Method for calculating trafficability of high-speed railway line

Abstract

The invention provides a method for calculating the trafficability of a high-speed railway line, and relates to the technical field of railway transportation. In the first stage, according to the profit of the space-time arc and the selection result of the space-time arc, the basic framework running diagram of the train running scheme is determined. In the second stage, the efficiency and accuracy of identifying the target space interval are improved through the capability utilization rate. And in the third stage, a second target solution is solved by constructing a second travel total profit function and a second constraint condition set, encrypted laying of the basic framework running diagram is realized, and a trafficability calculation result is obtained. According to the calculation method for the trafficability of the high-speed railway line provided by the invention, the calculation amount and the calculation complexity are reduced while the construction of a large-scale train working diagram is ensured.

Description

Technical Field

[0001] The present invention relates to the field of railway transportation technology, and in particular to a method for calculating the throughput capacity of a high-speed railway line. Background Art

[0002] The concept of railway transport capacity originates from production capacity and measures the maximum number of transport services a railway transport enterprise can provide during a planned period. Railway throughput capacity is a subcategory of railway transport capacity and is defined as the maximum number of standard weight trains or train pairs that can be processed by railway fixed equipment within a unit of time (usually a day or night), given a set type of locomotive and rolling stock, and a specific operational organization. Specifically, it refers to the maximum number of EMU trains that can be processed on a high-speed railway line within a day or night, given a set type of EMU and a specific operational organization.

[0003] The calculation of high-speed railway line capacity refers to the process of determining the value of high-speed railway line capacity indicators using appropriate technical methods. Accurate calculation of capacity is a prerequisite for designing transportation organization plans and capacity improvement measures.

[0004] Railway transport capacity calculation methods can currently be divided into three categories: analytical calculation, simulation, and graphical methods. The most accurate method is the graphical method. The graphical method has the following shortcomings. The graphical method does not adequately consider actual needs. Existing graphical method studies generally do not consider the heterogeneity between trains, such as the length and shortness of trains, their importance, and the factors affecting the increase or decrease in the number of trains. They cannot cover business needs and therefore cannot produce capacity calculation results that meet actual needs. The train timetable compilation problem is a large-scale combinatorial optimization problem. The graphical method takes all content into account at once, resulting in a combinatorial explosion of computational complexity and can only be limited to solving small-scale cases. It cannot produce feasible solutions to large-scale problems in the real world within an acceptable time.

[0005] The low efficiency of calculating existing railway transportation capacity leads to low efficiency in constructing train operation plans. Summary of the Invention

[0006] The present invention provides a method for calculating the throughput capacity of a high-speed railway line, so as to solve the defect of low efficiency in constructing a train operation plan in the prior art and improve the efficiency of constructing the train operation plan.

[0007] The present invention provides a method for calculating the throughput capacity of a high-speed railway line, comprising: determining a first travel total profit function and a first constraint condition set of the train based on the profit of the space-time arc of the space-time network of the high-speed railway line and the selection result of the space-time arc; solving the maximum value of the first travel total profit function based on the first constraint condition set to obtain a first target solution for the selection result of the train for the space-time arc; calculating the capacity utilization rate of the spatial segment of the space-time network within a set time range based on the first target solution, taking the spatial segment with a capacity utilization rate less than the set capacity utilization rate as the target spatial segment, and obtaining an existing train operation plan for the target spatial segment based on the first target solution; determining a second travel total profit function and a second constraint condition set based on the profit of the space-time arc of the space-time network corresponding to the target spatial segment and the set time range, the selection result of the space-time arc and the selection result of the operation plan; solving the maximum value of the second travel total profit function based on the second constraint condition set on the basis of the existing train operation plan to obtain a second target solution for the selection result of the train for the target space-time arc; and obtaining the maximum throughput capacity of the high-speed railway line based on the first target solution and the second target solution.

[0008] According to the method for calculating the capacity of a high-speed railway line provided by the present invention, the first constraint condition set includes basic constraint conditions and compatible constraint conditions, the compatible constraint conditions are used to characterize the incompatible information of space-time arc selection, and the maximum value of the first travel total profit function is solved based on the first constraint condition set, including: merging the compatible constraint conditions and the first travel total profit function into a travel total profit relaxation function according to the Lagrange multiplier; solving the maximum value of the travel total profit relaxation function based on the basic constraint conditions to obtain a relaxed solution; solving the maximum value of the first travel total profit function based on the relaxed solution of the travel total profit relaxation function and the first constraint condition set to obtain an initial solution; if the difference between the initial solution and the relaxed solution is greater than the set difference, updating the Lagrange multiplier to iteratively update the relaxed solution and the initial solution until the difference between the initial solution and the relaxed solution is less than or equal to the set difference, and taking the finally updated initial solution as the first target solution.

[0009] According to the method for calculating the throughput capacity of a high-speed railway line provided by the present invention, the basic constraint conditions are determined based on the following steps: based on the selection results of the space-time arc, it is determined that each train selects at most one starting station for departure; and the number of trains entering the transit station is equal to the number of trains leaving the transit station, thereby obtaining the basic constraint conditions.

[0010] According to the calculation method of the through-capacity of the high-speed railway line provided by the present invention, the compatible constraint condition is determined based on the following steps: based on the selection result of the space-time arc, it is determined that the number of trains existing at a station at the same time is less than the maximum storage capacity of the station; the number of trains departing at the same time in the departure interval time period of the line section is less than 1; the number of trains passing at the same time in the passing interval time period of the line section is less than 1; the number of trains arriving at the same time in the arrival interval time period of the line section is less than 1; if a train arrives at the rear station of the line section, the number of trains passing the rear station in the first time period after the arrival of the train is 0; if a train passes the rear station of the line section, the number of trains arriving at the rear station in the second time period after the train passes is 0; if a train departs from the front station of the line section, the number of trains passing the front station in the third time period after the departure of the train is 0; if a train passes the front station of the line section, the number of trains passing the front station in the fourth time period after the train passes is 0; and the number of trains existing in the same time period of the line section is less than 1, thereby obtaining the compatible constraint condition.

[0011] According to the method for calculating the throughput capacity of a high-speed railway line provided by the present invention, the capacity utilization rate of a spatial segment of a space-time network within a set time range is calculated based on a first target solution, including: obtaining at least one occupied time period of an existing train in the spatial segment based on the first target solution; adding at least one occupied time period to obtain the total occupied time of the spatial segment; if there is an overlapping time period between two occupied time periods, the overlapping time periods are only added once; determining the total available time of the spatial interval based on the set time range, the skylight time of the spatial segment and the invalid time of the spatial segment; and obtaining the capacity utilization rate based on the ratio of the total occupied time to the total available time.

[0012] According to the method for calculating the throughput capacity of a high-speed railway line provided by the present invention, the selection result of the operation plan includes the selection result of the speed level and the selection result of the stop plan.

[0013] According to the method for calculating the throughput capacity of a high-speed railway line provided by the present invention, the second set of constraints includes constraints on the selection results of the operating plan, and the constraints on the selection results of the operating plan are determined based on the following steps: based on the selection results of the operating plan corresponding to the target spatial segment and the set time range of the train, it is determined that each train can select at most one speed level and one stop plan; the train that has selected the speed level and stop plan must choose the transit stations with the same speed level and stop plan to stop; and the number of times all trains stop at the stations with the speed level and stop plan is greater than or equal to the required number of times at the station, thereby obtaining the constraints on the selection results of the operating plan.

[0014] According to the method for calculating the throughput capacity of a high-speed railway line provided by the present invention, the second constraint condition set also includes constraint conditions for the selection result of the space-time arc, and the constraint conditions for the selection result of the space-time arc are determined based on the following steps: based on the selection result of the space-time arc corresponding to the target spatial section and the set time range of the train, it is determined that each train selects at most one starting station for departure; the number of trains entering the passing station is equal to the number of trains leaving the passing station; the number of trains existing at a station at the same time is less than the maximum storage capacity of the station; the number of trains departing at the same time in the departure interval time period of the line section is less than 1; the number of trains passing at the same time in the passing interval time period of the line section is less than 1; The number of trains arriving simultaneously in the arrival interval time period between the two intervals is less than 1; if a train arrives at the rear station of the line section, the number of trains passing through the rear station in the first time period after the train arrives is 0; if a train passes through the rear station of the line section, the number of trains arriving at the rear station in the second time period after the train passes is 0; if a train departs from the front station of the line section, the number of trains passing through the front station in the third time period after the train departs is 0; if a train passes through the front station of the line section, the number of trains passing through the front station in the fourth time period after the train passes is 0; and the number of trains existing in the same time period of the line section is less than 1, and the constraint conditions for the selection result of the space-time arc are obtained.

[0015] According to the method for calculating the throughput capacity of a high-speed railway line provided by the present invention, on the basis of an existing train operation plan, the maximum value of the second travel total profit function is solved based on the second constraint condition set to obtain a second target solution for the train's selection result of the target space-time arc, including: dividing the set time range into multiple sub-time periods to divide the second travel total profit function and the second constraint condition set into multiple sub-functions, sub-constraint condition sets of the sub-functions and the solution order of the sub-functions; solving the unsolved sub-functions based on the solution order, the sub-constraint condition sets and the sub-optimal solutions of the solved sub-functions; and determining the second target solution based on the sub-optimal solutions of all sub-functions.

[0016] According to the method for calculating the throughput capacity of a high-speed railway line provided by the present invention, after solving the maximum value of the second travel total profit function based on the second constraint condition set and obtaining the second target solution of the train's selection result for the target space-time arc, it also includes: iteratively updating the capacity utilization of the target space segment based on the second target solution until the capacity utilization of the target space segment is greater than or equal to the set capacity utilization, and obtaining the updated second target solution; and obtaining the maximum throughput capacity of the high-speed railway line based on the first target solution and the updated second target solution.

[0017] The present invention provides a method for calculating the throughput capacity of a high-speed railway line. Based on the profit of a train's space-time arcs in a space-time network and the space-time arc selection results, a first total profit function for the train's trip and a first set of constraints are determined. The first total profit function is solved for maximum value based on the first set of constraints to obtain a first target solution for the train's selection of the space-time arcs. Based on the first target solution, the capacity utilization rate of a spatial segment of the space-time network within a set time range is calculated. Spatial segments with capacity utilization rates less than the set capacity utilization rate are designated as target spatial segments. Based on the first target solution, an existing train operation plan for the target spatial segment is obtained. Based on the profit of the train's space-time arcs in the space-time network corresponding to the target spatial segment and the set time range, the space-time arc selection results, and the selection results of the operation plan, a second total profit function and a second set of constraints are determined. Based on the existing train operation plan, the second total profit function is solved for maximum value based on the second set of constraints to obtain a second target solution for the train's selection of the target space-time arcs. The maximum throughput capacity of the high-speed railway line is obtained based on the first and second target solutions. In the first stage of the present invention, a basic framework operation diagram for determining a train operation plan is implemented based on the profit of the space-time arcs and the space-time arc selection results. In the second phase, capacity utilization improves the efficiency and accuracy of identifying the target spatial interval. In the third phase, by constructing a second trip total profit function and a second set of constraints, and then solving the second target solution, the basic framework operation diagram is densely laid out, resulting in the calculation of the throughput capacity. The method for calculating the throughput capacity of high-speed railway lines provided by this invention reduces the computational effort and complexity while ensuring the construction of large-scale train operation diagrams. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the present invention or the prior art, a brief introduction is given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0019] Figure 1 This is one of the flow charts of the method for calculating the throughput capacity of a high-speed railway line provided by the present invention.

[0020] Figure 2 This is the second flow chart of the method for calculating the throughput capacity of a high-speed railway line provided by the present invention.

[0021] Figure 3 This is one of the schematic diagrams of the space-time network of the train provided by the present invention.

[0022] Figure 4 It is a schematic diagram of the flow of calculating the total occupied time provided by the present invention.

[0023] Figure 5 It is a flow chart of calculating the maximum value of the total profit function of the second trip provided by the present invention.

[0024] Figure 6 This is the second schematic diagram of the space-time network of the train provided by the present invention.

[0025] Reference numerals: 101: Starting arc; 102: Interval arc; 103: Stop arc; 104: End arc. DETAILED DESCRIPTION

[0026] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0027] The following combination Figures 1-6 The method for calculating the throughput capacity of a high-speed railway line according to the present invention is described.

[0028] Figure 1 FIG. 1 is a flow chart of a method for calculating the throughput capacity of a high-speed railway line provided by the present invention, as shown in FIG. Figure 1 As shown, the method for calculating the throughput capacity of a high-speed railway line includes steps S100 to S600, and each step is specifically described as follows.

[0029] S100: Based on the profit of the space-time arc of the high-speed railway line train in the space-time network and the selection result of the space-time arc, determine the total profit function of the first trip of the train and the first constraint condition set.

[0030] like Figure 2 As shown, basic data such as the train's route data, operation plan, and train operating standards are input. The operation plan already specifies some long-distance trains with high operating efficiency (such as benchmark trains and cross-bureau trains). These trains have predefined speed levels, stop schedules, and departure times. This prioritizes the quality of these trains' operations. Therefore, these trains (representing the set of trains in the operation plan, and representing a specific train in the set) are assigned certain basic operating efficiency benefits. Penalties for deviations from the ideal departure time and penalties for additional travel time are also set. The goal is to ensure that all trains in the operation plan are deployed as successfully as possible with minimal deviation from the ideal, thereby meeting the line's core passenger needs and forming the basic framework diagram for the train operation plan.

[0031] The present invention calculates the capacity of a high-speed railway line in three stages. The first stage is to construct a basic operating diagram. The second stage is to identify target spatial segments with underutilized capacity within the basic operating diagram. The third stage is to encrypt and lay out train operation plans for these target spatial segments.

[0032] The basic framework of the train operation plan is constructed on the basis of the space-time network. Figure 3 As shown, the space-time network is a modeling method to solve the operation diagram problem, which constructs the railway infrastructure into a two-dimensional or three-dimensional space-time network, where the horizontal axis represents the time set. ; The vertical axis represents the train position (station) A collection of nodes in a network , represents the space-time position of the train, is the virtual starting point of the train, is the virtual destination of the train; the set of space-time arcs in the network Describe the train at the node and another node The process of transfer between (space-time arc) , The train number. Figure 3 The space-time network consists of three trains (Train 1, Train 2, and Train 3) and four stations (Station 1, Station 2, Station 3, and Station 4) within 15 minutes. A layer of space-time network is constructed for each train to represent the train's possible operation path. In order to represent the train's stay time at the station, the station-related nodes are divided into arrival node sets and departure node set ,For example, represents the departure node set of station 2, Represents the arrival node set of station 2.

[0033] like Figure 6 As shown, in the space-time network, each arc represents the running process of a train transferring from one node to another node. The space-time arcs of the train in the space-time network are divided into the starting arc set , terminal arc set , stop arc set and interval arc sets Four forms. The starting arc set includes multiple starting arcs 101. The ending arc set includes multiple ending arcs 104. The stop arc set includes multiple stop arcs 103. The interval arc set includes multiple interval arcs 102. In order to achieve the optimization goal, for each time-space arc Set a certain profit . Each type of space-time arc is calculated differently, where the starting arc represents the departure of the train, so the profit is the basic operation benefit minus the penalty for deviating from the ideal departure time. The ending arc represents the end of the train, and the profit is 0. The stop arc and the interval arc represent the operation process of the train, and the profit is the negative additional travel time. The basic framework operation diagram of the train operation plan is the process of determining whether the space-time arc in the space-time network is selected for each train. According to the profit of each space-time arc in the space-time network of multiple trains and the selection results of the space-time arc, the total profit function and the first constraint set of multiple trains are determined. The first objective function is to maximize the sum of the profits of all selected space-time arcs in the space-time network of multi-layer trains (maximum total benefit). The expression of the total profit function of the first trip is as follows.

[0034] ; in, is the total profit function of the first trip of multiple trains, is a space-time arc of the train, is the profit of the space-time arc, is the selection result of the space-time arc, Indicates that the space-time arc is selected, Indicates that the space-time arc is not selected. is a set of space-time arcs.

[0035] The first constraint condition set of the first travel total profit function includes at least one basic constraint condition and at least one compatible constraint condition.

[0036] Based on the above embodiment, the basic constraint condition is determined based on the following steps: based on the selection result of the space-time arc, it is determined that each train selects at most one starting station for departure; and the number of trains entering the transit station is equal to the number of trains leaving the transit station, thereby obtaining the basic constraint condition.

[0037] Based on the above embodiment, the compatible constraint condition is determined based on the following steps: based on the selection result of the space-time arc, it is determined that the number of trains existing at a station at the same time is less than the maximum storage capacity of the station; the number of trains departing at the same time in the departure interval time period of the line section is less than 1; the number of trains passing at the same time in the passing interval time period of the line section is less than 1; the number of trains arriving at the same time in the arrival interval time period of the line section is less than 1; if a train arrives at the rear station of the line section, the number of trains passing the rear station in the first time period after the train arrives is 0; if a train passes the rear station of the line section, the number of trains arriving at the rear station in the second time period after the train passes is 0; if a train departs from the front station of the line section, the number of trains passing the front station in the third time period after the train departs is 0; if a train passes the front station of the line section, the number of trains passing the front station in the fourth time period after the train passes is 0; and the number of trains existing in the same time period of the line section is less than 1, and the compatible constraint condition is obtained.

[0038] Each train can depart from at most one starting station, corresponding to formula (1). The number of trains entering a transit station is equal to the number of trains leaving the transit station, corresponding to formula (2). The number of trains simultaneously present at a station is less than the station's maximum capacity, corresponding to formula (3).

[0039] (1); (2); (3); in, is the selection result of the space-time arc, is the starting arc set, is the train number, Gather for the train, is a space-time arc, For trains Entering the space-time location The arc set of Represents the stations that the train passes through at a certain time. For trains Leaving the space-time location The arc set of For trains At the virtual starting point and virtual endpoint The set of space-time locations between is the set of stop arcs, Gather at the station, For trains exist Arrival time at the station ,exist Time from the station The result of the selection of the starting space-time arc, From the station The starting point, To reach the station Node, Characteristic station The maximum parking capacity, is the time set, For time.

[0040] According to the operation type of the train at the stations before and after the interval, the time and space arc passed by the train is the interval arc (line interval), and the line interval is Divided into the former station Starting arc set , former station Through the arc collection , rear station Arrival Arc Set , rear station Through the arc collection .

[0041] The number of trains departing simultaneously during the departure interval of a line section is less than 1, corresponding to formula (4). The number of trains passing simultaneously during the passing interval of a line section is less than 1, corresponding to formula (5). The number of trains arriving simultaneously during the arrival interval of a line section is less than 1, corresponding to formula (6). If a train arrives at the rear station of the line section, the number of trains passing through the rear station in the first time period after the train arrives is 0, corresponding to formula (7). If a train passes through the rear station of the line section, the number of trains arriving at the rear station in the second time period after the train passes is 0, corresponding to formula (8). If a train departs from the front station of the line section, the number of trains passing through the front station in the third time period after the train departs is 0, corresponding to formula (9). If a train passes through the front station of the line section, the number of trains passing through the front station in the fourth time period after the train passes is 0, corresponding to formula (10).

[0042] (4); (5); (6); (7); (8); (9); (10); in, For trains exist Arrival at the rear station ,exist Time from the previous station The result of the selection of the starting space-time arc, Arrival at the station Node, For the former station The starting point, is the set of line intervals, is the line section, For trains on the line In the former station The departure interval time period, Former station Starting arc set, Former station Through the arc set, For the rear station Arrival arc set, For the rear station Through the arc set, For trains on the line In the former station The passing interval time period, For trains on the line Arrived at the rear station The inter-arrival time period, and are the space-time arcs that exist simultaneously in the line interval, For line section The first time period after the train arrives at the rear station, To set a constant, used to control whether the constraint is effective. For line section The second time period after the train passes the rear station, For line section The third time period after the train departs from the previous station, For line section The fourth time period after the train passes the previous station.

[0043] Formula (4) represents the departure interval time period in the route section There is at most one departure arc from the previous station. Formula (5) represents the time interval of the passing interval in the line section. There is at most one passing arc in the line. Formula (6) represents the arrival interval time period in the line section. There is at most one arrival arc at the next station in the line interval. Formula (7) indicates that if a train arrives at the next station in the line interval, then in the first time period after the train arrives The arc passing through the rear station is 0. Formula (8) indicates that if a train passes through the rear station of the line section, then the second time period when the train passes the rear station The arrival arc of the next station is 0. Formula (9) indicates that if a train departs from the previous station of the line section, then in the third time period after the train departs The arc passing through the previous station is 0. Formula (10) indicates that if a train passes through the previous station of the line section, then in the fourth time period after the train passes The passing arc of the previous station is 0.

[0044] The number of trains existing in the same time period of the line section is less than 1, corresponding to formula (11).

[0045] (11); in, and are the space-time arcs that exist simultaneously in the line interval, Spacetime arc The corresponding departure time, Spacetime arc The corresponding arrival time, Spacetime arc The corresponding departure time, Spacetime arc The corresponding arrival time, is the set of line intervals, is the line section, For line section The space-time arc, Spacetime arc The probability of selection, Spacetime arc The probability of selection.

[0046] According to the above formulas (1) to (11), the first set of constraints for the first objective function (the first trip total profit function) is obtained.

[0047] The first constraint condition set of the present invention takes into account the actual conflicts of multiple trains passing through a station, which is beneficial to improving the accuracy of the subsequent solution of the total profit function of the first trip.

[0048] S200: Solving the maximum value of the total profit function of the first trip based on the first constraint condition set to obtain a first target solution for the train's selection result of the space-time arc.

[0049] The maximum value of the total profit function of the first trip is solved according to the first set of constraints to obtain the first target solution. The basic framework operation diagram of the train operation plan (the existing train operation plan) is obtained according to the first target solution.

[0050] S300: Calculate the capacity utilization of the spatial segments of the space-time network within a set time range based on the first target solution, take the spatial segments with a capacity utilization less than the set capacity utilization as target spatial segments, and obtain the existing train operation plan of the target spatial segments based on the first target solution.

[0051] The existing train operation plan derived from the first target solution may not yet achieve saturation on the high-speed railway line. Therefore, additional in-pipeline trains can be deployed within the spatial segments to achieve a saturated operation diagram. Therefore, the capacity utilization of each spatial segment in the existing train operation plan can be evaluated, and spatial segments with capacity utilization below the set capacity utilization can be identified to obtain target spatial segments. Subsequently, in-pipeline trains can be deployed within the target spatial segments.

[0052] S400: Determine a second travel total profit function and a second set of constraints based on the profit of the space-time arcs of the space-time network corresponding to the target spatial segment and the set time range, the selection results of the space-time arcs, and the selection results of the operation plan.

[0053] The operation plan includes speed levels and stop plan .like Figure 6 As shown, introducing speed levels in space-time networks and stop plan Each layer of the space-time network represents a choice of speed level and stop plan. The values ​​are 1, 2, 3 and 4 respectively, representing different stop options.

[0054] For the target spatial segment and set time range where the capacity utilization rate is less than the set capacity utilization rate, the second objective function (the second travel total profit function) and the corresponding second constraint condition set are constructed based on the profit of the space-time arc, the selection results of the space-time arc, and the selection results of the operation plan.

[0055] ; in, is the total profit function of the second trip of multiple trains, is a space-time arc of the train, is the profit of the space-time arc, is the selection result of the space-time arc, Indicates that the space-time arc is selected, Indicates that the space-time arc is not selected. is the space-time arc set corresponding to the target space segment and the set time range, is the set of trains corresponding to the target spatial segment and the set time range.

[0056] Based on the above embodiment, the selection result of the operation plan includes the selection result of the speed level and the selection result of the stop plan.

[0057] Based on the above embodiment, the second set of constraints includes the constraints of the selection results of the operation plan, and the constraints of the selection results of the operation plan are determined based on the following steps: based on the selection results of the operation plan corresponding to the target spatial segment and the set time range of the train, it is determined that each train can select at most one speed level and one stop plan; the train that has selected the speed level and stop plan must choose the transit station with the same speed level and stop plan to stop; and the number of times all trains stop at the stations with the speed level and stop plan is greater than or equal to the required number of times at the station, thereby obtaining the constraints of the selection results of the operation plan.

[0058] Based on the above embodiment, the second constraint condition set also includes constraint conditions for the selection results of the space-time arc, and the constraint conditions for the selection results of the space-time arc are determined based on the following steps: based on the selection results of the space-time arc corresponding to the target spatial segment and the set time range of the train, it is determined that each train selects at most one starting station for departure; the number of trains entering the passing station is equal to the number of trains leaving the passing station; the number of trains existing at a station at the same time is less than the maximum storage capacity of the station; the number of trains departing at the same time in the departure interval time period of the line section is less than 1; the number of trains passing at the same time in the passing interval time period of the line section is less than 1; and the number of trains arriving at the line section is less than 1. The number of trains arriving at the same time in the line section is less than 1; if a train arrives at the rear station of the line section, the number of trains passing through the rear station in the first time period after the train arrives is 0; if a train passes through the rear station of the line section, the number of trains arriving at the rear station in the second time period after the train passes is 0; if a train departs from the front station of the line section, the number of trains passing through the front station in the third time period after the train departs is 0; if a train passes through the front station of the line section, the number of trains passing through the front station in the fourth time period after the train passes is 0; and the number of trains existing in the same time period of the line section is less than 1, and the constraint conditions for the selection result of the space-time arc are obtained.

[0059] Determine the second set of constraints. The second set of constraints introduces the speed grade and stop plan . Each train chooses at most one starting station for departure, and at most one speed level and one stop plan, corresponding to formula (12). Trains that have selected a speed level and a stop plan must choose to stop at transit stations with the same speed level and stop plan, corresponding to formula (13). The number of stops of all trains at stations with the same speed level and stop plan is greater than or equal to the required number of stops at the station, corresponding to formula (14). The number of trains entering the transit station is equal to the number of trains leaving the transit station, corresponding to formula (15). The number of trains that exist at a station at the same time is less than the maximum vehicle storage capacity of the station, corresponding to formula (16).

[0060] (12); (13); (14); (15); (16); in, For trains Select a speed class and stop plan The probability of (the result of the selection of the operation plan), Indicates train Select a speed class and stop plan , Indicates train Do not select a speed class and stop plan , is the speed grade set, is the set of stop plans, is the starting arc set of the target space segment, is the train set corresponding to the target spatial segment and the set time range, is the selection result of the space-time arc, Select the speed level for the target space segment and stop plan And at the middle station The set of space-time arcs of the stops, To choose a ceasefire plan , speed level is Stations along the way The probability of Gather at the station, Characteristic station The number of demands, Characteristic station The maximum parking capacity, Selected speed class and the stop plan is Train exist Arrival time at the station ,exist Time from the station The result of the selection of the starting space-time arc, The train enters the space-time position The arc set of Represents the stations that the train passes through at a certain time. The time and space position of the train leaving The arc set of For the train at the virtual starting point and virtual endpoint The set of space-time locations between .

[0061] Furthermore, the number of trains departing simultaneously during the departure interval of the line section is less than 1, corresponding to formula (17). The number of trains passing simultaneously during the passing interval of the line section is less than 1, corresponding to formula (18). The number of trains arriving simultaneously during the arrival interval of the line section is less than 1, corresponding to formula (19). If a train arrives at the rear station of the line section, the number of trains passing through the rear station in the first time period after the train arrives is 0, corresponding to formula (20). If a train passes through the rear station of the line section, the number of trains arriving at the rear station in the second time period after the train passes is 0, corresponding to formula (21). If a train departs from the front station of the line section, the number of trains passing through the front station in the third time period after the train departs is 0, corresponding to formula (22). If a train passes through the front station of the line section, the number of trains passing through the front station in the fourth time period after the train passes is 0, corresponding to formula (23).

[0062] (17); (18); (19); (20); (twenty one); (twenty two); (twenty three); in, Selected speed class and stop plan Train exist Arrives at the next station in the target route section at the same time ,exist Time from the previous station on the route The result of the selection of the starting space-time arc, is the line interval set, is the line section, For trains on the line In the former station The departure interval time period, Former station Starting arc set, Former station Through the arc set, For the rear station Arrival arc set, For the rear station Through the arc set, For trains on the line In the former station The passing interval time period, For trains on the line Arrived at the rear station The inter-arrival time period, and are the space-time arcs that exist simultaneously in the line interval, For line section The first time period after the train arrives at the rear station, To set a constant, used to control whether the constraint is effective. For line section The second time period after the train passes the rear station, For line section The third time period after the train departs from the previous station, For line section The fourth time period after the train passes the previous station.

[0063] The number of trains existing in the same time period of the line section is less than 1, corresponding to formula (24).

[0064] (twenty four); in, and are the space-time arcs that exist simultaneously in the line interval, Spacetime arc The corresponding departure time, Spacetime arc The corresponding arrival time, Spacetime arc The corresponding departure time, Spacetime arc The corresponding arrival time, is the set of line intervals, is the line section, For line section The space-time arc, For trains Corresponding space-time arc The probability of selection, For trains Corresponding space-time arc The probability of selection, is the set of trains corresponding to the target spatial segment and the set time range.

[0065] According to the above formulas (12) to (24), the second set of constraints for the second objective function (the second trip total profit function) is obtained.

[0066] The second constraint condition set of the present invention takes into account the actual conflicts of multiple trains passing through the station, which is conducive to improving the accuracy of the subsequent solution of the second trip total profit function.

[0067] S500: On the basis of the existing train operation plan, solving the maximum value of the second trip total profit function based on the second constraint condition set, and obtaining a second target solution of the train selection result for the target space-time arc.

[0068] On the basis of the existing train operation plan, the maximum value of the second travel total profit function is solved according to the second constraint condition set to obtain the second target solution, and then the line is densely laid in the target space segment to obtain the saturated operation diagram of the target space segment.

[0069] For example, a long-line segment is identified as a target spatial segment, and long-line vehicles are added within the target spatial segment and a set time range until the long-line segment is densely populated. A short-line segment is identified as a target spatial segment, and short-line vehicles are added within the target spatial segment and a set time range until the short-line segment is densely populated.

[0070] Based on the above embodiment, after solving the maximum value of the second travel total profit function based on the second constraint condition set and obtaining the second target solution of the train's selection result for the target space-time arc, it also includes: iteratively updating the capacity utilization of the target space segment based on the second target solution until the capacity utilization of the target space segment is greater than or equal to the set capacity utilization, and obtaining the updated second target solution; obtaining the maximum passing capacity of the high-speed railway line based on the first target solution and the updated second target solution.

[0071] like Figure 2As shown, the capacity utilization of the spatial segments is iteratively updated based on the second target solution. Furthermore, the target spatial segments are iteratively updated until the capacity utilization of all spatial segments exceeds the set capacity utilization. The maximum capacity of the high-speed railway line (the saturated operation diagram for all spatial segments) is obtained based on the first target solution and the final updated second target solution.

[0072] S600: Obtaining the maximum throughput capacity of the high-speed railway line based on the first target solution and the second target solution.

[0073] The maximum throughput capacity of the high-speed railway line (saturated operation diagram of all spatial sections) is obtained based on the first objective solution and the second objective solution.

[0074] The method for calculating the throughput capacity of a high-speed railway line provided in an embodiment of the present invention determines a first travel total profit function and a first set of constraints for the train based on the profit of the space-time arc of the space-time network of the high-speed railway line and the selection result of the space-time arc; solves the maximum value of the first travel total profit function based on the first set of constraints to obtain a first target solution for the selection result of the train for the space-time arc; calculates the capacity utilization rate of the spatial segment of the space-time network within a set time range based on the first target solution, takes the spatial segment with a capacity utilization rate less than the set capacity utilization rate as the target spatial segment, and obtains the existing train operation plan of the target spatial segment based on the first target solution; determines a second travel total profit function and a second set of constraints based on the profit of the space-time arc of the space-time network corresponding to the target spatial segment and the set time range, the selection result of the space-time arc and the selection result of the operation plan; solves the maximum value of the second travel total profit function based on the second set of constraints on the basis of the existing train operation plan to obtain a second target solution for the selection result of the train for the target space-time arc; obtains the maximum throughput capacity of the high-speed railway line based on the first target solution and the second target solution. In the first phase of the present invention, a basic framework diagram for determining the train operation plan is implemented based on the profits of the space-time arcs and the results of the space-time arc selection. In the second phase, the efficiency and accuracy of identifying the target spatial interval are improved through capacity utilization. In the third phase, a second total travel profit function and a second set of constraints are constructed to solve the second target solution, thereby achieving an encrypted layout of the basic framework diagram and obtaining the result of the through-capacity calculation. The method for calculating the through-capacity of high-speed railway lines provided by the present invention reduces the amount of calculation and complexity while ensuring the construction of large-scale train diagrams.

[0075] Based on the above embodiment, the first constraint condition set includes basic constraints and compatible constraints, and the compatible constraints are used to characterize the incompatible information of space-time arc selection. The maximum value of the first trip total profit function is solved based on the first constraint condition set, including: merging the compatible constraints and the first trip total profit function into a travel total profit relaxation function according to the Lagrange multiplier; solving the maximum value of the travel total profit relaxation function based on the basic constraints to obtain a relaxed solution; solving the maximum value of the first trip total profit function based on the relaxed solution of the travel total profit relaxation function and the first constraint condition set to obtain an initial solution; if the difference between the initial solution and the relaxed solution is greater than the set difference, updating the Lagrange multiplier to iteratively update the relaxed solution and the initial solution until the difference between the initial solution and the relaxed solution is less than or equal to the set difference, and taking the final updated initial solution as the first target solution.

[0076] Optionally, before constructing the relaxation function for the total profit of the first trip, the constraints of Formula (7)-Formula (10) can be modified. Since the constants set in Formula (7)-Formula (10) are usually large, directly relaxing to the total profit function of the first trip will result in the inability to merge similar terms and the inability to calculate the value of the total profit function of the first trip. Therefore, these compatible constraints (Formula (7)-Formula (10)) can be modified in advance to set the constants Replace with the smallest value. For example, in formula (7) . In formula (8) . In formula (9) . In formula (10) .in, For trains on the line In the former station The passing interval time period, For trains on the line Arrived at the rear station The inter-arrival time period, For line section The first time period after the train arrives at the rear station, For line section The second time period after the train passes the rear station, For line section The third time period after the train departs from the previous station, For line section The fourth time period after the train passes the previous station.

[0077] In the first set of constraints, formula (1) and formula (2) are basic constraints. Formula (3)-Formula (11) are compatible constraints. According to the Lagrange multiplier, formula (3)-Formula (6), the modified formula (7)-Formula (10) and formula (11) are merged into the first trip total profit function. For example, the variables in formula (3)-Formula (6), the modified formula (7)-Formula (10) and formula (11) are The coefficient of is multiplied by the Lagrange multiplier and then summed with the variables in the total profit function of the first trip The coefficients of are combined to obtain the total travel profit relaxation function.

[0078] Set the initial value of the Lagrange multiplier to 0. According to the basic constraints (Formula (1) and Formula (2)), solve the maximum value of the trip total profit relaxation function and obtain the relaxation solution. This relaxation solution is used as the upper limit of the first objective solution of the original first trip total profit function.

[0079] Based on the relaxed solution, heuristic information for solving the original first-trip total profit function is obtained. This heuristic information includes the specific train placement sequence. Based on this heuristic information and the original first constraint set (Formulas (1) to (11)), the maximum value of the first-trip total profit function is solved to obtain an initial solution. This initial solution is used as the lower bound of the first objective solution of the original first-trip total profit function.

[0080] The difference between the relaxed solution (upper bound) and the initial solution (lower bound) is used to calculate the gap between the upper and lower bounds. If the difference between the relaxed solution and the initial solution is greater than the set difference, it indicates that the initial solution is not yet optimal. The Lagrange multiplier is updated to iteratively update the relaxed solution and the initial solution until the difference between the relaxed solution and the initial solution is less than or equal to the set difference, resulting in the final first target solution.

[0081] Optionally, the Lagrange multiplier is updated to iteratively update the relaxed solution and the initial solution until a set number of iterations is reached, and the initial solution obtained in the last iteration is used as the first target solution.

[0082] The present invention constructs a travel total profit relaxation function through Lagrange multipliers, simplifies the solution of the maximum value of the first travel total profit function, and reduces the amount of calculation.

[0083] Based on the above embodiment, the capacity utilization rate of the spatial segment of the space-time network within the set time range is calculated based on the first target solution, including: obtaining at least one occupied time period of the existing train in the spatial segment based on the first target solution; adding at least one occupied time period to obtain the total occupied time of the spatial segment; if there is an overlapping time period between two occupied time periods, the overlapping time period is only added once; based on the set time range, the skylight time of the spatial segment and the invalid time of the spatial segment, the total available time of the spatial interval is determined; based on the ratio of the total occupied time to the total available time, the capacity utilization rate is obtained.

[0084] The purpose of this embodiment is to quickly evaluate the capacity utilization of each space segment in an existing train operation plan.

[0085] According to the first target solution, the occupied time periods of existing trains in each spatial segment are obtained; the occupied time periods are added together to obtain the total occupied time of the spatial segment; if there is an overlapping time period between at least two occupied time periods, the overlapping time periods are added only once.

[0086] For example, Figure 4 As shown, for a single train, no matter how the train runs or how the line stations are set up, the train can be abstracted as an occupied time period on the time axis, thereby ignoring other details. The train's occupied time period is then used to determine whether there is a repeated occupancy relationship between trains, and the trains are divided into multiple immediately consecutive train groups. All trains in an immediately consecutive train group can be regarded as a combined train for the calculation of the occupied time period, so multiple occupied time periods are combined into one section, and then the occupied time periods of the immediately consecutive train groups are calculated separately. Because there is no repeated occupancy relationship between trains in different immediately consecutive train groups, the occupied time period can be accurately obtained by adding them up. This process does not require the judgment of complex relationships between trains, and avoids the calculation of repeated occupied time periods, which can effectively simplify the calculation process. As shown Figure 4 As shown, input the basic framework operation diagram corresponding to the first target solution. Sort the existing train operation plans in the basic framework operation diagram to obtain the sorted existing train operation plans. Group the sorted existing train operation plans and group the trains in the existing train operation plans into groups. Divided into 3 consecutive train groups ( ). Combine each group of consecutive trains into a combined train. For each combined train, calculate the occupied time period, which are 、 and The total occupancy time of the spatial segment is obtained by adding up the three occupancy time periods.

[0087] Based on the first objective solution, calculate the total occupancy time of the space segment in the basic framework diagram (the existing train operation plan). Divide the total occupancy time of the space segment by the available time of the space segment to obtain the capacity utilization rate of the space segment. Then, based on the total number of trains corresponding to the space segment and the capacity utilization rate, estimate the maximum number of trains that can be deployed if the total occupancy time in the space segment is fully utilized, i.e., the throughput capacity.

[0088] ; in, is the total occupation time of the space segment, is the total available time of the space segment, is the capacity utilization of the space segment, is the total number of trains corresponding to the spatial segment, If the total occupied time in the space section is occupied, the maximum number of trains that can be drawn, 1440 is the set time range (the number of minutes corresponding to 24 hours), is the skylight time of the space segment, is the invalid time of the space segment, is the length of the space segment, is the average speed of the train.

[0089] The present invention accurately calculates the total occupied time by using occupied time periods and overlapping time periods. By calculating the capacity utilization rate, the time utilization of the space segment is accurately evaluated, which is conducive to the subsequent dense laying of trains in the target space segment.

[0090] Based on the above embodiment, on the basis of the existing train operation plan, the maximum value of the second trip total profit function is solved based on the second constraint condition set to obtain the second target solution of the train's selection result for the target space-time arc, including: dividing the set time range into multiple sub-time periods to divide the second trip total profit function and the second constraint condition set into multiple sub-functions, sub-constraint condition sets of sub-functions and the solution order of sub-functions; solving the unsolved sub-functions based on the solution order, sub-constraint condition sets and sub-optimal solutions of the solved sub-functions; and determining the second target solution based on the sub-optimal solutions of all sub-functions.

[0091] The present invention solves the second objective solution of the second travel total profit function through a time domain rolling optimization algorithm.

[0092] like Figure 5As shown, the set time range (time domain) under study is divided into multiple sub-time periods, and trains are mapped in each sub-time period (subdomain) in sequence. Once a sub-time period has been fully mapped, no new trains can be added to that subdomain. Therefore, when mapping other subdomains, arcs can be constructed only within that subdomain, ignoring the constraints of previously solved subdomains, thus reducing the problem size. When calculating within a subdomain, the impact of trains in other mapped subdomains can be considered, and potentially conflicting trains can be used as known inputs to ensure that there are no conflicts with other subdomains. This divides the original problem into multiple subproblems, each of which can be optimally solved within a limited time. After all subdomains have been solved, the solutions to all subproblems are combined into a complete solution set, resulting in the second objective solution to the total profit function for the second trip.

[0093] Solving the second objective solution of the second trip total profit function includes the following steps.

[0094] Step 1: Determine the target time range for the second trip total profit function (the problem to be solved). For high-speed rail capacity calculations, the target time range is typically one hour, one peak period, or one day. Enter the target spatial segment, the target time range, the stop plan, and the first target solution.

[0095] Step 2: Divide the solution subdomain The time frame will be set based on the difficulty of the problem to be solved Divided into Sub-time periods (sub-domains), sub-domains can overlap but must cover the set time range ,Right now , thus forming Sub-problems , and calculate each time domain separately.

[0096] Step 3: Determine the order in which to solve the sub-functions (sub-problems). Before solving the sub-functions sequentially, the order can be determined. This method uses a greed-based heuristic to prioritize sub-time periods with limited capacity. If two sub-time periods have equally limited capacity, the earlier sub-time period is prioritized, thus ranking the sub-functions.

[0097] Step 4: Construct the sub-function . Set the time range for solving subproblems and problem parameters, and taking into account the trains that have been drawn in other sub-time periods, the sub-function construction is completed.

[0098] Step 5: Solve the subfunction Solve the sub-function (for example, solve the k-th sub-problem) by using the exact algorithm of the solver to solve the sub-function to ensure the superiority of the sub-optimal solution.

[0099] Step 6: Check whether the sub-optimal solution conflicts with other trains or the result is unsatisfactory. If so, return to step 4 to adjust the construction of the sub-function. For example, add the conflicting train to the front train pool, or adjust the schedule of the cross-line train. If satisfactory, add the running line drawn by the sub-function solution to the solution set and continue to solve other sub-functions (solve the k+1th sub-problem).

[0100] Step 7: Check whether all subproblems corresponding to the subtime periods have been solved. If so, the calculation is complete. Otherwise, return to Step 4 and continue solving the subfunctions. Output the final number of trains and timetable, and obtain the saturated operation diagram corresponding to the target spatial segment (second target solution).

[0101] According to the first target solution and the second target solution, the saturation operation diagrams of all spatial segments are obtained.

[0102] The present invention divides the set time range into multiple sub-time periods, and further decomposes the solution of the second trip total profit function into the solution of multiple sub-functions, thereby reducing the time complexity and space complexity of the solution of the second trip total profit function.

[0103] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for calculating the throughput capacity of a high-speed railway line, characterized in that: include: Based on the profit of the space-time arc of the high-speed railway line train in the space-time network and the selection result of the space-time arc, determine the total profit function of the first trip of the train and the first constraint condition set; Solving the maximum value of the first trip total profit function based on the first constraint condition set to obtain a first target solution for the train selection result of the space-time arc; calculating a capacity utilization rate of a spatial segment of the space-time network within a set time range based on the first target solution, taking a spatial segment with a capacity utilization rate less than the set capacity utilization rate as a target spatial segment, and obtaining an existing train operation plan for the target spatial segment based on the first target solution; Determining a second travel total profit function and a second set of constraints based on the profit of the space-time arcs of the space-time network corresponding to the target spatial segment and the set time range, the selection result of the space-time arcs, and the selection result of the operation plan; On the basis of the existing train operation plan, solving the maximum value of the second trip total profit function based on the second constraint condition set to obtain a second target solution for the train selection result of the target space-time arc; The maximum throughput capacity of the high-speed railway line is obtained based on the first target solution and the second target solution.

2. The method for calculating the throughput capacity of a high-speed railway line according to claim 1, characterized in that: The first constraint condition set includes basic constraint conditions and compatible constraint conditions, wherein the compatible constraint conditions are used to characterize incompatible information of the space-time arc selection. Solving the maximum value of the first trip total profit function based on the first constraint condition set includes: Combining the compatibility constraint condition and the first travel total profit function into a travel total profit relaxation function according to Lagrange multipliers; Solving the maximum value of the travel total profit relaxation function based on the basic constraint conditions to obtain a relaxation solution; Solving the maximum value of the first travel total profit function based on the relaxed solution of the travel total profit relaxation function and the first constraint condition set to obtain an initial solution; If the difference between the initial solution and the relaxed solution is greater than the set difference, the Lagrange multiplier is updated to iteratively update the relaxed solution and the initial solution until the difference between the initial solution and the relaxed solution is less than or equal to the set difference, and the final updated initial solution is used as the first target solution.

3. The method for calculating the throughput capacity of a high-speed railway line according to claim 2, characterized in that: The basic constraint condition is determined based on the following steps: based on the selection result of the space-time arc, determining that each train selects at most one starting station for departure; And the number of trains entering the transit station is equal to the number of trains leaving the transit station, thus obtaining the basic constraint condition.

4. The method for calculating the throughput capacity of a high-speed railway line according to claim 2, characterized in that: The compatibility constraint condition is determined based on the following steps: based on the selection result of the space-time arc, determining that the number of trains simultaneously existing at a station is less than the maximum vehicle storage capacity of the station; The number of trains departing simultaneously within the departure interval time period of the line section is less than 1; the number of trains passing simultaneously within the passing interval time period of the line section is less than 1; the number of trains arriving simultaneously within the arrival interval time period of the line section is less than 1; if a train arrives at the rear station of the line section, the number of trains passing through the rear station within the first time period after the train arrives is 0; if a train passes through the rear station of the line section, the number of trains arriving at the rear station within the second time period after the train passes is 0; if a train departs from the front station of the line section, the number of trains passing through the front station within the third time period after the train departs is 0; if a train passes through the front station of the line section, the number of trains passing through the front station within the fourth time period after the train passes is 0; and the number of trains existing in the same time period of the line section is less than 1, and the compatible constraint condition is obtained.

5. The method for calculating the throughput capacity of a high-speed railway line according to claim 1, characterized in that: The calculating, based on the first target solution, the capacity utilization rate of the spatial segment of the spatiotemporal network within a set time range includes: Obtaining at least one occupied time period of an existing train in the spatial segment based on the first target solution; Adding at least one of the occupied time periods to obtain the total occupied time of the spatial segment; if there is an overlapping time period between two of the occupied time periods, the overlapping time period is only added once; Determining the total available time of the space interval based on the set time range, the skylight time of the space segment, and the inactive time of the space segment; The capacity utilization rate is obtained based on the ratio of the total occupied time to the total available time.

6. The method for calculating the throughput capacity of a high-speed railway line according to claim 1, characterized in that: The selection result of the operation plan includes the selection result of the speed level and the selection result of the stop plan.

7. The method for calculating the throughput capacity of a high-speed railway line according to claim 6, characterized in that: The second set of constraints includes constraints on the selection result of the operation plan, and the constraints on the selection result of the operation plan are determined based on the following steps: Based on the selection results of the train's operation plan corresponding to the target spatial segment and the set time range, it is determined that each train can select at most one speed level and one stop plan; the train that has selected the speed level and stop plan must choose the same transit stations with the same speed level and stop plan to stop at; and the number of times all trains stop at stations with the speed level and stop plan is greater than or equal to the required number of times at the station, thereby obtaining the constraint conditions for the selection results of the operation plan.

8. The method for calculating the throughput capacity of a high-speed railway line according to claim 1, characterized in that: The second set of constraints further includes constraints on the selection result of the space-time arc, and the constraints on the selection result of the space-time arc are determined based on the following steps: Based on the selection result of the space-time arc corresponding to the target spatial segment and the set time range, each train is determined to select at most one starting station for departure; The number of trains entering the transit station is equal to the number of trains leaving the transit station; the number of trains existing at a station at the same time is less than the maximum storage capacity of the station; the number of trains departing simultaneously in the departure interval time period of the line section is less than 1; the number of trains passing simultaneously in the passing interval time period of the line section is less than 1; the number of trains arriving simultaneously in the arrival interval time period of the line section is less than 1; if a train arrives at the rear station of the line section, the number of trains passing the rear station in the first time period after the train arrives is 0; if a train passes the rear station of the line section, the number of trains arriving at the rear station in the second time period after the train passes is 0; if a train departs from the front station of the line section, the number of trains passing the front station in the third time period after the train departs is 0; if a train passes the front station of the line section, the number of trains passing the front station in the fourth time period after the train passes is 0; and the number of trains existing in the same time period of the line section is less than 1, and the constraint conditions of the selection result of the space-time arc are obtained.

9. The method for calculating the throughput capacity of a high-speed railway line according to claim 1, characterized in that: The method of solving the maximum value of the second trip total profit function based on the second constraint condition set on the basis of the existing train operation plan to obtain a second target solution for the train selection result of the target space-time arc includes: Dividing the set time range into a plurality of sub-time periods to divide the second trip total profit function and the second constraint condition set into a plurality of sub-functions, sub-constraint condition sets of the sub-functions, and a solving order of the sub-functions; Solving the unsolved sub-functions based on the solving order, the sub-constraint condition set, and the sub-optimal solution of the solved sub-functions; The second objective solution is determined based on the sub-optimal solutions of all sub-functions.

10. The method for calculating the throughput capacity of a high-speed railway line according to claim 1, characterized in that: After solving the maximum value of the second trip total profit function based on the second constraint condition set to obtain the second target solution of the train selection result for the target space-time arc, the method further includes: Iteratively updating the capacity utilization of the target space segment based on the second target solution until the capacity utilization of the target space segment is greater than or equal to the set capacity utilization, and obtaining an updated second target solution; The maximum throughput capacity of the high-speed railway line is obtained based on the first target solution and the updated second target solution.

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