Public transport vehicle scheduling optimization method based on inverse difference function image features

Abstract

The invention relates to the technical field of vehicle scheduling optimization, and discloses a public transport vehicle scheduling optimization method based on inverse difference function image features, which comprises the following steps: acquiring public transport line operation data; clustering the originating and ending stations according to the public transport line operation data, and determining a corresponding public transport departure time table according to the clustered originating and ending stations; according to the clustered originating and ending sites, establishing an inverse difference function image of each originating and ending site; carrying out inverse difference function peak value identification and decision variable marking on the inverse difference function images of the starting and ending stations; constructing a network flow model for public transport vehicle scheduling optimization according to the decision variable set, and calculating a minimum motorcade scale; and generating a multi-parking-lot collaborative scheduling train number chain according to the minimum fleet scale. According to the method, the image features of the inverse difference function are fully utilized, redundant variables of the network flow model are reduced, the network flow model is rapidly solved, and therefore the public transport vehicle scheduling problem is rapidly solved.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle scheduling optimization, and particularly relates to a public transportation vehicle scheduling optimization method based on the image features of the deficit function. Background Art

[0002] Vehicle scheduling optimization is an important issue in public transportation operation management activities. Its goal is to achieve the reasonable and efficient utilization of vehicle capacity resources by scientifically planning the production and operation plans of vehicles. With the acceleration of the urbanization process and the increase in the complexity of the public transportation network, the traditional manual scheduling mode is difficult to meet the large-scale and dynamic vehicle scheduling requirements. The automated scheduling method based on mathematical models and artificial intelligence algorithms has gradually become a more efficient solution to the public transportation vehicle scheduling optimization problem. The minimum fleet size, as the core index to measure the economy of the vehicle scheduling plan, directly affects the enterprise operation cost and becomes the primary goal of the mathematical optimization model.

[0003] The deficit function can be used to calculate the minimum fleet size required for a public transportation fleet to meet service demands. The deficit function is a step function with respect to the public transportation station. It takes time as the abscissa. When a vehicle departs from the station, its value increases by 1, and when a vehicle arrives at the station, its value decreases by 1. During the scheduling time period, the maximum value of the deficit function represents the minimum number of vehicles required for the corresponding public transportation station. Summing up the maximum values of the deficit function values of all stations gives the minimum fleet size required to execute the established service schedule. With the help of the function values of the deficit function, through independent calculations for each station and global accumulation, the required minimum fleet size can be quickly calculated.

[0004] The mathematical programming model based on the network flow model is another method for calculating the minimum fleet size of public transportation. This method abstracts train trips as nodes, converts the vehicle connection relationship into a directed edge, constructs a bipartite graph of train trip connections, and determines the maximum number of feasible connected train trips by solving the maximum flow of the bipartite graph, and then obtains the minimum fleet size (the total number of train trips minus the maximum flow value). Although this method can obtain an exact solution, it faces two major challenges: First, the spatio-temporal coupling of train trip connection constraints leads to an explosion in the model dimension. Especially for large-scale actual operation problems, the combination of vehicle-connected train trips grows exponentially, forming a huge decision variable and constraint matrix; Second, the efficiency of traditional solving algorithms (such as Ford-Fulkerson, Edmonds-Karp) drops sharply when dealing with ultra-large-scale networks and it is difficult to meet the rapid scheduling requirements.

[0005] In recent years, the update and replacement of optimized model commercial solvers have significantly improved the solving ability of the network maximum flow mathematical optimization model. By introducing extended models such as time-space networks and multi-commodity flows, practical constraints such as vehicle turnover and charging restrictions can be further refined. However, existing modeling strategies generally have the problem of redundant variables: for example, when the time interval between two trips is less than the minimum connection time or the yard capacity is saturated, the connection variables should be invalid, but traditional models still retain them in the feasible solution space, forcing the solver to traverse a large number of invalid paths during the branch and bound process. To address the problem of variable redundancy, existing optimization strategies mainly focus on heuristic pruning in the preprocessing stage, such as feasibility screening based on time windows and early exclusion of yard capacity constraints. Although this method can reduce the problem scale, its rule design highly depends on prior knowledge, lacks universality, and may misdelete potential optimal solutions. On the other hand, the image features of the deficit function have not been fully explored. Although existing research has pointed out the correlation between the deficit peak and the fleet size, there is still a lack of systematic research on how to transform the peak dynamic characteristics into variable reduction strategies. Especially in the scenario of multi-yard collaborative scheduling, traditional deficit functions only focus on the supply-demand balance of a single yard and fail to reveal the networked connection rules of cross-yard vehicle scheduling, and the model optimization space has not been fully released. Summary of the Invention

[0006] In view of the above deficiencies in the prior art, the present invention provides an optimization method for public transportation vehicle scheduling based on the image features of the deficit function. By combining the deficit function model with the network maximum flow model, the image features of the deficit function are fully utilized to reduce the redundant variables of the network maximum flow model, achieve rapid solution of the model, and thus achieve rapid solution of the public transportation vehicle scheduling problem.

[0007] To achieve the above invention purpose, the technical solution adopted by the present invention is as follows:

[0008] An optimization method for public transportation vehicle scheduling based on the image features of the deficit function, comprising the following steps:

[0009] Collect the operation data of public transportation lines;

[0010] Cluster the origin-destination yards according to the operation data of public transportation lines, and determine the corresponding public transportation departure schedules according to the clustered origin-destination yards;

[0011] Establish the deficit function images of each origin-destination yard according to the clustered origin-destination yards;

[0012] Identify the deficit function peaks and mark the decision variables for the deficit function images of each origin-destination yard;

[0013] Construct a network flow model for optimizing public transportation vehicle scheduling according to the decision variable set, and calculate the minimum fleet size;

[0014] Generate the train trip chains for multi-depot collaborative scheduling according to the minimum fleet size.

[0015] In an alternative way, the operation data of the public transport line includes:

[0016] The name of the public transport line, the departure and arrival timetables of the public transport in both directions during the full-day operation period, and the geographical location information of the origin and destination stations in both directions.

[0017] In an alternative way, establish the deficit function images of each origin and destination station according to the clustered origin and destination stations, including:

[0018] Statistically collect the times and train numbers of all arriving and departing trains at the same station;

[0019] Sort the time and its corresponding train number in ascending order based on the time column;

[0020] Calculate the deficit value corresponding to each time according to the calculation rule of the deficit value.

[0021] In an alternative way, perform deficit function peak identification and decision variable marking on the deficit function images of each origin and destination station, including:

[0022] Initialize the variable matrix to 0;

[0023] Take the index, total number of trains, train number, timetable, arrival / departure train determination, and deficit value of the deficit function of a station as input data;

[0024] Modify the deficit values corresponding to the consecutive identical train times in the time column to the deficit value corresponding to the last moment of this consecutive identical part, and return and store the processed data;

[0025] Identify all the maximum deficit values of the deficit function of the station and their corresponding times, indices, and train numbers. For the same maximum deficit function value of a station, take the situation where the arriving train is before the index position of the maximum deficit value and the departing train is after the index position of the maximum deficit value as the judgment condition, mark the variables corresponding to the arriving and departing trains that meet the judgment condition with 1, and finally return the decision variables with a value of 1 for all stations to the variable matrix.

[0026] In an alternative way, construct a network flow model for optimizing the public transport vehicle scheduling according to the set of decision variables, and calculate the minimum fleet size, including:

[0027] Construct a network flow model for optimizing the public transport vehicle scheduling according to the set of variables after removing redundant variables;

[0028] Solve the network flow model for optimizing the scheduling of public transportation vehicles to obtain the maximum number of feasible train connections.

[0029] Calculate the minimum fleet size based on the maximum number of feasible train connections.

[0030] In an alternative approach, construct a network flow model for optimizing the scheduling of public transportation vehicles based on a set of variables with redundant variables removed, specifically:

[0031]

[0032] The constraint condition is:

[0033] t j -(t i +t ij +z ij )≥(x ij -1)*M, i, j ∈ I

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] Where Max is the maximum value function, C(I) is the maximum number of feasible train connections in the set I of train trips in the public transportation network, x ij is a 0-1 variable indicating whether train trips i and j can be executed by the same vehicle, t i is the departure time of train trip i, t j is the departure time of train trip j, t ij is the travel time for train trip i to reach the station where train trip j is located, z ij is a judgment coefficient indicating whether train trips i and j are at the same station, and M is a set positive integer.

[0040] In an alternative approach, calculate the minimum fleet size based on the maximum number of feasible train connections, specifically:

[0041] Min F(I) = |I| - Max C(I)

[0042] Where Min is the minimum value function, F(I) is the minimum number of vehicles, |I| is the total number of all train trips in the set I of train trips in the public transportation network, Max is the maximum value function, and C(I) is the maximum number of feasible train connections in the set I of train trips in the public transportation network.

[0043] In an alternative approach, generating the multi-depot collaborative scheduling train number chain according to the minimum fleet size includes:

[0044] Obtain all the train number sets of the decision variables according to the minimum fleet size;

[0045] Establish a set of feasible directed edges based on all the train number sets of the decision variables;

[0046] Generate the multi-depot collaborative scheduling train number chain according to the set of feasible directed edges.

[0047] In an alternative approach, generating the multi-depot collaborative scheduling train number chain according to the set of feasible directed edges includes:

[0048] Traverse all the feasible directed edges, establish the out-edge adjacency list of each node, and count the in-degree of each node;

[0049] Select all the nodes with in-degree of 0 and having out-edges as the path starting points, start traversing from each starting point along the adjacency list, and record the path nodes;

[0050] Convert the path nodes into a node sequence to obtain the multi-depot collaborative scheduling train number chain.

[0051] The present invention has the following beneficial effects:

[0052] (1) The present invention adopts a redundant variable reduction strategy based on the image features of the inverse difference function. By utilizing the peak characteristics of the inverse difference function image, a redundant variable identification rule linked with the network flow model is constructed to accurately mark and eliminate invalid train number connection variables, reducing redundant variables while ensuring the completeness of the solution space, avoiding the suboptimal risk of heuristic pruning in the traditional branch and bound algorithm, and improving the model solving efficiency.

[0053] (2) The present invention adopts a multi-depot clustering collaborative scheduling optimization technology, innovatively combines the clustering of the geographical locations of the stations with the analysis of the inverse difference function, aggregates the scattered stations into regional nodes, and the inverse difference function image of the regional nodes reveals the network connection rules of vehicle scheduling, breaking through the limitation of the traditional single-station supply-demand balance, and significantly reducing the dimension and complexity of the multi-depot collaborative scheduling optimization problem.

[0054] (3) The present invention adopts a model acceleration and solving technology with nested solvers. By deeply integrating the preprocessing of the inverse difference function with the solving of the network flow model, dynamically pruning variables and constraints according to the redundant marking matrix during the modeling stage, and coupling the optimization capabilities of commercial solvers, it realizes the collaborative acceleration of variable reduction and solving algorithms, providing an efficient technical framework for solving large-scale public transport vehicle scheduling problems.

[0055] In summary, the public transportation vehicle scheduling method based on the image features of the inverse difference function proposed by the present invention helps to quickly solve the vehicle scheduling optimization problem of large-scale public transportation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 FIG. is a schematic flow chart of an optimization method for public transportation vehicle scheduling based on the image features of the inverse difference function;

[0057] Figure 2 FIG. is a schematic diagram of the inverse difference function image. DETAILED DESCRIPTION OF THE INVENTION

[0058] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0059] As Figure 1 shown, an optimization method for public transportation vehicle scheduling based on the image features of the inverse difference function provided by an embodiment of the present invention includes the following steps S1 to S5:

[0060] S1. Collect the operation data of the public transportation line;

[0061] In an alternative embodiment of the present invention, the operation data of the public transportation line collected in step S1 includes:

[0062] The name of the public transportation line, the departure schedules of the up and down directions during the full-day operation period, and the geographical location information of the origin and destination stations of the up and down directions.

[0063] S2. Cluster the origin and destination stations according to the operation data of the public transportation line, and determine the corresponding public transportation departure schedules according to the clustered origin and destination stations;

[0064] In an alternative embodiment of the present invention, the number of origin or destination stations involved in a large-scale public transportation network is too large. By clustering, the origin or destination stations belonging to one area can be regarded as one origin or destination station, which can reduce the number of stations and is beneficial to the solution of the subsequent public transportation vehicle scheduling optimization problem.

[0065] Step S2 determines the number of origin or destination stations for the final clustering based on the geographical location information of the origin and destination stations of the up and down lines through the elbow method. Then, clustering is performed according to the geographical location information of the origin and destination stations, and the origin or destination stations belonging to one area are regarded as one origin or destination station, reducing the number of stations involved in the large-scale public transportation network. And the corresponding public transportation departure schedules are sorted out according to the results of the origin and destination stations after clustering.

[0066] S3. Establish the deficit function image of each origin and destination station according to the origin and destination stations after clustering;

[0067] In an alternative embodiment of the present invention, step S3 stores the deficit function images of the stations one by one in the form of data columns based on the origin and destination stations after clustering; specifically, the abscissa time and the ordinate deficit value of the deficit function image of the station are stored in an Excel table in the form of a time column and a deficit value column. The data column form includes a train number column, a train time column, a deficit value column, an arrival / departure determination column, and an index column.

[0068] The deficit function is an image model, also known as a step function. The connotation of this step function is that at a single origin and destination station, if a vehicle departs from the station, the function value is increased by 1, and if a vehicle arrives at the station, the function value is decreased by 1; the function value of the deficit function represents the difference between the total number of departing vehicles and the number of arriving vehicles at the station before a certain moment (including this moment), and the function value corresponding to the peak is the minimum number of parked vehicles required to maintain the continuity of train numbers. Storing the time column and the function value column included in the deficit function image in the form of data columns is conducive to the subsequent identification of the deficit function peak and the marking of redundant variables.

[0069] This embodiment establishes the deficit function image of each origin and destination station according to the origin and destination stations after clustering, including:

[0070] Statistically collect the times and train numbers of all arriving and departing trains at the same station;

[0071] Sort the time and its corresponding train number in ascending order based on the time column;

[0072] Calculate the deficit value corresponding to each moment according to the calculation rule of the deficit value.

[0073] S4. Perform deficit function peak identification and decision variable marking on the deficit function images of each origin and destination station;

[0074] In an alternative embodiment of the present invention, in step S4, the peak value of the reverse difference function of each origin-destination station after clustering is identified and the decision variable is marked. For the same station, the connection of train arrivals where the arrival time of train i is later than the departure time of train j is called an infeasible train connection. This type of train connection cannot be continued in time and cannot be executed by the same vehicle. The corresponding decision variable x ij takes the value of 0; the connection of train arrivals where the arrival time of train i is earlier than the departure time of train j is called a feasible train connection. Due to the requirements of maximizing the number of train connections in the train maximum flow network model objective function and the constraint that each train can only be connected by one train before and after, not all feasible train connections can be connected. That is, the decision variable x ij of the feasible train connection is initially assigned a value of 0 or 1, and it is necessary to further solve through the train maximum flow network model to determine the value of the decision variable x ij corresponding to the feasible train connection. Benefiting from the graphical advantage of the reverse difference function image, the infeasible train connection and the feasible train connection are visualized, that is, the feasible solution space of the maximum flow network model can be determined through the reverse difference function image. As Figure 2 shown, for the reverse difference function image with the maximum reverse difference value being positive, the maximum reverse difference value represents the number of trains that the station needs to send out more at this moment, corresponding to the minimum number of on-site vehicles required for the station to maintain the operation plan. Combining the optimization idea of the maximum flow network model, the reverse difference function image is deeply analyzed, and it is obtained that the arriving train i before the maximum reverse difference value will not be connected to the arriving train j after the maximum reverse difference value. That is, in order to maximize the number of feasible train connections, the vehicle connecting the arriving train i before the maximum reverse difference value will connect the departing train j before the maximum reverse difference value, rather than the departing train j after the maximum reverse difference value.

[0075] In this embodiment, combining the optimization characteristics of the network flow model and the characteristics of the reverse difference function image, if the subscripts i and j of the variable x ij satisfy the rule: for the same peak value of the reverse difference function, the arriving train i is before the peak value and the departing train j is after the peak value, then the corresponding variable x ij is defined as the decision variable. That is, all variables x ij in the variable matrix are initially assigned a value of 0, and the variable x ij satisfying the constraint rule is assigned a value of 1. The variable assigned a value of 1 is the decision variable. Marking this type of decision variable and removing redundant variables can achieve the purpose of reducing the solution space while maintaining the completeness of the solution space of the maximum flow network model, thereby accelerating the solution.

[0076] On the basis of storing the reverse difference function of each station after clustering in data form, this embodiment uses the peak recognition algorithm to identify the peak value of the reverse difference function of each station. All decision variables x in the variable matrixij The initial value is 0. For the variable x that satisfies the constraint rule "for the same peak value of the inverse difference function, the arrival train number i is before the peak value and the departure train number j is after the peak value" ij is marked with 1, and finally all the marked results are returned to the same data set.

[0077] This embodiment performs inverse difference function peak recognition and decision variable marking on the inverse difference function images of each origin-destination station, including:

[0078] Initialize the variable matrix X ij to 0;

[0079] Take the index (n i ) of the inverse difference function of a station, the total number of train numbers (I, i ∈ I), the train number (c i ), the train timetable (t i ), the arrival / departure train determination (z i : for the arrival train number i at the same station, z i = 0; for the train number i departing from the same station, z i = 1) and the inverse difference value (d i ) as input data;

[0080] Preprocess the consecutive identical train times in the time column, that is, modify the inverse difference values corresponding to the consecutive identical train times to the inverse difference value corresponding to the last moment of the consecutive identical part, with the aim of ensuring that one moment value corresponds to one inverse difference value, and return and store the processed data;

[0081] Identify all the maximum inverse difference values of the station's inverse difference function and their corresponding moments, indices, and train numbers. For the same maximum inverse difference function value of a station, take the situation where the arrival train number c i , i ∈ (1, k - 1), z i = 0 is before the index position n of the maximum inverse difference value k and the departure train number c j , j ∈ (k + 1, I), z j = 1 is after the index position n of the maximum inverse difference value k as the judgment condition, and mark the x ij variables corresponding to the train numbers i and j that meet the judgment condition with 1. Finally, return the variable matrix X ij with the value of 1 for all decision variables x ij .

[0082] After the maximum inverse difference value and decision variable recognition operation of a station are completed, if there are new stations, select a new station and re-enter the data; if the decision variables of all stations have been recognized, output the final variable matrix X ij , and stop the process.

[0083] S5. Construct a network flow model for optimizing the scheduling of public transportation vehicles based on the set of decision variables, and calculate the minimum fleet size.

[0084] In an alternative embodiment of the present invention, step S5 constructs a network flow model for optimizing the scheduling of public transportation vehicles based on the train number data information of the public transportation network, and calculates the minimum number of vehicles required to maintain the operation of the public transportation network. When calling the optimization solver to model and solve the network flow model, based on the data set of decision variables identified in S3, only the x variables with non-redundant identifiers are defined during programming modeling, and the corresponding constraint conditions are constructed, so as to reduce the number of decision variables x and constraint conditions, reduce the solution space of the network flow model, and reduce the memory occupancy, thereby achieving the accelerated solution of the network flow model. ij variables and construct the corresponding constraint conditions, aiming to reduce the number of decision variables x ij and constraint conditions, reduce the solution space of the network flow model, and reduce the memory occupancy, so as to achieve the accelerated solution of the network flow model.

[0085] This embodiment constructs a network flow model for optimizing the scheduling of public transportation vehicles based on the set of decision variables, and calculates the minimum fleet size, including:

[0086] Construct a network flow model for optimizing the scheduling of public transportation vehicles based on the set of decision variables;

[0087] Solve the network flow model for optimizing the scheduling of public transportation vehicles to obtain the maximum feasible number of train connections;

[0088] Calculate the minimum fleet size according to the maximum feasible number of train connections.

[0089] This embodiment constructs a network flow model for optimizing the scheduling of public transportation vehicles based on the set of decision variables, specifically:

[0090]

[0091] The constraint condition is:

[0092] t j -(t i +t ij +z ij )≥(x ij -1)*M, i, j ∈ I

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] Among them, Max is the maximum value function, C(I) is the maximum feasible connection number of trips in the public transport network trip set I, and x ij is a 0-1 variable indicating whether trip i and trip j can be executed by the same vehicle. When trip i and trip j cannot be executed by the same vehicle, x ij takes the value of 0; t i is the departure time of trip i, and t j is the departure time of trip j. The departure time is discretized into minutes; t ij is the travel time for trip i to reach the station where trip j is located, and z ij is a judgment coefficient indicating whether trip i and trip j are at the same station. When trip i and trip j are at the same station, z ij takes the value of 0; when trip i and trip j are at different stations, z ij usually takes the empty running time of the vehicle between the stations where trip i and trip j are located; M is a set positive integer, usually taking a multiple of the operation cycle duration T. The first constraint is used to judge whether trip i and trip j can be executed by the same vehicle; the second and third constraint conditions limit that there can be at most one connecting trip before and after a trip. Through the above network maximum flow model, the maximum feasible connection number C(I) in the bipartite graph can be solved.

[0099] Based on the maximum feasible connection number C(I) of the bipartite graph obtained by solving in this embodiment, the minimum fleet size required to maintain the operation of all trips can be calculated, specifically:

[0100] Min F(I) = |I| - Max C(I)

[0101] Among them, Min is the minimum value function, F(I) is the minimum number of vehicles, |I| is the number of all trips in the public transport network trip set I, Max is the maximum value function, and C(I) is the maximum feasible connection number of trips in the public transport network trip set I.

[0102] In this embodiment, the constructed public transport vehicle scheduling optimization network flow model is solved using an optimization solver software, and data storage and analysis, inverse difference function peak identification, and redundant variable marking are implemented using programming software.

[0103] S6. Generate a multi-yard collaborative scheduling trip chain according to the minimum fleet size.

[0104] In an alternative embodiment of the present invention, step S6 of generating a multi-yard collaborative scheduling trip chain according to the minimum fleet size includes:

[0105] Obtain all trip sets of decision variables according to the minimum fleet size;

[0106] Establish a set of feasible directed edges based on all train trips in the decision variables;

[0107] Generate a multi-yard collaborative scheduling train trip chain according to the set of feasible directed edges.

[0108] In this embodiment, based on the solution result of the maximum flow model of the train trip network in step S4, obtain all subscript sets where the variable x ij = 1, obtain the connection situation of the train trip chain through the train trip chain generation algorithm, and obtain the train operation plan for multi-yard vehicle collaborative scheduling. In the network maximum flow model, x ij = 1 means that train trips i and j can be executed by the same vehicle, and such (i, j) are regarded as feasible directed edges. If the feasible directed edges satisfy the rule: the end point of one feasible directed edge is the starting point of another feasible directed edge, then these two feasible directed edges can be connected together to form a chain, that is, all directed edges satisfying the above rules are connected in sequence until there are no more feasible directed edges that can be continued, and the final train trip chain can be obtained. For example: there is a set of feasible directed edges [(1, 20), (20, 4), (4, 6), (5, 7)], then finally two train trip chains [1, 20, 4, 6] and [5, 7] can be obtained, as shown in Table 1.

[0109] Table 1

[0110]

[0111] This embodiment generates a multi-yard collaborative scheduling train trip chain according to the set of feasible directed edges, including:

[0112] Traverse all feasible directed edges, establish an out-edge adjacency list for each node, and count the in-degree of each node; the meaning of the node in-degree is the number of feasible directed edges converging to this node. Counting the in-degree of each node is to determine whether the node is the starting node of the train trip chain, that is, there are no feasible directed edges that will converge before the starting node of the train trip chain, and the corresponding in-degree is 0.

[0113] Select all nodes with an in-degree of 0 and having out-edges as the path starting points, start traversing along the adjacency list from each starting point, and record the path nodes;

[0114] Convert the path nodes into a node sequence to obtain a multi-yard collaborative scheduling train trip chain.

[0115] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows 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 the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0116] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0117] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operational steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0118] Specific embodiments are applied in the present invention to elaborate on the principles and implementation manners of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present invention.

[0119] Those of ordinary skill in the art will realize that the embodiments described herein are for helping readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various specific deformations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A public transport vehicle scheduling optimization method based on the image features of the inverse difference function, characterized in that It includes the following steps: Collect the operation data of public transportation lines; Cluster the origin and destination stations according to the operation data of public transportation lines, and determine the corresponding departure schedules of public transportation based on the clustered origin and destination stations; Establish the inverse difference function images of each origin and destination station according to the clustered origin and destination stations; Identify the peaks of the inverse difference functions and mark the decision variables for the inverse difference function images of each origin and destination station; Construct a network flow model for optimizing the scheduling of public transportation vehicles according to the set of decision variables, and calculate the minimum fleet size; Generate a multi-yard collaborative scheduling train number chain according to the minimum fleet size.

2. The optimized method for dispatching public transportation vehicles based on the image features of the inverse difference function according to claim 1, characterized in that, The operation data of public transportation lines includes: The name of the public transportation line, the up and down departure schedules of public transportation during the full-day operation period, and the geographical location information of the up and down origin and destination stations.

3. The optimization method for the scheduling of public transportation vehicles based on the image features of the inverse difference function according to claim 1, wherein Establish the inverse difference function images of each origin and destination station according to the clustered origin and destination stations, including: Statistically collect the arrival and departure times and train numbers of all trains at the same station; Sort the time and its corresponding train number in ascending order based on the time column; Calculate the inverse difference value corresponding to each moment according to the calculation rule of the inverse difference value.

4. A public transportation vehicle scheduling optimization method based on the image features of the inverse difference function according to claim 1, characterized in that, Identify the peaks of the inverse difference functions and mark the decision variables for the inverse difference function images of each origin and destination station, including: Initialize the variable matrix to 0; Take the index of the inverse difference function of a station, the total number of trains, the train number, the schedule, the arrival and departure train determination, and the inverse difference value as input data; Modify the inverse difference values corresponding to the consecutive same train times in the time column to the inverse difference value corresponding to the last moment of this consecutive same part, and return and store the processed data; Identify all the maximum inverse difference values and their corresponding times, indexes, and train numbers of the station's inverse difference function. For the same maximum inverse difference function value of a station, take the situation where the arrival train is before the index position of the maximum inverse difference value and the departure train is after the index position of the maximum inverse difference value as the judgment condition, mark the variables corresponding to the arrival and departure trains that meet the judgment condition with 1, and finally return the decision variables with a value of 1 for the station to the variable matrix.

5. The optimization method for public transport vehicle scheduling based on the image features of the inverse difference function according to claim 1, characterized in that, Construct a network flow model for optimizing the scheduling of public transportation vehicles according to the set of decision variables, and calculate the minimum fleet size, including: Construct a network flow model for optimizing the scheduling of public transportation vehicles according to the set of variables after removing redundant variables; Solve the network flow model for optimizing the scheduling of public transportation vehicles to obtain the maximum number of feasible train connections; Calculate the minimum fleet size according to the maximum number of feasible train connections.

6. The optimization method for public transport vehicle scheduling based on the image features of the inverse difference function according to claim 5, characterized in that, Construct a network flow model for optimizing the scheduling of public transportation vehicles according to the set of variables after removing redundant variables, specifically: The constraint conditions are: t j -(t i +t ij +z ij )≥(x ij -1)*M, i, j ∈ I Among them, Max is the maximum value function, C(I) is the maximum feasible connection number of trips in the public transport network trip set I, and x ij is a 0-1 variable indicating whether trips i and j can be executed by the same vehicle, t i is the departure time of trip i, t j is the departure time of trip j, t ij is the travel time from trip i to the station where trip j is located, z ij is the judgment coefficient indicating whether trips i and j are at the same station, and M is a set positive integer.

7. A public transportation vehicle scheduling optimization method based on the image features of the inverse difference function according to claim 5, characterized in that Calculate the minimum fleet size according to the maximum number of feasible train connections, specifically: MinF(I) = |I| - MaxC(I) Where, Min is the minimum value function, F(I) is the minimum number of vehicles, |I| is the total number of all trains in the public transportation network train set I, Max is the maximum value function, and C(I) is the maximum number of feasible train connections in the public transportation network train set I.

8. The optimization method for public transportation vehicle scheduling based on the image features of the inverse difference function according to claim 1, wherein Generate a multi-yard collaborative scheduling train number chain according to the minimum fleet size, including: Obtain all the train sets of the decision variables according to the minimum fleet size; Establish a set of feasible directed edges based on the set of all train trips of the decision variables; Generate a multi-yard collaborative scheduling train trip chain according to the set of feasible directed edges.

9. The optimization method for the scheduling of public transport vehicles based on the image features of the inverse difference function according to claim 8, characterized in that Generate a multi-yard collaborative scheduling train trip chain according to the set of feasible directed edges, including: Traverse all feasible directed edges, establish the out-edge adjacency list of each node, and count the in-degree of each node; Select all nodes with an in-degree of 0 and having out-edges as the path starting points, start from each starting point, traverse along the adjacency list, and record the path nodes; Convert the path nodes into a node sequence to obtain a multi-yard collaborative scheduling train trip chain.

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