CN115130263A

CN115130263A - Multi-traffic-facility equal-time-circle calculation method oriented to territorial space planning

Info

Publication number: CN115130263A
Application number: CN202210828575.7A
Authority: CN
Inventors: 马小毅; 汪振东; 刘明敏; 刘新杰; 江雪峰; 何鸿杰; 金安; 陈先龙; 宋程
Original assignee: Guangzhou Transportation Planning And Research Institute Co ltd
Current assignee: Guangzhou Transportation Planning And Research Institute Co ltd
Priority date: 2022-07-13
Filing date: 2022-07-13
Publication date: 2022-09-30
Anticipated expiration: 2042-07-13
Also published as: CN115130263B

Abstract

The invention discloses a method for calculating an equal time circle of a multi-traffic facility for territorial space planning, which comprises the following specific steps of: s1 iterating the node labels; s2 convex set or concave set equal time ring structure; s3 isochronous cycle expansion adjustment; s4, constructing and intersecting a Voronoi diagram; s5 conforms to a traffic network. The method for calculating the isochronal rings of the multiple traffic facilities based on the traffic network can be directly applied to a scene with multiple facilities, when network nodes in a facility coverage range are determined, the accuracy of the method is the same as that of a shortest-path algorithm, meanwhile, the algorithm complexity and the calculation time are greatly reduced, the isochronal ring structures such as convex sets and concave sets are carried out, the isochronal ring structure effect when a sparse road network and boundaries exist is improved, the isochronal rings are secondarily adjusted, the requirements of off-road travel behaviors of travelers and the attachment of the isochronal rings to the traffic network are considered, Voronoi graph structures are carried out and intersect with the maximized isochronal rings, and the overlapping of the isochronal rings among the facilities is eliminated.

Description

Multi-traffic-facility equal-time-circle calculation method oriented to territorial space planning

Technical Field

The invention belongs to the technical field of public transport facility planning, and particularly relates to a multi-transport facility equal-time-circle computing method for territorial space planning.

Background

1. Overview of public transportation facility planning

The public transport facility planning is a premise for efficiently and reliably constructing an urban public transport system, and aims to guide the reasonable setting of urban public transport facilities according to a judicious principle and ensure the functional applicability, the operation efficiency and the economic benefit of a station. One of the most important steps in the planning of a facility is to measure the service coverage of the facility. At present, a plurality of domestic cities carry out large-scale public transport planning, construction or improvement and perfection, and provide a rapid, scientific and quantitative method for measuring and calculating the service coverage of public transport facilities for planning workers, which is helpful for reducing the workload of the planning workers and improving the standard and scientificity of the facility planning work.

2. Site service scope computing overview

The calculation of the service range of the station is the work which must be carried out when planning public transport facilities, bus stations and rail transit stations. The service range of the station is generally represented by an isochronal circle, similar to a contour line used in mapping, where the isochronal circle represents a range where a traveler can reach a peripheral area from a transportation facility or represents a set of departure points of the peripheral area from the transportation facility within a certain travel cost range (represented by travel impedance such as available time and distance). The waiting circle is mainly used for determining the expected use frequency of the transportation facility and the convenience degree of using the transportation facility by surrounding travelers, and the waiting circle is highly positively correlated with the expected passenger flow and the economic benefit of the facility.

3. Brief introduction to the traditional equal time circle calculation theory research and practice method

At present, there is no systematic isochronous cycle calculation theory and practice method based on traffic network at home and abroad, as shown in fig. 1, the current general flow of isochronous cycle analysis and calculation at home and abroad is as follows:

(1) simple geometry buffer determination isochronous cycles

The method directly uses a geometric buffer zone (such as a circle with a certain radius) with a certain width, and determines the equal time circle of the facility by taking the facility position as the center.

(2) Determination of equal time circle by optimal short circuit algorithm

The minimum travel cost of the facility and the network nodes can be accurately determined by calculating the shortest distance between the facility position and the peripheral traffic network nodes, so that the equal-time circle is further determined according to the travel cost range limitation of the given equal-time circle. .

(3) Equal time circle for mature Geographic Information System (GIS) software measurement and calculation

The partially mature Geographic Information System (GIS) software (such as ArcGIS, QGIS and the like) provides the function of isochronous cycle calculation, and only the traffic network, the facility position and the trip cost threshold value need to be input, so that the software can automatically output isochronous cycles.

(4) Big data platform measures and calculates when circle

Map service providers such as God and Baidu estimate average travel cost among different nodes in a network by acquiring travel time of a large number of travelers at different positions in a traffic network, and determine a time circle such as a facility time circle only by searching and enumerating travel cost of the facility and the nodes of the peripheral network from existing data when calculating the time circle such as the facility.

(5) Traffic network rasterization simplification equal time circle calculation

By simplifying the complex traffic network into grids and replacing network nodes with more mass by grid centroids with smaller quantity, the calculation of the equal-time circle is simplified and quickly calculated.

4. Problems existing in the traditional equal time circle calculation practice method

The existing practical method, except that the shortest path algorithm determines the equal time circle, simplifies the equal time circle calculation process through certain simplification, pre-calculation and statistical methods, so that the equal time circle has low precision or abnormal shape, and the shortest path algorithm has long calculation time and is not practical. The specific problems of the above practical method are as follows:

(1) simple geometry buffer determination isochronous cycles

The method has obvious defects that travelers need to reach facilities or stations through a traffic network, and a buffer area cannot reflect the coverage area of the facilities under the actual traffic network, so that a geometric buffer area is far away from a real buffer area.

(2) Determination of equal time circle by optimal short circuit algorithm

The shortest path algorithm is high in calculation cost, a node set of a traffic network is set to be V, an edge set is set to be E, the fastest shortest path algorithm commonly used at present is a Dijkstra algorithm using a Fibonacci heap, time complexity is O (E + VlogV), wherein O represents an upper time complexity boundary, and obviously, when the traffic network is large in scale and the number of isochronous cycles to be determined is large, calculation time is long, and feasibility of practice is not achieved in an engineering sense. Meanwhile, the shortest path distance between the site facility and part of nodes is calculated, so that the calculation is repeated. In addition, a shortest-path algorithm based on a heuristic algorithm exists, but the calculation time is not obviously reduced compared with the Dijkstra algorithm, pre-calculation is generally needed, the obtained shortest-path distance is only an approximate estimation value, and high accuracy cannot be guaranteed.

When the Geographic Information System (GIS) software performs the equal-time-circle calculation, a large amount of time is consumed for network preprocessing and pre-calculation, and when the traffic network form is complex or sparse, the equal-time-circle form determined by the software is abnormal.

(4) Big data platform measures and calculates when circle

The cost for acquiring information from the map service provider platform by individuals and small-sized organizations is too high, and the travel time between network nodes cannot be updated or the timeliness is lost after a large amount of travel time data of travelers are lost. Meanwhile, the isochronous ring estimated by using the traveler travel data is based on the average travel cost rather than the shortest travel cost, and the size of the isochronous ring is smaller than that of a real isochronous ring.

(5) Traffic network rasterization simplified equal time circle calculation

The calculation of the isochronous ring by using the grid instead of the evolution of the actual traffic network is a simplified method, the accuracy of the isochronous ring obtained by calculation depends on the accuracy of the grid, and the grid simplifies the actual form of the traffic network, so that the form of the isochronous ring is not matched with the form of the actual traffic network.

The above methods are all defects existing in common isochronous ring calculation methods, and in addition, the method does not solve the problems of isochronous ring shape determination and secondary adjustment requirements after the calculation of the outline nodes of the composition isochronous ring is completed.

(1) Isochronous ring shape determination

The closed graph of the hour circle is divided into two forms: a convex set (covex hull) equal time circle and a concave set (concave hull) equal time circle, wherein the form of the convex set is represented in Euclidean space, and given any two network nodes, a line segment connecting the two network nodes is completely contained by the equal time circle. The concave set form represents an equal time circle that does not satisfy the convex set condition in the same space, i.e., a closed contour of minimum area encompasses all the facility coverage network node sets.

Because the convex set and concave set graphs are determined more complexly and need extra calculation amount, the common practice method does not discuss the shape of the equal time circle generally, but directly concatenates the points which are equal to or near the maximum coverage range of the equal time circle to determine the basic outline, when the road network is in a sparse area and under the scenes of river boundaries and the like, the distance between the nodes which are taken as the outline of the equal time circle and the facilities is possibly smaller than the maximum coverage range, so that the nodes which are taken as the outline nodes of the equal time circle cannot be judged to be the set of the equal time circle, and the problem can be completely solved by taking the convex set or concave set graphs on all the nodes in the coverage range of the facilities.

(2) Equal time circle secondary adjustment

The isochronous loop secondary adjustment is mainly divided into isochronous loop expansion adjustment and isochronous loop attachment to road network adjustment, and neither of these two types of secondary adjustment is discussed in the above common practice methods.

The purpose of the isochronous cycle scaling up adjustment is to take into account the off-road behavior of the traveler as much as possible. The distance between a certain traffic network node forming the contour of the equal time circle and the transportation facility may be smaller than the travel cost range of the equal time circle, the node serving as a terminal of the traffic network cannot be extended continuously on the traffic network, but a traveler can move continuously away from the traffic network, so the equal time circle may need to be enlarged and adjusted, the upper limit of the travel cost of the equal time circle is fully utilized, and the actual service coverage range of the facility is reflected.

The aim of adjusting the equal-time circle to the road network is to take the influence of the traffic network form on the equal-time circle form into consideration as much as possible and take the side of the traffic network as an equal-time circle closed contour.

(3) Isochronous cycle adjustment in multi-facility scenarios

In a multi-facility scenario, the isochrones between different facilities may overlap, resulting in repeated calculation of service coverage for all facilities, whereas the prior practical method only considers a single facility scenario.

To solve the above problems of the conventional isochronous ring calculation method, the technical difficulties are as follows:

1. compared with other simplified algorithms, the shortest-circuit algorithm has more accurate results, is more time-consuming, and needs to replace the shortest-circuit algorithm with an accurate algorithm with shorter time consumption;

2. the existing practical method determines a basic outline by searching points which are at a distance equal to or close to the maximum coverage range of the isochronous ring from the facility position and connecting the points in series clockwise or anticlockwise, but the series connection method can only keep good effect in a complete and dense area of a traffic network, and the shape of the isochronous ring needs to be directly determined through nodes in the maximum coverage range of the facility, so that the isochronous ring outline determination method is ensured to be effective in any scene;

3. the prior practical method does not consider the scene that a traveler breaks away from a traffic network to go off-road;

4. the existing practical method lacks a method for attaching the equal-time circle to a traffic network, which may cause that the equal-time circle comprises nodes with the distance from the facility exceeding the maximum service coverage;

5. under a multi-facility scene, the isochronous circles of different facilities may overlap, and the overlapping part needs to be reasonably divided.

Disclosure of Invention

Aiming at the problems, the invention provides a method for computing and analyzing the equal time rings of the multi-traffic facilities for the territorial space planning, which is characterized in that all traffic network nodes in the coverage range of the specified facilities are determined by using an iterative node marking method based on the existing traffic network and facility positions, and the equal time rings of convex sets or concave sets are constructed according to the required equal time ring forms and coverage nodes. After the equal time circle is constructed, the cross-country trip behavior of a traveler is considered, the equal time circle is expanded and adjusted, and the maximum equal time circle is obtained. Non-overlapping isochronal circles for each facility are then obtained by constructing a Voronoi diagram and intersecting the maximized isochronal circle, eliminating the inter-facility isochronal circle overlap. And finally, fitting the closed contour of the non-overlapped equal time ring to the nearest traffic network to obtain the network fitting equal time ring.

The technical scheme of the invention is as follows:

a multi-traffic facility equal time circle calculation method for territorial space planning comprises the following specific steps:

s1, determining network nodes in the facility coverage range, and carrying out iterative node marking;

specifying a transportation facility, the facility comprising: public transportation facilities, bus stops, rail transit stops;

continuously diffusing marks and updating the distance between the network nodes and the facilities outwards by taking the positions of the facilities as starting points until all the network nodes in the service coverage of the specified facilities are marked;

and S2 convex set or concave set equal time ring structure: the method comprises the following steps of (1) dividing the shape of an isochronous ring into a convex set and a concave set, wherein the convex set isochronous ring is used in a central area of a city, and the concave set isochronous ring is used in a suburban area; according to the marked network nodes, firstly adjusting the positions of the nodes temporarily positioned outside the coverage range of the facility service, then constructing an isochronous cycle closed graph of the convex set by using a Monotone chain algorithm according to a convex set form or a concave set form required by the isochronous cycle, and constructing the isochronous cycle closed graph by using a K neighbor improved algorithm to obtain the isochronous cycle of the convex set or the concave set;

s3 isochronous cycle expansion adjustment: constructing a buffer area for the contour node according to the obtained convex set or concave set isochronous ring, then constructing the convex set or concave set isochronous ring for the second time, and finally obtaining the maximum isochronous ring O of the facility _f ′；

S4Voronoi diagram construction and intersection: constructing a Voronoi diagram according to a plurality of facility positions, intersecting the Voronoi diagram of each facility with the maximized equal time circles obtained in the previous step, and obtaining non-overlapping equal time circles O by taking the intersection part _f ″；

S5 attaching to the traffic network: constructing a Markov model by taking an edge set in a traffic network as a boundary, and solving by using a Viterbi algorithm to obtain a network fit equal time circle O _f ″′；

Attaching the closed contour of the equal time circle to an adjacent traffic network, and forming a new equal time circle contour by using an edge set on the network; the structure of road network lamination equal time circle can be mainly divided into the following 3 main processes: matching traffic network range limitation, establishing a Markov model and solving by a Viterbi algorithm, which comprises the following steps:

s5.1 matching traffic network Range restrictions

Setting a network traffic network participating in the equal time circle calculation as G (V, E), setting a network node set as V, and setting a network edge set as E, wherein the specific steps are as follows:

1) obtaining non-overlapping isochronous circles for Voronoi graph construction and intersection based on buffer width Δ _R The drawing buffer area is expanded to obtain O _f "expanded region O _f,b ″；

2) Repetition ofStep 1), until obtaining O corresponding to each facility f _f,b ″；

Buffer O of all facilities f _f,b "is a union set of

Defining nodes and edges of a matching network as

And

s5.2 establishing Markov model and solving by Viterbi algorithm

Non-overlapping isochronous ring O corresponding to facility f _f First, a Markov model is defined:

1) defining emission probabilities, for non-overlapping isochronal rings O of facility f _f Let k _i Represents a composition O _f "i-th node of closed contour, number of nodes N _f A, is provided with M _r For an arbitrary node k _i Maximum search radius of, M _k For an arbitrary node k _i The maximum number of candidate matching nodes of (c), at k _i Radius of M _r Is selected from the range of (1) and k _i At most M with shortest straight line distance _k Taking individual traffic network nodes as candidate matching node set V _i ，V _i Any one candidate matching node is set as v _i (v _i ∈V _i ) And k is _i Has a linear distance d (k) _i ,v _i )，v _i The emission probability is:

where σ represents the maximum allowable error between the contour of the non-overlapping equal time circle and the fitted road network when matching is performed, and the physical meaning of the formula is expressed in terms of v _i And k is _i Is determined by the distance v _i As k is _i Probability of matching points, where ep (v) _i ) Must be provided withSatisfies ep (v) _i )≥ep _min ；

2) Define transition probabilities for k _i And k _i+1 Candidate matching node v between _i And v _i+1 Let their shortest path distance in the traffic network be sp (v) _i ,v _i+1 ) If v is _i As k is _i Matching point of v _i+1 As k is _i+1 The probability of matching points is:

3) taking any series of candidate matching nodes as O according to the emission probability and the transition probability defined above _f "score of matching points attached to the network:

matching point sequence with highest score

v _i Denotes the time k when s is the highest _i Corresponding candidate matching nodes are used as the closed contour of road network fitting equal time circle;

and the transmission probability, the transition probability and the score are defined as a Markov model, a matching point sequence corresponding to the highest score is solved by using a Viterbi algorithm, and finally road network fitting equal time circles of all facilities are obtained.

Preferably, the step S1 iterates the node marking as follows:

1) determining a network node set V participating in the calculation of the equal time circle;

2) selecting a facility F (F belongs to F) from all facilities F, calculating a network node in a specified facility service coverage range of the facility F, taking the facility F as a node in a current node set C, setting a prepared iteration node set T when only one node of the facility F exists in the current node set C;

3) for each available network node V ∈ V, there isMark theta _v Setting the flags of all network nodes to theta _v M, while marking the facility f with the mark θ _f Set to 0;

4) is provided with

Extracting a node C from C (C belongs to C), and recording the adjacent network node set of C as

Updating the mark value theta of all arbitrary nodes a (a belongs to A) in the set A _a The update method is theta _a ＝min(θ _c +d _ac ,θ _a )，d _ac Is the distance from a to c; let d _max For a specified facility coverage, θ is satisfied for set A _a ≤d _max If T does not have a, adding a to T;

5) repeating the step 4) until all nodes C in the C are traversed, firstly updating the V by the method of V \ C, and then updating the C by the method of C ═ T;

6) repeating the steps 4) -5) until

When the flag value satisfies theta _v The node v < M is a network node which can be covered by the facility f, and the set of the nodes is marked as K _f At this time K _f Middle part network node K (K belongs to K) _f ) May be a sign value of _k ＞d _max ；

7) Repeating steps 2) -6) until all network nodes covered by the facility within the coverage area of the specified facility f are found.

Preferably, the specific steps of the circle construction such as the convex set or the concave set in step S2 are as follows:

s2.1, adjusting the node position outside the coverage range of facility service;

covering the network node set K for each facility f obtained in step S1 _f Node K in (K ∈ K) _f ) When the flag value exists [ theta ] _k ＞d _max Then, the nodes are adjusted to ensure thatFall into d _max Within the range of (1); the specific steps are as follows:

1) selecting one facility F (F belongs to F) from all facilities F, wherein the covered network node set is K _f ；

2) Satisfies theta for the flag value _k ＞d _max Node K (K ∈ K) _f ) First, the retuning value Δ θ is calculated _k -d _max ；

3) Selecting a marker value smaller than theta from a set of adjacent network nodes of k _k Is marked as a set A ', and the edge e with the end points of the nodes a' (a '. epsilon.A') and k _a′k Adding a new network node at a distance delta from the node K as an adjusted overlay network node, and adding the new network node to the node K _f Simultaneously from K _f Deleting a node k;

4) repeating the steps 1) -3) until all network nodes covered by the facility are adjusted;

s2.2, constructing a convex set equal time circle closed graph;

s2.3 a closed graph structure of the isochronous ring.

Preferably, step S2.2 the circle-like closed figure of the convex set is constructed as follows:

calculating time circles such as a convex set by adopting a Monotone chain algorithm;

1) selecting a certain facility f to obtain K after the node position outside the coverage area is adjusted _f ；

2) Calculating K _f Angle value mu of all nodes k in _k And from small to large pairs K _f The middle node carries out reordering, and the geographic coordinate of the node k is set as (x) _k ,y _k )，μ _k The calculation method comprises the following steps:

3) set of nodes O _f Is provided with O _f ＝K _f Setting i to 1 and j to 0;

4) set l ═ i +1) mod | O _f |，u＝(i-1)mod|O _f L, set k _i Represents K _f In (1)The ith node, calculating a vector

And

a vector product of, if

Node k _i From O _f Deleting and setting j to 0, otherwise setting j to j + 1;

5) set i ═ i +1) mod | O _f |；

6) If j is less than | K _f I, repeating the steps 4) -5), otherwise, ending the step, and collecting the nodes O _f Namely the outline of the equal time circle of the convex set;

obtaining a node set O through the steps _f The formed closed graph is the convex set equal time circle of the facility f.

Preferably, step S2.3 notch-set isochronous bounding graphs are constructed as follows:

calculating a concave set equal time circle by adopting a K neighbor improvement algorithm, and recording an algorithm function as Concavehall (K) _f β), β being a parameter of a neighbor algorithm for determining the number of neighbor points considered in the analysis, the specific steps being:

1) let k _i Represents K _f P is K _f The serial number of the minimum node of the middle vertical coordinate is set as a node set O _f ＝{k _p H, will k _p From K _f Deleting, setting current node c ═ k _p And λ ═ 0, m ═ 2;

2) if m is 5, the node k is connected _p Is added to K _f ；

3) Finding out the nearest beta nodes of the node c, marking as a set A, and according to the angle mu of each node a (a belongs to A) _a Sorting from big to small, and setting the geographic coordinate of the node a as (x) _a ,y _a )，μ _a The calculation method is as follows:

4) setting i to 0 and q to 1;

5) if q is 1 and i < | a |, then go to step 6), otherwise go to step 13);

6) updating i by i-i +1 if the ith node a in A is _i The same as c, setting l to 1, otherwise, setting l to 0;

7) setting j to 2 and q to 0;

8) if q is 0 and j < (| O) _f L-l), then jump to step 9), otherwise jump to step 11);

9) let o _i Represents O _f The ith node in (1), if the vector

And

crossing, setting q to 1, otherwise, setting q to 0;

10) j is updated, the updating method is j +1, and the step 8) is skipped;

11) if q is 1, the algorithm ConcaveHull (K) is called _f ,β+1)；

12) Updating the current node c by the method that c is a _i Update λ by an update method of

Updating m, wherein the updating method is m-m +1, and adding the current node c to O _f From K, the current node c is connected _f Deleting, returning to step 5);

13) setting g to be 1, updating i, and updating the method to be i to be | K _f |；

14) If g is 1 and i is greater than 0, jumping to step 15), otherwise jumping to step 17);

15) judging node k _i Whether or not at O _f In a closed graph formed by the nodes in the graph, if yes, setting g to be 1, and otherwise, setting g to be 0;

16) updating i, wherein the updating method is i-1, and jumping to the step 14);

17) if g is equal to 0, the algorithm ConcaveHull (K) is called _f ,β+1)；

Obtaining a node set O through the steps _f The formed closed graph is a concave-set equal-time circle of the facility f.

Preferably, the steps of adjusting the isochronous rate expansion in step S3 are as follows:

method for adjusting isochronous cycle expansion and obtaining node set O by solving isochronous cycle closed graph structure _f Namely, the method is carried out on the basis of nodes forming a convex set, a concave set and the like closed graph:

1) let O _f Isochronal contour of convex or concave sets obtained for isochronal closed-figure construction of facility f, if O _f For convex time-rings, then set up

If O is _f For concave and integrated time-equaling ring, set K _f ′＝K _f ；

2) To O _f Each node O (O e O) in (c) _f ) With a marking value theta obtained by an iterative node marking algorithm _o Let the maximum enlargement value be Δ _M Calculating the expansion value Δ ═ min (Δ ═ min) _M ,θ _o -d _max ) Creating a buffer area for the node o according to the size of delta, wherein the buffer area is a plurality of equilateral polygons with o as the center according to preset precision, the point forming the buffer area is a node set B, and the point is added to K _f ′；

3) Repeating the step 2) until O _f Creating the buffer areas of all the nodes in the network;

4) according to O _f Using a convex set or concave set isochronal circle solution algorithm used in an isochronal circle closed graph structure, inputting K _f ' and calculating the corresponding equal time circle to obtain the maximum equal time circle O of the enlarged adjustment _f ′。

Preferably, the Voronoi diagram of step S4 is constructed and intersected, and the specific steps are as follows:

s4.1 construction based on Voronoi diagrams of facility locations

Let f _i For the ith set of all utility points FFacility, for arbitrary facility f _i Voronoi region of

Points inside and on the sides of the region

And facilities f _i Is a distance of

Not more than r and other facilities f _j I.e.:

the algorithm for solving the Voronoi diagrams of all the facility points is a Delaunay triangulation algorithm, and the specific steps are as follows:

1) connecting facility points in the F to construct a Delaunay triangular network DT (F), wherein in the Delaunay triangular network, any Delaunay triangle T (T belongs to DT (F)) corresponds to an external circle OC _T Without any facility points inside, i.e.

Set the Voronoi diagram as

R consists of a series of Voronoi edges;

2) calculating and determining the centers of all circumscribed circles, namely the outsentrics of all Delaunay triangles;

3) for any Delaunay triangle T, the three sides composing T are e _i (i is 1,2,3) if at edge e _i There is another Delaunay triangle T' adjacent to T, i.e. e _i T ═ n T ', the line connecting the outer centers of T' and T is added to R, if at the edge e _i If there is no other Delaunay triangle, then e _i The perpendicular bisector of (c) is added to R;

4) repeating the step 3) until all Delaunay triangles are traversed and all Voronoi edges are found, and further obtaining the Voronoi area corresponding to each facility f

There is no intersection between Voronoi regions of any two facilities;

s4.2 intersection operation

Setting the maximum isochronous cycle of the isochronous cycle closed pattern structure acquisition facility f as O _f Voronoi region R of facility f _f And O _f Intersecting to obtain non-overlapping equal time rings O _f ″＝R _f ∩O _f 。

Preferably, in step S5, the viterbi algorithm specifically includes the steps of:

1)V _i (j) represents V _i J (th) candidate matching node in (V) _i Has a transmission probability vector of X _i Size is V _i Number of candidate matching nodes | V in (1) _i When V is _i (j)＝v _i When it is clear there is X _i (j)＝ep(v _i )，V _i To V _i+1 Has a transition probability matrix of Y _i,i+1 Of size | V _i |×|V _i+1 When V is _i (j)＝v _i ，V _i+1 (m)＝v _i+1 When it is apparent that there is Y _i,i+1 (j,m)＝tp(v _i ,v _i+1 )；

2) Empty list T ₁ For storing intermediate variables of the Viterbi Algorithm, setting T ₁ (1)＝X ₁ (ii) a Output road network joint equal time ring O _f "' is set to a size N _f An empty list of;

3) let i equal 2, set T ₁ (i)＝T ₁ (i-1)·Y _i,i+1 ·X _i+1 Is provided with

O _f ″′(i-1)＝argmax(T ₁ (i-1)·Y _i,i+1 ·X _i+1 )；

4) If i is less than or equal to N _f Setting i to i +1, repeating the steps, and otherwise, turning to the next step；

5) Is provided with

O _f ″′(N _f ) The network nodes in the network are closed outlines of road network fitting equal time circles;

6) and (5) repeating the steps 1-5 until road network attaching equal time circles of all facilities are obtained.

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

(1) can be applied to multi-facility scenes and has high calculation speed

The multi-traffic facility equal-time-circle calculation analysis method based on the traffic network replaces the shortest-circuit algorithm used by a common practice method with an innovative iteration node marking method, even under extreme conditions (namely the coverage range of facility service is infinite, all nodes in the traffic network need to be marked), the time complexity of the iteration node marking method is O (V eta), wherein eta is the average number of adjacent nodes of network nodes, and the time complexity is O (E + VlogV) when the shortest-circuit algorithm calculates a pair of shortest paths and distances, so that the calculation cost of the iteration node marking method is far less than that of the shortest-circuit algorithm. Meanwhile, the isochronous cycle calculation among multiple facilities belongs to mutually independent tasks, and parallel calculation can be realized.

(2) Accurate shape of the equal time ring

The multi-traffic facility equal-time-circle calculation and analysis method based on the traffic network introduces a convex set and concave set closed graph determination algorithm, so that reasonable and accurate construction effects of the equal-time circles when a sparse road network and boundaries exist are ensured, and the existing practical method roughly and simply connects nodes near the service coverage of the facilities, so that the equal-time circles are unreasonable in shape.

(3) Providing a secondary adjustment method to meet different requirements

The multi-transportation facility equal-time circle calculation analysis method based on the transportation network uses a Voronoi diagram construction method and a method of intersecting with a maximized equal-time circle, eliminates the overlapping of the equal-time circles among facilities, and prevents the service coverage areas among different facilities from not overlapping. Meanwhile, the cross-country trip behavior of the travelers is considered, and the waiting time circle is properly enlarged, so that the waiting time circle is more similar to the actual situation. In addition, the functions of calculating the time circle with the network as the boundary are provided by constructing a hidden Markov model and solving by using a Viterbi algorithm and attaching the time circle to the edge of the traffic network.

Drawings

FIG. 1 is a schematic diagram of a conventional calculation method for an equal time circle.

FIG. 2 is a flow chart of a multi-facility equal time circle calculation method.

Fig. 3 is a flow chart of an iterative node labeling method.

FIG. 4 is a schematic diagram of a convex set isochronal circle and a concave set isochronal circle.

Fig. 5 is a flowchart of the isochronous ring structure of the convex set or the concave set and the isochronous ring expansion adjustment.

Fig. 6 is a schematic diagram of adjusting the position of the out-of-coverage node.

FIG. 7 is a schematic diagram of buffer creation for an isochronous ring profile node.

FIG. 8 is a schematic diagram of the convex set isochronous cycle expansion adjustment.

Fig. 9 is a schematic diagram of the adjustment for enlarging the ring when the groove is set.

FIG. 10 is a Voronoi diagram construction and intersection construction flow diagram.

Fig. 11 is a schematic diagram of the Delaunay triangulation algorithm.

Fig. 12 is a flowchart of the isochronous lane overlay traffic network.

FIG. 13 is a schematic diagram of matching traffic network range definitions.

FIG. 14 is a diagram illustrating the results of the iterative node labeling method.

FIG. 15 is a diagram of convex set maximization isochronal results.

FIG. 16 is a graph showing the result of the trough-maximizing isochronous circles.

Fig. 17 is a schematic view of Voronoi regions of each facility.

FIG. 18 is a diagram of convex set non-overlapping isochronous circles results.

FIG. 19 is a graph showing the results of the non-overlapping iso-clock circles for the notch set.

Fig. 20 is a schematic diagram showing the result of the circles when the convex set road network is attached.

FIG. 21 is a schematic diagram showing the result of the circle when the valley concentration road network is bonded.

Detailed Description

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

The invention relates to a method for calculating and analyzing a multi-traffic facility equal time circle facing to territorial space planning, which is used for constructing a facility equal time circle according to a specified facility service coverage area based on the existing traffic network and facility positions.

Multi-facility equal time circle calculation method

General idea

The invention relates to a method for calculating and analyzing an equal time circle of a plurality of traffic facilities facing to territorial space planning, which realizes the equal time circle structure of the plurality of traffic facilities through a model formed by five main steps, as shown in figure 2, the method specifically comprises the following steps:

1. and (3) iterative node marking: continuously diffusing the marks outwards and updating the distance between the network nodes and the facility positions by taking the facility positions as starting points until all the network nodes in the specified facility service coverage range are marked;

2. convex set or concave set isochronal ring structure: according to the marked network nodes, firstly adjusting the positions of the nodes temporarily outside the coverage range of the facility service, then constructing an equal time circle closed graph by using a corresponding algorithm according to the convex set form or the concave set form required by the equal time circle, and obtaining the convex set or the concave set equal time circle;

3. and (3) expanding and adjusting the equal time circle: if the cross-country trip characteristics of the travelers are considered, the equal time circle is expanded and adjusted to obtain the maximum equal time circle;

voronoi diagram construction and intersection: constructing a Voronoi diagram according to a plurality of facility positions, intersecting the Voronoi diagram of each facility with the maximized equal time circles obtained in the previous step, and taking an intersection part to obtain non-overlapping equal time circles;

5. laminating a traffic network: and if the equal time circle needs to take an edge set in the traffic network as a boundary, constructing a Hidden Markov Model (HMM), and solving by using a Viterbi (Viterbi) algorithm to obtain the network fit equal time circle.

The method aims to quickly construct multiple facilities and equal time circles in various forms meeting different requirements.

The invention relates to a method for calculating and analyzing a multi-traffic facility equal time circle facing to territorial space planning, which is described in detail below.

Iterative node marking

The flow chart of the iterative node labeling method is shown in fig. 3, and the specific steps are as follows:

1. determining a network node set V participating in the calculation of the equal time circle;

2. selecting a facility F (F belongs to F) from all facility points F to calculate network nodes in the designated facility service coverage range, wherein the facility F is used as one node in a current node set C, only one node of the facility F exists in the current node set C, and a preparation iteration node set T is set;

3. for each available network node V ∈ V, there is a label θ _v Setting the flags of all network nodes to theta _v Where M is a large number, while marking the facility f with a mark θ _f Set to 0;

4. is provided with

Updating the mark value theta of all arbitrary nodes a (a belongs to A) in the set A _a The update method is theta _a ＝min(θ _c +d _ac ,θ _a )，d _ac Is the distance from a to c. Let d _max For a specified facility coverage, θ is satisfied for set A _a ≤d _max If T does not have a, adding a to T;

5. repeating the step 4 until all nodes C in the C are traversed, firstly updating the V by the method of V \ C, and then updating the C by the method of C ═ T;

6. repeating the steps 4-5 until

7. Repeating steps 2-6 until all network nodes covered by the facility within the coverage area of the specified facility f are found to be dominant.

Convex or concave isochronous ring configuration and isochronous ring expansion adjustment

As shown in fig. 4, the isochronal rings are classified into convex (concave) or concave (convex) sets, the convex isochronal rings are usually used in urban central areas where the traffic network is dense and complete and the periphery has no geographic boundaries, and the concave isochronal rings are usually used in urban suburban areas where the traffic network is sparse and the periphery has more geographic boundaries, such as rivers and mountains.

The convex set form represents that in euclidean space, given any two network nodes, the line segment connecting them is completely encompassed by the isochronous circles. The concave set form represents an equal time circle that does not satisfy the convex set condition in the same space, i.e., a closed contour with a minimum area encompasses all the facility coverage network node sets.

Since the algorithm used for the isochronous ring expansion adjustment is related to the isochronous ring shape, the two main steps of the isochronous ring structure of convex set or concave set and the isochronous ring expansion adjustment will be described together.

As shown in fig. 5, the structure of the isochronous cycle of the convex set or the concave set is mainly divided into 2 processes, namely, the node position adjustment outside the coverage range and the structure of the isochronous cycle closed graph; and (4) performing expansion adjustment on the isochronous cycle, constructing a buffer area for the outline node of the isochronous cycle according to the obtained isochronous cycle of the convex set or the concave set, then performing isochronous cycle construction of the convex set or the concave set for the second time, and finally obtaining the maximum isochronous cycle of the facility.

(1) Convex or concave isochronous ring structure

1. Out-of-coverage node position adjustment

Covering network node set K for each facility f obtained by iterative node marking algorithm _f Node K in (K ∈ K) _f ) The flag value may be θ _k ＞d _max Therefore, it is necessary to adjust these nodes to ensure that they fall into d _max In the presence of a surfactant.

The specific adjustment method is shown in fig. 6, and the specific steps are as follows:

5) selecting one facility F (F belongs to F) from all the facility points F, wherein the covered network node set is K _f ；

6) Satisfies theta for the flag value _k ＞d _max Node K (K ∈ K) _f ) First, the retuning value Δ θ is calculated _k -d _max ；

7) Selecting a marker value smaller than theta from a set of adjacent network nodes of k _k Is marked as a set A ', and the edge e with the end points of the nodes a' (a '. epsilon.A') and k _a′k Adding a new network node at a distance delta from the node K as an adjusted overlay network node, and adding the new network node to the node K _f Simultaneously from K _f Deleting a node k;

8) and repeating the steps 1-3 until all network nodes covered by the facility are adjusted.

2. Convex set equal time ring closed figure structure

The algorithm for calculating the time circles such as the convex set is a Monotone chain algorithm, and the specific steps are as follows:

7) selecting a certain facility f to obtain K after the node position outside the coverage area is adjusted _f ；

8) Calculating K _f Angle value mu of all nodes k in _k And from small to large pairs K _f The middle node carries out reordering, and the geographic coordinate of the node k is set as (x) _k ,y _k )，μ _k The calculation method comprises the following steps:

9) set node set O _f Is provided with O _f ＝K _f Setting i to 1 and j to 0;

10) set l ═ i +1) mod | O _f |，u＝(i-1)mod|O _f L, set k _i Represents K _f In (1)The ith node, calculating a vector

And

a vector product of, if

Node k _i From O _f Deleting and setting j to 0, otherwise setting j to j + 1;

11) set i ═ i +1) mod | O _f |；

12) If j is less than | K _f If not, ending the node set O _f Namely the outline of the equal time circle of the convex set;

3. Concave-collecting isochronous ring closed figure structure

The algorithm used for calculating the notch set isochronous ring is a K neighbor improvement algorithm proposed by Moreira Adriano and Santos Maribel, and the algorithm function is recorded as Concavehall (K) _f β), β being a parameter of a neighbor algorithm for determining the number of neighbor points considered in the analysis for controlling the accuracy of the computation of the time circle, ConcaveHull (K), of the concave set _f Beta) the specific steps of the algorithm are:

18) let k _i Represents K _f P is K _f The serial number of the minimum node of the middle vertical coordinate is set as a node set O _f ＝{k _p H, will k _p From K _f Deleting, setting current node c ═ k _p And λ ═ 0, m ═ 2;

19) if m is 5, the node k is connected _p Is added to K _f ；

20) Finding out the nearest beta nodes of the node c, marking as a set A, and according to the angle mu of each node a (a belongs to A) _a Sorting from big to small, and setting the geographic coordinate of the node a as (x) _a ,y _a )，μ _a The calculation method is as follows:

21) setting i to 0 and q to 1;

22) if q is 1 and i is less than | A |, skipping to step 6, otherwise skipping to step 13;

23) updating i by i-i +1 if the ith node a in A is _i The same as c, setting l to 1, otherwise, setting l to 0;

24) setting j to 2 and q to 0;

25) if q is 0 and j < (| O) _f L), jumping to step 9, otherwise jumping to step 11;

26) let o _i Represents O _f The ith node in (1), if the vector

And

crossing, setting q to 1, otherwise, setting q to 0;

27) j is updated, the updating method is that j is j +1, and the step 8 is skipped;

28) if q is 1, the algorithm ConcaveHull (K) is called _f ,β+1)；

29) Updating the current node c by the method that c is a _i Update λ by an update method of

Updating m, wherein the updating method is m-m +1, and adding the current node c to O _f Connecting the current node c from K _f Deleting, returning to step 5;

30) setting g to be 1, updating i, and updating the method to be i to be | K _f |；

31) If g is 1 and i is greater than 0, jumping to step 15, otherwise, jumping to step 17;

32) judging node k _i Whether or not at O _f In a closed graph formed by the inner nodes, if yes, g is set to be 1, and otherwise, g is set to be 0;

33) updating i, wherein the updating method is that i is i-1, and jumping to step 14;

34) if g is equal to 0, the algorithm ConcaveHull (K) is called _f ,β+1)；

(2) Isochronous cycle expansion adjustment

Considering the off-road characteristic of the travelers, namely, after arriving at a certain network node, the travelers can continuously move to the place where the network node and the network edge do not exist, and the traffic basic network cannot possibly contain all roads for the travelers to travel in reality, so that the equal-time circle is expanded and adjusted according to the characteristic, and the facility coverage range which can better reflect the real travel characteristic of the travelers can be obtained.

Isochronous-loop expansion adjustment on node set O obtained by solving isochronous-loop closed graph structure _f (i.e., nodes that form a closed graph such as a convex set, a concave set, etc.). The specific adjustment method is shown in fig. 7, 8 and 9, and the specific steps are as follows:

5) let O _f Isochronal contour of convex or concave sets obtained for isochronal closed-figure construction of facility f, if O _f For convex time-rings, then set up

If O is _f For concave-concentration equal-time ring, set K _f ′＝K _f ；

6) To O _f Each node O (O e O) in (c) _f ) With a marking value theta obtained by an iterative node marking algorithm _o Let the maximum enlargement value be Δ _M Calculating the expansion value Δ ═ min (Δ) _M ,θ _o -d _max ) And creates a buffer for node o (a polygon with several sides centered on o according to a predetermined precision) according to the size of Δ, the points constituting the buffer being a set of nodes B to be added to K _f ′；

7) Repeating the step 2 until O _f Creating the buffer areas of all the nodes in the network;

8) according to O _f Using a convex set or concave set isochronal circle solution algorithm used in an isochronal circle closed graph structure, inputting K _f ' and calculating the corresponding equal time circle to obtain the maximum equal time circle O of the enlarged adjustment _f ′。

Voronoi diagram construction and intersection

When the two facilities are too close to each other, the corresponding isochronous circles may overlap, resulting in the service range of the facilities being considered repeatedly, which does not meet the characteristic that travelers prefer to select the nearest transportation facility for traveling. The method of adjusting this overlap is Voronoi diagram construction and intersection. The Voronoi diagram construction and intersection can be mainly explained in 2 main flows, that is, non-overlapping equal time circles are acquired based on the facility location Voronoi diagram construction and intersection operation, as shown in fig. 10.

1. Voronoi graph construction based on facility location

Let f _i For the facilities of the ith set of all facility points F, for any facility F _i Voronoi region of

Points inside and on the sides of the region

And facilities f _i Is a distance of

Not more than r and other facilities f _j I.e.:

there is no possibility that portions overlapping each other occur between the Voronoi regions.

An algorithm for solving Voronoi diagrams of all facility points is a Delaunay triangulation algorithm, as shown in fig. 11, and the specific steps are as follows:

5) connecting facility points in the F to construct a Delaunay triangular network DT (F), wherein in the Delaunay triangular network, any Delaunay triangle T (T belongs to DT (F)) corresponds to an external circle OC _T Without any facility points inside, i.e.

Set the Voronoi diagram as

It is clear that the final R should consist of a series of Voronoi edges;

6) calculating and determining the centers of all circumscribed circles, namely the outsentrics of all Delaunay triangles;

7) for any Delaunay triangle T, the three sides composing T are e _i (i-1, 2,3) if on side e _i There is another Delaunay triangle T' adjacent to T, i.e. e _i T ═ n T ', an outer connecting line of T' and T is added to R, if at edge e _i If there is no other Delaunay triangle, then e _i The perpendicular bisector of (c) is added to R;

8) repeating the step 3 until all Delaunay triangles are traversed and all Voronoi edges are found, and further obtaining the Voronoi area corresponding to each facility f

There is no intersection between Voronoi regions of any two facilities.

2. Intersection operation

Let O be the maximum isochronous cycle of the isochronous cycle closed pattern structure acquisition means f _f Using the characteristic that no intersection exists between Voronoi areas to connect the Voronoi areas R of the facility f _f And O _f Intersecting to obtain non-overlapping equal time rings O _f ″＝R _f ∩O _f 。

Conformable traffic network

After the non-overlapping equal time circle is obtained, the closed contour of the non-overlapping equal time circle is not an edge set on the traffic network, and in order to reflect the coverage area of facilities under the actual traffic network more truly, the closed contour of the equal time circle needs to be attached to the adjacent traffic network, and a new equal time circle contour is formed by using the edge set on the network. The construction of the road network fitting equal time circle can be mainly described by dividing into 3 main processes, namely matching the traffic network range limitation, establishing an HMM model and solving by a Viterbi algorithm, as shown in FIG. 12.

1. Matching traffic network range limits

If the network traffic network participating in the equal time circle calculation is G ═ V, E, the set of network nodes is V, the set of network edges is E, when the non-overlapping equal time circle is attached to the network, only the network edges around the contour of the equal time circle are matched, and the network edges and points in other ranges are useless, so that the range of the matching network needs to be limited, and the matching calculation amount is reduced, as shown in fig. 13, the black pattern is the non-overlapping equal time circle, the dark traffic network is the limiting matching network, and the light traffic network is the excluded traffic network, the specific steps are as follows:

3) obtaining non-overlapping isochronous circles for Voronoi graph construction and intersection based on buffer width Δ _R The drawing buffer area is expanded to obtain O _f "expanded region O _f,b ″；

4) Repeating the step 1 until obtaining O corresponding to each facility f _f,b ″；

Buffer O of all facilities f _f,b "is a union set of

Defining nodes and edges of a matching network as

And

2. establishing HMM model and Viterbi algorithm solution

Non-overlapping isochronous ring O corresponding to facility f _f The principle of fitting the closed contour to the adjacent road network is to collect the edges and all parts of the closed contour in the traffic networkMatching one by one, finding the edge set combination most similar to the closed contour shape, and realizing the process by establishing an HMM model and solving the model by using a Viterbi algorithm, firstly defining the HMM model:

4) defining the emission probability, for non-overlapping isochronous rings O of the facility f _f Let k _i Represents a composition O _f "i-th node of closed contour, number of nodes N _f Each is provided with M _r For an arbitrary node k _i Maximum search radius of, M _k For an arbitrary node k _i The maximum number of candidate matching nodes of (c), at k _i Radius of M _r Is selected from the range of (1) and k _i At most M with shortest straight line distance _k Taking individual traffic network nodes as candidate matching node set V _i ，V _i Any one candidate matching node is set as v _i (v _i ∈V _i ) And k is _i Has a linear distance d (k) _i ,v _i )，v _i The emission probability is:

where σ represents the maximum allowable error between the non-overlapping equal time circle contour and the fitted road network when matching is performed, and the physical meaning of the formula is expressed in terms of v _i And k _i Is determined by the distance v _i As k is _i Probability of matching points, where ep (v) _i ) Ep (v) must be satisfied _i )≥ep _min 。

5) Defining transition probabilities for k _i And k _i+1 Candidate matching node v therebetween _i And v _i+1 Let their shortest path distance in the traffic network be sp (v) _i ,v _i+1 ) If v is _i As k is _i Matching point of v _i+1 As k is _i+1 The probability of a matching point is:

6) transmission according to the above definitionProbability and transition probability, any series of candidate matching nodes as O _f "the score of the matching points fit to the network is:

sequence of matching points with the highest apparent score

(v _i Denotes the time k when s is the highest _i The corresponding candidate matching node) is taken as the closed contour of the road network fitting hour circle.

The emission probability, the transition probability and the score are defined as an HMM model, an algorithm used for solving the matching point sequence corresponding to the highest score is a Viterbi algorithm, and the algorithm specifically comprises the following steps:

7)V _i (j) denotes V _i J (th) candidate matching node, V _i Has a transmission probability vector of X _i Size is V _i Number of candidate matching nodes | V in (1) _i When V is _i (j)＝v _i When it is evident that there is X _i (j)＝ep(v _i )，V _i To V _i+1 Has a transition probability matrix of Y _i,i+1 Of size | V _i |×|V _i+1 When V is _i (j)＝v _i ，V _i+1 (m)＝v _i+1 When it is apparent that there is Y _i,i+1 (j,m)＝tp(v _i ,v _i+1 )；

8) Empty list T ₁ For storing intermediate variables of Viterbi algorithm, setting T ₁ (1)＝X ₁ . Output road network joint equal time ring O _f "' is set to a size N _f An empty list of;

9) let i equal 2, set T ₁ (i)＝T ₁ (i-1)·Y _i,i+1 ·X _i+1 Is provided with O _f ″′(i-1)＝argmax(T ₁ (i-1)·Y _i ,i+1·X _i+1 )；

10) If i is less than or equal to N _f If the current value is not equal to i +1, repeating the steps, and otherwise, turning to the next step;

11) is provided with

O _f ″′(N _f ) The network nodes in the road network are closed outlines of road network fitting equal time circles;

12) and (5) repeating the steps 1-5 until road network attaching equal time circles of all facilities are obtained.

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

example (b):

considering 243 rail transit network stations, 587282 nodes and 644023 edges of a road network in a certain area, taking the rail transit stations as facilities, taking the road network as a traffic network, designating the service coverage range of the facilities as 500 meters, calculating the time circle of each facility and the like.

The calculation result of the iterative node marking method is shown in fig. 14, the iterative node marking method calculates and marks the distance between a road network node around a certain facility and the facility position, the calculation and marking of the distance between the road network node around the facility and the facility position are completed in only about 15 minutes, the same result obtained by using the mature commercial geographic information system software ArcGIS needs about 1 hour, when the iterative node marking method is used for calculating the distance between the nodes around each site, the parallel calculation technology can be applied, and the calculation time can be further greatly reduced along with the increase of the calculation resources.

As shown in fig. 15 and 16, the calculation results of the iso-circle structure and the iso-circle expansion adjustment of the convex or concave set are obtained, and the post-iso-circle expansion adjustment (the outline of the hollow portion) is obviously expanded to an area where no road network edge exists, as compared with the pre-iso-circle expansion adjustment (the outline of the solid portion), so as to take the off-road travel behavior of the traveler into consideration.

The result of the Voronoi diagram structure is shown in fig. 17, no overlapping region occurs between the Voronoi diagrams of each facility, the result of intersecting the Voronoi diagrams with the maximized equal-time circles is shown in fig. 18 and 19, compared with the maximized equal-time circles, the intersected non-overlapping equal-time circles are reasonably divided into unreasonable overlapping portions, and no overlapping portion exists between the non-overlapping equal-time circles of each facility.

The equal-time-circle-fit road network results are shown in fig. 20 and 21, the non-overlapping equal-time circles of each facility are fit to the road network, and the contour of the equal-time circles of the road network fit is composed of road network edges.

the traffic network-based multi-traffic facility equal time circle calculation analysis method can be directly applied to determination of the service coverage area of the traffic facility, the determination of the equal time circle is completely based on the traffic network used by travelers, and the calculation result is high in precision and high in calculation speed and is used in various scenes and a plurality of traffic facilities.

It will be apparent to those skilled in the art that various changes and modifications can be made in the embodiments of the invention without departing from the inventive concept of the present application, and these embodiments are intended to be covered by the claims of the present application.

Claims

1. A method for calculating equal time circles of multiple traffic facilities facing territorial space planning is characterized by comprising the following specific steps:

and S2 convex set or concave set equal time ring structure: the method comprises the following steps of (1) dividing the shape of an isochronous ring into a convex set and a concave set, wherein the isochronous ring of the convex set is used in a central area of a city, and the isochronous ring of the concave set is used in a suburban area; according to the marked network nodes, firstly, adjusting the positions of the nodes temporarily positioned outside the coverage area of the facility service, then, according to the convex set form or the concave set form required by the isochronous ring, constructing the convex set isochronous ring closed graph by using a Monotone chain algorithm, and constructing the isochronous ring closed graph by using a K neighbor improvement algorithm to obtain the convex set or the concave set isochronous ring;

s3 isochronous cycle expansion adjustment:constructing a buffer area for the contour node according to the obtained convex set or concave set isochronous ring, then constructing the convex set or concave set isochronous ring for the second time, and finally obtaining the maximum isochronous ring O of the facility _f ′；

S4Voronoi diagram construction and intersection: constructing a Voronoi diagram according to a plurality of facility positions, intersecting the Voronoi diagram of each facility with the maximized equal time circle obtained in the previous step, and obtaining a non-overlapping equal time circle O by taking the intersection part _f ″；

Attaching the closed contour of the equal time circle to an adjacent traffic network, and forming a new equal time circle contour by using an edge set on the network; the structure of road network lamination equal time circle can be mainly divided into the following 3 main processes: matching traffic network range limitation, establishing a Markov model and solving a Viterbi algorithm, and specifically comprising the following steps:

s5.1 matching traffic network Range restrictions

The network traffic network participating in the equal time circle calculation is set as G ═ V, E, the network node set is set as V, the network edge set is set as E, and the specific steps are as follows:

1) constructing and intersecting Voronoi graphs to obtain non-overlapping isochronous circles according to buffer width delta _R The drawing buffer area is expanded to obtain O _f "expanded region O _f,b ″；

2) Repeating the step 1) until obtaining O corresponding to each facility f _f,b ″；

Buffer O of all facilities f _f,b "is a union set of

Defining nodes and edges of a matching network as

And

s5.2 establishing Markov model and solving by Viterbi algorithm

Non-overlapping isochronous ring O for facility f _f First, a Markov model is defined:

1) defining the emission probability, for non-overlapping isochronous rings O of the facility f _f Let k _i Represents a composition O _f "i-th node of closed contour, number of nodes N _f A, is provided with M _r For an arbitrary node k _i Maximum search radius of, M _k For an arbitrary node k _i The maximum number of candidate matching nodes of, at k _i Radius of M _r Is selected from the range of (1) and k _i At most M with shortest linear distance _k Taking individual traffic network nodes as candidate matching node set V _i ，V _i Any one candidate matching node is set as v _i (v _i ∈V _i ) And k is _i Has a linear distance d (k) _i ,v _i )，v _i The emission probability is:

where σ represents the maximum allowable error between the contour of the non-overlapping equal time circle and the fitted road network when matching is performed, and the physical meaning of the formula is expressed in terms of v _i And k is _i Is determined by the distance v _i As k is _i Probability of matching points, where ep (v) _i ) Ep (v) must be satisfied _i )≥ep _min ；

2) Defining transition probabilities for k _i And k _i+1 Candidate matching node v therebetween _i And v _i+1 Let their shortest path distance in the traffic network be sp (v) _i ,v _i+1 ) If v is _i As k is _i Matching point of v _i+1 As k is _i+1 The probability of a matching point is:

3) taking any series of candidate matching nodes as O according to the emission probability and the transition probability defined above _f "the score of the matching points fit to the network is:

matching point sequence with highest score

2. The method for calculating the equal time circle of the multi-traffic facility facing the territorial space planning of claim 1, wherein the steps are as follows

The specific steps of the iterative node marking of S1 are as follows:

3) for each available network node V ∈ V, there is a label θ _v Setting the flags of all network nodes to theta _v While marking the facility f with the mark θ _f Set to 0;

4) is provided with

Extracting a node C from C (C epsilon)C) C set of adjacent network nodes as

Updating the mark value theta of any node a (a epsilon A) in the set A _a The update method is theta _a ＝min(θ _c +d _ac ,θ _a )，d _ac Is the distance from a to c; let d _max For a given facility coverage, θ is satisfied for set A _a ≤d _max If T does not have a, adding a to T;

6) repeating the steps 4) -5) until

3. The method for calculating the equal-time circle of the multi-traffic facility facing the territorial space planning of claim 1, wherein the step S2 is that the specific steps of the structure of the equal-time circle of the convex set or the concave set are as follows:

covering the network node set K for each facility f obtained in step S1 _f Node K in (K ∈ K) _f ) When the flag value exists [ theta ] _k ＞d _max Then, these nodes are adjusted to ensure that they fall into d _max Within the range of (1); the method comprises the following specific steps:

1) selecting one facility F (F E F) from all facilities F, and the network node covered by the facility FSet of points is K _f ；

2) Satisfies theta for the flag value _k ＞d _max Node K (K ∈ K) _f ) First, the retuning value Δ ═ θ is calculated _k -d _max ；

3) Selecting a marker value smaller than theta from a set of adjacent network nodes of k _k Is marked as a set A ', and the edge e with the end points of the nodes a' (a 'belongs to A') and k _a′k Adding a new network node at a distance delta from the node K as an adjusted overlay network node, and adding the new network node to the node K _f Simultaneously from K _f Deleting a node k;

s2.2, constructing a convex set equal time circle closed graph;

s2.3 a closed graph structure of a concave-concentration isochronous ring.

4. The method for calculating the equal time circle of the multi-traffic facility facing the territorial space planning of claim 3, wherein the closed graph of the convex set equal time circle in the step S2.2 is constructed as follows:

3) set of nodes O _f Is provided with O _f ＝K _f Setting i to 1 and j to 0;

4) set l ═ i +1) mod | O _f |，u＝(i-1)mod|O _f L, set k _i Represents K _f The ith node inCalculating vector quantity

And

a vector product of (a) if

Node k _i From O _f Delete and set j to 0, otherwise set

j＝j+1；

5) Set i ═ i +1) mod | O _f |；

5. The method for calculating the equal-time circle of the multi-traffic facility facing the territorial space planning of claim 3, wherein the step S2.3 of constructing the closed graph of the concave-set equal-time circle is as follows:

calculating the concave set equal time circle by adopting a K nearest neighbor improvement algorithm, and recording the algorithm function as Concavehull (K) _f β), β being a parameter of a neighbor algorithm for determining the number of neighbor points considered in the analysis, the specific steps being:

1) let k _i Represents K _f P is K _f The serial number of the minimum node of the middle vertical coordinate is set as a node set O _f ＝{k _p H, will k _p From K _f Deleting, setting current node c as k _p And λ ═ 0, m ═ 2;

2) if m is 5, the node k is connected _p To K _f ；

3) Finding out the nearest beta nodes of the node c, marking as a set A, and according to the angle mu of each node a (a epsilon A) _a Sorting from big to small, and setting the geographic coordinate of the node a as (x) _a ,y _a )，μ _a The calculation method is as follows:

4) setting i to 0 and q to 1;

5) if q is 1 and i < | a |, then go to step 6), otherwise go to step 13);

7) setting j to 2 and q to 0;

9) let o _i Represents O _f The ith node in (1), if the vector

And

crossing, setting q to 1, otherwise, setting q to 0;

10) j is updated, the updating method is j +1, and the step 8) is skipped;

11) if q is 1, the algorithm ConcaveHull (K) is called _f ,β+1)；

12) Updating the current node c by using the method that c is equal to a _i Update λ by the update method of

14) If g is 1 and i is greater than 0, jumping to step 15), otherwise, jumping to step 17);

15) judging node k _i Whether or not at O _f In a closed graph formed by the inner nodes, if yes, g is set to be 1, and otherwise, g is set to be 0;

17) if g is equal to 0, the algorithm ConcaveHull (K) is called _f ,β+1)；

6. The method for calculating the equal-time circle of the multi-traffic facility facing the territorial space planning of any one of claims 1 to 5, wherein the step S3 of expanding and adjusting the equal-time circle comprises the following specific steps:

If O is _f For concave-concentration equal-time ring, set K _f ′＝K _f ；

4) according to O _f The type of the isochronal rings, the solution using convex or concave isochronal rings used in the closed graph structure of the isochronal ringsMethod, input K _f ' and calculating the corresponding equal time circle to obtain the maximum equal time circle O of the enlarged adjustment _f ′。

7. The method for calculating the equal-time circle of the multi-transportation facility facing the territorial space planning as recited in any one of claims 1 to 5, wherein the Voronoi diagram of the step S4 is constructed and intersected, and the specific steps are as follows:

s4.1 constructing based on Voronoi diagram of facility position

Points inside and on the sides of the region

And facilities f _i Is a distance of

Not more than r and other facilities f _j I.e.:

Set the Voronoi diagram as

R consists of a series of Voronoi edges;

2) calculating and determining the centers of all circumscribed circles, namely the outer centers of all Delaunay triangles;

3) for any Delaunay triangle T, the three sides composing T are e _i (i-1, 2,3) if on side e _i There is another Delaunay triangle T' adjacent to T, i.e. e _i T ═ n T ', an outer connecting line of T' and T is added to R, if at edge e _i If there is no other Delaunay triangle, then e _i The perpendicular bisector of (c) is added to R;

There is no intersection between Voronoi regions of any two facilities;

s4.2 intersection operation

Let O be the maximum isochronous cycle of the isochronous cycle closed pattern structure acquisition means f _f Voronoi region R of facility f _f And O _f Intersecting to obtain non-overlapping equal time rings O _f ″＝R _f ∩O _f 。

8. The method for calculating the equal time circle of the multi-traffic facility facing the territorial space planning of any one of claims 1 to 5, wherein in the step S5, the Viterbi algorithm comprises the following specific steps:

1)V _i (j) denotes V _i J (th) candidate matching node, V _i Has a transmission probability vector of X _i Size is V _i Number of candidate matching nodes | V in (1) _i When V is _i (j)＝v _i When it is clear there is X _i (j)＝ep(v _i )，V _i To V _i+1 Has a transition probability matrix of Y _i,i+1 Of size | V _i |×|V _i+1 When V is _i (j)＝v _i ，V _i+1 (m)＝v _i+1 When it is apparent that there is Y _i,i+1 (j,m)＝tp(v _i ,v _i+1 )；

3) let i equal 2, set T ₁ (i)＝T ₁ (i-1)·Y _i,i+1 ·X _i+1 Is provided with O _f ″′(i-1)＝argmax(T ₁ (i-1)·Y _i,i+1 ·X _i+1 )；

4) If i is less than or equal to N _f Setting i to i +1, and repeating the steps, otherwise, turning to the next step;

5) is provided with