CN113987729B

CN113987729B - Large-scale urban rail network automatic generation method based on land utilization

Info

Publication number: CN113987729B
Application number: CN202111613349.9A
Authority: CN
Inventors: 景国胜; 马小毅; 刘明敏; 何鸿杰; 李彩霞; 刘新杰; 金安; 陈先龙; 李磊; 陈建均; 张科; 吴恩泽
Original assignee: GUANGZHOU TRANSPORT PLANNING RESEARCH INSTITUTE
Current assignee: Guangzhou transportation planning and Research Institute Co.,Ltd.
Priority date: 2021-12-28
Filing date: 2021-12-28
Publication date: 2022-03-01
Anticipated expiration: 2041-12-28
Also published as: CN113987729A

Abstract

The invention discloses a large-scale urban rail network automatic generation method based on land utilization, which comprises the following six steps: s1, establishing a mathematical model; s2, carrying out clustering analysis to obtain a plurality of site clusters; s3, solving the minimum spanning tree for each site cluster, and combining the minimum spanning trees; s4, network correction is carried out on the network scheme generated after the combination; s5, calculating the total length of the corrected generated network scheme, and if the total length is less than the minimum total length, updating the optimal generated network scheme and the minimum total length; s6, if the iteration times do not reach the upper limit, returning to the step S3, iterating the steps S3-S5 for a plurality of times, otherwise, ending the process; the generation method can be used for quantitatively designing the urban rail network based on a site selection scheme of land utilization, so that the problems that the scheme is difficult to optimize due to high difficulty of a subjective design planning scheme, various site and network structure forms, more influence factors and the like are solved, and the scientificity and the rationality of the urban rail network planning are improved.

Description

Large-scale urban rail network automatic generation method based on land utilization

Technical Field

The invention belongs to the technical field of urban rail network planning, and particularly relates to a large-scale urban rail network automatic generation method based on land utilization.

Background

Overview of urban railway line network planning

Urban rail network planning is a precondition for efficiently and reliably constructing an urban rail system, and aims to guide reasonable construction of the urban rail network according to a judicious principle and guarantee functional applicability, operation rationality and engineering feasibility of the network. In the present stage, a plurality of cities in China are planning or constructing large-scale urban rails, and a scientific and quantitative urban rail line network planning method is provided for planning workers, so that the workload of the planning workers is reduced, and the standard and scientificity of line network planning work are improved.

The main research content of urban rail network planning is overall network design, which refers to designing a network capable of achieving certain construction and operation targets according to the determined geographical positions of sites.

Network design requires that a mathematical model (e.g., an integer programming model) be established to solve an optimal network solution under given objectives (e.g., construction cost, construction length, maximum flow, etc.).

Brief introduction to research and practice of traditional urban rail network design

As shown in fig. 1, the urban rail network design in the theoretical research of traditional urban rail network planning includes three main directions, one is based on the network structure, the other is guided by the construction cost, and the third is to consider the operation possibility.

(1) Network design based on network structure

Under the given target (such as construction cost, construction length, maximum flow and the like), a general mathematical model (such as an integer programming model) is established to solve the optimal network scheme.

(2) Cost-oriented network design

And the planners propose a plurality of network schemes, calculate and evaluate the total cost of different schemes according to various cost indexes, and select the network design scheme with the lowest total cost.

(3) Network design taking into account operational possibilities

And designing the public transport network according to the influence of the existing traffic facilities, the current passenger flow corridor distribution form and the geographic form of the planned area on the engineering feasibility.

At present, the urban rail network planning practice in China adopts a qualitative and quantitative combined method, namely a series of urban rail network planning alternative schemes are compiled through the qualitative method, then a quantitative index evaluation system is adopted to select a preferred scheme from the alternative schemes, and the preferred scheme is analyzed and adjusted, and the specific flow can be summarized as shown in fig. 2.

Problems of traditional urban rail network design research and practice method

For the traditional urban rail line network planning theory research, the research object of urban rail network design is too ideal and simple, the scale of the research range is smaller, the calculation complexity is too high, and the reasonable form and the smoothness degree of the network are not considered during the network design; the reasonable topology and engineering operation feasibility of the network are not considered at the same time.

Similar to the existing problems of theoretical research, the existing urban railway line network planning practice method has the following problems:

(1) the initial planning scale is small, and the foresight is lacked, and the specific problems include:

1. the urban land utilization changes frequently, the urban updating speed is high, and the old network planning scheme has insufficient support for urban development;

2. the planning of the network preset scale lacks analysis in traffic quantification and does not consider urban expansion;

3. due to the lack of stable track network guidance, transfer conditions are not reserved basically, so that the subsequent stations and the first-stage project mainly adopt channel transfer and the transfer is inconvenient;

4. the network has single level, is lack of urban fast lines, and has no obvious difference between the skeleton line and the common line.

(2) Planning one section, constructing one section, operating one section, lacking integrity, the concrete problem includes:

1. the later adjustment planning is optimized and adjusted on the basis of the original network, and the defects of the original network are overcome with extremely high difficulty;

2. transfer conditions are not reserved, so that the construction of transfer and connection projects of subsequent stations and earlier projects is difficult;

3. the stable urban rail network is the basis and foundation for construction planning and compilation, and in the aspect of rail transit, the selection of second-stage engineering construction projects and the stability of a scheme are influenced due to the fact that the planning and compilation of the rail network is delayed;

4. the mode of connecting the new city line and the central city area line is single, the mode of connecting the city new city line or the peripheral line and the central city line or the current main line network is single, and most of the connection modes are single line connection. The biggest problem brought by the connection transfer mode is that as the transfer points are positioned at the edge of a city, and a large number of employment posts are lacked at the periphery of the transfer station, most passengers need to select to transfer to other lines to enter a central city, which brings larger passenger flow and operation pressure to the transfer lines and the transfer stations;

5. the capacity of transfer stations is insufficient, so that network bottleneck is caused, and as part of the transfer stations are used as transportation hubs, sectional planning can cause a plurality of lines to be continuously added to a single hub transfer station, so that the transfer capacity of the transfer station is insufficient, and the transfer station becomes the network bottleneck.

Disclosure of Invention

In order to solve the problems of the theoretical research and practice method of the traditional urban rail network design, the technical difficulties are as follows:

1. the scale of the network is increased, the design difficulty of a planning scheme is increased, and especially the early network planning is mainly based on subjective design;

2. along with the enlargement of the site scale, the more combinations of the net structure forms which need to be considered, the difficulty in supporting the evaluation system of the existing net planning scheme;

3. when large-scale network planning is carried out, transfer sites and transfer forms are difficult to determine;

4. the urban traffic track network planning scheme has a plurality of influence factors, so that the hub scheme is difficult to stabilize, and the related track scheme is also difficult to stabilize.

Aiming at the problems, the invention provides a large-scale urban rail network automatic generation method based on land utilization, which is used for quantitatively designing the urban rail network based on a site selection scheme of the land utilization so as to solve the problems of difficult scheme optimization and the like caused by high difficulty of a subjective design planning scheme, various site and network structure forms and more influence factors and improve the scientificity and the rationality of the urban rail network planning.

The technical scheme of the invention is as follows:

a large-scale urban rail network automatic generation method based on land utilization is disclosed, the rail network automatic generation method can automatically generate an integral rail network based on a site selection scheme; the site selection scheme comprises a site number, a name and a corresponding space geographic position coordinate; the detailed steps are as follows:

s1, selecting a clustering algorithm according to the site selection scheme, and establishing a mathematical model;

s1.1 site set in site selection scheme is

The expected generated orbit network is represented as a decision variable matrix X, and a certain corresponding element in the matrix is

The practical meaning is as follows:

s1.2, carrying out multiple constraints on the model, wherein the constraints comprise accessibility constraints among sites, degree constraints of the sites, line angle constraints and inter-site distance constraints, and the constraints are satisfied by a network correction method;

s1.3 for urban rail transit, the goal of rail network generation is to obtain a generation network of minimized length:

in the formula (I), the compound is shown in the specification, c _ij-stationsiAnd sitejThe construction cost is fixed per unit length;

d _ij-stationsiAnd sitejThe length of the line between the two lines;

s2, performing cluster analysis and obtaining a plurality of site clusters;

s2.1, according to the spatial geographical position coordinates of the sites, performing spatial hierarchical division on the sites in the site selection scheme, dividing all the sites into different site groups, and pre-constructing and generating an initial form of a network;

s2.2, the most suitable clustering algorithms corresponding to different types of rail transit networks are different, and the most suitable clustering algorithms are selected according to the following situations:

1) a track network consisting of circular, curved and strip lines: based on single connection criteria in the hierarchical cluster;

2) radioactive and mixed orbital networks: the K-Means algorithm;

3) multi-center mass track network: any algorithm other than the spectral clustering algorithm may be used;

s2.3, after the used clustering algorithm is determined, evaluating the clustering effect by using an average contour coefficient, and selecting an optimal clustering algorithm hyper-parameter according to the evaluation result, wherein the contour coefficient is calculated by the following formula:

in the formula (I), the compound is shown in the specification,a _i-sites within the same clusteriAverage distance to sites within other clusters;

b _i-stationsiAnd siteiCluster of the nearest clusterAverage distance of all stations within;

s3, solving the minimum spanning tree for each site cluster, and combining the minimum spanning trees until the sites can reach each other;

solving of the minimum spanning tree is based on a station group obtained by clustering analysis, and the method specifically comprises the following steps:

s3.1 clustering analysis: clustering all stations forming the rail transit network, and clustering and partitioning by adopting a proper clustering algorithm according to the relative positions of the stations;

s3.2 solving the minimum spanning tree: solving the minimum spanning tree of each cluster by using a Kruskal algorithm, and decomposing a total problem of constructing the minimum spanning tree for all the sites into sub-problems of constructing the minimum spanning tree for each smaller cluster;

s3.3 sub-minimum spanning tree merging: merging the minimum spanning trees obtained by solving the subproblems into spanning trees of all the sites, wherein the total length of edges of the spanning trees is close to the minimum spanning trees directly constructed for all the sites, and the merging principle is that all the sites can be reached with each other, and the total length of a network is increased to be minimized;

s4, network correction is carried out on the network scheme generated after the combination;

s5, calculating the total length of the corrected generated network scheme, and if the total length is less than the minimum total length, updating the optimal generated network scheme and the minimum total length;

and S6, if the iteration times do not reach the upper limit, returning to the step S3, iterating the steps S3-S5 for multiple times, and otherwise, ending the process to obtain the optimal generated network scheme and the minimum total length.

Preferably, step S4 performs network modification on the network solution generated after the merging, and the steps are as follows:

and (3) repairing a triangular branch: three sites can be mutually reachable only by connecting two shorter sides, and sites which do not meet the requirements are corrected;

acute angle branch correction: correcting error branches with the number of stations being only 2 extending from acute angle parts at the intersection of the multiple lines, and fusing the error branches to adjacent lines;

and (3) line cross repairing: repairing and fusing a large number of aggregated and adjacent abnormal cross points at a position with high network density;

redundant branch merging: removing redundant connection between two parallel straight line sections, and adjusting;

starting and finishing site screening: if the station with the degree of 1 is not a starting and ending station, new connection with surrounding stations is required to be established under the condition of meeting the constraint so as to prolong the length of a potential line;

acute angle line repairing: the edge set of the network partial area does not meet the angle constraint, the angle is too small, and the edge set which does not meet the constraint needs to be repaired;

potential line lengthening: when the minimum spanning tree solving algorithm is applied to the checkerboard type network instead of the radial type network, the generated network cannot form the checkerboard type network, most sites are not directly connected with each other, long-distance line segments passing through more sites cannot be formed, potential lines are short, and some network parts need to be continued as far as possible.

Preferably, in step S1.2, the inter-site reachability constraint, the site degree constraint, the line angle constraint, and the inter-site distance constraint are as follows:

1) inter-site reachability constraint: all sites must be accessed by the network, namely any two sites can be reached; setting the reachable matrix corresponding to the network X as A, wherein A can be obtained by calculation through a Warshall algorithm, and the site is the siteiAndjwhen they are mutually reachable, the elements of Aa _ij=1, otherwisea _ij= 0; the constraint may be expressed as:

2) degree constraint of the site: the maximum number of edges in the network with a certain site as an end point; the constraint may be expressed as:

in the formula (I), the compound is shown in the specification,P _max-maximum degree of a station;

3) and (3) line angle constraint: the Euler path in the network is not an intersection part, and the angle cannot be too large; setting the distance matrix between the stations as D if the stationsiAnd sitejThere is an adjacency between them, the elements of whichd _ijRepresenting the adjacency distance between the stations; if siteiAnd sitejThere is no adjacent relation between them, d _ijrepresenting the linear distance between the stations; if it isi=jThen, thend _ij =0(ii) a For three consecutive stations on the Euler pathi，j，hThe following relationship should be satisfied:

in the formula, omega is the maximum steering angle of the Euler path non-intersection part in the network;

4) and (3) station spacing constraint: the connection length between any two stations cannot be too long; the constraint may be expressed as:

in the formula (I), the compound is shown in the specification,d _max-maximum inter-site distance between any two sites.

Taking a certain actual rail transit network as an example, compared with the prior art, the invention adopting the technical scheme has the following beneficial effects:

1. clustering analysis: and (3) clustering 228 sites by adopting a K-Means clustering algorithm, wherein the sites are divided into 14 different site groups, so that the expected generated network has preliminary hierarchical division, and the minimum spanning tree calculation cost is reduced.

2. Solving the child minimum spanning tree: and solving the minimum spanning tree for each station group to obtain all the sub-minimum spanning trees of the whole network, wherein the sum of the lengths of all the sub-minimum spanning trees is only 75.6 percent of the original network scheme.

3. Child minimum spanning tree merging: and combining the sub minimum spanning trees to enable the sites in different site groups to be mutually reachable to obtain an initial generated network, wherein the length of the initial generated network is only 82.1% of that of the original network scheme.

4. And (3) generating network correction: and correcting unreasonable branches of the initial generation network to ensure that the branches have engineering and operation feasibility, the optimal generation network length is only 92.0 percent of the original network scheme, the network form is similar to the original network scheme, and the branches have reasonable transfer station setting.

Compared with the existing built network, the automatic generation method of the wire network can reduce the total mileage of the wire network by about 8.04 percent, can build a large amount of track construction cost if being implemented in actual construction, and can obtain the positions of transfer stations and junction stations in advance and reserve engineering redundancy in advance.

Drawings

Fig. 1 is a schematic diagram of the main contents of a conventional urban rail network design.

Fig. 2 is a flow chart of a conventional urban rail network planning.

Fig. 3 is a flow chart of urban rail network generation.

Fig. 4 is a schematic diagram of a minimal spanning tree construction based on clustering.

FIG. 5 is a schematic diagram of triangular branch repair.

FIG. 6 is a schematic diagram of a sharp branch modification.

Fig. 7 is a schematic diagram of line crossing repair.

FIG. 8 is a diagram of redundant branch merging.

FIG. 9 is a schematic diagram of a start and end site screen.

Fig. 10 is a schematic diagram of acute angle line repair.

Fig. 11 is a schematic diagram of potential wiring extensions.

Fig. 12 is a schematic diagram of a city rail network generation flow.

Fig. 13 is a schematic illustration of a mass transit station scheme used in a particular embodiment.

FIG. 14 is a schematic diagram of the cluster effect evaluation of different hyper-parameters.

FIG. 15 is a schematic diagram of site clustering results.

FIG. 16 is a schematic diagram of cluster-based sub-minimum spanning tree solution results.

FIG. 17 is a diagram of a merged child minimum spanning tree.

FIG. 18 is a schematic diagram of an iterative solution convergence process.

Figure 19 is a schematic diagram of a net length minimum generation network.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and examples.

The invention relates to a large-scale urban rail network automatic generation method based on land utilization, the detailed flow of which is shown in figure 3, the rail network automatic generation method can automatically generate an integral urban rail network based on a site selection scheme; the site location scheme refers to site numbers, names and corresponding geographic position coordinates.

Urban rail network generation method overall flow

The general flow of the urban rail network generation method is shown in fig. 12, and mainly includes six steps, which are:

s2, performing cluster analysis and obtaining a plurality of site clusters;

The detailed steps are as follows:

s1, selecting a clustering algorithm according to the site selection scheme, and establishing a mathematical model, wherein the steps are as follows:

set the site set in the site selection scheme as

The practical meaning is as follows:

the model requires a plurality of constraints (e.g., inter-site reachability constraints, site degree constraints, line angle constraints, inter-site distance constraints, etc.) to be satisfied by the below-described generation network modification method in S4.

3) and (3) line angle constraint: euler path non-intersection in a networkA point part, the angle cannot be too large; setting the distance matrix between the stations as D if the stationsiAnd sitejThere is an adjacency between them, the elements of whichd _ijRepresenting the adjacency distance between the stations; if siteiAnd sitejThere is no adjacent relation between them, d _ijrepresenting the linear distance between the stations; if it isi=jThen, thend _ij =0(ii) a For three consecutive stations on the Euler pathi，j，hThe following relationship should be satisfied:

For urban rail transit, the fixed cost has a greater proportion than the variable cost, while the variable cost has a lesser proportion. Once a certain line is built, the influence of the traffic volume of the one-way section in unit time on the total cost in a short period is small, and the main factor to be considered is the total length of the rail transit network, so the goal of urban rail network generation is to obtain a generation network with the minimum length:

d _ij-stationsiAnd sitejThe length of the line between the two lines;

s2, performing cluster analysis and obtaining a plurality of site clusters, wherein the steps are as follows:

the cluster analysis is an unsupervised learning method for grouping sample points, and in the method, the cluster analysis performs spatial hierarchical division on sites in a site selection scheme according to the spatial geographic positions of the sites, and divides all the sites into different site groups. The cluster analysis has the effect of reducing the solving scale of the minimum spanning tree and constructing the initial form of the spanning network in advance.

The most suitable clustering algorithms corresponding to different types of rail transit networks are different, and are usually selected according to the following situations:

1. a rail transit network consisting of circular, curved and strip lines: based on single connection criteria in the hierarchical cluster;

2. radioactive and hybrid rail transit networks: the K-Means algorithm;

3. multi-center mass rail transit network: any algorithm other than the spectral clustering algorithm may be used.

After the used clustering algorithm is determined, an average contour coefficient is needed to evaluate the clustering effect, an optimal clustering algorithm hyper-parameter is selected according to the evaluation result, and the contour coefficient is calculated by the following formula:

b _i-stationsiAnd siteiAverage distance between all the stations in the cluster which is adjacent and closest to the cluster;

s3, solving the minimum spanning tree for each site cluster, merging each minimum spanning tree until the sites can reach each other, and the steps are as follows:

the minimum spanning tree solving method is a method for finding the minimum spanning tree of the undirected and edge-weighted graph, in the network solved by the method, all the sites can reach each other, and the total length of the network is minimized. Solving of the minimum spanning tree is based on a station group obtained by clustering analysis, and the method is shown in the attached figure 4 and comprises the following specific steps:

1. decomposition (cluster analysis): clustering all stations forming the rail transit network, and clustering and partitioning by adopting a proper clustering algorithm according to the relative positions of the stations;

2. resolution (minimum spanning tree solution): solving the minimum spanning tree of each cluster by using a Kruskal algorithm, and decomposing a total problem of constructing the minimum spanning tree for all the sites into sub-problems of constructing the minimum spanning tree for each smaller cluster;

3. merging (child minimum spanning tree merging): merging the minimum spanning trees obtained by solving the subproblems into spanning trees of all the sites, wherein the total length of edges of the spanning trees is close to the minimum spanning trees directly constructed for all the sites, and the merging principle is that all the sites can be reached with each other, and the total length of a network is increased to be minimized;

s4 performs network modification on the combined network solution, including the following steps:

the network generated in the above steps may have network structures or branches that do not meet the engineering feasibility requirements, and need to be corrected to eliminate unreasonable branches. The correction method and corresponding application are as follows:

1. and (3) repairing a triangular branch: three sites can be mutually reachable only by connecting two shorter sides, and sites which do not meet the requirements are corrected. As shown in fig. 5, when three sites are connected by three edges or the sum of the lengths of two edges connected is not reduced to the minimum value, the branch needs to be repaired according to the following process:

(1) searching all triangle branches;

(2) in the triangular branch, if three stations are connected by one side every two, the side with the largest length is removed. If the three stations are connected by only two sides and keep mutually reachable, and the sum of the two sides is not the sum of the lengths of the two shorter sides of the triangle formed by the three stations, the two sides of the current situation are changed into the two shorter sides under the condition of meeting the constraint.

2. Acute angle branch correction: correcting the error branches with the number of stations being only 2 extending from the acute angle part at the intersection of the multiple lines, and fusing the error branches to the adjacent lines, as shown in fig. 6, specifically correcting the error branches as follows:

(1) searching all acute angle branches;

(2) disconnecting the edge connecting the intersection point and the starting and ending point of the line in the acute angle branch, so that the starting and ending point of the line is isolated from the generated network;

(3) under the condition of satisfying the constraint, the isolated point is connected with the closest point except the original connection intersection point, the length of the line is prolonged as much as possible, and the removal of redundant edges is attempted according to the triangle rule.

3. And (3) line cross repairing: the generated network has a large density, and a phenomenon that a large number of line intersections are gathered and closely adjacent to each other occurs. These abnormal intersections increase the difficulty of routing, reduce the possible length of the lines, and increase the non-linear coefficients of the lines, and in order to avoid such adverse effects, repair and fusion of these abnormal intersections is required. As shown in fig. 7, the specific correction steps are as follows:

(1) finding all eligible adjacent potential transfer point combinations (shown in fig. 7 as black dots);

(2) calculating the distances between the transfer point combinations and other surrounding stations, sequencing the transfer point combinations from small to large, and giving higher priority to the point pairs with smaller distances;

(3) disconnecting the connection of the current transfer point combination, trying to connect other sites, and replacing the connection of the original transfer point combination with the new connection if the number of cross points can be reduced by the newly connected edges and the constraint condition is met;

(4) repeating steps 1-3 until all outlier intersections are eliminated.

4. Redundant branch merging: removing redundant connection between two parallel straight line segments, and adjusting, as shown in fig. 8, the specific correction steps are as follows:

(1) searching all redundant branches existing as shown in fig. 8, namely, a station exists between two parallel potential lines and is connected with the two lines;

(2) calculating the sum of the distances between the station and the nearest station of the two parallel potential lines, and sequencing the stations from small to large, and giving higher priority to the redundant branch with the larger distance sum;

(3) for a redundant branch, the station is merged into a line on the shorter distance side, and the connection connecting the two lines is deleted.

(4) And repeating the steps 1-2 until the redundant branch is eliminated or the upper limit of the correction times is reached.

5. Starting and finishing site screening: if the station with the degree of 1 is not the starting and ending station, a new connection needs to be established with the surrounding stations under the condition that the constraint is met so as to prolong the length of the potential line, as shown in fig. 9.

6. Acute angle line repairing: the edge set of the network partial area does not satisfy the angle constraint, the angle is too small, and the edge set which does not satisfy the constraint needs to be repaired, as shown in fig. 10, the specific correction steps are as follows:

(1) searching all acute angle parts which do not meet the constraint of the line angle;

(2) traversing all the sites except the sites forming the acute angle edge set by taking the sites forming the acute angle vertex as a center and sequencing the sites from small to large according to the distance, trying to replace the original connection with the traversed sites and the new connection positioned at the vertex sites, and correcting under the condition of meeting the constraint;

(3) repeating steps 1-2 until all sharp-angled connections are corrected.

7. Potential line lengthening: when the minimum spanning tree solving algorithm is applied to the checkerboard network instead of the radial network, the generated network cannot form the checkerboard network, most sites are not directly connected with each other, long-distance line segments passing through more sites cannot be formed, and potential lines are short, so that some network parts need to be continued as much as possible, as shown in fig. 11;

The networks obtained by the solutions of S3-S5 are not fixed, and the total length of the networks generated each time is inconsistent due to the randomness of the algorithm used, so that the above steps need to be iterated for many times to obtain the network with the minimum total length.

The invention will now be described in further detail with reference to the following examples:

example (b):

referring to fig. 13, considering that the number of the stations corresponding to the rail transit network in a certain area is 228, the total current mileage is about 508.28 km. The expected shape of the network is a hybrid radioactive rail transit network without obvious loop lines, the network is formed into a net in the central area, and the peripheral area is arranged in a linear mode.

And because the expected shape of the wire net is a mixed type radioactive rail transit network, the 228 stations are clustered by adopting a K-Means clustering algorithm so as to reduce the minimum spanning tree calculation amount. The contour coefficient is used to evaluate the clustering effect of the K-Means algorithm when different hyper-parameters (expected clustering number) are selected, the clustering number interval is set to be [10, 30], and the evaluation result is shown in FIG. 14.

Fig. 14 shows that the clustering effect is best when the number of expected clusters is 14, and the contour coefficient is 0.449. The expected clustering number is set to be 14, 228 sites are clustered by using a K-Means clustering algorithm, and the clustering result is shown in FIG. 15. As can be seen from fig. 15, the clusters in the central area are in the shape of lumps, and the clusters in the peripheral area are in the shape of lines, which conform to the main characteristics of the hybrid radioactive rail transit network.

Solving the minimum spanning tree for each cluster in FIG. 15 results in all the child minimum spanning trees for the entire net, as shown in FIG. 16. In fig. 16, sites of different clusters, i.e., different sub-minimum spanning trees, are not reachable from each other, and the sum of the lengths of all the sub-minimum spanning trees is 384.488 km. The sub-minimum spanning trees are merged to make the sites of different sub-minimum spanning trees mutually reachable, and as shown in fig. 17, the total length of the merged sub-minimum spanning trees is increased by 32.950km, and the total length of the net is increased by 417.439 km.

If the minimum spanning tree is directly solved for all the sites without first performing cluster analysis, the total length of the net is 419.738km, which is very close to the total length of the net obtained by solving the minimum spanning tree based on the cluster analysis, which shows that the method not only can effectively reduce the calculation complexity, but also the result is very close to the actual minimum value.

Iterative solution is performed according to the flow of fig. 12, and in the iterative solution process, the total length of the target value generation network is continuously reduced, and the target value generation network rapidly converges to an optimal value, as shown in fig. 18. As shown in fig. 19, the total length of the lines of the generated network obtained by iterative solution is 467.892km, which is a saving of 8.04% relative to the total length of the current situation, and the shape of the generated network is approximately the same.

Compared with the prior art, the invention adopting the technical scheme has the following technical advantages:

It will be apparent to those skilled in the art that various modifications and improvements can be made to the embodiments of the present invention without departing from the inventive concept of the present application, which falls within the scope of the present application.

Claims

1. A large-scale urban rail network automatic generation method based on land utilization is disclosed, the rail network automatic generation method can automatically generate an integral rail network based on a site selection scheme; the site selection scheme comprises a site number, a name and a corresponding space geographic position coordinate; the method is characterized by comprising the following detailed steps:

s1.1 site set in site selection scheme is

The practical meaning is as follows:

d _ij-stationsiAnd sitejThe length of the line between the two lines;

s2, performing cluster analysis and obtaining a plurality of site clusters;

2) radioactive and mixed orbital networks: the K-Means algorithm;

2. The land-utilization-based large-scale urban rail network automatic generation method according to claim 1, wherein step S4 is to modify the network generated after merging, and the steps are as follows:

3. A land-utilization-based large-scale urban rail network automatic generation method according to any one of claims 1-2, characterized in that in step S1.2, the inter-site accessibility constraint, site degree constraint, line angle constraint and inter-site distance constraint are as follows: