A high-speed freight train scheduling optimization method and device based on an alternative set

Abstract

The application relates to a high-speed freight train operation optimization method and device based on an alternative set, and the method comprises the following steps: establishing a high-speed freight train operation optimization nonlinear model; linearizing the nonlinear model by applying a train alternative set to obtain a linear model; performing multi-target processing and fitness value setting on the linear model to obtain a corresponding solution, wherein the solution is the result obtained by optimization. The application takes the minimum high-speed freight train operation cost and total freight transportation time as the target, considers the freight flow demand satisfaction, train carrying capacity, station operation capacity, section passing capacity, train operation condition, operation section and stop station and other constraints, designs a freight train operation scheme optimization model, and cooperatively optimizes train types, operation sections, operation frequencies, stop station schemes and demand distribution. Meanwhile, the train alternative set is applied to linearize the nonlinear term, so that the model complexity and solution difficulty are reduced.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of train scheduling scheme, and particularly relates to a high-speed rail freight train scheduling optimization method and device based on an alternative set. BACKGROUND

[0002] The railway train scheduling scheme optimization problem can be simply expressed as: under the transportation demand between different nodes in a given transportation network, based on certain optimization objectives, considering relevant constraint conditions, finally selecting a group of paths and the number of trains of different forms on the paths to meet the transportation demand. From the perspective of decision content, it mainly involves five parts of train formation structure, route selection, frequency setting, stop mode and demand allocation, wherein the train formation structure determines the train carrying capacity, which is usually known and fixed in the solution, the route selection determines the origin and destination points, the sections and intermediate stations of train operation, the frequency setting determines the number of trains on each selected route within the study period, the stop mode determines whether the intermediate stations on the route are stopped, and the demand allocation determines the OD amount served by each train based on the passenger and freight demand matrix. From the perspective of railway attributes and service objects, the research objects of railway train scheduling scheme can be mainly divided into passenger trains of conventional speed railway, freight trains of conventional speed railway, passenger trains of high-speed railway and freight trains of high-speed railway.

[0003] Existing researches focus on the decision content of train formation structure, origin and destination point selection, running route, frequency setting, stop scheme and freight flow allocation in the scheduling scheme optimization, and a large number of researches are carried out through different assumption conditions and key decision selections, and rich research results are obtained in the optimization model construction and solution algorithm design. Among them, the research progress of railway passenger trains is particularly perfect, and the research on railway freight train scheduling scheme optimization is relatively weak, especially the comprehensive optimization research on all decision contents is relatively less, which needs to be further enriched.

[0004] The existing railway freight train scheduling scheme optimization faces many practical technical problems, such as the lack of coordination of multi-dimensional resource constraints such as station operation capacity, locomotive turnover and line capacity, the poor matching of the scheme and physical conditions, the difficulty in balancing the core objectives such as transportation cost, timeliness and energy efficiency, the limited comprehensive benefits, the complex coupling relationship between train running section, stop scheme and freight flow allocation, which leads to the difficulty in generating feasible schemes, and the low solution efficiency of traditional methods under large-scale solution space, which is difficult to support efficient decision-making needs. Therefore, how to apply corresponding technical methods to reduce the model complexity and solution scale has become a difficult problem to be solved in the field of railway train scheduling scheme optimization. SUMMARY

[0005] In order to overcome the above problems existing in the prior art, the application provides a high-speed freight train operation optimization method and device based on an alternative set, which are used for solving the above problems existing in the prior art.

[0006] A high-speed freight train operation optimization method based on an alternative set, the method comprising:

[0007] S1. Establishing a high-speed freight train operation optimization nonlinear model;

[0008] S2. Linearizing the nonlinear model by applying a train alternative set to obtain a linear model;

[0009] S3. Performing multi-objective processing and adaptive value setting on the linear model;

[0010] S4. Applying the set model to a selected actual high-speed railway line case for solving to obtain an actual high-speed railway freight train operation optimization scheme and a freight flow distribution scheme. As described above, the aspect and any possible implementation mode further provide an implementation mode, the S1 comprising:

[0011] S11. Constructing a physical network, a demand network, a train network and a service network;

[0012] S12. Establishing a minimum high-speed freight train operation cost objective function and a minimum total freight transportation time objective function, establishing demand satisfaction constraints, station and section passing capacity constraints, train carrying capacity constraints, train operation economic benefit constraints and train section operation condition constraints;

[0013] S13. Constructing a nonlinear model according to the network constructed in S11 and the objective function and constraints established in S12.

[0014] As described above, the aspect and any possible implementation mode further provide an implementation mode, the S2 comprising:

[0015] S21. Defining the high-speed freight train alternative set as a plurality of high-speed trains with known freight objects, origin-destination points and operation sections, motor train unit types, motor train unit consist and stop station schemes;

[0016] S22. Converting the decision variables involved in the alternative trains in the train alternative set: train stop train demand service train passing section and train origin-destination point into train operation frequency;

[0017] S23. Linearizing the freight demand satisfaction nonlinear constraints and the train carrying capacity nonlinear constraints.

[0018] Aspects and any possible implementation thereof as described above, further provide an implementation, the S3 comprises:

[0019] S31. decomposing the linearized model into a first single-objective optimization model and a second single-objective optimization model;

[0020] S32. solving the objective function of the first single-objective optimization model to obtain a minimum value of the high-speed freight train operation cost;

[0021] S33. solving the objective function of the second single-objective optimization model to obtain a minimum value of the total transport time of the high-speed freight train.

[0022] Aspects and any possible implementation thereof as described above, further provide an implementation, the objective function of the first single-objective optimization model is Z1 represents the minimum cost of the high-speed freight train operation, representing the freight train k g the number of departures in the statistical period, representing the fixed cost of the freight train departure; representing the variable cost of the freight train departure related to distance, yuan / train kilometer; representing the variable cost of the freight train departure related to station stop; representing the freight train k g whether to pass through the section z i , taking the value of 0 or 1; zl i represents the distance between i station and i+1 station, K G representing the set of high-speed freight trains, k g represents the index of K G , representing the freight train k g whether to stop at i station, taking the value of 0 or 1.

[0023] Aspects and any possible implementation thereof as described above, further provide an implementation, the objective function of the second single-objective optimization model is Z2 represents the minimum total transport target time of all goods, S represents the set of high-speed stations, e, i, j represents the index of S, |S| represents the number of stations; representing the freight flow from the station i to the station j assigned to the freight train k g above; representing the freight train k g whether to serve the freight demand g ij ; zl e represents the distance between i station and i+1 station; used to judge whether the train k g stops at e station; for judging whether the train k g passes the section z e ; V G represents the average running speed of the freight train; represents the additional start-stop time caused by the intermediate stop of the freight train.

[0024] As the above-mentioned aspects and any possible implementation, further provided is an implementation, wherein an expression of a decision variable of the first single-objective optimization model is: and S represents a set of high-speed railway stations, e, i, j represent indexes of S, and |S| represents a number of stations; O represents a starting station of a high-speed railway line; D represents a terminal station of the high-speed railway line; for judging whether the train k g stops at the i station; for judging whether the train k g passes the section z i ; for judging whether the i station is a starting station of the train k g ; for judging whether the i station is a terminal station of the train k g , and K G represents a set of high-speed freight trains, k g represents an index of K G ; represents a freight flow allocated to the train k g from the i station to the j station; G represents a set of freight demands; and N represents a set of natural numbers.

[0025] The application further provides a device for optimization of high-speed freight train scheduling based on an alternative set, which is used to implement the method and comprises:

[0026] a building module, configured to build a high-speed freight train scheduling optimization nonlinear model;

[0027] a linearization module, configured to linearize the nonlinear model by using a train alternative set to obtain a linear model;

[0028] a setting module, configured to perform multi-objective processing and value setting on the linear model;

[0029] a solving module, configured to apply the set model to a selected actual high-speed railway line case to obtain an actual high-speed freight train scheduling optimization scheme and a freight flow allocation scheme.

[0030] The application further provides a computer storage medium, wherein a computer program is stored on the medium, and the computer program is executed by a processor to implement the method.

[0031] The application also provides an electronic device, which comprises:

[0032] a memory storing executable instructions;

[0033] a processor running the executable instructions in the memory to implement the method.

[0034] Advantages of the application

[0035] The high-speed railway freight train operation optimization method of the application takes the minimum high-speed freight train operation cost and total freight transportation time as the target, considers the freight flow demand satisfaction, train carrying capacity, station operation capacity, section passing capacity, train operation condition, operation section and stopping station constraints, designs a train operation scheme optimization model, and cooperatively optimizes train types, operation sections, operation frequency, stopping station scheme and demand distribution. Meanwhile, the train candidate set is applied to linearize the nonlinear terms, so as to reduce the model complexity and solution difficulty.

[0036] Compared with the prior art, the application has the advantages that:

[0037] The high-speed railway freight train operation scheme model constructed by the application has multiple terms generated by multiplication of decision variables in the objective function, freight demand satisfaction constraint, train carrying capacity constraint, section passing capacity constraint and station operation capacity constraint, and has conditional constraints containing decision variables in the train service OD stopping station constraint, train origin-destination stopping station constraint, train stopping range constraint and train passing section range constraint, so the model belongs to a nonlinear mixed integer programming model. The nonlinear objective and constraint in the model are linearized by the application, the nonlinear terms such as operation section selection and stopping station constraint are converted into 0-1 variables and linear expressions, so a linear programming model is obtained, and the non-convexity of the nonlinear model can be effectively eliminated. Meanwhile, the train operation mode is pre-screened and coded by using the candidate set, the originally high-dimensional discrete decision variables are converted into index variables of limited combinations, the variable scale is reduced by more than 50%, the solution space is compressed to a high-quality feasible region by the pre-screening mechanism based on the candidate set, so as to reduce the solution complexity and avoid missing potential optimal schemes. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is a high-speed freight train operation set diagram of the application;

[0039] Figure 2 is a high-speed freight train operation set diagram of the application;

[0040] Figure 3is a method flow chart of the present application;

[0041] Figure 4 is a four-layer network structure diagram of the physical-demand-train-service of the present application. DETAILED DESCRIPTION

[0042] In order to better understand the technical solutions of the present application, the present application includes but is not limited to the specific embodiments in the following, and similar technologies and methods should be considered as within the scope of the present application. In order to make the technical problems, technical solutions and advantages of the present application more clear, the following will be described in detail in conjunction with the drawings and specific embodiments.

[0043] It should be clear that the embodiments described in the present application are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0044] The terms used in the embodiments of the present application are only for the purpose of describing specific embodiments, and are not intended to limit the present application. The singular forms "a", "an" and "the" used in the embodiments of the present application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise.

[0045] As Figure 3 shown, the present application provides a high-speed rail freight train operation optimization method based on an alternative set, which comprises:

[0046] S1. Establishing a high-speed rail freight train operation optimization nonlinear model;

[0047] S2. Linearizing the nonlinear model by applying a train alternative set to obtain a linear model;

[0048] S3. Multi-objective processing and fitness value setting for the linear model;

[0049] S4. Applying the set model to the selected actual high-speed railway line case for solving to obtain an actual high-speed rail freight train operation optimization scheme and a freight flow distribution scheme.

[0050] Further, the S1 comprises:

[0051] S11. Constructing a physical network, a demand network, a train network and a service network;

[0052] S12. Establish a minimum high-speed freight train operation cost objective function and a minimum total freight transport time objective function, establish demand satisfaction constraints, station and section passing capacity constraints, train carrying capacity constraints, train operation economic benefit constraints and train section running condition constraints;

[0053] S13. Construct a nonlinear model according to the network constructed in S11 and the objective function and constraints established in S12.

[0054] Further, the S2 comprises:

[0055] S21. Define the high-speed freight train candidate set as a plurality of high-speed trains with known freight objects, origin-destination points and running sections, motor train unit types, motor train unit consist and stop station schemes;

[0056] S22. Transform the decision variables involved in the candidate trains in the train candidate set: train stop train demand service train passing section and train origin-destination point into train operation frequency;

[0057] S23. Linearize the freight demand satisfaction nonlinear constraints and the train loading capacity nonlinear constraints.

[0058] Specifically, the implementation process of the present application is as follows:

[0059] A high-speed freight train operation optimization method based on a candidate set, the specific steps of which are as follows:

[0060] (1) Clearly define the optimization range, optimization conditions and optimization steps, and model the high-speed freight train operation scheme optimization problem, including two objective functions: minimizing the total high-speed train operation cost and minimizing the freight demand travel time, as well as demand satisfaction constraints, station and section passing capacity constraints, train carrying capacity constraints, train operation economic benefit constraints and train section running condition constraints;

[0061] (2) Linearize the nonlinear objectives and constraints involved in the constructed optimization model by applying the train candidate set idea, reduce the solution space and improve the solving efficiency;

[0062] (3) Perform multi-objective processing and fitness value setting on the linearized optimization model obtained in the above step;

[0063] (4) Select an actual high-speed railway line for case analysis to obtain corresponding parameter data, and substitute them into the set model obtained in step (3) to solve, and obtain the high-speed railway freight train operation scheme and freight flow distribution scheme.

[0064] wherein,

[0065] The specific steps of constructing the high-speed freight train operation optimization model in step (1) are as follows:

[0066] Step one: Construction of a four-layer network of "physical-demand-train-service". The first layer is the railway infrastructure, called the physical network, including stations and section lines connecting the stations. The second layer is the OD demand, called the demand network, including the OD demand of freight flow between nodes. The third layer provides train line planning with different operation modes (origin-destination, passing section, stop scheme) for the OD demand, called the train network. The fourth layer provides service network for the demand with the arrangement of line planning, and the service network is composed of service arcs from all train lines. The passenger and freight transport selection is affected by the total travel time of different service arcs with the same OD in the fourth layer. The fourth layer determines how to allocate passenger and freight demand to each train, which is the network for demand allocation. The physical network provides infrastructure constraints for the train network, the demand network defines the optimization goal, the train network generates supply resources for the service network, and the service network finally completes demand allocation.

[0067] Figure 4 A simple high-speed rail network is shown, which has 4 stations along a corridor, wherein a represents the physical network, b represents the demand network, c represents the train network, and d represents the service network.

[0068] In a given railway corridor from station A to station D, the OD demand between nodes is known, the high-speed train loading capacity is 600, and it is assumed that three different train lines with different origin-destination, running section, and stop mode are provided. Train 1 starts at station A, stops at station B, and ends at station C; train 2 starts at station A, stops at station C, and ends at station D; and train 3 starts at station A, stops at station B, and ends at station D. In the service network, two different distribution schemes of three train line service arcs can be observed: scheme 1 has 2 trains of train 1, 1 train of train 2, and 1 train of train 3, and scheme 2 has 1 train of train 1, 2 trains of train 2, and 1 train of train 3.

[0069] Step two: In order to describe and build the model more clearly, the hypothesis conditions are set, which involve four aspects of line, station, train and demand. In terms of line, the high-speed railway network to be solved is assumed to be a known one-way line, and the running direction of high-speed train, the total number of stations on the line, the sequence of each station in the direction, and the running distance between each station are known. In terms of station, it is assumed that the stations stopped by high-speed express trains have the operation capacity and conditions matching the high-speed express demand. In terms of train, it is assumed that the train running speed is a fixed value given in advance, and the train interval pure running time is determined by the interval length and the fixed speed of the train. In addition, the stopping time and additional starting and stopping time of high-speed train are calculated according to the difference of train types. In terms of demand, it is assumed that the passenger and freight flow demand between each station OD (i.e. the starting and ending point) on the line is known and does not change, and there is no transfer and transshipment in the whole transportation process.

[0070] Step three: Under the above assumption conditions of the four aspects, a nonlinear mixed integer comprehensive optimization model M1 is built, and the parameters and main formulas involved in the model are as follows:

[0071] Model parameters: S represents the set of high-speed railway stations, e, i, j represent the index of S, |S| represents the number of stations; O represents the starting station of high-speed railway line; D represents the terminal station of high-speed railway line; Z represents the interval set, z i represents the interval from i station to i+1 station; ZL represents the interval distance set, zl i represents the distance of the interval from i station to i+1 station; G represents the freight demand set, g ij represents the freight flow demand from i station to j station; K G represents the set of high-speed freight trains, k g represents the index of K G , |K G | represents the number of freight trains; N represents the set of natural numbers; represents the fixed cost of freight transportation, unit: yuan / ton; represents the variable cost of freight transportation, which is related to distance, unit: yuan / ton kilometer; represents the fixed cost of freight train operation, unit: yuan / train; represents the variable cost of freight train operation related to distance, unit: yuan / train kilometer; represents the variable cost of freight train operation related to stopping, unit: yuan / train time; represents the upper limit of the capacity of interval z i , unit: number of trains; represents the upper limit of the operation capacity of station i in unit period, unit: number of trains; N G represents the fixed load weight of freight train, unit: ton; This represents the lower limit of the total number of stops for a freight train throughout its journey, in times. This represents the maximum number of stops a freight train can make along its entire route, expressed in times. This represents the lower limit of the total mileage traveled by a freight train, in kilometers. V represents the maximum mileage for a freight train, in kilometers; G This represents the average operating speed of freight trains, in kilometers per hour. This represents the stopping time of a freight train at an intermediate station, in minutes. This represents the additional time for freight trains to stop at intermediate stations, in minutes; M represents an infinite positive number.

[0072] The model's decision variables are those related to the train line sections and stops: where Represents freight train k g Whether station i stops is a 0-1 variable; it takes the value 1 if the station stops and 0 if the station does not stop. Represents freight train k g Does it pass through the interval z? i A 0-1 variable is a variable that takes the value 1, not 0. Does station i represent a freight train? g The starting station, a 0-1 variable, takes the value 1, not 0; Does station i represent a freight train? g The destination station is a 0-1 variable, meaning it takes the value 1, not 0. Decision variables related to train frequency include: Represents freight train k g The number of trains operated within the statistical period is an integer variable. Decision variables related to train freight flow allocation include: Represents freight train k g Can it serve the needs of cargo flow? ij A 0-1 variable is a variable that takes the value 1, not 0. Representative assigned to freight train k g The freight flow from station i to station j is an integer variable.

[0073] The objective function of the nonlinear mixed-integer synthesis optimization model M1 is as follows:

[0074] (1) Total operating cost of high-speed trains

[0075] Freight costs consist of the actual operating costs of each freight train. These costs include fixed operating costs, distance-related variable costs, station-related variable costs, and cargo loading and unloading costs. The formula for calculating the operating costs of high-speed rail freight trains is as follows:

[0076]

[0077] The objective function can be written as:

[0078]

[0079] (2) Total freight transport time

[0080] Ignoring the cost of cargo damage, cargo transfer related costs, etc., the generalized cost of freight transport is only represented by the sum of train running time, station stop time, and additional start-stop time. According to the system optimal principle of demand allocation, the minimum objective of the total freight transport time is represented by Z2 as follows:

[0081]

[0082] The model constraints are as follows:

[0083] The constraints of high-speed train operation scheme include three types of constraints: meeting freight demand, transport capacity limitation, and basic train operation conditions. Meeting freight demand is the core objective of the design of the operation scheme; transport capacity limitation refers to the passing capacity of each station and each section, as well as the train carrying capacity; and the basic train operation conditions include train operation section range, train stop requirements, train stop number, and train operation mileage. To ensure that all freight demand is met and the train runs safely, the constraint conditions for building the operation scheme model are analyzed in detail below.

[0084] (1) Freight demand satisfaction constraint

[0085] According to the basic requirements of the operation scheme, all demands can be served by trains, so it is necessary to ensure that the flow demand on any OD pair can be met and arranged on the designated freight train, i.e.,

[0086]

[0087] (2) Train carrying capacity constraint

[0088] To ensure the accuracy of the freight allocation scheme, the carrying capacity of any train passing through each section must be greater than the actual carrying capacity, i.e.,

[0089]

[0090] (3) Section passing capacity constraint

[0091] The number of high-speed trains passing through any section must be less than the section passing capacity, i.e.,

[0092]

[0093] (4) Station operation capacity constraint

[0094] The number of trains stopping at any station for relevant operations is less than the station operation capacity of the station, i.e.

[0095] (5) Train stopping number constraint

[0096] The number of stops of any train is within a certain interval i.e.

[0097]

[0098] (6) Train mileage constraint

[0099] Any train is within a reasonable mileage , i.e.

[0100]

[0101] (7) Train service OD stopping constraint

[0102] High-speed train must stop at the origin and destination of any OD pair in the service section to complete the OD transportation service, otherwise, only when the train stops at a certain OD pair, the train can serve the OD pair, i.e. wherein, represents whether freight train k g stops at j station, 0-1 variable, 1 for stopping, 0 for not stopping.

[0103] (8) Train origin-destination number constraint

[0104] Train can only have one originating station and one terminal station on its running line, and the origin-destination of any train has only one, i.e.

[0105] (9) Train origin-destination sequence constraint

[0106] To express the uniform and fixed direction of train running in the running section, it is stipulated that any train runs from its originating station to the terminal station, and the starting point of the train on its running line must be before the terminal point, i.e. wherein, is a 0-1 variable indicating whether j station is the terminal station of freight train k g , 1 for yes, 0 for no.

[0107] (10) Train origin-destination stopping constraint

[0108] Train completes departure and terminal operations at the origin-destination, and any train must stop at the origin-destination of the running line, i.e. if or

[0109] (11) Train stop range constraint

[0110] The start and end points of a train determine the running section of the train on the line. The train cannot stop outside the start and end points of the line it runs on, i.e. If And e < i Wherein, Indicates whether to stop at e station, 0-1 variable, is 1, not 0; If And j > i

[0111] (12) Train passing section range constraint

[0112] The start and end points of a train determine the running section of the train on the line. The train cannot stop outside the start and end points of the line it runs on, i.e. Wherein, Indicates whether e station is the starting station of the freight train, 0-1 variable, is 1, not 0.

[0113] (13) Model decision variable range

[0114] The train running frequency, freight flow allocation scheme, stop selection, service OD, passing section, start and end point, etc. Decision information is written into the model of this paper as the decision variable of high-speed rail train operation scheme model. The specific value range of each decision variable is as follows:

[0115] 1) Train running frequency decision variable:

[0116] 2) Freight flow decision variable:

[0117] 3) Train stop decision variable:

[0118] 4) Train demand service decision variable

[0119] 5) Train passing section decision variable

[0120] 6) Train start and end point decision variable

[0121] As described above, the high-speed rail freight train operation scheme optimization model M1 includes the following contents:

[0122] Objective function: formula (2), (3)

[0123] Constraint condition: formula (4)-(17)

[0124] Decision variables: Formulas (18)-(24)

[0125] The specific steps for linearization using the train candidate set described in step (2) are as follows:

[0126] Step 1: Define the high-speed rail freight train candidate set as follows: the high-speed rail trains in the set have known freight objects, origin and destination points and operating sections, EMU type, EMU formation, and station stopping scheme.

[0127] Step Two: In actual operation, there may be multiple feasible train operation modes, but resources are limited, so it is necessary to select the most suitable solution. Therefore, the potential candidate solutions in the train alternative set are considered, including the train stops at the relevant stations. Train demand service Train passes through the section Train origin and destination and The four types of decision variables are transformed into train operation frequency. Since the multiplication terms (nonlinear terms) of the decision variables contained in the objective function and constraints in model M1 are all related to the above four types of decision variables, after the decision variable transformation of the train candidate set, these nonlinear multilinear terms are basically transformed into linear objectives and constraints.

[0128] Step 3: Further linearize other nonlinear constraints, namely, the freight demand with multiple terms satisfying the nonlinear constraint formula (4) and the train loading capacity nonlinear constraint formula (5). Thus, all nonlinear objective functions and constraints in model M1 are converted into linear forms, thereby transforming the original nonlinear mixed integer programming model M1 into a linear mixed integer programming model M2. This simplifies the solution difficulty, reduces computational complexity, and transforms high-dimensional nonlinear problems into low-dimensional linear problems, avoiding the branch and bound algorithm from getting stuck in local optima or exponential computation time due to nonconvexity.

[0129] The linearization process for constraint formulas (4) and (5) is as follows:

[0130] For a high-speed train passing through a certain origin-destination (OD), if train k g Unable to serve OD needs g ij ,but At this time, train k g Loading OD requirements g ij Traffic If train k is 0; g Able to serve OD needs g ij ,but Furthermore, the following service-traffic logical coupling constraints exist:

[0131]

[0132] In combination with the coupling constraints described above, the freight flow demand satisfaction constraint formula (4) is transformed into

[0133] The train carrying capacity constraint (5) is transformed into Wherein, Ori represents the starting station of the line, and Des represents the terminal station of the line.

[0134] The train opening frequency decision variable (18) is transformed into:

[0135] Wherein, N represents a set of natural numbers.

[0136] Thus, the nonlinear model M1 is converted into a linear model M2 through linearization, and the M2 includes the following contents:

[0137] Objective function: (2), (3)

[0138] Constraint condition: (25)-(27), (6), (7)

[0139] Decision variable: (28), (19)

[0140] The selection of the candidate train in the high-speed train candidate set is determined by the train stop number constraint (8) and the train travel mileage constraint (9) in the model M1, and all trains satisfying the two constraint conditions are added to the "candidate set" as candidate trains.

[0141] The specific steps of multi-objective processing and fitness value setting for the linearization-processed optimization model obtained in step (3) are as follows:

[0142] Step one: using the priority method to decompose the linear equivalent model M2 based on the candidate set with multiple objectives into two single-objective optimization models M3 and M4.

[0143] The model M3 includes the following contents:

[0144] Objective function: formula (2)

[0145] Constraint condition: all constraints of the model M2, i.e. formula (25)-(27), (6) and (7)

[0146] Decision variable: formula (28), (19)

[0147] The model M4 includes the following contents:

[0148] Objective function: formula (3)

[0149] Constraints: all constraints of the inherited model M2, equations (25)-(27), (6), (7), and the following new constraints are added to control that the total cost does not exceed the optimal value of model M3:

[0150]

[0151] wherein Z1 * is the optimal objective value obtained by solving M3.

[0152] Decision variables: equations (28), (19).

[0153] The steps for solving the multi-objective linear model M2 using the priority method are as follows: first, optimize the objective function (2) alone, i.e., solve model M3, to obtain the minimum value of the high-speed freight train operation cost; then, under the condition of considering the new constraint (29), optimize the objective function (3) alone, i.e., solve model M4, to obtain the minimum value of the total freight transport time.

[0154] By decomposing the multi-objective model M2 into two single-objective models M3 and M4 using the priority method, the goal of prioritizing the minimization of the total operation cost is achieved, and the total freight transport time is further optimized on the basis of the optimal operation cost, which simplifies the solving process of the single-objective model and avoids the complexity of multi-objective algorithms. This processing process conforms to the decision-making logic of "cost control first and time efficiency second" in actual operation. While ensuring the quality of the solution, the computational complexity is significantly reduced.

[0155] The following specific examples are used to illustrate:

[0156] A one-way high-speed rail line is selected on a certain high-speed rail line, which is connected by six stations LZ, LN, CQ, GY, GL, and GZ. The distances between the stations on the line are known.

[0157] Since high-speed rail freight trains and mixed freight services have not yet been fully implemented, this study focuses on the national express delivery volume that high-speed rail freight can serve as the source of goods. It obtains the intercity express delivery volume of the top 100 cities in terms of national express delivery volume and related cities along the example route for 2023-2024. Considering factors such as express delivery volume, total freight volume, regional GDP, tertiary industry added value, total retail sales of consumer goods, per capita disposable income of urban and rural households, per capita consumption expenditure, and resident population of each city, principal component analysis is used to calculate the intercity express delivery volume of each city in 2023. Taking into account the timeliness, economy, and safety of four modes of transportation—road, air, high-speed rail, and conventional rail mail trains—a share-rate model is designed to calculate the intercity express delivery volume that can be served by high-speed rail freight. Furthermore, a gravity model is used to calculate the express delivery volume between cities, ultimately determining the OD demand for freight flow between stations along the example route. Since demand forecasting and share-rate calculation are not the focus of this study, the unit-per-cycle freight OD demand is given as initial known conditions.

[0158] In addition, considering the large-scale increase in model decision variables and constraints with the increase in the number of stations and trains, in order to enable the model to be solved accurately, the time period is further divided into 4-hour units per day, and the first time period from 6:00 am to 10:00 am is selected for example calculation.

[0159] The relevant parameters are shown in Tables 1 to 3. In the example design, various parameters such as high-speed rail operating line conditions, train (carriage) operation parameters, and freight transportation costs are specified. For the convenience of solving the example, it is assumed that the throughput capacity of each station in each section is the same within a unit cycle, and the high-speed rail freight train has an 8-car formation with each carriage having the same configuration.

[0160] Table 1 Example Station and Section Information Table

[0161]

[0162] Table 2 Example Cargo Flow OD Demand Table (Unit: tons / unit cycle)

[0163]

[0164] Table 3. Train and Line Related Parameters

[0165]

[0166]

[0167] (2) Analysis of solution results

[0168] To verify the effectiveness of the model and the design algorithm, the above example is taken as the experimental background, and the data or information in Tables 1 to 3 are taken as known variables. The Cplex 12.8.0.0 engine is called by Python language programming, and is run on a computer configured with Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz 2.21GHz, 8GB RAM, and Windows 10 system. It should be noted that the solution process of the Cplex mathematical optimization engine is first to solve the linear programming problem of relaxing the integer constraint according to the model, and then to use the branch and bound method to further solve the integer solution of the linear optimal problem. Since the branch and bound solution is large in scale, two solution end criteria, Gap solution termination condition and Time solution termination condition, are set at the beginning of the solution. If the Gap between the upper bound and the lower bound is less than the Gap termination condition within the Time range, the current approximate optimal integer solution is output. If the approximate optimal solution within the Gap range cannot be obtained within the Time range, the best approximate integer solution at the end of the Time is output.

[0169] In the example solution, the Gap termination range is set to 0.5%, and the Time termination range is set to 600 seconds. The Cplex mathematical optimization engine is called by Python language to solve the models M3 and M4, and the results including the initial train candidate set, the freight train operation scheme, and the freight train flow allocation scheme are obtained. The results and the scheme details are shown in Figure 1 and Figure 2 . Figure 1 The results show the train stop scheme, and a total of 6 freight trains are operated. Train f_1 runs from LN station to GZ station with a stop at GY station; train f_2 runs from CQ station to GY station; train f_3 runs from LN station to GZ station with a stop at CQ station; train f_4 runs from LZ station to GL station with a stop at GY station; train f_5 runs from LZ station to GZ station with stops at CQ station and GL station; and train f_6 runs from LZ station to GZ station with stops at LN station and GL station. The specific freight flow allocation of each high-speed rail freight train is shown in Figure 2As shown, the LN station-GY station transport section of the train f_1 allocates goods 79t, the GY station-GZ station transport section allocates goods 75t; the CQ station-GY station transport section of the train f_2 allocates goods 48t; the LN station-CQ station transport section of the train f_3 allocates goods 80t, and the CQ station-GZ station transport section allocates goods 72t; the LZ station-GY station transport section of the train f_4 allocates goods 63t, and the GY station-GL station transport section allocates goods 80t; the LZ station-CQ station transport section of the train f_5 allocates goods 80t, the CQ station-GL station transport section allocates goods 62t, and the GL station-GZ station transport section allocates goods 52t; the LZ station-LN station transport section of the train f_6 allocates goods 77t, the LN station-GL station transport section allocates goods 80t, and the GL station-GZ station transport section allocates goods 54t. Meanwhile, the objective function value of the high-speed rail freight train scheduling scheme model is [730504, 58727.8], that is, the total operation cost of the high-speed rail freight train is 730504 yuan per unit period, and the total transport time of the goods is 58727.8 tons per minute per unit period, which serves all the freight demands on the case line in the current research period. The above values are the optimal solution of the model solving.

[0170] Therefore, by using the above scheduling scheme and the goods flow allocation scheme, the total operation cost of the high-speed rail freight train is 730504 yuan per unit period, and the total transport time of the goods is 58727.8 tons per minute per unit period, thereby achieving the optimization purpose.

[0171] As an embodiment of the present application, the present application further provides a high-speed rail freight train scheduling optimization device based on an alternative set, which is used to realize the method and comprises:

[0172] A building module is configured to build a high-speed rail freight train scheduling optimization nonlinear model;

[0173] A linearization module is configured to linearize the nonlinear model by using a train alternative set to obtain a linear model;

[0174] A setting module is configured to perform multi-objective processing and adaptive value setting on the linear model;

[0175] A solving module is configured to apply the set model to a selected actual high-speed railway line case for solving to obtain an actual high-speed rail freight train scheduling optimization scheme and a goods flow allocation scheme.

[0176] As an embodiment of the present application, the present application further provides a computer storage medium, wherein a computer program is stored on the medium, and the computer program is executed by a processor to realize the method.

[0177] As an embodiment of the present disclosure, the present disclosure also provides an electronic device, comprising:

[0178] a memory storing executable instructions;

[0179] a processor running the executable instructions in the memory to implement the method.

[0180] The above description shows and describes several preferred embodiments of the present disclosure, but as previously described, it should be understood that the present disclosure is not limited to the forms disclosed herein, should not be considered as excluding other embodiments, and can be used in various other combinations, modifications and environments, and can be modified within the scope of the application described herein, by the above teaching or related technical or knowledge. The modifications and changes made by those skilled in the art without departing from the spirit and scope of the present disclosure shall fall within the scope of the appended claims of the present disclosure.

Claims

1. A method for optimization of high-speed freight train scheduling based on candidate set, characterized in that, The method comprises: S1. establishing a high-speed freight train operation optimization nonlinear model, comprising: S11. constructing a physical network, a demand network, a train network, and a service network, wherein the physical network is a first layer, comprising stations and section lines connecting the stations; the demand network is a second layer, comprising freight flow network demand between nodes; the train network is a third layer, used to provide the demand network with train line planning with different operation modes; the service network is a fourth layer, providing a service network for the demand along with the arrangement of the line plan; setting a hypothetical condition, wherein, in terms of the line: the high-speed railway network to be solved is assumed to be a known single-direction line, the running direction of the high-speed train, the total number of stations on the line, the sequence of each station in the direction, and the running distance between each station are known; in terms of the station: it is assumed that the stations stopped by the high-speed freight train all have the operation capacity and conditions matching the high-speed freight demand; in terms of the train: it is assumed that the train running speed is a fixed value given in advance, the train section pure running time is determined by the section length and the fixed train speed, and the station stopping time and additional stopping time of the high-speed train are calculated according to the fixed values of different train types; in terms of the demand: it is assumed that the passenger flow demand and the freight flow demand between the starting point and the terminal point of each station on the line are known and do not change, and there is no transfer and transshipment in the whole transportation process; S12. under the above hypothetical condition, a minimum high-speed freight train operation cost objective function and a minimum total freight transportation time objective function are established, and demand satisfaction constraints, station and section passing capacity constraints, train carrying capacity constraints, train operation economic benefit constraints, and train section running condition constraints are established; S13. a nonlinear model is constructed according to the network constructed in S11 and the objective functions and constraints established in S12; S2. a linear model is obtained by linearizing the nonlinear model using a train candidate set, comprising: S21. defining the high-speed freight train candidate set as a plurality of high-speed trains with known freight objects, origin-destination points, and running sections, motor train unit types, motor train unit marshalling, and station stopping schemes; S22. Transforming the decision variables involved in the candidate trains in the train candidate set: train stop , train demand service , train passing section , and train origin-destination point and into train operating frequency , ; For other nonlinear constraints, i.e. freight demand satisfaction nonlinear constraint formula with multiple terms , train loading capacity nonlinear constraint formula Further linearization processing, wherein, representing freight train Whether it can serve the freight flow demand , representing the freight flow from station i to station j allocated to freight train , representing the number of freight trains Running in the statistical cycle; representing the freight train loading weight, G represents the freight demand set, Indicates the freight flow demand from station i to station j; representing the high-speed rail freight train set, Indicates The index of, S represents the high-speed rail station set, e, i, j represents the index of S, Indicates the terminal station of the line; S3. performing multi-objective processing and adaptive value setting on the linear model; S4. applying the set model to a selected actual high-speed railway line case for solving to obtain an actual high-speed railway freight train operation optimization scheme and a freight flow distribution scheme.

2. The method of claim 1, wherein, The S3 comprises: S31. decomposing the linearized model into a first single-objective optimization model and a second single-objective optimization model; S32. solving the objective function of the first single-objective optimization model to obtain the minimum value of the high-speed freight train operation cost; S33. solving the objective function of the second single-objective optimization model to obtain the minimum value of the total freight transportation time of the high-speed freight train.

3. The method of claim 2, wherein, The objective function of the first single-target optimization model is Z1 represents the minimum cost of high-iron freight train operation, represents the fixed cost of freight train operation; represents the variable cost of freight train operation related to distance; represents the variable cost of freight train operation related to stopping; represents the freight train whether to pass through the section , taking 0 or 1 as the value; represents the distance between i station and i+1 station, represents the freight train whether to stop at i station, taking 0 or 1 as the value.

4. The method of claim 3, wherein, The objective function of the second single-target optimization model is Z2 represents the total transport minimum target time of all goods, and |S| represents the number of stations. represents the distance between i station and i+1 station; for judging whether the train stops at e station; for judging whether the train passes through the section ; represents the average running speed of the freight train; represents the start-stop additional time generated by the intermediate stop of the freight train, represents the stop time when the freight train stops at the intermediate station.

5. The method of claim 4, wherein, An expression of the decision variable of the first single-objective optimization model is: and O represents a starting station of a high-speed railway line. D represents the terminal station of the high-speed railway line; represents the freight train whether to stop at i station; represents the freight train whether to pass through the section ; whether i station is the starting station of the freight train ; whether i station is the terminal station of the freight train , and N represents a set of natural numbers.

6. A device for optimization of high-speed freight train operation based on candidate set, characterized in that, The device is used to implement the method in any one of claims 1-5, comprising: a model establishing module, used to establish a high-speed freight train operation optimization nonlinear model; a linearization module, used to linearize the nonlinear model using a train candidate set to obtain a linear model; a setting module, used to perform multi-objective processing and adaptive value setting on the linear model; A solution module is configured to apply the set model to a selected actual high-speed railway line case for solution, and obtain an actual high-speed railway freight train operation optimization scheme and a freight flow distribution scheme.

7. A computer storage medium, characterized in that The medium stores a computer program, and the computer program is executed by a processor to implement the method in any one of claims 1-5.

8. An electronic device, comprising: The electronic device includes: A memory storing executable instructions; A processor running the executable instructions in the memory to implement the method in any one of claims 1-5.

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