Extra high-speed train arrangement method and apparatus taking passenger demands under time window constraint into consideration

Abstract

Provided in the present application are an extra high-speed train arrangement method and apparatus taking passenger demands under a time window constraint into consideration. The method comprises: constructing a first extra train arrangement optimization model with the goal of maximizing profits, and constructing a second extra train arrangement optimization model with the goal of meeting passenger travel demands to the greatest possible extent; determining constraint conditions, and acquiring overflow passenger travel demands and existing train operation data, wherein the passenger travel demands comprise riding time windows and riding departure and arrival demands, and the existing train operation data comprises train routes, a train stop scheme set and train section operation times; and on the basis of the constraint conditions, the passenger travel demands and the train operation data, respectively solving the first extra train arrangement optimization model and the second extra train arrangement optimization model, so as to obtain a first extra train arrangement scheme and a second extra train arrangement scheme. Therefore, an extra train arrangement scheme which takes economic benefits into consideration and meets passenger travel demands is achieved.

Description

Method and device for increasing high-speed train operation with time window constraints considering passenger demand

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to a Chinese patent application filed with the Patent Office of China on December 26, 2023, with application number 202311807883.2 and entitled “Method and device for increasing the number of high-speed trains with time window constraints considering passenger demand”, the entire contents of which are incorporated by reference in this disclosure. Technical Field

[0003] The present application relates to the field of railway operation diagram compilation, and in particular to a method and device for increasing the operation of high-speed trains with time window constraints taking into account passenger demand. Background Art

[0004] High-speed rail timetables are closely aligned with passenger travel needs and are crucial for ensuring a high-quality travel experience. Typically, high-speed rail timetables are developed before ticket sales open and adjusted as necessary based on actual passenger flow during the ticket sales period. Given the high priority of passenger trains, when passenger travel needs cannot be met, timetable adjustments typically do not involve canceling existing trains. Instead, additional trains are added to accommodate excess passenger demand.

[0005] High-speed rail is a public service, prioritizing passenger travel needs. However, high-speed rail is currently generally operating at a loss, and the railway sector's economic benefits must also be considered when compiling and adjusting timetables.

[0006] In related technologies, for the problem of scheduling additional trains on an existing timetable, the traffic capacity management algorithm uses the desired train schedule and a tolerable error as input, and provides a timetable adjustment plan that maximizes overall benefits by weighing the benefits of the service and the gap between the actual schedule and the operator's desired schedule. Additional train service scheduling technology allows the timetable of existing trains to be modified, introducing time window constraints on their actual departure times, and adding trains on this basis. However, in actual operation, the departure times of existing trains are basically not modified; and passenger demand has time window constraints. Passengers will only choose to travel on this train when the train's departure time is within the time window. Therefore, the existing method of adding trains is difficult to truly meet passenger travel needs and ignores the economic benefits of the railway sector. Summary of the Invention

[0007] In view of the above problems, an embodiment of the present application provides a method and device for increasing the number of high-speed trains with time window constraints taking into account passenger demand, so as to overcome the above problems or at least partially solve the above problems.

[0008] In a first aspect of an embodiment of the present application, a method for increasing the number of high-speed trains with time window constraints considering passenger demand is disclosed, the method comprising:

[0009] Constructing a first train increase optimization model with the goal of maximizing profits, and a second train increase optimization model with the goal of maximizing passenger travel needs;

[0010] Determine constraints, and obtain overflow passenger travel demand and existing train operation data, wherein the passenger travel demand includes a boarding time window and a boarding departure and arrival demand, and the existing train operation data includes a train route, a train stop plan set, and a train interval operation time;

[0011] According to the constraints, the passenger travel demand and the train operation data, the first train increase optimization model and the second train increase optimization model are solved respectively to obtain a first train increase plan and a second train increase plan.

[0012] Optionally, an optimization model for increasing the number of first trains with the goal of maximizing profit is constructed, including:

[0013] Constructing a first sub-model based on train operation costs and passenger ticket revenue, wherein the first sub-model aims to maximize profits;

[0014] constructing a second sub-model based on the time when the train arrives at the station, the time when the train leaves the station, and the selected train stop plan, wherein the second sub-model aims to minimize the total travel time;

[0015] The first train increase optimization model is obtained according to the first sub-model and the second sub-model.

[0016] Optionally, an optimization model for adding a second train with the goal of maximizing passenger travel demand is constructed, including:

[0017] A third sub-model is constructed based on the number of reserved tickets for the train, wherein the third sub-model aims to maximize the satisfaction of passenger travel needs;

[0018] constructing a fourth sub-model according to the selected train stop plan, wherein the fourth sub-model aims to minimize the number of additional trains;

[0019] constructing a fifth sub-model according to the time when the train arrives at the station, the time when the train leaves the station, and the selected train stop plan, wherein the fifth sub-model aims to minimize the total travel time;

[0020] The second train increase optimization model is obtained according to the third sub-model, the fourth sub-model and the fifth sub-model.

[0021] Optionally, determine constraints, including:

[0022] determining a stop plan constraint condition, wherein the stop plan constraint condition is used to constrain each train to select only one train stop plan from the train stop plan set;

[0023] Determining timetable constraints, wherein the timetable constraints are used to constrain the time when a train arrives at a station, the time when a train leaves a station, and the time when a train runs between stations;

[0024] Determining a passenger travel time window constraint condition, wherein the passenger travel time window constraint condition is used to constrain the matching relationship between the train and the passenger travel demand;

[0025] Determining a ticket allocation constraint condition, wherein the ticket allocation constraint condition is used to constrain the relationship between the number of tickets reserved for a train and the number of passengers traveling;

[0026] A train sequence constraint condition is determined, where the train sequence constraint condition is used to constrain the activation sequence of trains.

[0027] Optionally, the schedule constraints include:

[0028] The time when the train arrives at the station cannot be later than the start time of maintenance, and the time when the train leaves the station cannot be earlier than the end time of maintenance;

[0029] The duration of the stop between the time the train arrives at the station and the time the train leaves the station cannot be less than the shortest stop duration and cannot be greater than the longest stop duration;

[0030] The train interval running time between the time when the train leaves the station and the time when the train arrives at the next station cannot be less than the shortest train interval running time and cannot be greater than the longest train interval running time;

[0031] The departure interval between two adjacent trains cannot be less than the shortest departure interval, and the arrival interval between two adjacent trains cannot be less than the shortest arrival interval.

[0032] Optionally, the passenger travel time window constraint includes:

[0033] When the train's stop stations match the departure and arrival requirements, and the train's stop time window matches the boarding time window, the train meets the passengers' travel needs.

[0034] Optionally, the ticket allocation constraints include:

[0035] The number of tickets reserved for a train does not exceed the number of passengers required;

[0036] The number of passenger demands satisfied by the train does not exceed the capacity of the train;

[0037] The number of tickets reserved for a train is non-zero if and only if the train's stop stations match the boarding departure and arrival requirements and the train's stop time window matches the boarding time window.

[0038] Optionally, solving the first train increase optimization model according to the constraint conditions, the passenger travel demand, and the train operation data includes:

[0039] Solving the first sub-model according to the constraints, the passenger travel demand, and the train operation data to obtain a first optimal solution, the first optimal solution including: a stop plan of the first additional train, a travel order of the first additional train, and a number of tickets provided by the first additional train to meet the passenger travel demand;

[0040] Substitute the first optimal solution into the second sub-model for solution to obtain the timetable of the first additional train;

[0041] A first train additional plan is obtained according to the timetable of the first additional train and the first optimal solution.

[0042] Optionally, solving the second train increase optimization model according to the constraint conditions, the passenger travel demand, and the train operation data includes:

[0043] Solving the third sub-model and the fourth sub-model according to the constraints, the passenger travel demand, and the train operation data to obtain a second optimal solution, the second optimal solution including: a stop plan for the second additional train, a travel order for the second additional train, and a number of tickets provided by the second additional train to meet the passenger travel demand;

[0044] The second optimal solution is brought into the fifth sub-model for solving to obtain the timetable of the second additional train;

[0045] A second train additional plan is obtained according to the timetable of the second additional train and the second optimal solution.

[0046] In a second aspect of an embodiment of the present application, a device for increasing the number of high-speed trains with time window constraints taking into account passenger demand is disclosed, the device comprising:

[0047] A construction module is used to construct a first train increase optimization model with the goal of maximizing profit, and to construct a second train increase optimization model with the goal of maximizing passenger travel demand;

[0048] a determination module, configured to determine constraint conditions and obtain overflow passenger travel demands and existing train operation data, wherein the passenger travel demands include boarding time windows and boarding departure and arrival requirements, and the existing train operation data includes train routes, train stop plan sets, and train interval operation times;

[0049] A solution module is used to solve the first train increase optimization model and the second train increase optimization model according to the constraints, the passenger travel demand and the train operation data, to obtain the first train increase plan and the second train increase plan.

[0050] The embodiments of the present application include the following advantages:

[0051] In an embodiment of the present application, considering adding trains to meet excess passenger demand with time window constraints, first, a first train addition optimization model with the goal of maximizing profit is constructed, and a second train addition optimization model with the goal of maximizing passenger travel demand is constructed; then, the constraints are determined, and the overflow passenger travel demand and existing train operation data are obtained, the passenger travel demand includes the boarding time window and the boarding departure and arrival demand, and the existing train operation data includes the train route, the train stop plan set, and the train interval operation time; finally, according to the constraints, the passenger travel demand and the train operation data, the first train addition optimization model and the second train addition optimization model are solved respectively to obtain the first train addition plan and the second train addition plan.

[0052] Since the first train addition optimization model aims to maximize profits, and the second train addition optimization model aims to maximize passenger travel demand, the resulting first and second train addition plans can meet passenger travel needs while also taking into account the railway sector's economic benefits to varying degrees. Furthermore, the first and second train addition plans are derived based on passenger travel demand and existing operational data. Therefore, the provided train addition plans meet passenger travel needs (i.e., satisfy passengers' travel time windows) without changing the existing train schedule. This achieves a train addition plan that considers economic benefits and meets passenger travel needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0054] FIG1 is a flowchart of a method for increasing the number of high-speed trains with time window constraints considering passenger demand provided by an embodiment of the present application;

[0055] FIG2 is a schematic diagram of the Shenyang South-Dalian North section railway line provided in an embodiment of the present application;

[0056] FIG3 is a schematic diagram of a set of train stop solutions provided in an embodiment of the present application;

[0057] FIG4 is a schematic diagram of the results of Experiment 1 provided in an embodiment of the present application;

[0058] FIG5 is a schematic diagram of the results of Experiment 2 provided in an embodiment of the present application;

[0059] FIG6 is a schematic diagram of the results of Experiment 3 provided in an embodiment of the present application;

[0060] FIG7 is a schematic diagram of the results of Experiment 4 provided in an embodiment of the present application;

[0061] FIG8 is a schematic diagram of the results of Experiment 5 provided in an embodiment of the present application;

[0062] FIG9 is a schematic diagram of the results of Experiment 6 provided in an embodiment of the present application;

[0063] FIG10 is a schematic diagram of the results of Experiment 7 provided in an embodiment of the present application;

[0064] FIG11 is a schematic diagram of the results of Experiment 8 provided in an embodiment of the present application;

[0065] FIG12 is a schematic structural diagram of a high-speed train additional operation device with time window constraints that takes into account passenger demand, provided in an embodiment of the present application. DETAILED DESCRIPTION

[0066] To make the above-mentioned purposes, features, and advantages of this application more clearly understood, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of this application.

[0067] The embodiment of the present application provides a method for increasing the operation of high-speed trains with time window constraints considering passenger demand. As shown in FIG1 , FIG1 is a flowchart of the steps of the method for increasing the operation of high-speed trains with time window constraints considering passenger demand provided by the embodiment of the present application, including steps S110 to S130:

[0068] Step S110: constructing a first train increase optimization model with the goal of maximizing profits, and constructing a second train increase optimization model with the goal of maximizing the satisfaction of passengers' travel needs.

[0069] In the embodiment of the present application, the public welfare and general loss status of high-speed rail are taken into consideration, and the economic benefits of the railway department are taken into account to varying degrees while meeting the travel needs of passengers, and two train increase optimization models are provided, namely the first train increase optimization model and the second train increase optimization model. For the convenience of calculation, it is assumed that the first train increase optimization model and the second train increase optimization model are constructed on a corridor-type railway. A corridor-type railway means that all stations are distributed on a railway line, and there is a line for each of the up and down lines that are parallel to each other and do not affect each other, and all trains use the same starting and ending stations. In addition, it is assumed that all available trains are high-speed trains and have the same attributes. The existing fare setting is adopted based on the selection of the train stop plan (for example, the second-class seat fare is uniformly used for calculation).

[0070] The model parameters involved in the first train additional operation optimization model and the second train additional operation optimization model include: S station set, i.e., stations on the train route; S0 train’s starting station; S l The train's final destination; L is a set of optional train stop plans. A train may pass through multiple stations along its route, but it may not stop at all stations. Therefore, multiple trains on the same route involve multiple train stop plans. C N N0 is the set of candidate additional trains; N0 is the set of existing scheduled trains; N is the set of all available trains, including candidate additional trains and existing scheduled trains, that is, N = C N N0∪N0; W boarding time window width; h d The minimum interval between trains departing from the same station; h a The minimum interval time between trains arriving at the same station; U l,s The constant value is 0-1, and the value is 1 if the stop plan l stops at station s, otherwise it is 0; d i,s The departure time of train i at station s is i∈N0,s∈S and s≠S l ;a i,s The arrival time of train i at station s is i∈N0,s∈S and s≠S0; The maximum stay time of a train at a station; T stop The shortest stay time of a train at a station; p = (o, d, t) represents the passenger demand of departing from station o to station d at time t, p∈P; P is the set of all pending passenger demands; Q is the list of the number of passengers with different demands, Q p The number of passengers representing the travel demand p; M is a large constant; T start The earliest time (in minutes) that a train is allowed to depart from the starting station; Tend The latest time (in minutes) that a train is allowed to arrive at the terminal; The maximum time required for a train to run from station m to station n using operation plan l; l,m,n The shortest time required for a train to run from station m to station n using operation plan l; Ca is the passenger capacity of the train (regardless of seat class); C is the operating cost of running a train; Pr i,j,l The average price per passenger (second-class seat) for a trip from station i to station j in route plan l.

[0071] The decision variables of the first train additional operation optimization model and the second train additional operation optimization model include related variables and sequence variables of the additional train operation diagram.

[0072] Among them, the variables related to the additional train operation diagram include: i,l ∈{0,1}, that is, it is 1 when train i chooses stop plan l to depart, otherwise it is 0, i∈C N N0;d i,s is the departure time of train i at station s, i∈C N N0,s∈S and s≠S l ;a i,s is the arrival time of train i at station s, i∈C N N0, s∈S and s≠S0, the above variables determine the choice of stop plan for all spare trains and the arrival and departure time at each station. In addition, it also includes the variable π i,j,s , which means that on the segment (s, s+1), if train i departs before train j, it is 1, otherwise it is 0, i∈C N N0,j∈N,s∈S and s≠S l .

[0073] Sequential variables can more conveniently describe the distance between trains. On a single-track railway, trains are only allowed to overtake within stations and are not allowed to pass on the tracks. Therefore, it is only necessary to determine the departure time sequence of the two trains at the station to simultaneously determine the arrival order of the two trains at the next station.

[0074] In an optional embodiment, constructing a first train additional operation optimization model with the goal of maximizing profit includes:

[0075] Constructing a first sub-model based on train operation costs and passenger ticket revenue, wherein the first sub-model aims to maximize profits;

[0076] constructing a second sub-model based on the time when the train arrives at the station, the time when the train leaves the station, and the selected train stop plan, wherein the second sub-model aims to minimize the total travel time;

[0077] The first train increase optimization model is obtained according to the first sub-model and the second sub-model.

[0078] In an embodiment of the present application, the first train increase optimization model includes a first sub-model and a second sub-model. The first sub-model is used to optimize the profits of the railway department, and the second sub-model is used to further optimize the total travel time of the train in its optimal solution space while optimizing the profits, so as to maximize the profits and reduce the train's running time in the section and the stop time at the station as much as possible without causing conflicts.

[0079] For example, the first sub-model z1 and the second sub-model z2 are respectively expressed as:

[0080] Among them, Cx i,l represents the train operation cost of train i choosing the l-stop plan; y i,p represents the number of tickets reserved by train i for demand p; y i,p Pr p.o,p.d,l Represents ticket revenue; variable x i,l ∈{0,1} is 1 when train i chooses stop plan l to depart, otherwise it is 0, i∈C N N0; is the departure time of train i at station s, i∈C N N0,s∈S and s≠S l ; is the arrival time of train i at station s, i∈C N N0,s∈S and s≠S0.

[0081] In an optional embodiment, constructing an optimization model for increasing the number of second trains with the goal of maximizing passenger travel demand includes:

[0082] A third sub-model is constructed based on the number of reserved tickets for the train, wherein the third sub-model aims to maximize the satisfaction of passenger travel needs;

[0083] constructing a fourth sub-model according to the selected train stop plan, wherein the fourth sub-model aims to minimize the number of additional trains;

[0084] constructing a fifth sub-model according to the time when the train arrives at the station, the time when the train leaves the station, and the selected train stop plan, wherein the fifth sub-model aims to minimize the total travel time;

[0085] The second train increase optimization model is obtained according to the third sub-model, the fourth sub-model and the fifth sub-model.

[0086] In this embodiment of the present application, the second train addition optimization model includes a third sub-model, a fourth sub-model, and a fifth sub-model. The third sub-model maximizes the total number of passengers carried; the fourth sub-model considers minimizing the number of additional trains, reducing operating costs by reducing the number of additional trains operated by the railway department; and the fifth sub-model considers minimizing the total travel time of all spare trains to improve operational efficiency.

[0087] For example, the third sub-model z3, the fourth sub-model z4 and the fifth sub-model z5 are respectively expressed as:

[0088] Among them, y i,p represents the number of tickets reserved by train i for demand p; variable x i,l ∈{0,1} is 1 when train i chooses stop plan l to depart, otherwise it is 0, i∈C N N0; is the departure time of train i at station s, i∈C N N0,s∈S and s≠S l ; is the arrival time of train i at station s, i∈C N N0,s∈S and s≠S0.

[0089] Step S120: Determine the constraints, and obtain the overflow passenger travel demand and existing train operation data, wherein the passenger travel demand includes the boarding time window and the boarding departure and arrival requirements, and the existing train operation data includes the train route, the train stop plan set, and the train interval operation time.

[0090] In the embodiment of the present application, the constraint conditions are used to constrain the stop plan, timetable, passenger travel time window, ticket allocation and train activation order of the additional trains. When solving the first train additional optimization model and the second train additional optimization model, the first constraint condition is calculated as the constraint.

[0091] The overflow passenger travel demand is obtained from the passenger data of those who purchase “standby” tickets. Currently, the high-speed rail provides a “standby” ticket purchase plan. The passenger data of those who purchase “standby” tickets can provide overflow passenger travel demand information, which includes the passenger’s departure and destination stations (i.e., the departure and arrival demand), and the passenger’s expected boarding time (i.e., the boarding time window).

[0092] Existing train operation data includes train routes, train stop plan sets, and train interval operation time. Among them, the train route refers to the route of the train, including the train's departure station, terminal station, and transit stations; the train will pass through multiple stations when traveling, but the train will not stop at all stations. Therefore, the train stop plan set refers to the possible stop plans of the train on a train route. The stop plan of the additional train is selected from the existing train stop plan set; the train interval operation time includes the train operation schedule and the train operation time in each operation interval.

[0093] In an optional embodiment, the constraints are determined, including items A1 to A5:

[0094] Item A1: Determine a stop plan constraint condition, where the stop plan constraint condition is used to constrain each train to select only one train stop plan from the train stop plan set.

[0095] In the embodiment of the present application, the additional train stop plan is to select one from the existing train stop plan set for execution (or none of them can be selected, i.e., no train will be dispatched). i,l To indicate whether train i has selected the stop plan l. For each train, considering only the downlink, at most one stop plan can be selected.

[0096] For example, the stop plan constraints can be expressed as:

[0097] When x i,l When it is equal to 0, it means that no stop plan is selected. i,l When it is equal to 1, it means that stop plan l is selected. i,s ≤T end It means that the departure time is less than the latest allowed arrival time of the latest train at the terminal station.

[0098] Item A2: Determine timetable constraints, which are used to constrain the time when a train arrives at a station, the time when a train leaves a station, and the time when a train runs between stations.

[0099] In the embodiment of the present application, the timetable determines the arrival time and departure time of each train at each station (a i,s ,d i,s ), in order to ensure operational safety and service quality, it is necessary to take into account the constraints of train maintenance window time, train overtaking, safe vehicle distance, station services, etc.

[0100] Specifically, the schedule constraints include the following items B1 to B4:

[0101] Item B1: The time when the train arrives at the station cannot be later than the start time of maintenance, and the time when the train leaves the station cannot be earlier than the end time of maintenance.

[0102] For example, if train i stops at station s, the time a at which the train arrives at the station is i,s No later than the maintenance start time T end Expressed as:

[0103] The time the train leaves the station d i,s Cannot be earlier than the maintenance end time T start Expressed as:

[0104] Item B2: The duration of the stop between the time the train arrives at the station and the time the train leaves the station cannot be less than the shortest stop duration and cannot be greater than the longest stop duration.

[0105] For example, the stop duration cannot be less than the minimum stop duration, which is expressed as:

[0106] Among them, d i,s -a i,s represents the duration of train i’s stop at station s; T stop Indicates the shortest stop time; x i,l U l,s Indicates whether train i stops at station s when it chooses stop plan l. If it stops, then x i,l U l,s is equal to 1, otherwise it is equal to 0.

[0107] For example, the stop duration cannot be greater than the maximum stop duration, which is expressed as:

[0108] in, Indicates the maximum stop duration.

[0109] Item B3: The train interval running time between the time the train leaves the station and the time the train arrives at the next station cannot be less than the shortest train interval running time and cannot be greater than the longest train interval running time.

[0110] For example, the train interval running time cannot be less than the shortest train interval running time, which is expressed as:

[0111] Among them, a i,s+1 The time it takes for train i to reach the next station s+1; d i,s represents the time when train i leaves station s; a i,s+1 -d i,s Indicates the train interval running time; Transl,m,n represents the shortest time required to travel from station m to station n, that is, the shortest train interval running time; x i,l Trans l,m,n It represents the shortest time required for train i to travel from station m to station n when it chooses stop plan l.

[0112] For example, the train interval running time cannot be greater than the longest train interval running time, which is expressed as:

[0113] in, It represents the longest time required for a train to run from station m to station n using operation plan l, that is, the longest train interval operation time; It represents the maximum time required for train i to travel from station m to station n when it chooses stop plan l.

[0114] Item B4: The departure interval between two adjacent trains cannot be less than the shortest departure interval, and the arrival interval between two adjacent trains cannot be less than the shortest arrival interval.

[0115] For example, train i and train j are two adjacent trains. If train i is in front of train j, the departure interval between the two adjacent trains cannot be less than the shortest departure interval, which can be expressed as:

[0116] That is, the departure time of train i at station s is earlier than the departure time of train j at station s minus the shortest departure interval h d .

[0117] If train j is ahead of train i, the interval between two adjacent trains cannot be less than the shortest interval, which can be expressed as:

[0118] That is, the departure time of train j at station s is earlier than the departure time of train i at station s minus the shortest departure interval h d .

[0119] If train i is ahead of train j, the arrival interval between two adjacent trains cannot be less than the shortest arrival interval, which can be expressed as:

[0120] That is, the time when train i arrives at station s+1 is earlier than the time when train j arrives at station s minus the shortest arrival interval h a .

[0121] If train j is ahead of train i, the arrival interval between two adjacent trains cannot be less than the shortest arrival interval, which can be expressed as:

[0122] That is, the time when train j arrives at station s+1 is earlier than the time when train i arrives at station s minus the shortest arrival interval h a .

[0123] Among them, π i,j,s Indicates that on the segment (s, s+1), if train i departs before train j, it is 1, otherwise it is 0, i∈C N N0,j∈N,s∈S and s≠S l π j,i,s Indicates that on the segment (s, s+1), if train j departs before train i, it is 1, otherwise it is 0, i∈C N N0,j∈N,s∈S and s≠S l .

[0124] Therefore, π i,j,s and π j,i,s The following relationship exists:

[0125] Item A3: Determine the passenger travel time window constraint condition, which is used to constrain the matching relationship between the train and the passenger travel demand.

[0126] In the embodiment of this application, passenger travel demand is mainly characterized by two aspects: one is space demand: the train needs to stop at the passenger's departure station and destination station, and the other is time demand: the passenger has specific requirements for the departure time.

[0127] Specifically, the passenger travel time window constraint condition includes: the train meets the passenger travel demand when the train's stop stations match the departure and arrival requirements, and the train's stop time window matches the boarding time window. For example, the train's stop stations matching the departure and arrival requirements are expressed as:

[0128] Among them, z i,p ∈{0,1}, which means it is 1 when train i meets the demand p, otherwise it is 0; x i,l U l,o Indicates whether train i departs from station o when it chooses stop plan l. If it departs from station o, then x i,l U l,o is equal to 1, otherwise equal to 0; x i,l U l,d Indicates whether train i stops at station d when it chooses stop plan l. If it stops at station d, then x i,l U l,d is equal to 1, otherwise equal to 0. Only when x i,l U l,ois equal to 1, and x i,l U l,d Only when it is equal to 1, the passenger's departure and arrival demand from station o to station d is met, that is, the demand p is met.

[0129] For example, the train stop time window matches the boarding time window as follows:

[0130] Among them, d i,p.o The train i that meets the demand p is the departure time from station o, that is, the train's stop time window. The train's stop time window needs to match the passenger's boarding time window. The boarding time window is obtained by using the passenger's original train departure time t as the center and setting a time window width of W. For example, if the original train departure time is 8 o'clock and the time window width is 2 hours, it is considered that the passenger's expected travel time window is from 7 o'clock to 9 o'clock.

[0131] Item A4: Determine the passenger ticket allocation constraint conditions, which are used to constrain the relationship between the number of passenger tickets reserved for a train and the number of passengers traveling.

[0132] In the embodiment of the present application, the purpose of the first train additional operation optimization model and the second train additional operation optimization model is to solve the operation diagram of the additional trains in the face of additional passenger demand, that is, the timetable of each additional train. Therefore, the present application considers the timetable that is closely related to the travel demand of passengers. An important connection between the two is the allocation method of the passenger demand to be solved, that is, the variable y i,p It represents the satisfaction of passenger travel demand p by train i, that is, the number of tickets reserved by train i for passenger travel demand p.

[0133] Specifically, the ticket allocation constraints include the following items C1 to C3:

[0134] Item C1: The number of tickets reserved for the train does not exceed the number of passengers demanded.

[0135] For example, the number of reserved tickets for a train does not exceed the number of passengers required, which is expressed as:

[0136] That is, the number of tickets reserved by train i for passenger travel demand p is less than or equal to the number of passengers with demand p.

[0137] Item C2: The number of passenger demands satisfied by the train does not exceed the capacity of the train.

[0138] For example, the number of passenger demands satisfied by a train that does not exceed the train's capacity is expressed as:

[0139] That is, the number of tickets reserved by train i for passenger travel demand p is less than or equal to the train passenger capacity Ca of the train.

[0140] Item C3: The number of reserved tickets for a train is non-zero if and only if the train's stop stations match the boarding departure and arrival requirements and the train's stop time window matches the boarding time window.

[0141] For example, the number of reserved tickets for a train is non-zero if and only if the train's stop stations match the boarding departure and arrival requirements and the train's stop time window matches the boarding time window, which is expressed as:

[0142] That is to say, z i,p When it is equal to 1, it means that train i meets the passenger travel demand p, that is, the train's stop stations match the departure and arrival requirements and the train's stop time window matches the i's boarding time window. At this time, train i is the reserved passenger ticket.

[0143] Item A5: Determine the train sequence constraint conditions, which are used to constrain the activation order of trains.

[0144] In the embodiment of this application, all trains have the same capacity and the same attributes. All spare trains are numbered and sorted. The schedules of any two trains, such as train i(m) and train i(n), can be interchanged without affecting the final solution. However, if this is not restricted, a large number of optimal solutions with the same effect will appear, slowing down the solution. Therefore, after sorting the spare trains, this application stipulates that the trains with the highest ranking will be prioritized. That is, if spare train i is not activated, then train i+1 will not be activated (and subsequent trains will not be activated either).

[0145] Step S130: According to the constraints, the passenger travel demand and the train operation data, the first train increase optimization model and the second train increase optimization model are solved respectively to obtain a first train increase plan and a second train increase plan.

[0146] In this embodiment of the present application, passenger travel demand and the train operation data are incorporated into a first train addition optimization model. The first train addition optimization model is then solved using the constraints as constraints to obtain a first train addition plan. The first train addition plan includes the stop plan for the newly added trains, the travel sequence of the additional trains, the number of tickets provided by the additional trains to meet passenger travel needs, and the timetable for the additional trains. Because the first train addition optimization model is designed to maximize profits, the first train addition plan aims to meet passenger travel demand to the greatest extent possible while maximizing the economic benefits of the railway sector.

[0147] Similarly, passenger travel demand and the train operation data are fed into the second train addition optimization model. Using the constraints as constraints, the second train addition optimization model is solved to obtain a second train addition plan. The second train addition plan includes the stop plan for the newly added trains, the travel sequence of the newly added trains, the number of tickets available for the newly added trains to meet passenger travel needs, and the timetable for the newly added trains. Since the second train addition optimization model aims to maximize passenger travel demand, the second train addition plan aims to maximize the economic benefits of the railway sector while maximizing passenger travel demand.

[0148] In an optional embodiment, the first train increase optimization model is solved according to the constraint conditions, the passenger travel demand, and the train operation data, including steps D1 to D3:

[0149] Step D1: Solving a first sub-model based on the constraints, the passenger travel demand, and the train operation data to obtain a first optimal solution, wherein the first optimal solution includes: a stop plan for the first additional train, a travel order for the first additional train, and a number of tickets provided by the first additional train to meet the passenger travel demand;

[0150] Step D2: Substitute the first optimal solution into the second sub-model for solution to obtain the timetable of the first additional train;

[0151] Step D3: Obtain a first train additional plan based on the first additional train schedule and the first optimal solution.

[0152] In this embodiment of the present application, the first train addition optimization model includes a first sub-model and a second sub-model. The first sub-model is designed to maximize profit, and the first sub-model is solved first to obtain the first optimal solution for maximizing profit. The second sub-model is then used to further optimize the total train travel time, maximizing profit and minimizing train travel time within the section and station stop time as much as possible without generating conflicts, to obtain the timetable for the first additional trains, and then to obtain the first train addition plan. The first train addition plan includes data such as the number of additional trains, the additional train stop plan, and the additional train timetable.

[0153] In an optional embodiment, solving the second train increase optimization model according to the constraint conditions, the passenger travel demand and the train operation data includes steps E1 to E3:

[0154] Step E1: Solving the third sub-model and the fourth sub-model based on the constraints, the passenger travel demand, and the train operation data to obtain a second optimal solution, where the second optimal solution includes: a stop plan for the second additional train, a travel order for the second additional train, and a number of tickets provided by the second additional train to meet the passenger travel demand;

[0155] Step E2: Substitute the second optimal solution into the fifth sub-model for solution to obtain the timetable of the second additional train;

[0156] Step E3: Obtain a second train additional plan based on the second additional train schedule and the second optimal solution.

[0157] In this embodiment of the present application, the first train addition optimization model includes a third sub-model, a fourth sub-model, and a fifth sub-model. The third sub-model is designed to maximize passenger travel demand, while the second sub-model is designed to minimize the number of additional trains. Prioritizing the third and fourth sub-models, the solution is solved to obtain a second optimal solution that maximizes passenger travel demand and, to a certain extent, meets economic needs. The fifth sub-model is then used to further optimize the total train travel time, maximizing profit and minimizing train travel time within the section and station stop time without generating conflicts. This results in a timetable for the second additional trains, and further, a second train addition plan. The second train addition plan includes data such as the number of additional trains, the additional train stop plan, and the additional train timetable.

[0158] In summary, the embodiment of the present application considers adding trains to meet excess passenger demand with time window constraints. First, a first train addition optimization model with the goal of maximizing profit is constructed, and a second train addition optimization model with the goal of maximizing passenger travel demand is constructed. Then, the constraints are determined, and the overflow passenger travel demand and existing train operation data are obtained. The passenger travel demand includes the boarding time window and the boarding departure and arrival demand. The existing train operation data includes the train route, the train stop plan set, and the train interval operation time. Finally, according to the constraints, the passenger travel demand and the train operation data, the first train addition optimization model and the second train addition optimization model are solved respectively to obtain the first train addition plan and the second train addition plan. Since the first train addition optimization model aims to maximize profit and the second train addition optimization model aims to maximize passenger travel demand, the first train addition plan and the second train addition plan obtained by solving can meet the passenger travel demand while taking into account the economic benefits of the railway department to varying degrees. Furthermore, the first and second additional train operation plans are derived based on passenger travel demand and existing operational data. Therefore, the proposed additional train operation plans meet passenger travel demand (i.e., meet passengers' travel time windows) without changing the existing train timetable. This creates a train operation plan that considers economic benefits and meets passenger travel needs.

[0159] Next, taking the Shenyang South-Dalian North section of the railway line as an example, the method for increasing the number of high-speed trains with time window constraints considering passenger demand in an embodiment of the present application is described in detail.

[0160] First, obtain existing train operation data, namely, train routes, train stop plan sets, and train interval operation times. As shown in Figure 2, Figure 2 is a schematic diagram of the Shenyang South-Dalian North section railway line provided in an embodiment of the present application. In this Shenyang South-Dalian North section railway line, the train will pass through 8 stations, and the train will not stop at all stations during the journey. Figure 3 shows the 8 existing stop plans on this route. The train interval operation time is the timetable, and the recent timetable of existing trains can be obtained from the ticket purchasing software (such as the 12306 platform).

[0161] Secondly, obtain the travel demand by train. The passenger flow data of high-speed trains is currently unavailable, and the embodiment of this application adopts an estimation method. First, based on the selected 8 stop plans, for any driving interval, count how many of the 8 stop plans can realize the OD pair (i.e., the departure and arrival demand of the train), and use this number as the approximate proportion of the passenger flow between each driving interval. On this basis, the travel demand of passengers of different scales is obtained by modifying the base number. For each OD pair, the stop plans that stop at its starting and ending points are screened out, and the boarding time in the existing timetable corresponding to these stop plans is used as the optional time. The travel time demand of passengers is given by random sampling. For example, there are 4 trains departing from Shenyang South Station and stopping at Liaoyang Station. Their departure times from Shenyang South are 7:21 (441 minutes), 7:27 (447 minutes), 9:47 (587 minutes) and 19:50 (1190 minutes), respectively. The minutes corresponding to the departure time are in brackets. Given the passenger travel demand between Shenyang South Station and Liaoyang Station, one of these four times is randomly selected as the expected travel time for this group of passengers. The calculation parameters are then set based on the existing train operation data, as shown in Table 1.

[0162] Table 1 Calculation parameter settings

[0163] Finally, we conducted 10 sets of experiments for analysis and calculation. Experiments 1–8 compared the performance of the first and second train optimization models for different passenger flow inputs. Experiments 9 and 10 compared the improvement in model solution efficiency achieved by sequentially enabling constraints. The experimental parameters are shown in Table 2.

[0164] Table 2 Experimental parameter settings

[0165] All experiments were conducted on the same machine with the following configuration: Windows 11, a 12th Gen Intel(R) Core(TM) i9-12900H 2.50GHz processor, and 32.0GB of RAM. Python 3.9.8 was used to run the Gurobi solver, with a maximum solution time of 1 hour.

[0166] The experimental results for Experiments 1–8 are shown in Figures 4–11. The solid lines represent the timetable distribution of existing trains, and the dotted lines represent the timetable distribution of newly added trains. A comparison of railway sector profits and costs for Experiments 1–8 is shown in Table 3, and a comparison of passenger travel demand satisfaction is shown in Table 4. A comparison of solution times for Experiments 9 and 10 is shown in Table 5.

[0167] Table 3 Comparison of profits and costs in the railway sector

[0168] Table 4 Comparison of passenger travel demand satisfaction ratios

[0169] Table 5 Comparison of solution time

[0170] Experimental results show that the first train addition optimization model attempts to increase train occupancy by extending train operating time spans, thereby reducing overall train usage and increasing railway profits. Profitability shows a steady upward trend as passenger volume increases. Regarding passenger demand satisfaction, while profit-first approaches do not maximize passenger demand, overall, the proportion of passenger demand satisfaction remains consistently above 50%, with the model prioritizing the needs of larger numbers of passengers traveling farther. The overall satisfaction ratio increases with increasing passenger volume, and remains relatively stable even when passenger volume decreases. However, certain time spans on timetable curves can increase travel time for long-distance passengers, reducing their satisfaction.

[0171] The biggest advantage of the second train addition optimization model is its ability to meet passenger travel needs to the greatest extent possible. The passenger-priority model also attempts to increase the time span of train operations to reduce costs. However, due to the priority of maximizing passenger demand, timetable curves with excessively long time spans do not appear. Optimization of the number of trains is limited, and overall, the number of additional trains is greater than that of the profit-priority model. In terms of economic benefits, the passenger-priority model performs poorly compared to the profit-priority model, especially when passenger demand is small. However, compared to directly adding trains that would result in overflow, the passenger-priority model still reduces the number of additional trains. The "unbundling" approach provides room for model optimization.

[0172] By comparing the model solution time, it can be seen that by adding grouping and sorting of trains with the same attributes and enabling constraints in sequence, good results are achieved in both the profit-first and passenger-first models, greatly shortening the solution time and improving the solution efficiency.

[0173] The present application also provides a device for increasing the number of high-speed trains with time window constraints taking into account passenger demand, as shown in FIG12 . FIG12 is a schematic structural diagram of a device for increasing the number of high-speed trains with time window constraints taking into account passenger demand provided by the present application. The device includes:

[0174] A construction module 1210 is configured to construct a first train additional operation optimization model with the goal of maximizing profit, and a second train additional operation optimization model with the goal of maximizing passenger travel demand.

[0175] Determination module 1220, configured to determine constraint conditions and obtain overflow passenger travel demands and train operation data, wherein the passenger travel demands include: boarding time windows and boarding departure and arrival requirements; and the train operation data includes train routes, train stop plan sets, and train interval operation times;

[0176] The solution module 1230 is used to solve the first train increase optimization model and the second train increase optimization model according to the constraints, the passenger travel demand and the train operation data, and obtain the first train increase plan and the second train increase plan.

[0177] In an optional embodiment, the constructing the model includes:

[0178] A first sub-model is constructed, for constructing a first sub-model based on train operation costs and passenger ticket revenue, wherein the first sub-model aims to maximize profit;

[0179] a second sub-model construction, configured to construct a second sub-model according to the time when the train arrives at the station, the time when the train leaves the station, and the selected train stop plan, wherein the second sub-model aims to minimize the total travel time;

[0180] The third sub-model is constructed to obtain the first train increase optimization model based on the first sub-model and the second sub-model.

[0181] In an optional embodiment, the constructing the model includes:

[0182] The fourth sub-model is used to construct a third sub-model according to the number of tickets reserved for the train, wherein the third sub-model aims to maximize the satisfaction of passenger travel needs;

[0183] a fifth construction sub-model, configured to construct a fourth sub-model according to the selected train stop plan, wherein the fourth sub-model aims to minimize the number of additional trains;

[0184] a sixth construction sub-model, configured to construct a fifth sub-model according to the time when the train arrives at the station, the time when the train leaves the station, and the selected train stop plan, wherein the fifth sub-model aims to minimize the total travel time;

[0185] The seventh sub-model is constructed to obtain the second train increase optimization model based on the third sub-model, the fourth sub-model and the fifth sub-model.

[0186] In an optional embodiment, the determining module includes:

[0187] A first determining submodule is configured to determine a stop plan constraint condition, wherein the stop plan constraint condition is configured to constrain each train to select only one train stop plan from the train stop plan set;

[0188] A second determining submodule is used to determine a timetable constraint condition, wherein the timetable constraint condition is used to constrain the time when the train arrives at the station, the time when the train leaves the station, and the train interval running time;

[0189] A third determination submodule is configured to determine a passenger travel time window constraint condition, wherein the passenger travel time window constraint condition is used to constrain the matching relationship between the train and the passenger travel demand;

[0190] A fourth determination submodule is used to determine a ticket allocation constraint condition, wherein the ticket allocation constraint condition is used to constrain the relationship between the number of tickets reserved for a train and the number of passengers traveling;

[0191] The fifth determining submodule is used to determine a train sequence constraint condition, where the train sequence constraint condition is used to constrain the activation order of the trains.

[0192] In an optional embodiment, the schedule constraint conditions include:

[0193] The time when the train arrives at the station cannot be later than the start time of maintenance, and the time when the train leaves the station cannot be earlier than the end time of maintenance;

[0194] The duration of the stop between the time the train arrives at the station and the time the train leaves the station cannot be less than the shortest stop duration and cannot be greater than the longest stop duration;

[0195] The train interval running time between the time when the train leaves the station and the time when the train arrives at the next station cannot be less than the shortest train interval running time and cannot be greater than the longest train interval running time;

[0196] The departure interval between two adjacent trains cannot be less than the shortest departure interval, and the arrival interval between two adjacent trains cannot be less than the shortest arrival interval.

[0197] In an optional embodiment, the passenger travel time window constraint includes:

[0198] When the train's stop stations match the departure and arrival requirements, and the train's stop time window matches the boarding time window, the train meets the passengers' travel needs.

[0199] In an optional embodiment, the ticket allocation constraints include:

[0200] The number of tickets reserved for a train does not exceed the number of passengers required;

[0201] The number of passenger demands satisfied by the train does not exceed the capacity of the train;

[0202] The number of tickets reserved for a train is non-zero if and only if the train's stop stations match the boarding departure and arrival requirements and the train's stop time window matches the boarding time window.

[0203] In an optional embodiment, the solution module includes:

[0204] a first solving sub-model, configured to solve the first sub-model according to the constraint conditions, the passenger travel demand, and the train operation data to obtain a first optimal solution, wherein the first optimal solution includes: a stop plan of the first additional train, a travel order of the first additional train, and a number of tickets provided by the first additional train to meet the passenger travel demand;

[0205] A second solving sub-model is used to bring the first optimal solution into the second sub-model for solving, so as to obtain a timetable for the first additional train;

[0206] The third solving sub-model is used to obtain a first train additional train plan based on the timetable of the first additional train and the first optimal solution.

[0207] In an optional embodiment, the solution module includes:

[0208] a fourth solving sub-model, configured to solve the third sub-model and the fourth sub-model based on the constraint conditions, the passenger travel demand, and the train operation data to obtain a second optimal solution, wherein the second optimal solution includes: a stop plan for the second additional train, a travel order of the second additional train, and a number of tickets provided by the second additional train to meet the passenger travel demand;

[0209] a fifth solving sub-model, configured to bring the second optimal solution into the fifth sub-model for solving, to obtain a timetable for the second additional train;

[0210] The sixth solving sub-model is used to obtain a second train additional train plan based on the timetable of the second additional train and the second optimal solution.

[0211] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0212] Although preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they become aware of the basic inventive concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the embodiments of the present invention.

[0213] Finally, it should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or terminal device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or terminal device that includes the element.

[0214] The above is a detailed introduction to a method and device for increasing the number of high-speed trains with time window constraints that take into account passenger demand provided by the present application. This article uses specific examples to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method of the present application and its core idea; at the same time, for general technical personnel in this field, based on the ideas of the present application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present application.

Claims

1. A method for adding high-speed rail trains considering passenger demand with time window constraints, characterized in that The method includes: Constructing a first train additional operation optimization model aiming at maximizing profit, and constructing a second train additional operation optimization model aiming at maximizing the satisfaction of passengers' travel demands; Determining constraint conditions, and obtaining the overflow of passengers' travel demands and the existing train operation data, where the passengers' travel demands include the travel time window and the travel departure and arrival demands, and the existing train operation data includes train routes, a set of train stop plans, and train section running times; According to the constraint conditions, the passengers' travel demands and the train operation data, solving the first train additional operation optimization model and the second train additional operation optimization model respectively to obtain a first train additional operation plan and a second train additional operation plan.

2. The method according to claim 1, wherein Constructing a first train additional operation optimization model aiming at maximizing profit includes: Constructing a first sub-model based on train operation costs and ticket revenues, where the first sub-model aims at maximizing profit; Constructing a second sub-model based on the arrival time of the train at the station, the departure time of the train from the station, and the selected train stop plan, where the second sub-model aims at minimizing the total travel time; Obtaining the first train additional operation optimization model according to the first sub-model and the second sub-model.

3. The method according to claim 1, characterized in that, Constructing a second train additional operation optimization model aiming at maximizing the satisfaction of passengers' travel demands includes: Constructing a third sub-model based on the number of reserved tickets for the train, where the third sub-model aims at maximizing the satisfaction of passengers' travel demands; Constructing a fourth sub-model based on the selected train stop plan, where the fourth sub-model aims at minimizing the number of additional trains; Constructing a fifth sub-model based on the arrival time of the train at the station, the departure time of the train from the station, and the selected train stop plan, where the fifth sub-model aims at minimizing the total travel time; Obtaining the second train additional operation optimization model according to the third sub-model, the fourth sub-model and the fifth sub-model.

4. The method according to claim 1, wherein Determining constraint conditions includes: Determining stop plan constraint conditions, which are used to constrain that each train can only select one train stop plan from the set of train stop plans; Determining timetable constraint conditions, which are used to constrain the arrival time of the train at the station, the departure time of the train from the station, and the train section running time; Determining passenger travel time window constraint conditions, which are used to constrain the matching relationship between the train and the passengers' travel demands; Determining ticket allocation constraint conditions, which are used to constrain the relationship between the number of reserved tickets for the train and the number of passengers' travel demands; Determining train order constraint conditions, which are used to constrain the activation order of the trains.

5. The method according to claim 4, characterized in that, The timetable constraint conditions include: The arrival time of the train at the station cannot be later than the start time of maintenance, and the departure time of the train from the station cannot be earlier than the end time of maintenance; The stop duration between the arrival time of the train at the station and the departure time of the train from the station cannot be less than the shortest stop duration and cannot be greater than the longest stop duration; The running duration of the train in the train section between the time when the train leaves the station and the time when the train arrives at the next station shall not be less than the shortest train section running duration and shall not be greater than the longest train section running duration; The departure interval duration between two adjacent trains shall not be less than the shortest departure interval duration, and the arrival interval duration between two adjacent trains shall not be less than the shortest arrival interval duration.

6. The method according to claim 4, wherein The passenger travel time window constraint conditions include: When the train's stopping station matches the travel departure and arrival requirements and the train's stop time window matches the travel time window, the train meets the passenger travel requirements.

7. The method according to claim 4, characterized in that The ticket allocation constraint conditions include: The number of tickets reserved for the train does not exceed the number of passenger requirements; The number of passengers whose travel requirements are met by the train does not exceed the capacity of the train; The number of tickets reserved for the train is non-zero if and only if the train's stopping station matches the travel departure and arrival requirements and the train's stop time window matches the travel time window.

8. The method according to claim 2, wherein Solving the first train additional operation optimization model according to the constraint conditions, the passenger travel requirements and the train operation data includes: Solving the first sub-model according to the constraint conditions, the passenger travel requirements and the train operation data to obtain the first optimal solution, where the first optimal solution includes: the stop plan of the first additional train, the running order of the first additional train, and the number of tickets provided by the first additional train for the passenger travel requirements; Substituting the first optimal solution into the second sub-model for solution to obtain the timetable of the first additional train; Obtaining the first train additional operation plan according to the timetable of the first additional train and the first optimal solution.

9. The method according to claim 3, characterized in that, Solving the second train additional operation optimization model according to the constraint conditions, the passenger travel requirements and the train operation data includes: Solving the third sub-model and the fourth sub-model according to the constraint conditions, the passenger travel requirements and the train operation data to obtain the second optimal solution, where the second optimal solution includes: the stop plan of the second additional train, the running order of the second additional train, and the number of tickets provided by the second additional train for the passenger travel requirements; Substituting the second optimal solution into the fifth sub-model for solution to obtain the timetable of the second additional train; Obtaining the second train additional operation plan according to the timetable of the second additional train and the second optimal solution.

10. A high-speed rail train additional operation device considering passenger demands with time window constraints, characterized in that, The device includes: A construction module for constructing a first train additional operation optimization model with the goal of maximizing profit and a second train additional operation optimization model with the goal of maximizing the satisfaction of passenger travel requirements; A determination module for determining the constraint conditions and obtaining the overflow passenger travel requirements and train operation data, where the passenger travel requirements include: the travel time window and the travel departure and arrival requirements, and the train operation data includes the train route, the set of train stop plans, and the train section running time; A solution module, configured to solve the first train additional operation optimization model and the second train additional operation optimization model respectively according to the constraint conditions, the passenger travel demands and the train operation data, so as to obtain a first train additional operation plan and a second train additional operation plan.

Images