A Method and System for Constructing Constrained Feasible Path Sets Based on Urban Rail Network Model

Abstract

This invention discloses a method and system for constructing a constrained feasible path set based on an urban rail transit network model. The method includes the following steps: loading basic information on urban rail transit system stations and lines; analyzing the spatial logical relationships between the network, stations, and lines based on the characteristics of the urban rail transit network to construct a spatial topology model of the urban rail transit system network; and using a constrained breadth-first search algorithm to search for a set of feasible paths between OD pairs that satisfy the maximum number of transfers constraint, and selecting the shortest path between OD pairs. This invention can search for a set of feasible paths between OD pairs in an urban rail transit network, providing a basis for building a rail transit network simulation platform and analyzing passenger flow characteristics.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit network model construction, and in particular to a method and system for constructing feasible path sets for urban rail transit. Background Technology

[0002] With the advancement of urbanization, China's urban population continues to rise, leading to increased daily travel demands from urban residents. As an important means of alleviating urban traffic congestion, urban rail transit has developed rapidly in recent years, with many cities already having established and operational rail transit networks.

[0003] To better analyze passenger flow in urban rail transit networks, it is necessary to accurately grasp passenger travel paths within the network. Therefore, searching for feasible travel paths between different origin-destination (OD) pairs is essential. Existing technologies only search for the shortest path between OD pairs as the travel path for passengers between those pairs. However, in reality, urban rail transit networks have multiple feasible paths for each OD pair, and not every passenger chooses the shortest path. Therefore, it is necessary to identify the travel paths that passengers might choose in real-world scenarios, thus constructing a set of feasible paths between OD pairs. Summary of the Invention

[0004] The problem to be solved by this invention is to propose a method and system for constructing a set of feasible urban rail transit routes with constraints, so as to provide a basis for the construction of urban rail transit network simulation platform and passenger flow travel characteristic analysis.

[0005] The present invention adopts the following technical solution:

[0006] A method for constructing a constrained feasible path set based on an urban rail network model includes the following steps:

[0007] S1. Acquire and analyze the basic data of urban rail transit network stations and lines, and clean the input data to obtain the data format required by the model.

[0008] S2. Based on the characteristics of urban rail transit networks, analyze the spatial logical relationships between the network, stations, and lines, establish the mapping relationships between network entities including lines, stations, and platforms, and construct a spatial topology model of the urban rail transit network.

[0009] S3. Using a constrained breadth-first search algorithm, search for a set of feasible paths between OD pairs that satisfy the maximum number of transfers constraint, and select the shortest path between OD pairs.

[0010] Furthermore, in step S1, the urban rail transit network station data includes: station number, station longitude, station latitude, and the line to which it belongs, represented as:

[0011] VS = {[v1,Lon1,Lat]}1, l1],…,[v i Lon i ,Lat i ,l j ]}

[0012] Among them, v i Indicates the station number, Lon i Indicates the longitude of the station, Lat i Representing the latitude of a station, i = 1, 2, ..., n, where n is the number of stations, l j This represents the line to which a station belongs in the road network, j = 1, 2, ..., m, where m is the total number of lines in the road network.

[0013] Furthermore, the spatial logical relationships between the road network, stations, and lines in step S2 include:

[0014] (1) At the network level, all lines constitute a road network, and the set of lines is represented as:

[0015] L = {l1, l2, ..., l m}

[0016] Among them, l j Let l be a line in a road network, j = 1, 2, ..., m. j Includes the following attribute values: line name, and the ACC number of the rail transit clearing system; the ACC number of each station is uniquely encoded for all stations in the network.

[0017] (2) At the line level, multiple stations constitute a line, and line l j The set of sites is represented as:

[0018]

[0019] in, Indicates line l j The i-th station in the series, where i = 1, 2, ..., n j n j For line l j The number of sites in;

[0020] station Includes the following attribute values: station name, line number, station ACC number, station intra-line number, and whether it is a transfer station; the station intra-line number is coded according to the order of the up and down directions of the line, and the station code is not unique; the code for transfer stations is different in different lines.

[0021] (3) The road network includes all stations, and the set of all stations in the road network is represented as:

[0022]

[0023] Based on the spatial logical relationships between the road network, stations, and lines described above, the spatial logical relationships between stations and lines in the road network are expressed as follows:

[0024] φ(L,V)

[0025] Wherein, φ represents the nonlinear relationship between the line and the station;

[0026] The road network spatial model is constructed as follows:

[0027] N = {φ(L,V)}

[0028] Where N represents the road network, L represents the set of lines, and V represents the set of stations in the subway network.

[0029] Furthermore, step S2 involves constructing a spatial topology model of the urban rail transit network, specifically including:

[0030] Based on the above road network spatial model, a directed graph of the road network space is constructed, represented as follows:

[0031] G(V,A)

[0032] Where A is a directed connection in the subway network, that is, the set of train track areas between stations;

[0033] Construct the adjacency matrix M of G(V,A) c Sum distance matrix M d , is represented as:

[0034]

[0035] Among them, c ij =1 indicates that stations i and j are directly connected, and the opposite is represented by 0;

[0036] d ij This represents the distance of the directed edge from station i to station j. If the two stations are directly connected, the distance between the edges of adjacent stations is the distance a between the stations. ij Conversely, it is +∞;

[0037] The spatial logical relationships between stations and lines in the road network, together with the directed graph of the road network, constitute the spatial topology model of the road network, as shown below:

[0038] O={φ(L,V),G(V,A)}

[0039] In the directed graph G(V,A), v∈V represents the node of the graph and a∈A represents the edge of the graph. There are edges connecting adjacent stations in both the up and down directions. Virtual platforms are set up at transfer stations to describe the passenger transfer behavior within the transfer station.

[0040] Furthermore, in step S3, a constrained breadth-first search algorithm is used to search for the set of feasible paths between all OD pairs in the network. The specific algorithm includes the following sub-steps:

[0041] S301: Initialization, load the directed spatial graph G(V,A) of the road network constructed in step S2, set the maximum number of transfers X for passengers in the road network, and input the set R of road network OD pairs. w ;

[0042] S302: Loop R w OD in w ij (v i ,v j Then, steps S303 to S307 are executed to generate a decision tree for feasible paths between OD pairs:

[0043] S303: Create an empty queue Q with OD as the starting point v i As the root node, it is placed in Q. An array C is defined to represent the number of path transfers, and C = 0 is set.

[0044] S304: When queue Q is not empty, the following steps S305 to S307 are performed in a loop:

[0045] S305: Retrieve the node from Q and determine if it is the destination v. j If yes, execute the algorithm as follows: step S307; otherwise, execute the algorithm as follows: step S306.

[0046] S306: Take the node taken from Q as the parent node v p Search for sites whose parent node is connected to G(V,A). As its direct child node Let n be the nth child node of the s-th parent node, and put it into queue Q, where n s The child node's sequence number is used; it is determined whether the child node is a transfer station. If it is, the transfer count of that node is incremented by one; otherwise, no operation is performed; the distance from the parent node's station to the child node's station is calculated. Number of transfers The child node site number is recorded together. In the corresponding child node;

[0047] S307: End the search, determine feasible paths, and decide the number of transfers (c) for each leaf node. r Check if r = 1, 2, ..., x is less than or equal to the maximum number of transfers, where x is the number of leaf nodes. If yes, keep the branch; otherwise, prune it.

[0048] S308: Read the feasible path decision tree generated in step S302. Each leaf node branch corresponds to a feasible path. Read and save the path station numbers in reverse order from the leaf node to the root node, as OD pairs.ij The feasible paths between them are stored in the corresponding OD pair feasible path set P. w The algorithm ends here.

[0049] This invention also includes a constrained feasible path set construction system based on an urban rail network model, constructed using the aforementioned constrained feasible path set construction method, comprising a road network data loading module, a network spatial topology model construction module, and a network OD pair feasible path search module, wherein:

[0050] The road network data loading module loads urban rail transit network station data and basic line data.

[0051] The network space topology model construction module constructs a network space topology model of urban rail transit based on the road network infrastructure, including the logical mapping relationship between lines, stations and platforms.

[0052] The feasible path search module between OD pairs in the network uses a constrained breadth-first search algorithm to search for the set of feasible paths between all OD pairs in the urban rail transit network.

[0053] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0054] 1. This invention employs a constrained breadth-first search algorithm to search for all feasible paths between OD pairs in an urban rail transit network and selects the shortest path between OD pairs.

[0055] 2. This invention provides a basis for the construction of a rail transit network simulation platform and the analysis of passenger flow characteristics, and has strong practical application significance. Attached Figure Description

[0056] Figure 1 This is a flowchart of the method for constructing a spatial topology model of an urban rail transit network according to the present invention;

[0057] Figure 2 This invention provides a directed graph of the urban rail transit network.

[0058] Figure 3 This is a feasible path decision tree diagram in the feasible path set search algorithm between OD pairs of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the application will be further described in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in this invention. All non-innovative embodiments based on this invention by other researchers in the art are within the protection scope of this invention.

[0060] like Figure 1 As shown, the technical solution of the present invention is: a method for constructing a constrained feasible path set based on an urban rail network model, comprising the following steps:

[0061] S1. Acquire and analyze the basic data of urban rail transit network stations and lines, and clean the input data to obtain the data format required by the model.

[0062] S2. Based on the characteristics of urban rail transit networks, analyze the spatial logical relationships between the network, stations, and lines, establish the mapping relationships between network entities including lines, stations, and platforms, and construct a spatial topology model of the urban rail transit network.

[0063] S3. Using a constrained breadth-first search algorithm, search for a set of feasible paths between OD pairs that satisfy the maximum number of transfers constraint, and select the shortest path between OD pairs.

[0064] In a preferred embodiment of the present invention, step S1, the urban rail transit network station data includes: station number, station longitude, station latitude, and its corresponding line, represented as:

[0065] VS={[v1,Lon1,Lat1,l1],...,[v i Lon i Lat i , l j ]}

[0066] Among them, v i Indicates the station number, Lon i Indicates the longitude of the station, Lat i Represents the latitude of a station, i = 1, 2, ..., n, where n is the number of stations, l j This represents the line to which a station belongs in the road network, j = 1, 2, ..., m, where m is the total number of lines in the road network.

[0067] It should be noted that the urban rail transit network is divided into three levels in space, from high to low: “network, line, and station”. The network includes different operating lines. The urban rail transit network spatial model is represented by N = {φ(L, V)}, where N represents the network, L represents the set of lines, and V represents the set of stations. The lines and stations form the network through a non-linear relationship φ.

[0068] From the logical relationships between lines, stations, and the network in the road network N={φ(L,V)}, the basic properties of the network can be derived. Specifically, the spatial logical relationships between the network, stations, and lines in step S2 include the following:

[0069] (1) At the network level, all lines constitute a road network, and the set of lines is represented as:

[0070] L = {l1, l2, ..., l} m}

[0071] Among them, l j Let l be a line in the road network, j = 1, 2, ..., m. j Includes attribute values:

[0072] Line l j Includes the following attribute values: line name, ACC number of the rail transit clearing system; the ACC number of the station is used to uniquely encode all stations in the network;

[0073] (2) At the line level, multiple stations constitute a line, and line l j The set of sites is represented as:

[0074]

[0075] in, Indicates line l j The i-th station in the series, i = 1, 2, ..., n j n j For line l j The number of sites in;

[0076] station The system includes the following attribute values: station name, line number, station ACC number, station intra-line number, and whether it is a transfer station. The station intra-line number is encoded according to the order of the up and down directions of the line, and the station code is not unique. The code for transfer stations is different in different lines. Based on the above attributes of the lines and stations, the system can perform a query function for station and line information in the network.

[0077] (3) The road network includes all stations, and the set of all stations in the road network is represented as:

[0078]

[0079] Based on the spatial logical relationships between the road network, stations, and lines described above, the spatial logical relationships between stations and lines in the road network are expressed as follows:

[0080] φ(L, V)

[0081] Where φ represents the nonlinear relationship between the line and the station.

[0082] The road network spatial model is constructed as follows:

[0083] N = {φ(L, V)}

[0084] Where N represents the road network, L represents the set of routes, and V represents the set of stations.

[0085] Then, in step S2, a spatial topology model of the urban rail transit network is constructed, specifically including:

[0086] Based on the above road network spatial model, a directed graph of the road network space is constructed, represented as follows:

[0087] G(V, A)

[0088] Where V is the set of stations in the metro network, and A is the directed edge in the metro network, that is, the set of train track areas between stations;

[0089] Construct the adjacency matrix M of G(V, A) c Sum distance matrix M d , is represented as:

[0090]

[0091] It should be noted that c ij =1 indicates that stations i and j are directly connected, and the opposite is represented by 0, which means they are not directly connected.

[0092] d ij This represents the distance of the directed edge from station i to station j. If the two stations are directly connected, the distance between the edges of adjacent stations is the distance a between the stations. ij Conversely, it is +∞;

[0093] Furthermore, based on the spatial logical relationships between stations and lines in the road network and the directed graph of the road network, a spatial topology model of the road network is constructed, as follows:

[0094] O = {φ(L, V), G(V, A)}

[0095] In the directed graph G(V, A), v∈V represents the node of the graph and a∈A represents the edge of the graph. There are edges connecting adjacent stations in both the up and down directions. Virtual platforms are set up at transfer stations to describe the passenger transfer behavior within the transfer station.

[0096] Specifically, such as Figure 2 As shown, Line A and Line B connect at transfer station v. T In a directed graph, the transfer station v is connected. T The description is that there are stations on both Line A and Line B. and and virtual platform v T Two-way connection, the walking time for passengers transferring between the two lines is v, which is the time from the platform of the preceding service train to the virtual platform. T Walking time plus time from virtual station v T Walking time to the platform of the subsequent service train.

[0097] Similarly, lines A, B, and C connect at transfer station v. T In a directed graph, the transfer station v is connected. T The description indicates that stations are located on lines A, B, and C. and and and virtual platform v T The connection allows passengers to transfer between the three lines, with the walking time from the platform of the preceding service train to the virtual platform being v. T Walking time plus time from virtual station v T Walking time to the platform of the subsequent service train.

[0098] In another preferred embodiment of the present invention, step S3 employs a constrained breadth-first search algorithm to search for the set of feasible paths between all OD pairs in the network. The specific algorithm includes the following sub-steps:

[0099] S301: Initialization, load the directed spatial graph G(V,A) of the road network constructed in step S2, set the maximum number of transfers X for passengers in the road network, and input the set R of road network OD pairs. w ;

[0100] S302: Loop R w OD in w ij (v u ,v j ), and execute steps S303 to S307 to generate as follows Figure 3 The OD pair feasible path decision tree shown:

[0101] S303: Create an empty queue Q with OD as the starting point v i As the root node, it is placed in Q. An array C is defined to represent the number of path transfers, and C = 0 is set.

[0102] S304: When queue Q is not empty, the following steps S305 to S307 are performed in a loop:

[0103] S305: Retrieve the node from Q and determine if it is the destination v. j If yes, execute the algorithm as follows: step S307; otherwise, execute the algorithm as follows: step S306.

[0104] S306: Take the node taken from Q as the parent node v p Search for sites whose parent node is connected to G(V,A). As its direct child node Let n be the nth child node of the s-th parent node, and put it into queue Q, where n sThe child node's sequence number is used; it is determined whether the child node is a transfer station. If it is, the transfer count of that node is incremented by one; otherwise, no operation is performed; the distance from the parent node's station to the child node's station is calculated. Number of transfers The child node site number is recorded together. In the corresponding child node;

[0105] S307: End the search, determine feasible paths, and decide the number of transfers (c) for each leaf node. r Check if r = 1, 2, ..., x is less than or equal to the maximum number of transfers, where x is the number of leaf nodes. If yes, keep the branch; otherwise, prune it.

[0106] S308: Read the feasible path decision tree generated in step S302. Each leaf node branch corresponds to a feasible path. Read and save the path station numbers in reverse order from the leaf node to the root node, as OD pairs. ij The feasible paths between them are stored in the corresponding OD pair feasible path set P. w The algorithm ends here.

[0107] As a preferred embodiment of the present invention, the present invention also provides a constrained feasible path set construction system based on an urban rail network model, constructed using any of the above-mentioned constrained feasible path set construction methods, including a road network data loading module, a network spatial topology model construction module, and a network OD pair feasible path search module, wherein...

[0108] The road network data loading module loads urban rail transit network station data and basic line data.

[0109] The network space topology model construction module constructs a network space topology model of urban rail transit based on the road network infrastructure, including the logical mapping relationship between lines, stations and platforms.

[0110] The feasible path search module between OD pairs in the network uses a constrained breadth-first search algorithm to search for the set of feasible paths between all OD pairs in the urban rail transit network.

[0111] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for constructing a constrained feasible path set based on an urban rail network model, characterized in that, Includes the following steps: S1. Acquire and analyze the basic data of urban rail transit network stations and lines, and clean the input data to obtain the data format required by the model. Urban rail transit network station data includes: station number, station longitude, station latitude, and the line to which it belongs, represented as: （1） in, Indicates the station number. Indicates the longitude of the station. Represents the latitude of the station, i=1,2,..., , For the number of sites, Indicates the line to which a station belongs in the road network. , This represents the total number of lines in the road network. S2. Based on the characteristics of urban rail transit networks, analyze the spatial logical relationships between the network, stations, and lines, establish the mapping relationships between network entities including lines, stations, and platforms, and construct a spatial topology model of the urban rail transit network. The spatial logical relationships between road networks, stations, and lines include: (1) At the network level, all lines constitute a road network, and the set of lines is represented as: （2） in, For a certain line in the road network, ,line Corresponding attribute values: route name and station ACC number; the station ACC number uniquely encodes all stations in the road network; (2) At the line level, multiple stations constitute a line. The set of sites is represented as: （3） in, Indicates the line The first in One site, , For the line The number of sites in; station Corresponding attribute values: station name, line number, station ACC number, station line number, and whether it is a transfer station; The station numbers within the line are coded according to the order of the up and down directions of the line, and the codes are not unique; The transfer station has different codes on different lines; (3) The road network includes all stations, and the set of all stations in the road network is represented as: （4） Based on the spatial logical relationships between the road network, stations, and lines described in formulas (2) to (4), the spatial logical relationships between stations and lines in the road network are expressed as follows: （5） in, This indicates the nonlinear relationship between lines and stations; The road network spatial model is constructed as follows: （6） in, Indicates road network, Represents a set of routes. A collection of stations in the subway network; S3. Using a constrained breadth-first search algorithm, search for a set of feasible paths between OD pairs that satisfy the maximum number of transfers constraint, and select the shortest path between OD pairs.

2. The method for constructing a constrained feasible path set based on an urban rail network model as described in claim 1, characterized in that, The step S2, which involves constructing a spatial topology model of the urban rail transit network, specifically includes: Based on the above road network spatial model, a directed graph of the road network space is constructed, represented as follows: （7） in, A directed edge in a subway network, which is the set of train track areas between stations; Build adjacency matrix Sum distance matrix , is represented as: （8） in, Indicates site If two lines are directly connected, then they are not directly connected, and this is represented by 0. Indicates site to station The distance between directed edges is the distance between adjacent stations if two stations are directly connected. Conversely, it is ; The spatial logical relationships between stations and lines in the road network, together with the directed graph of the road network, constitute the spatial topology model of the road network, as shown below: （9） Among them, the directed graph of the road network space China and Israel Representing the nodes of a graph, using The graph represents the connections between adjacent stations in both the up and down directions. Virtual platforms are set up at transfer stations to describe passenger transfer behavior within the transfer station.

3. The method for constructing a constrained feasible path set based on an urban rail network model as described in claim 2, wherein step S3 employs a constrained breadth-first search algorithm to search for the feasible path set between all OD pairs in the network, and the specific algorithm includes the following sub-steps: S301: Initialization, loading the directed spatial graph of the road network constructed in step S2. Set the maximum number of transfers X for passengers traveling on the road network, and input the set of OD pairs for the road network. ; S302: Cycle OD pairs in Then, steps S303 to S307 are executed to generate a decision tree for feasible paths between OD pairs: S303: Create an empty queue Q, with OD as the starting point. As the root node, it is placed in Q. An array C is defined to represent the number of transfers along the path, and C = 0 is set. S304: When queue Q is not empty, the following steps S305 to S307 are performed in a loop: S305: Retrieve the node from Q and determine if it is the destination. If yes, execute the algorithm as follows: step S307; otherwise, execute the algorithm as follows: step S306. S306: Take the node taken from Q as the parent node. Searching for the parent node Connected sites As its direct child node For the first The first parent node Each child node is added to queue Q, where The child node's sequence number is used; it is determined whether the child node is a transfer station. If it is, the transfer count of that node is incremented by one; otherwise, no operation is performed; the distance from the parent node's station to the child node's station is calculated. Number of transfers Record the sub-node site numbers together. In the corresponding child node; S307: End the search, determine feasible paths, and decide the number of transfers for leaf nodes. Is it less than or equal to the maximum number of transfers? The number of leaf nodes; if so, retain the feasible path; otherwise, perform pruning. S308: Read the feasible path decision tree generated in step S302. Each leaf node branch corresponds to a feasible path. Read and save the path station numbers in reverse order from the leaf node to the root node, as OD pairs. The feasible paths between them are stored in the corresponding OD pair feasible path set. The algorithm ends here.

4. A system for constructing a constrained feasible path set based on an urban rail network model, characterized by employing the constrained feasible path set construction method according to any one of claims 1 to 3, wherein... This includes a road network data loading module, a network spatial topology model construction module, and a feasible path search module between network OD pairs; The road network data loading module loads urban rail transit network station data and basic line data. The network space topology model construction module constructs a network space topology model of urban rail transit based on the road network infrastructure, including the logical mapping relationship between lines, stations and platforms. The feasible path search module between OD pairs in the network uses a constrained breadth-first search algorithm to search for the set of feasible paths between all OD pairs in the urban rail transit network.

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