimization method, a two-stage model is proposed to balance train efficiency and robustness. The first stage decision is the time minutes included in the planned timetable, with the goal of minimizing the travel time while ensuring train safety. After the planned timetable is given, the second stage decision is the timetable adjustment to ensure train safety after a small disturbance occurs, with the goal of minimizing the deviation between the adjusted timetable and the planned timetable, i.e., minimizing the delay. An efficient solution method is designed for the characteristics of the model.

[0062] Based on the above technical concept, embodiments of this application provide a method for compiling train timetables based on a distributed bar optimization model, such as... Figure 1 As shown, Figure 1 A flowchart of a train timetable compilation method based on a split-bar optimization model provided in this application includes steps S101 to S103:

[0063] Step S101: For the timetable compilation and rescheduling decision-making process, construct a data-driven 1-Wasserstein two-stage sub-Brussels bar train timetable optimization model centered on experience distribution. The two-stage sub-Brussels bar train timetable optimization model aims to minimize the total travel time and total delay of trains.

[0064] In this embodiment, train timetable compilation refers to the compilation of train schedules, rescheduling decisions refer to the scheduling methods of trains within each operating section, and data-driven means that the model is built based on limited historical data. This robust optimization model based on the 1-Wasserstein distribution set, compared to traditional models that use the empirical distribution of historical data as the true probability distribution of travel time, can generate a planned train timetable that remains robust in scenarios outside of historical data even with limited historical data, meaning it exhibits less delay. Compared to other robust optimization models that do not use probability distribution information, it achieves stronger robustness by extending the planned train travel time by less.

[0065] Specifically, the two-stage sub-Blu-ray train timetable optimization model includes: a first-stage optimization model and a second-stage optimization model. For example, the two-stage sub-Blu-ray train timetable optimization model is expressed as:

[0066]

[0067] Where, minx∈x Q I (x) represents the model in the first optimization stage. For the second-stage optimization model, x represents the planned timetable, indicating the arrival and departure times of each train at each station in the timetable. χ is the feasible region of x as defined by operating regulations and safety constraints. Q I (x) represents the traffic efficiency loss function of the planned timetable x, ξ is a random vector representing the travel time of each train between adjacent stations, and Q II (x, ξ) represents the total degree of delay function given a planned timetable x and the known ξ. Let F represent a set of distribution functions, containing the empirical distribution F formed by N historical data points. N Centered on Ξ, with Ξ as the support set, and the Wasserstein distance not exceeding ε N The probability distribution function, specifically, in this embodiment, the support set Ξ is considered as a rectangular support set, that is... Where vector ξ This represents the lower bound of the running time of each train in each section. The upper boundary.

[0068] It should be noted that this embodiment addresses the problem of train timetable creation on a single-track line (either northbound or southbound). The set of all trains operating on this dedicated single-track line is used... This indicates that there is a series of stations on the dedicated single-track line, and the stations divide the dedicated single-track line into track sections. The set of all track sections is represented by [the symbol used in the original text]. This is used to represent the train's journey. The train departs from one station, stops at several stations along the way, and terminates at another station. To conform to practical application scenarios, this embodiment does not assume that the starting and ending stations of all trains are the first and last stations on a dedicated one-way line. The planned train stopping scheme has been given in the first stage of timetable development, including the starting station (first section f) of each train i. i Terminal station (last section l) i (and the stopping time at intermediate stops.) Let {f} represent the set of all intervals traversed by train i. i f i +1, ..., l i}, Let j represent the set of all trains that pass through section j. This represents all train-section pairs, i.e. The decision vector x in the first stage contains two parts: the time when train i enters track section j. and the time when train i leaves track section j The vector is represented as bI and e I In the second stage, the actual train travel time ξ is a random vector, with values ​​ranging from... Among them, the components of ξ are ξ i，j This represents the actual travel time of train i on interval j, which is a random variable, and its corresponding value range is... Suppose that N samples ξ are observable from historical operational data, which together form the historical dataset.

[0069] In this embodiment, the two-stage split-Blu-ray train timetable optimization model includes a first-stage optimization model and a second-stage optimization model. The construction of the two-stage split-Blu-ray train timetable optimization model includes: constructing the first-stage optimization model and constructing the second-stage optimization model.

[0070] (1) Constructing the first-stage optimization model. The first-stage optimization model aims to minimize the travel time while ensuring train safety. The construction of the first-stage optimization model includes: determining the train travel constraints and constructing the traffic efficiency loss function.

[0071] First, determine the constraints for train operation. Due to practical operational limitations and safety considerations, train operation needs to meet constraints A1 to A4:

[0072] A1: The departure time of each train from the starting station must not be earlier than the given time st. i ,Right now:

[0073]

[0074] A2: The travel time of each train in each section must not be less than the shortest possible travel time, and the stop time at each station must not be less than the required stopping time, that is:

[0075]

[0076]

[0077] Where, d i，j This represents the shortest stopping time for train i at the terminal station of section j. If the train does not stop at that station, then d i，j The value is 0.

[0078] A3: Overtaking can only occur within stations, and adjacent trains on the same section must maintain a certain interval. Therefore, for And i1≠i2, the following constraints should be satisfied:

[0079]

[0080]

[0081]

[0082] in, This is a 0-1 decision variable introduced for assistance. When it equals 1, it indicates that train i1 runs before train i2 in interval j. M is a sufficiently large number. It is the minimum allowed departure interval between trains i1 and i2 on section j. It is the minimum arrival interval.

[0083] A4: The total running time of all trains shall not exceed the sum of the proportion of the shortest travel time and the proportion of the shortest stop time, that is:

[0084]

[0085] Where c1 and c2 are given constants greater than 1.

[0086] Secondly, a traffic efficiency loss function is constructed, wherein the decision vector of the traffic efficiency loss function is the time when each train enters each track section and the time when the train leaves the track section.

[0087] Specifically, to ensure good solvability of the model, this embodiment assumes that the decision variable y is given, and an approximate solution can be obtained by solving a simpler model. When y is given, the train's running order on each section is determined; therefore, the set... It can be represented as an ordered set in Let $\frac{1}{j}$ represent the first train running on interval $j$, and so on. Considering the constraints from A1 to A4, the feasible region of the first-stage optimization model is... Represented as:

[0088]

[0089] Therefore, the first-stage traffic efficiency loss function Q I (x), that is, Q I (b I e I The first-stage traffic efficiency loss function consists of two parts: the dwell time of each train at its originating station, and the total travel time of each train. Therefore, the first-stage traffic efficiency loss function is expressed as:

[0090]

[0091] Where, r i and w i It is the set corresponding coefficient.

[0092] (2) Constructing the second-stage optimization model. The second-stage optimization model aims to minimize the deviation between the adjusted timetable and the planned timetable based on actual conditions. It includes: constructing the total delay degree function and determining the actual operating constraints.

[0093] First, a total delay severity function is constructed. The decision vector of the total delay severity function is the time when each train enters each track section and the time when each train leaves the track section after the second stage adjustment.

[0094] Specifically, the second phase of decision-making is based on a given planned timetable (b I , I Once the actual shortest travel time ξ is known, the adjusted train timetable aims to minimize the total delay time relative to the planned timetable. This embodiment considers small, random disturbances, as large disturbances could lead to severe delays or even cancellations. Therefore, large disturbances are better suited for complex rescheduling methods to regenerate the timetable. Including large disturbances could result in an overly conservative planned timetable, wasting railway resources. Under the premise of small disturbances, this embodiment assumes that the timetable adjustment follows a simple rule: the departure order of each train in each section remains unchanged from the original plan. If the original planned timetable is infeasible given the actual travel time ξ, the planned departure time is postponed to make the actual timetable safe and feasible.

[0095] The decision variables in the second stage include a vector b. II and e II , representing the start and end times of each train's journey on each route section after adjustment. For example, the total delay severity function for the second stage is expressed as:

[0096]

[0097] Secondly, the actual operational constraints must be determined. To ensure train safety, actual train operation must meet constraints B1 to B3:

[0098] B1: The actual departure time of each train from the station must not be earlier than the scheduled time, and the actual arrival time at the station must not be earlier than the scheduled time, that is:

[0099]

[0100]

[0101] B2: The actual travel time of each train in each section shall not be less than the shortest possible travel time, and the actual stop time at each station shall not be less than the required stop time, that is:

[0102]

[0103]

[0104] B3: Overtaking can only occur within a station, and two adjacent trains on the same section must maintain a certain headway.

[0105]

[0106]

[0107] The feasible region of the second stage, consisting of constraints B1 to B3, is available. express.

[0108] In an optional embodiment, since the two-stage sub-Blubar train timetable optimization model established in step S101 contains random variables and cannot be solved directly using a common solver, it is necessary to transform the two-stage sub-Blubar train timetable optimization model containing random variables into a semi-infinite programming two-stage sub-Blubar optimization model without random variables before solving the two-stage sub-Blubar train timetable optimization model.

[0109] For example, the two-stage partial blue bar optimization model of semi-infinite programming without random variables is expressed as:

[0110]

[0111] st

[0112]

[0113] λ≥0

[0114] (b I e I )∈χ

[0115] in, Historical data set One of the samples, (b) I e I ) represents the planned timetable, b I and e I These represent the times when each train enters and leaves each track section, respectively, QI(b) I e I ) is the planned timetable (b I e I The efficiency loss function of s n and As intermediate variables in the model transformation process, For a given planned timetable (b) I e I ) and known The total delay degree function under the following circumstances It is stipulated by operating regulations and safety constraints (b) I e I The feasible region of ).

[0116] In this embodiment, when the radius ε of the Wasserstein uncertainty set N When the value is not 0, it means that the empirical distribution of historical data differs from the actual distribution. Then, by solving the above-mentioned two-stage sub-Brussels bar optimization model without random variables, the optimal solution of the two-stage sub-Brussels bar optimization model can be obtained, which is the train schedule.

[0117] Step S102: Input the train route plan and historical train operation data into the two-stage sub-Blu-ray train timetable optimization model. The route plan includes: the set of trains to be scheduled, the route sections of each train, and the driving and stopping data of each train. The historical data is the actual driving data of each train in each driving section.

[0118] Since the problem involves creating train timetables for a specific dedicated railway line, the train route plan is known, i.e., the set of trains for which timetables need to be created. The route sections of each train Train travel and stopping data (stopping time of each train at stations along the route) (If train i does not stop at station j, then d) i，j Take 0), the earliest departure time allowed for each train at its first station. i The departure and arrival interval h of adjacent trains on the same section b h e All of these are known.

[0119] This embodiment is based on this and is a collection. The train schedule is determined by the planned arrival and departure times of each train at each station along its route. The travel time for each train on each section is uncertain and is based on N historical data points. Specifically, the train route plan and historical train operation data are input into a two-stage semi-infinite programming sub-Bruker optimization model without random variables to obtain the train schedule.

[0120] Step S103: Solve the two-stage sub-Bruker train timetable optimization model by designing iterative solution algorithms for the main problem and sub-problems to obtain the train timetable plan.

[0121] In this embodiment, solving the two-stage sub-Blule bar train timetable optimization model refers to solving a two-stage sub-Blule bar optimization model of a semi-infinite programming problem without random variables. Since the constraints in a two-stage sub-Blule bar optimization model of a semi-infinite programming problem without random variables are infinite, further algorithm design is required to enable a general solver to solve this model.

[0122] In one optional embodiment, the iterative solution algorithm for the main design problem and subproblems includes:

[0123] (1) Design a subproblem solving model and obtain multiple vertices of the constraint parameters of the semi-infinite programming two-stage sub-Bruker optimization model through a hybrid programming solver.

[0124] Specifically, the subproblem is to obtain the vertices of a polyhedron by using a mixed-integer programming solver. and vertex and (i.e., the vertices of the constraint parameters of the two-stage partial Bruker optimization model of semi-infinite programming), and an upper bound (UB) of the original problem, specifically, for each The subproblem n to be solved is:

[0125]

[0126] st

[0127]

[0128]

[0129]

[0130] in, It is optimal. The upper bound of . In the algorithm for the general two-stage split-Brussels model, it takes a sufficiently large number. Because the chosen . The smaller the value, the higher the efficiency of the solution. Therefore, this embodiment, considering the characteristics of the train timetable problem, designs a method for finding the compact value. The algorithm.

[0131] Enter a place, seek The algorithms include:

[0132] Before starting the algorithm, we first construct a directed graph. The method involves the length of the edge in the directed graph being related to the parameter b. I e I h b h eThe structure of a directed graph is related to ξ.

[0133] Node set Include Each node represents a decision variable for the first stage. and In a directed graph, there is a corresponding node vb. i，j and ve i，j In addition, there is a virtual node o.

[0134] The set of directed edges ε: There is an edge between node o and any other node, i.e., o→vb. i，j o→ve i，j The length of the side is and For any e i，j →vb i，j+1 There is a long side d i，j+1 Directed edges; for any vb i，j →ve i，j There is a line of length ξ i，j For any and Each has a length of and The directed edge.

[0135] If there is a directed path from node A to B in the graph, then A is called the upstream node of B and B is called the downstream node of A.

[0136] beg The algorithm specifically includes steps C1 to C3:

[0137] Input: The nth sample and the upper realm The train's running sequence y in each section, and a feasible planned train timetable b. I e I ;

[0138] C1: Construct graph G, for any gather Represents node ve i,j The set consisting of all its downstream nodes;

[0139] C2: For all Let the side lengths ξi and j in graph G be... Calculate the distance from point o to each node. The longest path, denoted as For all Let the side length ξ in graph G be...i，j Set as ξ i，j Calculate the distance from point o to each node. The longest path is denoted as l(o, v);

[0140] C3: sequentially Complete steps C31 to C34 as follows:

[0141] C31: Assignment

[0142] C32: For all Let the side length ξ in graph G be... i，j Set as Compute node vei,j to its downstream nodes The longest path, denoted as

[0143] C33: For any Execution step C331:

[0144] C331: If Then update Otherwise update

[0145] C34: sequentially Perform steps C341 to C342:

[0146] C341: For node vb i′，j′ ,if Established, or ve i′,j′ -1 and vb last(i′，j′)，j′ Both belong to D′ i，j Then update D′ i，j :D′ i，j ←D′ i，j ∪{vb i′，j′ C342: For node ve i,,j′ ,if Established, or VB i′，j′ and ve last(i′,j′),j′ Both belong to D′ i，j Then update D′ i，j :D′ i，j ←D′ i，j U{ve i′,j′ Otherwise, update.

[0147] Output:

[0148] In this embodiment, the algorithm used to solve the upper bound of the optimal solution of the subproblem narrows the feasible region of the subproblem by obtaining the parameters, thereby greatly shortening the solution time of the subproblem and improving the solution efficiency.

[0149] (2) The two-stage sub-Brubar optimization model of the semi-infinite programming is transformed into a two-stage sub-Brubar optimization model with finite constraints to obtain the main problem solution model.

[0150] Specifically, the main problem-solving model includes a first type of constraint and a second type of constraint;

[0151] The first type of constraint is based on the Benders decomposition framework, where each pair of vertices... It corresponds to one constraint and does not introduce new decision variables;

[0152] The second constraint is based on a row-column generation decomposition framework, where each vertex... Corresponding to a constraint, a new decision variable is introduced. The new decision variables satisfy the constraints corresponding to the second-stage optimization model.

[0153] In this embodiment, since the original optimization problem (a two-stage partial Brussels optimization model of semi-infinite programming) actually contains an infinite number of constraints, the main problem is a relaxation problem of the original optimization problem, containing only a limited number of constraints, and is a linear programming problem. In this embodiment, a commercial solver (such as CPLEX) is used to solve the main problem, yielding a feasible planned train timetable (b) for the original optimization problem. I e I ), and a lower bound (LB) for the original optimization problem.

[0154] For example, the main problem solution model is as follows:

[0155]

[0156] st

[0157] First type of constraint:

[0158] The second type of constraint:

[0159]

[0160] λ≥0

[0161] (b I e I )∈χ

[0162] Where Ωn represents a given pair of vertices. The set of subscripts, Given a rectangular polyhedron One of the vertices, Given the feasible region of the dual problem of the second-stage optimization problem. The vertices are all generated by solving subproblems. It is Ω n A subset of is the index of the vertices generated by the subproblem in the latest S-round iterations; the first constraint is based on the Benders decomposition framework, and each pair of vertices... The first type of constraint corresponds to one constraint and does not introduce new decision variables; the second type of constraint is based on a row-column generation decomposition framework, where each vertex... Corresponding to a constraint, a new decision variable is introduced. The new decision variables satisfy the constraints corresponding to the second-stage optimization model, and the second type of constraint... The larger the value of S, the longer the time required to compute the main problem in a single iteration, but the fewer times the main problem needs to be computed in an iterative algorithm. It is the objective function of the dual problem of the second-stage optimization problem.

[0163] Specifically, the expression for the dual problem of the second-stage optimization problem is as follows:

[0164]

[0165] st

[0166] The third type of constraint:

[0167]

[0168] The fourth type of constraint:

[0169]

[0170] p b p e p ξ p d ≥0

[0171] p hb p he ≥0

[0172] in, `a` is the indicator function; it takes the value 1 when A is true, and 0 otherwise. `last(i, j)` represents the index of the train preceding train `i` running on interval `j`. If train `i` is the first train in the interval, the decision variable containing the index `last(i, j)` in the constraint is 0. `next(i, j)` represents the index of the train following train `i` running on interval `j`. If train `i` is the last train in the interval, the decision variable containing the index `next(i, j)` in the constraint is 0. The objective function is... The expression is as follows:

[0173]

[0174] Among them, feasible region It is the set of decision variables that satisfy the third and fourth constraints, i.e.:

[0175] p that satisfies the third and fourth constraints b p e p ξ p d p hb p he}

[0176] (3) Solve the main problem model based on the multiple vertices.

[0177] Specifically, the solution includes the following steps D1 to D4:

[0178] D1: Input N historical data records The train departure sequence y in each section, an initial feasible timetable. The radius ε of the distribution set N ≥0, error control parameter ∈≥0, ∈ g ≥0, parameters of the main problem module

[0179] D2: Initialize parameters: λ←0, ω←0, s n ←+∞, gap n ←+∞, LB←-∞, UB←+∞;

[0180] D3: Perform the following steps sequentially until (UB-LB) / LB≤∈ and Iteration stops at time:

[0181] D31: Apply sequentially to all The algorithm in section 2-2-1) is used to find the answer. As a parameter of the subproblem;

[0182] D32: Apply sequentially to all Using a mixed-integer programming solver, solve for a given train timetable (b I e I The problem involves optimizing the subproblem n under parameter λ. The solver is configured to solve the problem when the objective function value exceeds s. n Time or error gap n When = 0, the solution is interrupted, and a feasible solution p and γ for the subproblem are obtained, denoted as . and Then according to calculate if but Otherwise, it is 0. Furthermore, the objective function value at the time of interruption can also be obtained from the solver's output. and the error gap during interruption n ;

[0183] D33: For all Update Ω n ←Ω n ∪{ω};

[0184] D34: Update

[0185] D35: If (UB-LB) / LB≤∈and Then proceed to step D4;

[0186] D36: Using existing vertices, solve for parameters Ωn and The main problem is to obtain a new feasible train timetable (b) I e I ), and (s, λ);

[0187] D37: Update

[0188] D38: ω←ω+1;

[0189] D4: Output the planned timetable (b I e I ).

[0190] In this embodiment, the main problem uses a combination of two constraints in utilizing the vertices generated by the subproblems. The advantage of the first constraint is that it does not introduce new decision variables, making the solution to the main problem faster. The advantage of the second constraint is that the solution obtained by the main problem is closer to the optimal solution of the original problem, and the lower bound is larger, thus enabling the main-subproblem iterative algorithm to converge in fewer iterations. Therefore, the combination of these two constraints in this embodiment can combine their advantages, thereby enabling the overall algorithm to converge at a faster speed.

[0191] In this embodiment, for the two-stage sub-Bruker optimization model of semi-infinite programming, an algorithm is designed to obtain the optimal solution with an error within ∈ by iteratively solving the subproblems and the main problem, that is, to obtain the optimal schedule (b) with an error within ∈. I e I ).

[0192] In one alternative embodiment, such as Figure 2 As shown, the solution to the two-stage sub-Blu-ray train timetable optimization model includes steps S1 to S5:

[0193] Step S1: Determine the train departure sequence and initial arrival and departure timetable. Establish a sample mean approximation model based on historical train operation data. Solve the sample mean approximation model using mixed integer linear programming to obtain the initial train operation timetable.

[0194] In this embodiment, to ensure the two-stage Brussels-Barred train timetable optimization model has good solvability, the train departure order y is given. An approximate solution is obtained by solving a simpler model to determine the departure order y. Specifically, when the Wasserstein radius of the distribution set is 0, the two-stage Brussels-Barred train timetable optimization model degenerates into a sample mean approximation model. This is based on historical train operation data. Establish a sample mean approximation model, which is expressed as follows:

[0195]

[0196] st satisfies constraints A1 to A4.

[0197]

[0198] Then, mixed-integer linear programming is used to solve the approximate model of the sample mean. When the model is large, i.e., the number of samples, vehicles, or intervals is large, the solution time may be too long. In this case, obtaining a satisfactory feasible solution is sufficient. Specifically, an optimal gap can be set in the solver. When the solver obtains a feasible solution that satisfies the optimal gap, the solver will stop and output the feasible solution: y and (b I e I )'. Where y is the train departure sequence, (b I e I )' is the initial train timetable. In subsequent steps, the initial train timetable is optimized to obtain the final train timetable.

[0199] Step S2: Set the solver initialization parameters by inputting the train departure sequence, initial arrival and departure timetable, and historical train operation data into the solver.

[0200] First, input the following into the solver: the departure sequence y of each train on each section and the initial train timetable (b). I e I )′, N historical data The radius ε of the set N ≥0, error control parameter ∈≥0, ∈ g ≥0, parameters of the main problem module

[0201] Then, set the solver initialization parameters: λ←0, ω←0. s n ←+∞, gap n ←+∞, LB←-∞, UB←+∞.

[0202] Step S3: Call the mixed integer programming solver to solve the subproblem solving model, obtain multiple vertices of the constraint parameters of the semi-infinite programming two-stage sub-Bruker optimization model, update the parameters of the mixed integer programming solver, and determine whether the iteration has terminated. If the iteration termination condition is met, execute step S5; otherwise, execute step S4.

[0203] In this embodiment, a mixed-integer programming solver is used to solve all subproblems sequentially. To solve for the initial train timetable (b) I e I The optimization problem of subproblem n under parameter λ.

[0204] First, the solution for the vertices includes (1) to (3):

[0205] (1) The mixed-integer programming solver is set as follows: when the objective function value exceeds s n Time or error gap n When = 0, the solution is interrupted;

[0206] (2) The output of the mixed-integer programming solver is: the objective function value at the time of interruption. and the error gap during interruption n A feasible solution p and γ to the subproblem is denoted as p. and (i.e., the vertex);

[0207] (3) Output result processing: According to calculate if but Otherwise, it is 0.

[0208] Then, update the parameters of the mixed-integer programming solver and determine whether the iteration terminates, including

[0209] For all subproblems Update Ω n ←Ω n ∪{ω};

[0210]

[0211]

[0212] If (UB-LB) / LB≤∈and End the algorithm and proceed to step S5; otherwise, proceed to step S4.

[0213] Step S4: Input the multiple vertices into the linear programming solver to solve the main problem model, obtain a new train timetable, update the solver parameters, determine whether the iteration has terminated, if the iteration termination condition is met, execute step S5, otherwise return to step S3.

[0214] First, based on the multiple vertices obtained in step S3 and The solution is obtained using a linear programming solver, specifically by solving for the parameter Ω. n and The main problem is to solve a new feasible train timetable (b). I e I ), and (s, λ).

[0215] Then, update the solver parameters and determine whether the iteration has terminated, including:

[0216] ω←ω+1;

[0217] If (UB-LB) / LB≤∈, and End the algorithm and proceed to step S5; otherwise, return to step S3.

[0218] Step S5: Output the current train timetable (b I e I ).

[0219] In this embodiment, the final output of the current train timetable (b) I e I ), is in the initialization of the initial train timetable (b I e I The train timetable (b) is obtained by optimizing the existing timetable. I e I It can better balance traffic efficiency and robustness.

[0220] For example, an experiment was conducted using the Xuzhou East-Shanghai Hongqiao section of the high-speed railway as an example. This section has 12 stops. The stop schedules of all trains passing through a certain section of the Xuzhou East-Shanghai Hongqiao line on a Saturday were obtained from 12306. If a train stops at a certain station, the minimum stop time is set to 2 minutes, i.e., d. i，j =2, the shortest departure and arrival interval h between adjacent trains b and h e All are 8 minutes. Based on the train end times displayed on 12306 for the Xuzhou East-Shanghai Hongqiao section, the trains are sorted in ascending order, and the first 10, 20, 40, 60, and 80 trains are selected respectively to generate timetable formulation problems of different scales.

[0221] Unlike algorithms designed for typical two-stage biscrow optimization models, this embodiment accelerates the algorithm in two aspects: in the subproblems The parameter M is not arbitrarily chosen as a sufficiently large number, but rather calculated through a designed algorithm. Using this parameter in subproblems can significantly reduce their time complexity. The main problem employs a hybrid approach of two constraints (i.e., the first and second constraints), which reduces the overall time of the iterative algorithm compared to using only one constraint, i.e., setting S to 0 or +∞. Table 1 shows the solution time (in seconds) of the algorithm for problems of different sizes. The solution time is limited to 3 hours. If the algorithm fails to converge after 3 hours, the optimal gap of the currently found solution is output (shown in parentheses in the table). Table 1 demonstrates that the improvement to the main problem (i.e., S not being 0 or ∞) is effective at medium-sized problems, and the improvement to the subproblems... Choosing a constant M that is not arbitrarily large can significantly improve the solution performance of the model. When the problem size is large, such as the example of 40 or 60 trains, the algorithm cannot converge within 3 hours without improvement, but with improvement, the convergence time is less than 50% of 3 hours.

[0222] Table 1: Performance comparison of algorithm improvements under different sample sizes

[0223]

[0224] Taking 10 trains as an example, Table 2 shows the performance of timetables generated by different models on test samples outside of historical samples under different real-world distributions, addressing the uncertainty of travel time. Both test samples and historical samples are sampled from the same distribution. In the table, AVE represents the average objective function value of the timetable on the test samples, and Q90 represents the objective function value of the timetable on the 90th best test sample (for example, with 50 test samples, the performance of a given timetable on these 50 test samples corresponds to 50 objective function values; these are sorted from smallest to largest, and the 45th value is output). In Table 2, SAA represents the sample mean approximation model, RO represents the robust optimization model, LR represents the lightly robust model, and DR is the two-stage sub-robust train timetable optimization model of this embodiment. As can be seen from Table 2, the timetable obtained by the two-stage sub-robust train timetable optimization model of this embodiment performs better on test samples outside of historical samples and has stronger robustness.

[0225] Table 2: Performance of different models on test samples

[0226]

[0227] In this embodiment, a robust timetable is developed using limited historical travel time data when train travel time is uncertain. First, a data-driven, experience-based 1-Wasserstein two-stage sub-Bruker robust train timetable optimization model is constructed for the timetable development and rescheduling decision-making process. This model aims to minimize the total train travel time and the total delay level. Then, iterative algorithms for solving the main problem and sub-problems are designed to solve the model, resulting in the planned train timetable. Because the model is a two-stage sub-Bruker optimization model based on the 1-Wasserstein distribution set, compared to models that use the experience distribution of historical data as the true probability distribution of travel time, this model maintains robustness in scenarios outside of historical data, i.e., lower delay levels, even with limited historical data. Compared to robust optimization models that do not use probability distribution information, this model achieves stronger robustness by extending the planned train travel time less. Furthermore, by designing iterative algorithms for subproblems and the main problem to solve the model, the infinitely constrained programming problem that cannot be solved by general solvers can obtain the optimal solution by solving a linear programming main problem and a mixed integer programming subproblem through multiple rounds of iteration, thus saving solution time.

[0228] Specifically, compared to models that do not use historical data, the timetable obtained by the method in this embodiment can avoid unnecessary extensions in travel time. The robustness of the train timetable is achieved by adding an appropriate buffer time to the timetable, allowing sufficient time to avoid potential delays. Historical data can partially reflect the actual travel time; utilizing this information allows for more targeted allocation of travel time, resulting in a higher conversion rate of sacrificing efficiency for robustness.

[0229] Compared to directly using empirical distributions as the true distribution, the train timetable obtained in this embodiment remains robust in extended scenarios beyond historical data. Traditional methods utilizing historical data treat the empirical distribution formed by historical data as the true probability distribution of travel times. When the amount of data is small, the difference between the empirical distribution and the true distribution is significant. This leads to timetables obtained using this traditional method performing poorly for disturbances that may occur but have not historically occurred, resulting in severe delays. The two-stage partially robust train timetable optimization model in this embodiment fills this gap. By assuming that the distance between the true distribution and the empirical distribution does not exceed a given radius, the model maintains good robustness in the face of uncertainties not reflected in historical data.

[0230] By designing a decomposition algorithm (main problem and subproblems), an infinitely constrained programming problem that is unsolvable by general solvers can be solved by iteratively solving a linear programming main problem and a mixed integer programming subproblem to obtain the optimal solution. The proposed algorithm for finding the upper bound of the optimal solution of the subproblems narrows the feasible region of the subproblems, thus significantly reducing the solution time and improving efficiency. In utilizing the vertices generated by the subproblems, the main problem employs a hybrid approach to constraints. The first constraint avoids introducing new decision variables, resulting in a faster solution to the main problem. The second constraint provides a solution closer to the optimal solution of the original problem, yielding a larger lower bound, allowing the iterative algorithm to converge in fewer iterations. This hybrid use of constraints combines their advantages, enabling the overall algorithm to converge quickly.

[0231] This application also provides a train timetable compilation device based on a split-bar optimization model, such as... Figure 3 As shown, Figure 3 A schematic diagram of a train timetable compilation device based on a split-bar optimization model provided in this application embodiment, the device comprising:

[0232] Model building module 31 is used to build a data-driven 1-Wasserstein two-stage sub-Brussels bar train timetable optimization model centered on experience distribution for the process of train chart compilation and rescheduling decision-making. The two-stage sub-Brussels bar train timetable optimization model aims to minimize the total travel time and total delay of trains.

[0233] The parameter input module 32 is used to input the train route plan and historical train operation data into the two-stage sub-Blu-ray bar train timetable optimization model. The route plan includes: the set of trains to be scheduled, the route sections of each train, and the driving and stopping data of each train. The historical data is the actual driving data of each train in each driving section.

[0234] The model solving module 33 is used to solve the two-stage sub-Bruker train timetable optimization model by designing iterative solving algorithms for the main problem and sub-problems, and to obtain the train timetable plan.

[0235] In one optional embodiment, the model building module includes:

[0236] The first function construction module is used to construct the traffic efficiency loss function, wherein the decision vector of the traffic efficiency loss function is the time when each train enters each track section and the time when the train leaves the track section;

[0237] The first constraint determination module is used to determine the train operation constraints, including: the departure time of each train from the starting station must not be earlier than a given time; the travel time of each train in each section must not be less than the shortest possible travel time, and the stop time at the station must not be less than the required stopping time; overtaking can only occur within the station, and two adjacent trains in the same section must maintain a certain headway; the total running time of each train must not exceed the sum of the proportion of the shortest travel time and the proportion of the shortest stop time.

[0238] In one optional embodiment, the model building module includes:

[0239] The second function construction module is used to construct the total delay severity function, wherein the decision vector of the total delay severity function is the time when each train enters each track section and the time when each train leaves the track section after the second stage adjustment.

[0240] The second constraint determination module is used to determine the actual operating constraints, including: the actual time of departure from the station for each train must not be earlier than the planned time, and the actual time of arrival at the station must not be earlier than the planned time; the actual travel time of each train in each section must not be less than the shortest possible travel time, and the actual stop time at the station must not be less than the required stop time; overtaking can only occur within the station, and two adjacent trains in the same section must maintain a certain headway.

[0241] In one optional embodiment, the model solving module includes:

[0242] The subproblem module is used to design the subproblem solution model and obtain multiple vertices of the constraint parameters of the semi-infinite programming two-stage sub-Bruker optimization model through a hybrid programming solver.

[0243] The main problem module is used to transform the two-stage sub-Brussels bar optimization model of the semi-infinite programming into a two-stage sub-Brussels bar optimization model with finite constraints, thereby obtaining the main problem solution model;

[0244] The calculation module is used to solve the main problem solution model based on the multiple vertices.

[0245] In one optional embodiment, the main problem module includes:

[0246] The first submodule is used to determine the first type of constraint based on the Benders decomposition framework, where each pair of vertices corresponds to one constraint, and no new decision variables are introduced.

[0247] The second submodule is used to determine the second type of constraint based on the row and column generation decomposition framework, where each vertex corresponds to a constraint, and to introduce new decision variables that satisfy the constraints corresponding to the second-stage optimization model.

[0248] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0249] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0250] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0251] The above provides a detailed description of the train timetable compilation method and apparatus based on the sub-Bruker optimization model provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for compiling train timetables based on a distributed bar optimization model, characterized in that, This method is used to create train timetables for dedicated single-track lines. The set of all trains operating on the dedicated single-track line is denoted by I. The dedicated single-track line has a series of stations, which divide the line into track sections, and the set of all track sections is denoted by J. Trains originate from a station, stop at several stations along the way, and terminate at another station. To conform to practical application scenarios, it is not assumed that the starting and ending stations of all trains are the first and last stations on the dedicated single-track line. The method includes: To address the timetable creation and rescheduling decision-making process, a data-driven, experience-distribution-centered 1-Wasserstein two-stage sub-Brussels timetable optimization model is constructed. This model aims to minimize the total travel time and total delays of trains. Train route plans and historical train operation data are input into the model. The route plans include: the set of trains to be scheduled, the routes of each train, and the travel and stopping data for each train. The historical data consists of the actual travel data of each train within each travel section. By designing iterative solutions for the main problem and sub-problems, the two-stage sub-Bruker train timetable optimization model is solved to obtain the train timetable plan. The first stage of the two-stage decomposed train timetable optimization model aims to minimize travel time while ensuring operational safety. The planned train stop schedules are provided in the first stage of timetable development, including information for each train. The first interval The last interval And the stopping time at intermediate stops; Indicates train The set of all intervals traversed. , Indicates passing through the train section The collection of all trains, the collection This represents all train-section pairs, i.e. ; Decision vector for the first stage The decision-making process includes two parts: train Entering the orbital section The moment and trains Leaving the orbital section The moment , The vector is represented as and Constructing the first-stage optimization model includes: A traffic efficiency loss function is constructed, wherein the decision vector of the traffic efficiency loss function is the time when each train enters each track section and the time when the train leaves the track section; the traffic efficiency loss function consists of two items: the dwell time of each train at its originating station and the total travel time of each train. Determine the constraints for train operation, including: Each train must not depart from the initial station earlier than the given time. The travel time of each train in each section shall not be less than the shortest possible travel time, and the stop time at the station shall not be less than the required stop time. Overtaking is only allowed within stations, and two adjacent trains on the same section must maintain a certain interval. The total running time of all trains shall not exceed the sum of the proportion of the shortest travel time and the proportion of the shortest stop time; The second stage of the two-stage timetable optimization model aims to minimize the deviation between the adjusted timetable and the planned timetable based on actual conditions. In the second stage, the actual train travel time... It is a random vector with a value range of 1. ,in, The amount It refers to a train. In the interval The actual driving time is a random variable, and its corresponding range of values ​​is... It can be observed from historical operational data. N strip The samples, which together form the historical dataset. Construct the second-stage optimization model, including: Construct a total delay severity function, the decision vector of which is the time when each train enters each track section and the time when each train leaves the track section after the second stage adjustment; Determine the actual operational constraints, including: The actual departure time of each train from the station shall not be earlier than the scheduled time, and the actual arrival time at the station shall not be earlier than the scheduled time; The actual travel time of each train in each section shall not be less than the shortest possible travel time, and the actual stop time at the station shall not be less than the required stop time. Overtaking is only allowed within stations, and two adjacent trains on the same section must maintain a certain interval. Solving the two-stage sub-Blu-ray train timetable optimization model involves the following steps: Step S1: Determine the train departure sequence and initial arrival and departure timetable. Establish a sample mean approximation model based on historical train operation data. Solve the sample mean approximation model using mixed integer linear programming to obtain the initial train operation timetable. Step S2: Set the solver initialization parameters by inputting the train departure sequence, initial train timetable, and historical train operation data into the solver; Step S3: Call the mixed integer programming solver to solve the subproblem solving model, obtain multiple vertices of the constraint parameters of the semi-infinite programming two-stage sub-Bruker optimization model, update the parameters of the mixed integer programming solver, and determine whether the iteration has terminated. If the iteration termination condition is met, execute step S5; otherwise, execute step S4. Step S4: Input the multiple vertices into the linear programming solver to solve the main problem model, obtain a new train timetable, update the solver parameters, determine whether the iteration has terminated, and if the iteration termination condition is met, proceed to step S5; otherwise, return to step S3. Step S5: Output the current train timetable. In the initial train timetable The current train timetable is obtained through optimization based on the existing timetable. It can better balance traffic efficiency and robustness.

2. The method according to claim 1, characterized in that, The two-stage sub-Bluerg train timetable optimization model includes: a first-stage optimization model and a second-stage optimization model. The two-stage sub-Bluerg train timetable optimization model is expressed as follows: in, This is the model for the first optimization stage. For the second stage of model optimization, This is a planned timetable, indicating the arrival and departure times of each train at each station in the timetable. It is stipulated by operating regulations and safety constraints regarding feasible domain, Indicates the planned timetable The traffic efficiency loss function, It is a random vector representing the travel time of each train between adjacent stations. Indicates a given planned timetable With known The total delay degree function under the following circumstances Describe a set of distribution functions, containing... Empirical distribution formed by historical data Centered on, with For the support set, the Wasserstein distance does not exceed The probability distribution function.

3. The method according to claim 1, characterized in that, Before solving the two-stage sub-Blu-ray train timetable optimization model, the following steps are also included: The two-stage partial Brussels bar optimization model containing random variables is transformed into a semi-infinite programming two-stage partial Brussels bar optimization model without random variables. The semi-infinite programming two-stage partial Brussels bar optimization model without random variables is expressed as follows: st in, Historical data set One of the samples, For the planned timetable, and These are the times when each train enters and leaves each track section. For the planned timetable The efficiency loss function, and As intermediate variables in the model transformation process, Given a planned timetable and known The total delay degree function under the following circumstances It is stipulated by operating regulations and safety constraints. The feasible domain.

4. The method according to claim 3, characterized in that, The iterative solution algorithm for the main design problem and its subproblems includes: Design a subproblem-solving model and obtain multiple vertices of the constraint parameters of the semi-infinite programming two-stage sub-Bruker optimization model through a hybrid programming solver; The two-stage partial Brussels bar optimization model of the semi-infinite programming is transformed into a two-stage partial Brussels bar optimization model with finite constraints, and the main problem solution model is obtained. The main problem is solved using the multiple vertices.

5. The method according to claim 4, characterized in that, The main problem-solving model includes a first type of constraint and a second type of constraint; The first type of constraint is based on the Benders decomposition framework, with each pair of vertices corresponding to one constraint, and does not introduce new decision variables; The second type of constraint is based on a row-column generation decomposition framework, with each vertex corresponding to a constraint, and introduces new decision variables that satisfy the constraints corresponding to the second-stage optimization model.

6. A train timetable compilation device based on a distributed bar optimization model, characterized in that, This device is used to create train timetables on dedicated single-track lines. The set of all trains operating on the dedicated single-track line is denoted by I. The dedicated single-track line has a series of stations, which divide the line into track sections, and the set of all track sections is denoted by J. Trains originate from a station, stop at several stations along the way, and terminate at another station. To conform to practical application scenarios, it is not assumed that the starting and ending stations of all trains are the first and last stations on the dedicated single-track line. The device includes: The model building module is used to construct a data-driven, experience-distribution-centered 1-Wasserstein two-stage sub-Brussels bar train timetable optimization model for the process of train chart compilation and rescheduling decision-making. The two-stage sub-Brussels bar train timetable optimization model aims to minimize the total train travel time and the total delay degree. The parameter input module is used to input the train route plan and historical train operation data into the two-stage sub-Blu-ray bar train timetable optimization model. The route plan includes: the set of trains to be scheduled, the route sections of each train, and the driving and stopping data of each train. The historical data is the actual driving data of each train in each driving section. The model solving module is used to solve the two-stage sub-Bruker train timetable optimization model by designing iterative solving algorithms for the main problem and sub-problems, and to obtain the train timetable plan. The first stage of the two-stage decomposed train timetable optimization model aims to minimize travel time while ensuring operational safety. The planned train stop schedules are provided in the first stage of timetable development, including information for each train. The first interval The last interval And the stopping time at intermediate stops; Indicates train The set of all intervals traversed. , Indicates passing through the train section The collection of all trains, the collection This represents all train-section pairs, i.e. ; Decision vector for the first stage The decision-making process includes two parts: train Entering the orbital section The moment and trains Leaving the orbital section The moment , The vector is represented as and Constructing the first-stage optimization model includes: A traffic efficiency loss function is constructed, wherein the decision vector of the traffic efficiency loss function is the time when each train enters each track section and the time when the train leaves the track section; the traffic efficiency loss function consists of two items: the dwell time of each train at its originating station and the total travel time of each train. Determine the constraints for train operation, including: Each train must not depart from the initial station earlier than the given time. The travel time of each train in each section shall not be less than the shortest possible travel time, and the stop time at the station shall not be less than the required stop time. Overtaking is only allowed within stations, and two adjacent trains on the same section must maintain a certain interval. The total running time of all trains shall not exceed the sum of the proportion of the shortest travel time and the proportion of the shortest stop time; The second stage of the two-stage timetable optimization model aims to minimize the deviation between the adjusted timetable and the planned timetable based on actual conditions. In the second stage, the actual train travel time... It is a random vector with a value range of 1. ,in, The amount It refers to a train. In the interval The actual driving time is a random variable, and its corresponding range of values ​​is... It can be observed from historical operational data. N strip The samples, which together form the historical dataset. Construct the second-stage optimization model, including: Construct a total delay severity function, the decision vector of which is the time when each train enters each track section and the time when each train leaves the track section after the second stage adjustment; Determine the actual operational constraints, including: The actual departure time of each train from the station shall not be earlier than the scheduled time, and the actual arrival time at the station shall not be earlier than the scheduled time; The actual travel time of each train in each section shall not be less than the shortest possible travel time, and the actual stop time at the station shall not be less than the required stop time. Overtaking is only allowed within stations, and two adjacent trains on the same section must maintain a certain interval. Solving the two-stage sub-Blu-ray train timetable optimization model involves the following steps: Step S1: Determine the train departure sequence and initial arrival and departure timetable. Establish a sample mean approximation model based on historical train operation data. Solve the sample mean approximation model using mixed integer linear programming to obtain the initial train operation timetable. Step S2: Set the solver initialization parameters by inputting the train departure sequence, initial train timetable, and historical train operation data into the solver; Step S3: Call the mixed integer programming solver to solve the subproblem solving model, obtain multiple vertices of the constraint parameters of the semi-infinite programming two-stage sub-Bruker optimization model, update the parameters of the mixed integer programming solver, and determine whether the iteration has terminated. If the iteration termination condition is met, execute step S5; otherwise, execute step S4. Step S4: Input the multiple vertices into the linear programming solver to solve the main problem model, obtain a new train timetable, update the solver parameters, determine whether the iteration has terminated, and if the iteration termination condition is met, proceed to step S5; otherwise, return to step S3. Step S5: Output the current train timetable. In the initial train timetable The current train timetable is obtained through optimization based on the existing timetable. It can better balance traffic efficiency and robustness.

7. The apparatus according to claim 6, characterized in that, The model building module includes: The first function construction module is used to construct the traffic efficiency loss function, wherein the decision vector of the traffic efficiency loss function is the time when each train enters each track section and the time when the train leaves the track section; The first constraint determination module is used to determine the train operation constraints, including: the departure time of each train from the starting station must not be earlier than a given time; the travel time of each train in each section must not be less than the shortest possible travel time, and the stop time at the station must not be less than the required stopping time; overtaking can only occur within the station, and two adjacent trains in the same section must maintain a certain headway; the total running time of each train must not exceed the sum of the proportion of the shortest travel time and the proportion of the shortest stop time.

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