A method for calculating the number of trains assigned to a line in an intelligent rail express system

Abstract

The present invention relates to the field of intelligent rail transit technology, and specifically to a method for calculating the number of trains assigned to lines in an intelligent rail express system. The method includes calculating the minimum number of line-operated trains required to execute all service trips; constructing a dual-objective linear programming model whose objective function is to minimize the number of line-operated trains and minimize the number of train charging tasks, and calculating multiple different feasible numbers of trains in operation and the corresponding total number of train charging tasks; using a deficit function graphical scheduling model to draw a deficit function image of each origin and destination station; drawing a two-dimensional Pareto solution set image, and determining the number of trains in operation in combination with the deficit function image; and calculating the number of trains assigned to lines in an intelligent rail express system. The present invention comprehensively considers constraints such as the charging demand and turnaround preparation time of the intelligent rail train, combines the deficit function model with the mathematical programming model, and can more accurately determine the scale of the intelligent rail line-assigned fleet.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent rail transit, and in particular to a method for calculating the number of trains assigned to a line of an intelligent rail express system. Background Art

[0002] In recent years, with the development of emerging technologies, a new mode of transportation, the Autonomous Rail Rapid Transit (ART), has been successfully developed and started to operate in some cities at home and abroad. The ART system uses virtual track technology to guide and control ART vehicles through automatic and virtual tracking technology, breaking the limitations of traditional tracks. Another feature of ART is that it allows vehicles to be flexibly marshaled to provide variable passenger capacity, better meet passenger needs and reduce the number of empty seats in vehicles. ART not only has lower construction and operating costs than traditional rail transit, but also has a higher passenger capacity than buses. ART not only combines the flexibility of buses and the high efficiency of rail transit, but also has a lower construction cost than light rail. In addition, ART can also bring many economic, environmental and social benefits, such as reducing traffic congestion, reducing parking requirements, reducing greenhouse gas emissions, and promoting public transportation-oriented development. Therefore, it is an extremely attractive urban public transportation mode.

[0003] In the initial operational planning stage of the smart rail, traffic planners need to predict passenger flow demand based on actual conditions, and then design network routes, formulate vehicle operation schedules, and determine the size of the attached fleet. Among them, the determination of the size of the line's attached fleet is very important. Because on the one hand, the vehicle purchase cost is the main cost of the operating company; on the other hand, the size of the attached fleet also directly affects the service level of the smart rail line. An insufficient size of the attached fleet will lead to reduced operating efficiency and longer passenger waiting time, which will in turn cause a decline in the overall service quality. An overly large attached fleet will lead to vacant vehicles and unnecessary vehicle purchase costs, which will ultimately affect the economic feasibility of the overall smart rail system. Therefore, it is of great significance to determine a reasonable size of the attached fleet for the smart rail line.

[0004] The traditional calculation method is to divide the train turnaround time by the train departure interval to obtain the number of operating vehicles required for the line. However, the limitation of this calculation method is that it regards the train turnaround time as a fixed value. However, in actual use, the turnaround time of each train is not exactly the same due to the need for charging, which makes it difficult to directly apply the traditional calculation method to the calculation of the number of vehicles assigned to the smart rail line. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for calculating the number of trains assigned to an intelligent rail express system line, which comprehensively considers constraints such as the charging requirements and turnaround preparation time of the intelligent rail trains, and combines the deficit function model with the mathematical programming model, so as to more accurately determine the scale of the intelligent rail line assigned fleet.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0007] A method for calculating the number of trains assigned to a line of an intelligent rail express system comprises the following steps:

[0008] Generate train service information for the full-day operation period according to the line operation period and train departure interval of the intelligent rail express system, and calculate the minimum number of line operation trains required to execute all service trips based on the train service trip data information;

[0009] A dual-objective linear programming model with the objective function of minimizing the number of trains in operation on the line and minimizing the number of train charging tasks is constructed. Based on the minimum number of trains in operation on the line, multiple different feasible numbers of trains in operation and the corresponding total number of train charging tasks are calculated;

[0010] Use the deficit function graphical dispatch model to draw the deficit function image of each departure and arrival station;

[0011] According to multiple different feasible numbers of trains and the corresponding total number of train charging tasks, a two-dimensional Pareto solution set graph is drawn, and the number of trains to be used is determined in combination with the deficit function graph;

[0012] According to the number of spare trains and trains under repair in the intelligent rail express system, the number of trains assigned to the intelligent rail express system line is calculated based on the determined number of operating trains.

[0013] Preferably, the minimum number of line operation trains required to execute all service trains is calculated based on the train service train data information, including the following steps:

[0014] Based on the train service data information, a network flow integer programming model without considering charging is constructed;

[0015] Solve the network flow integer programming model without considering charging to obtain the maximum feasible number of train connections;

[0016] The minimum number of line-operated trains required to execute all service trips is calculated based on the maximum feasible number of train connections.

[0017] As a preferred embodiment, the network flow integer programming model without considering charging is constructed as follows:

[0018]

[0019] The constraints are:

[0020] x j -(x i +t i +△t i +z ij )≥(x ij -1)*M 1 ,i,j∈I

[0021]

[0022] Among them, Max is the maximum value function, C VS (I) is the number of feasible train connections, I is the set of train service numbers, x ij is a 0-1 variable indicating whether train number i and train number j are executed by the same train, x j is the departure time of train number j, x i is the departure time of train number i, t i is the travel time of train number i, △t i is the turnaround preparation time of train number i, z ij is the judgment coefficient of whether train number i and train number j are located at the same station, M 1 is a set positive parameter, and T is the duration of the operation cycle.

[0023] As a preferred embodiment, the minimum number of line operation trains required to execute all service trips is calculated based on the maximum feasible train connection number:

[0024] Min F VS (I)=|I|-MaxC VS (I)

[0025] Among them, Min is the minimum function, F VS (I) is the number of trains in service on the line, |I| is the number of all trains in the train service set I, Max is the maximum value function, C VS (I) is the number of feasible train connections.

[0026] Preferably, a dual-objective linear programming model is constructed with the objective function of minimizing the number of line operating trains and minimizing the number of train charging tasks, and a plurality of different feasible numbers of operating trains and corresponding numbers of train charging tasks are calculated based on the minimum number of line operating trains, including the following steps:

[0027] Construct a dual-objective linear programming model with the objective function of minimizing the number of trains used on the line and minimizing the number of train charging tasks;

[0028] The objective function of minimizing the number of trains used on the line in the dual-objective linear programming model is transformed into a constraint condition, and a single-objective linear programming model with the objective function of minimizing the number of train charging tasks is obtained;

[0029] Based on the minimum number of trains in operation on the line, the number of feasible train connections is gradually increased in steps of 1, and a single-objective linear programming model with the objective function of minimizing the number of train charging tasks is solved to obtain multiple different feasible numbers of trains in operation and the corresponding numbers of train charging tasks.

[0030] As a preferred embodiment, a dual-objective linear programming model is constructed with the objective function of minimizing the number of line operating trains and minimizing the number of train charging tasks, specifically:

[0031]

[0032] The constraints are:

[0033]

[0034] Among them, Min is the minimum function, F VS (I) is the number of trains in service on the line, |I| is the number of all trains in the train service set I, Max is the maximum value function, x ij is a 0-1 variable indicating whether train number i and train number j are executed by the same train, F BS The number of charging tasks for the train, y ij is a 0-1 variable indicating whether train number i is connected to train number j and the train is charged, x j is the departure time of train number j, x i is the departure time of train number i, t i is the travel time of train number i, Δt i is the turnaround preparation time of train number i, z ij is the judgment coefficient of whether train number i and train number j are located at the same station, Q is the maximum battery capacity of the train, is the remaining power of the train after the train number i is executed, P is the rated charging power of the charging pile, M 2 is a positive integer, is the remaining power of the train before the train number i, qi is the power consumed by each trip of train number i, α is the safety power threshold coefficient of the train, is the remaining power of the train before the execution of train number j, u ij is the remaining power of the train from train number i to train number j, r ij is a 0-1 variable indicating whether the train number i is connected and has a charging task, and T is the duration of the operation cycle.

[0035] Preferably, the deficit function graphical scheduling model is used to draw the deficit function image of each origin and destination station, including:

[0036] With time as the horizontal axis and the difference between the total number of departing trains and the total number of arriving trains at the originating and terminating stations before the set time as the vertical axis, the inverse function graph of each originating and terminating station is plotted.

[0037] Preferably, according to a plurality of different feasible numbers of trains and the corresponding total number of train charging tasks, a two-dimensional Pareto solution set image is drawn, and the number of trains to be used is determined in combination with the inverse function image, including the following steps:

[0038] With the number of feasible trains as the horizontal coordinate and the total number of train charging tasks as the vertical coordinate, multiple different numbers of feasible trains and the corresponding total number of train charging tasks are plotted in the form of points on a two-dimensional coordinate system to obtain a two-dimensional Pareto solution set image;

[0039] A solution is selected from the two-dimensional Pareto solution set image, and the number of trains to be used is determined according to the number of feasible trains to be used for the selected solution.

[0040] As a preferred embodiment, according to the number of spare trains and the number of trains under repair of the intelligent rail express system, the number of trains assigned to the line of the intelligent rail express system is calculated based on the determined number of operating trains, specifically:

[0041] Add the number of spare trains and trains under repair of the intelligent rail express system to the determined number of operating trains to obtain the number of trains assigned to the intelligent rail express system line.

[0042] As a preferred method, the number of spare trains of the intelligent rail express system is calculated as follows:

[0043]

[0044] Among them, N 备 is the number of spare trains, N 运 is the number of trains in operation, δ 备 is the reserve rate;

[0045] The calculation method for the number of trains under repair in the intelligent rail express system is:

[0046]

[0047] Among them, N 修 is the number of trains under repair, h i is the maintenance cycle coefficient of maintenance process i, t i is the detention time for repair process i.

[0048] The present invention has the following beneficial effects:

[0049] 1. The present invention proposes a new calculation method for determining the size of the fleet assigned to the smart rail line, which is used to determine the number of vehicles (trains) required for the smart rail line. The method takes into account three different fleet size components, including the number of operating vehicles, the number of spare vehicles, and the number of vehicles under repair.

[0050] 2. Based on the network flow mathematical programming model, the present invention considers the charging demand of the smart rail train, proposes a new dual-objective linear programming model, and transforms the dual-objective linear programming model into a single-objective linear programming model. This model can not only calculate the number of smart rail vehicles, but also optimize the total number of charging times of the smart rail train. In addition, the "two-dimensional Pareto solution set diagram" proposed by the present invention can also help assist operating management companies to choose a plan for the number of smart rail vehicles that is more in line with reality.

[0051] 3. The present invention makes full use of the advantages of the graphical representation of the deficit function model. By drawing the corresponding deficit function image for each station, it can not only intuitively and visually analyze the train ownership of each station in the smart rail line in different time periods, that is, the abundance or shortage of trains, but also obtain the number of smart rail vehicles that should be equipped at each station during the full-day operation period. This brings great convenience to the research work on the scale of the station fleet in the road network and the scheduling operation of the operating staff. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 A flow chart of a method for calculating the number of trains assigned to a line of an intelligent rail express system;

[0053] Figure 2 This is the deficit function diagram of the starting station of the smart rail line;

[0054] Figure 3 This is the deficit function diagram of the terminal station of the smart rail line. DETAILED DESCRIPTION

[0055] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0056] Due to the charging requirements of the smart rail trains, the turnaround time of each trip is not exactly the same, which makes the traditional method of calculating the fleet size by fixed vehicle turnaround time and departure interval not applicable to the smart rail line. Therefore, the present invention expands the network flow mathematical programming model and makes full use of the advantages of the graphical representation of the deficit function to better solve the problem of calculating the number of vehicles assigned to the smart rail line with charging requirements.

[0057] like Figure 1 As shown, a method for calculating the number of trains assigned to a line of an intelligent rail express system provided by an embodiment of the present invention includes the following steps S1 to S5:

[0058] S1. Generate train service information for the full-day operation period according to the line operation period and train departure interval of the intelligent rail express system, and calculate the minimum number of line operation trains required to execute all service trains based on the train service train data information;

[0059] In an optional embodiment of the present invention, the present embodiment calculates the minimum number of line operation trains required to execute all service trains based on the train service train number data information, including the following steps:

[0060] Based on the train service data information, a network flow integer programming model without considering charging is constructed;

[0061] Solve the network flow integer programming model without considering charging to obtain the maximum feasible number of train connections;

[0062] The minimum number of line-operated trains required to execute all service trips is calculated based on the maximum feasible number of train connections.

[0063] In this embodiment, the network maximum flow model for the minimum fleet size problem is constructed using three attributes of the service train data information and a judgment coefficient. The three attributes of the train data information are the departure time x of train number i and the departure time x of train number i. i , trip time t i , the turnaround preparation time △t of train number i i ; The judgment coefficient of whether train number i and j are located at the same station is z ij , judgment coefficient z ij The purpose is to constrain the station of train number u and j to be the same station, that is, empty running of trains is not allowed. The mathematical expression of the specific model is as follows:

[0064]

[0065] The constraints are:

[0066] x j -(x i +t i +△ti +z ij )≥(x ij -1)*M 1 ,i,j∈I

[0067]

[0068]

[0069] Among them, Max is the maximum value function, C VS (I) is the number of feasible train connections, I is the set of train service numbers, x ij is a 0-1 variable indicating whether train number i and train number j are executed by the same train. If so, x ij =1, otherwise x ij =0,x ij The value is mainly determined based on the departure time of trains i and j, the travel time of train i, the turnaround time after train i ends, and the judgment coefficient of whether trains i and j are located at the same station; x j is the departure time of train number j, x i is the departure time of train number i, t i is the travel time of train number i, Δt i is the turnaround preparation time of train number i, z ij is the judgment coefficient of whether train number i and train number j are located at the same station. If train number i and train number j are located at the same station, then z ij =0, otherwise the value is usually the duration of the operation cycle; M 1 It is a positive parameter set, and its value is usually several times the length of the operating cycle; T is the length of the operating cycle.

[0070] By solving the above model, we can get the maximum feasible train connection number C: VS (I), which is the corresponding maximum network flow in the network flow model.

[0071] Based on the maximum feasible train connection number C obtained by solution calculation VS (I), the minimum fleet size required can be calculated as follows:

[0072] MinF VS (I)=|I|-MaxC VS (I)

[0073] Among them, Min is the minimum function, F VS (I) is the number of trains in service on the line, |I| is the number of all trains in the train service set I, Max is the maximum value function, C VS (I) is the number of feasible train connections.

[0074] S2. Construct a dual-objective linear programming model with the objective function of minimizing the number of line operating trains and minimizing the number of train charging tasks, and calculate multiple different feasible numbers of operating trains and the corresponding total number of train charging tasks based on the minimum number of line operating trains;

[0075] In an optional embodiment of the present invention, this embodiment constructs a dual-objective linear programming model whose objective function is to minimize the number of line operating trains and minimize the number of train charging tasks, and calculates multiple different feasible numbers of operating trains and corresponding numbers of train charging tasks based on the minimum number of line operating trains, including the following steps:

[0076] Construct a dual-objective linear programming model with the objective function of minimizing the number of trains used on the line and minimizing the number of train charging tasks;

[0077] The objective function of minimizing the number of trains used on the line in the dual-objective linear programming model is transformed into a constraint condition, and a single-objective linear programming model with the objective function of minimizing the number of train charging tasks is obtained;

[0078] Based on the minimum number of trains in operation on the line, the number of feasible train connections is gradually increased in steps of 1, and a single-objective linear programming model with the objective function of minimizing the number of train charging tasks is solved to obtain multiple different feasible numbers of trains in operation and the corresponding numbers of train charging tasks.

[0079] In this embodiment, the power consumption, safety power threshold, charging power of charging piles, etc. of the smart rail train are fully considered, the network flow integer programming model of step S1 is expanded, and a dual-objective linear programming model with the objective function of minimizing the fleet size and minimizing the number of train charging tasks is constructed. Based on the calculation results in step S1, multiple feasible options for the number of smart rail trains and the number of charging tasks considering the train charging needs are calculated. The specific dual-objective linear programming model is as follows:

[0080]

[0081] The constraints are:

[0082] Train chain constraints:

[0083]

[0084] The constraints on whether trains i and j can connect:

[0085]

[0086] The constraints of train connections being greater than charging tasks:

[0087]

[0088] Power consumption constraints:

[0089]

[0090] The remaining power of the vehicle is limited by:

[0091]

[0092] Among them, Min is the minimum function, F VS (I) is the number of trains in service on the line, |I| is the number of all trains in the train service set I, Max is the maximum value function, x ij is a 0-1 variable indicating whether train number i and train number j are executed by the same train, F BS The number of charging tasks for the train, y ij is a 0-1 variable indicating whether train number i is connected to train number j and the train is charged, x j is the departure time of train number j, x i is the departure time of train number i, t i is the travel time of train number i, Δt i is the turnaround preparation time of train number i, z ij is a 0-1 variable indicating whether train number i and train number j are located at the same station, Q is the maximum battery capacity of the train, is the remaining power of the train after the train number i is executed, P is the rated charging power of the charging pile, M 2 is a positive integer, is the remaining power of the train before train number i, q i is the power consumed by each trip of train number i, α is the safety power threshold coefficient of the train, is the remaining power of the train before the execution of train number j, u ij is the remaining power of the train from train number i to train number j, r ij is a 0-1 variable indicating whether the train number i is connected and has a charging task, and T is the duration of the operation cycle.

[0093] In the above model, the two objective functions are to minimize the number of trains used on the smart rail line and to minimize the total number of charging times of the smart rail trains. The departure time of train number i, j is x i , x j , assuming that the departure time is discretized into minutes. The train chain connection constraint ensures that each train can only be connected to one train before and after. The judgment basis for whether train number i and , can be connected is based on the departure time of train number i and , the travel time of train number i, the turnaround preparation time after the end of train number i, the judgment coefficient of whether train number i and , are located in the same station, and the charging time of the train number. If train number i and j can be executed by the same vehicle, x ij =1 or 0; if train numbers i and j cannot be carried out by the same vehicle, then xij = 0; if the train is charged after executing train number i and then executes train number j, then y ij =1; if the train does not need to be charged after completing the train number i, then y ij = 0. The constraint that the train connection is greater than the charging task means that the need for charging is considered only when the trains are connected, and the charging problem is not considered if there is no connection between the trains. The power consumption constraint ensures that the remaining power of the train does not fall below the preset power safety threshold. The remaining power constraint of the vehicle ensures that the train has enough power to perform the task of the next train before executing the corresponding train.

[0094] In this embodiment, by converting the objective function of the number of vehicles used on the smart rail line in the objective function of the above model into a constraint condition, the following single-objective linear programming model for calculating the total number of charging times of smart rail trains during the full-day operation period can be obtained:

[0095]

[0096] Add the following constraints to the existing ones:

[0097]

[0098] In step S1, the number of feasible train connections C VS Based on the solution of (I), the number of feasible train connections C VS (I) By increasing the step size by 1, the different numbers of smart rail vehicles and the corresponding charging times can be solved.

[0099] S3. Use the deficit function graphical dispatch model to draw the deficit function image of each departure and arrival station;

[0100] In an optional embodiment of the present invention, the present embodiment uses the deficit function graphical scheduling model to draw the deficit function image of each origin and destination station, including:

[0101] With time as the horizontal axis and the difference between the total number of departing trains and the total number of arriving trains at the originating and terminating stations before the set time as the vertical axis, the inverse function graph of each originating and terminating station is plotted.

[0102] In this embodiment, the deficit function model is a graphical model, also known as a step function. The connotation of this step function is: at a single station, if a vehicle is dispatched from the station, the function value is increased by 1; if a vehicle arrives at the station, the function value is reduced by 1. Its biggest advantage is that it can intuitively and visually analyze the vehicle ownership of each station in the line network at different time periods, that is, the abundance or shortage of the number of vehicles. This brings great convenience to the research work on the scale of station vehicles in the road network and the scheduling operation of the operating staff. The deficit function image is a two-dimensional image, in which the horizontal axis represents time, and the vertical axis represents the difference between the total number of departure vehicles and the number of vehicles arriving before a certain time station (including this time). According to the train service train information of the full-day operation period generated by the line operation period and train departure interval of the intelligent rail express system, the deficit function image of all the starting and ending stations of the line can be drawn. Figure 2 and Figure 3 The deficit function diagram of the starting station and the terminal station of a certain intelligent rail line is given.

[0103] This embodiment takes advantage of the graphical representation of the deficit function model to draw a corresponding deficit function graph for each station, thereby obtaining the number of smart rail line operation vehicles that should be equipped at each station.

[0104] S4. Draw a two-dimensional Pareto solution set image based on a plurality of different feasible numbers of trains and the corresponding total number of train charging tasks, and determine the number of trains to be used in combination with the deficit function image;

[0105] In an optional embodiment of the present invention, this embodiment draws a two-dimensional Pareto solution set image according to a plurality of different feasible numbers of trains and the corresponding total number of train charging tasks, and determines the number of trains in use in combination with the inverse difference function image, including the following steps:

[0106] With the number of feasible trains as the horizontal coordinate and the total number of train charging tasks as the vertical coordinate, multiple different numbers of feasible trains and the corresponding total number of train charging tasks are plotted in the form of points on a two-dimensional coordinate system to obtain a two-dimensional Pareto solution set image;

[0107] A solution is selected from the two-dimensional Pareto solution set image, and the number of operating trains is determined according to the number of feasible operating trains of the selected solution.

[0108] In this embodiment, for each solution including the number of trains in use on the smart rail line and the total number of charging tasks for the smart rail trains, a two-dimensional Pareto solution set image including these two objectives is drawn. The minimum number of trains in use on the line in the two-dimensional Pareto solution set image refers to the total number of trains in use that perform all service trips. The total number of trains in use can also be understood as the sum of the number of trains in use equipped by all stations in the line; and the deficit function image can give the number of trains in use required for each station in the line, which is a decomposition of the total number of trains in use; therefore, the dispatcher can select the number of trains in use scheme that meets the actual needs based on the obtained two-dimensional Pareto solution set image and the deficit function image of each station under different circumstances.

[0109] This embodiment calculates the total number of charging tasks of the corresponding smart rail train for each new smart rail train fleet size plan obtained by adjustment in step S2. Then, the two indicators are used as horizontal and vertical coordinates, and the values ​​obtained by each adjustment and solution are plotted in the form of points on a two-dimensional coordinate graph to obtain the Pareto optimal solution set for the two indicators. The dispatcher selects a solution from the Pareto optimal solution set according to actual needs, and uses the corresponding smart rail line fleet size plan as the final fleet size plan.

[0110] S5. According to the number of spare trains and trains under repair of the intelligent rail express system, the number of trains assigned to the intelligent rail express system line is calculated based on the determined number of operating trains.

[0111] In an optional embodiment of the present invention, the embodiment calculates the number of trains assigned to the intelligent rail express system line based on the number of spare trains and the number of trains under repair of the intelligent rail express system and the number of operating trains determined, specifically:

[0112] Add the number of spare trains and trains under repair of the intelligent rail express system to the determined number of operating trains to obtain the number of trains assigned to the intelligent rail express system line.

[0113] In this embodiment, the number of spare trains and the number of trains under repair of the smart rail train are calculated based on the maintenance schedule and maintenance system of the smart rail train.

[0114] A spare car is a train that is used to replace a faulty train when a train breaks down and is put into service on the main line as a reserve to ensure normal operation of the line. The spare rate in the same operating period is a fixed value and is calculated according to a certain spare rate. The number of spare cars is calculated as follows:

[0115]

[0116] Among them, N 备 is the number of spare trains, N 运 is the number of trains in operation, δ备 is the reserve rate;

[0117] Regarding the number of vehicles under repair, except for the train inspection, all levels of maintenance are only carried out during the statutory working hours, that is, the annual maintenance working time is 250 days (the whole year is calculated as 365 days). Based on the total workload of maintenance at all levels throughout the year, the formula for calculating the average number of vehicles under repair per day is as follows:

[0118]

[0119] Among them, N 修 is the number of trains under repair, N 运 is the number of trains in operation, h i is the maintenance cycle coefficient of maintenance process i, t i is the detention time for repair process i.

[0120] Finally, add up the number of operating vehicles, spare vehicles, and vehicles under repair to get the number of trains assigned to the smart rail line:

[0121] N 配 =N 运 +N 备 +N 修

[0122] In this embodiment, the network maximum flow model of the minimum fleet size problem is solved by using optimization solver software, and the inverse difference function image and the two-dimensional Pareto solution set image are drawn by using drawing software tools.

[0123] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0124] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0125] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0126] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, 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 invention.

[0127] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for calculating the number of trains assigned to a line of an intelligent rail express system, characterized in that: The following steps are involved: Generate train service information for the full-day operation period according to the line operation period and train departure interval of the intelligent rail express system, and calculate the minimum number of line operation trains required to execute all service trips based on the train service trip data information; A dual-objective linear programming model with the objective function of minimizing the number of trains in operation on the line and minimizing the number of train charging tasks is constructed. Based on the minimum number of trains in operation on the line, multiple different feasible numbers of trains in operation and the corresponding total number of train charging tasks are calculated; Use the deficit function graphical dispatch model to draw the deficit function image of each departure and arrival station; According to multiple different feasible numbers of trains and the corresponding total number of train charging tasks, a two-dimensional Pareto solution set graph is drawn, and the number of trains to be used is determined in combination with the deficit function graph; According to the number of spare trains and trains under repair in the intelligent rail express system, the number of trains assigned to the intelligent rail express system line is calculated based on the determined number of operating trains.

2. The method for calculating the number of trains assigned to a line of an intelligent rail express system according to claim 1, characterized in that: Calculating the minimum number of line operation trains required to execute all service trains based on train service train number data information includes the following steps: Based on the train service data information, a network flow integer programming model without considering charging is constructed; Solve the network flow integer programming model without considering charging to obtain the maximum feasible number of train connections; The minimum number of line-operated trains required to execute all service trips is calculated based on the maximum feasible number of train connections.

3. The method for calculating the number of trains assigned to a line of an intelligent rail express system according to claim 2, characterized in that: The specific integer programming model for network flow without considering charging is as follows: The constraints are: x j -(x i +t i +△t i +z ij )≥(x ij -1)*M1,i,j∈I Among them, Max is the maximum value function, C VS (I) is the number of feasible train connections, I is the set of train service numbers, x ij is a 0-1 variable indicating whether train number i and train number j are executed by the same train, x j is the departure time of train number j, x i is the departure time of train number i, t i is the travel time of train number i, △t i is the turnaround preparation time of train number i, z ij is the judgment coefficient of whether train number i and train number j are located at the same station. If train number i and train number j are located at the same station, then z ij =0, otherwise it takes the value of the operating cycle duration, M1 is the set positive parameter, and T is the operating cycle duration.

4. The method for calculating the number of trains assigned to a line of an intelligent rail express system according to claim 2, characterized in that: The minimum number of line operation trains required to execute all service trips is calculated based on the maximum number of feasible train connections: Min F VS (I)=|I|-Max C VS (I) Among them, Min is the minimum function, F VS (I) is the number of trains in service on the line, |I| is the number of all trains in the train service set I, Max is the maximum value function, C VS (I) is the number of feasible train connections.

5. The method for calculating the number of trains assigned to a line of an intelligent rail express system according to claim 1, characterized in that: A dual-objective linear programming model with the objective function of minimizing the number of line operating trains and minimizing the number of train charging tasks is constructed. Based on the minimum number of line operating trains, multiple different feasible numbers of operating trains and the corresponding total number of train charging tasks are calculated, including the following steps: Construct a dual-objective linear programming model with the objective function of minimizing the number of trains used on the line and minimizing the number of train charging tasks; The objective function of minimizing the number of trains used on the line in the dual-objective linear programming model is transformed into a constraint condition, and a single-objective linear programming model with the objective function of minimizing the number of train charging tasks is obtained; Based on the minimum number of trains in operation on the line, the number of feasible train connections is gradually increased in steps of 1, and a single-objective linear programming model with the objective function of minimizing the number of train charging tasks is solved to obtain multiple different feasible numbers of trains in operation and the corresponding total number of train charging tasks.

6. A method for calculating the number of trains assigned to a line of an intelligent rail express system according to claim 5, characterized in that: A dual-objective linear programming model with the objective function of minimizing the number of line operating trains and minimizing the number of train charging tasks is constructed, specifically: The constraints are: Among them, Min is the minimum function, F VS (I) is the number of trains in service on the line, |I| is the number of all trains in the train service set I, Max is the maximum value function, x ij is a 0-1 variable indicating whether train number i and train number j are executed by the same train, F BS The number of charging tasks for the train, y ij is a 0-1 variable indicating whether the train will be charged after completing the train number i and the train number. j is the departure time of train number j, x i is the departure time of train number i, t i is the travel time of train number i, △t i is the turnaround preparation time of train number i, z ij is the judgment coefficient of whether train number i and train number j are located at the same station, Q is the maximum battery capacity of the train, is the remaining power of the train after the train number i is executed, P is the rated charging power of the charging pile, M2 is a set positive integer, is the remaining power of the train before train number i, q i is the power consumed by each trip of train number i, α is the safety power threshold coefficient of the train, is the remaining power of the train before the execution of train number j, u ij is the remaining power of the train from train number i to train number j, r ij is a 0-1 variable indicating whether train number i and train number j are connected and have charging tasks, and T is the duration of the operation cycle.

7. The method for calculating the number of trains assigned to a line of an intelligent rail express system according to claim 1, characterized in that: The deficit function diagram scheduling model is used to draw the deficit function image of each departure and arrival station, including: With time as the horizontal axis and the difference between the total number of departing trains and the total number of arriving trains at the originating and terminating stations before the set time as the vertical axis, the inverse function graph of each originating and terminating station is plotted.

8. The method for calculating the number of trains assigned to a line of an intelligent rail express system according to claim 1, characterized in that: According to a plurality of different feasible numbers of trains and the corresponding total number of train charging tasks, a two-dimensional Pareto solution set image is drawn, and the number of trains to be used is determined in combination with the deficit function image, including the following steps: With the number of feasible trains as the horizontal coordinate and the total number of train charging tasks as the vertical coordinate, multiple different numbers of feasible trains and the corresponding total number of train charging tasks are plotted in the form of points on a two-dimensional coordinate system to obtain a two-dimensional Pareto solution set image; A solution is selected from the two-dimensional Pareto solution set image, and the number of operating trains is determined according to the number of feasible operating trains of the selected solution.

9. The method for calculating the number of trains assigned to a line of an intelligent rail express system according to claim 1, characterized in that: According to the number of spare trains and trains under repair of the intelligent rail express system, the number of trains assigned to the intelligent rail express system line is calculated based on the determined number of operating trains, specifically: Add the number of spare trains and trains under repair of the intelligent rail express system to the determined number of operating trains to obtain the number of trains assigned to the intelligent rail express system line.

10. The method for calculating the number of trains assigned to a line of an intelligent rail express system according to claim 1, characterized in that: The calculation method for the number of spare trains in the intelligent rail express system is: Among them, N 备 is the number of spare trains, N 运 is the number of trains in operation, δ 备 is the reserve rate; The calculation method for the number of trains under repair in the intelligent rail express system is: Among them, N 修 is the number of trains under repair, h i is the maintenance cycle coefficient of maintenance process i, t i is the detention time for repair process i.

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