CN114001747A - Urban road network multisource shortest path obtaining method based on common calculation and dijkstra algorithm - Google Patents

Urban road network multisource shortest path obtaining method based on common calculation and dijkstra algorithm Download PDF

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CN114001747A
CN114001747A CN202111368321.3A CN202111368321A CN114001747A CN 114001747 A CN114001747 A CN 114001747A CN 202111368321 A CN202111368321 A CN 202111368321A CN 114001747 A CN114001747 A CN 114001747A
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intersection
source point
shortest path
weight
intersections
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CN114001747B (en
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丁建勋
殷慧娟
黄林煊
颜江楠
樊哲延
曾嘉涵
查菲菲
徐小明
龙建成
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Hefei University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
    • G01C21/34—Route searching; Route guidance
    • G01C21/3407—Route searching; Route guidance specially adapted for specific applications
    • G01C21/3415—Dynamic re-routing, e.g. recalculating the route when the user deviates from calculated route or after detecting real-time traffic data or accidents
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
    • G01C21/34—Route searching; Route guidance
    • G01C21/3446—Details of route searching algorithms, e.g. Dijkstra, A*, arc-flags, using precalculated routes

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Abstract

The invention discloses a method for acquiring a multisource shortest path of an urban road network based on common calculation and dijkstra algorithm, which comprises the following steps: 1, acquiring a real-time urban road network map, and selecting a plurality of source point intersections; 2 if all predecessor intersections of an adjacent intersection of the intersections which obtain the weight of the shortest path in the previous iteration obtain the weight of the shortest path of the source point, updating the weight of the shortest path from the source point to the adjacent intersection, or else updating the upper bound of the weight of the shortest path of the adjacent intersection, and selecting the minimum weight which is updated to the shortest path; 3 backtracking the shortest path obtained by the iteration, and searching and updating the weight of the shortest path from other source points in the path to the intersection; and 4, when the shortest paths from all the source points to all the intersections in the intersection set are obtained, ending the search and outputting, and otherwise, continuing the iteration. The method can effectively improve the calculation efficiency of large-scale road network navigation planning and meet the travel demands of different travel points of multiple users at the same time.

Description

Urban road network multisource shortest path obtaining method based on common calculation and dijkstra algorithm
Technical Field
The invention belongs to the field of vehicle navigation path optimization, and particularly relates to a method for acquiring a multisource shortest path of an urban road network based on common calculation and dijkstra algorithm.
Background
With the continuous expansion of the scale of urban road networks and the corresponding increase of road network nodes, the existing shortest path navigation system firstly utilizes a single-source shortest path algorithm or a full-source shortest path algorithm to meet the travel requirements of users, the calculation workload is huge, and the real-time and efficient requirements of people on navigation software are difficult to meet. The common full-source shortest path algorithm is used in a large-scale urban road network, particularly when nodes of the road network are dense, the calculation range is wide, time consumption and resource occupation are correspondingly increased, and the method for exchanging the quantity of resources for the efficiency and the quality is a common coping scheme.
Different scholars design different algorithms in solving the shortest path of the vehicle navigation core problem, and the single-source shortest path algorithm is independently adopted one by one in application of the single-source shortest path algorithm, so that calculated weights can be repeatedly calculated, and a large amount of calculation redundancy is caused; the full-source shortest path algorithm (from all points to all points) performs unnecessary single-source point shortest path algorithm, and the calculated amount is increased, so that the method is not suitable for the concept of real-time navigation.
Meanwhile, the same algorithm is single in the path of obtaining the shortest path at present, and the traditional Dijisra algorithm only obtains the shortest path step by searching leaf nodes, so that the efficiency is low. The improvement of the relevant scholars on the basis of the method is still based on the point, the efficiency improvement effect is not good, and the parallel implementation is not facilitated.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides an urban road network multisource shortest path acquisition method based on common calculation and dijkstra algorithm, so that the problem of vehicle-mounted navigation path optimization can be solved by obtaining the weight of the shortest path through multiple paths, the calculation efficiency of large-scale road network navigation planning is effectively improved, and the travel requirements of different travel points of multiple users at the same time are met.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a method for acquiring a multisource shortest path of an urban road network based on common calculation and dijkstra algorithm, which is characterized by comprising the following steps of:
step 1: constructing an urban road network, defining parameters and initializing;
acquiring real-time road network data and obtaining an urban road network G ═ (V, A, W), V represents an intersection set, and V ═ V1,v2,v3,…,vi,…,vR}，viDenotes the ith intersection, i is 1,2,3, …, R is the total number of intersections in the urban road network G, a denotes the set of links between intersections, and a is { (v)i,vj)|i,j＝1,2,3,…,R}，(vi,vj) Indicates the ith intersection viTo the jth intersection vjW represents a set of weights for links between intersections, W ═ ωi,j|i,j＝1,2,3,…,R}，ωi,jAs directed links (v)i,vj) If the ith intersection viTo the jth intersection vjThere is a directed road section (v) in betweeni,vj) Then the jth intersection vjIs the ith intersection viAdjacent intersection, i-th intersection viFor the jth intersection vjPrecursor of (2)At an intersection, and ωi,jNot less than 0; if the ith intersection viTo the jth intersection vjThere is no directed link (v) betweeni,vj) Then let ω bei,jInfinity, +,; defining the current iteration times as t;
step 2: acquiring a source point intersection set:
k source point intersections are selected and a source point intersection set V ' ═ V ' is formed 'k1,2, …, K, where v'kRepresenting the kth source point intersection in the source point intersection set V ', and enabling the kth source point intersection V'kThe serial number in the intersection set V is skI.e. by
Figure BDA0003361675280000021
Figure BDA0003361675280000022
Represents the s th in the intersection set VkAt each intersection, K is more than 1 and less than or equal to R;
and step 3: initializing the weights from the source point intersection to each intersection of the t iteration:
defining the kth source point intersection V ' in the source point intersection set V ' at the t iteration 'kThe ith intersection V in the intersection set ViThe upper bound of the weight of the shortest path of (1) is
Figure BDA0003361675280000023
And initialize
Figure BDA0003361675280000024
Is + ∞;
defining the kth source point intersection V 'in the source point intersection set V'kThe ith intersection V in the intersection set ViWeight of the shortest path of Pk(vi) And initializes Pk(vi) Is + ∞;
initializing t ═ 1;
initializing kth source point intersection v 'under the t iteration'kTo skV. of each intersectionskThe upper bound of the weight of the shortest path of (1) is
Figure BDA0003361675280000025
The kth source point intersection V ' in the source point intersection set V ' at the t iteration 'kTo skIndividual intersection
Figure BDA0003361675280000026
Has the weight of the shortest path of
Figure BDA0003361675280000027
And will bekIndividual intersection
Figure BDA0003361675280000028
Add to t-1 iterations before crossing v 'with the kth Source Point'kIntersection set for obtaining weight of shortest path for source point
Figure BDA0003361675280000029
And intersecting v 'with the k source point in the t-1 iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000210
Definition of Lk,iRepresenting the kth source point intersection V 'in the source point intersection set V'kThe ith intersection V in the intersection set ViAnd initializing intersection sets of shortest paths
Figure BDA00033616752800000211
And 4, step 4: intersecting v 'with k source point in t-1 iterations'kIntersection set for obtaining weight of shortest path for source point
Figure BDA0003361675280000031
All intersections in (1) perform forward search and update the weight of the shortest path:
step 4.1: initializing k to 1;
step 4.2: if t-1 times beforeIntersection v 'with k-th source point under iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA0003361675280000032
If the intersection set V contains all the intersections in the intersection set V, the kth source point intersection V ' in the source point intersection set V ' is subjected to intersection treatment 'kEnding the shortest path search of the source point, and turning to the step 6, otherwise, turning to the step 4.3;
step 4.3: initializing intersection v 'with k source point in t iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA0003361675280000033
Recording the k source point intersection v 'in the t-1 iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA0003361675280000034
The number of intersections in (1) is Mt-1(ii) a Taking out the m-th intersection and marking as
Figure BDA0003361675280000035
Order the m-th intersection
Figure BDA0003361675280000036
The serial number in the intersection set V is
Figure BDA0003361675280000037
Namely, it is
Figure BDA0003361675280000038
Step 4.3.1: initializing m to 1;
step 4.3.2: traverse the m-th intersection
Figure BDA0003361675280000039
And selecting all the adjacent intersections from the intersection set which does not belong to
Figure BDA00033616752800000310
And join into an adjacency set
Figure BDA00033616752800000311
Step 4.3.2.1: fetching contiguous collections
Figure BDA00033616752800000312
At the q-th intersection in (1), recording the adjacency set
Figure BDA00033616752800000313
Middle q intersection
Figure BDA00033616752800000314
The set of the front driving intersections is
Figure BDA00033616752800000315
Make the adjacent set
Figure BDA00033616752800000316
Middle q intersection
Figure BDA00033616752800000317
The serial number in the intersection set V is rqI.e. by
Figure BDA00033616752800000318
Step 4.3.2.2: initializing q to be 1;
step 4.3.2.3: traversing precursor intersection set
Figure BDA00033616752800000319
If all the intersections in (1) are set in the front-driving intersection
Figure BDA00033616752800000320
All intersections in (1) belong to the intersection v 'of the kth source point under the first t-1 iterations'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000321
Then step 4.4 is carried out, otherwise step 4.5 is carried out;
step 4.4: acquiring v 'from k-th source point intersection'kObtaining a k source point intersection v 'from all the precursor intersections'kThe shortest path weight of the intersection which is the weight of the shortest path of the source point:
step 4.4.1: precursor-memory intersection set
Figure BDA00033616752800000322
The number of the intersections in the tree is B, and a precursor intersection set is taken out
Figure BDA0003361675280000041
The b-th intersection in (1)
Figure BDA0003361675280000042
The serial number of the intersection in the intersection set V is nbI.e. by
Figure BDA0003361675280000043
Step 4.4.2: initializing b to be 1;
step 4.4.3: if it is
Figure BDA0003361675280000044
Then will be
Figure BDA0003361675280000045
Is assigned to
Figure BDA0003361675280000046
And memory forerunner intersection
Figure BDA0003361675280000047
Sequence number n of intersection set VbAssigning to the r-th in the intersection set VqIndividual intersection
Figure BDA0003361675280000048
Number n of temporary predecessor intersectionb,min(ii) a Wherein the content of the first and second substances,
Figure BDA0003361675280000049
represents the kth source point intersection v'kN-th in intersection set VbThe weight of the shortest path of each intersection,
Figure BDA00033616752800000410
represents the n-th in the intersection set VbIndividual intersection
Figure BDA00033616752800000411
To the r < th > rqIndividual intersection
Figure BDA00033616752800000412
The weight of (a) is determined,
Figure BDA00033616752800000413
represents the kth source point intersection v'kR-th in intersection set VqIndividual intersection
Figure BDA00033616752800000414
The weight of the shortest path of (1);
step 4.4.4: b +1 is assigned to B, the step 4.4.3 is carried out until B is equal to B, and therefore the k source point intersection v 'is output'kR-th in intersection set VqIndividual intersection
Figure BDA00033616752800000415
Weight of shortest path of
Figure BDA00033616752800000416
And number nb,minAnd will r beqIndividual intersection
Figure BDA00033616752800000417
Adding the source point intersection V ' to the kth source point intersection V ' in the source point intersection set V 'kN-th in intersection set Vb,minIndividual intersection
Figure BDA00033616752800000418
Intersection set of shortest paths of
Figure BDA00033616752800000419
Thereby obtaining the kth source point intersection V 'in the source point intersection set V'kR-th in intersection set VqIndividual intersection
Figure BDA00033616752800000420
Intersection set of shortest paths of
Figure BDA00033616752800000421
Namely, it is
Figure BDA00033616752800000422
Will r toqIndividual intersection
Figure BDA00033616752800000423
To k source point intersection v'kSet of weights to get the shortest path for a source point
Figure BDA00033616752800000424
And intersecting v 'with the k source point in the t iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000425
Namely, it is
Figure BDA00033616752800000426
Figure BDA00033616752800000427
Turning to step 4.6;
step 4.5: if it is not
Figure BDA00033616752800000428
Then will be
Figure BDA00033616752800000429
Is assigned to
Figure BDA00033616752800000430
Otherwise, turning to step 4.6;
step 4.6: if Q is not equal to Q, assigning Q +1 to Q, and turning to step 4.3.2.3, otherwise, assigning M +1 to M, and judging that M is larger than Mt-1If yes, executing step 4.7; otherwise, turning to the step 4.3.2;
step 4.7: selecting an intersection with the minimum upper bound of the weight of the shortest path from the intersection set V under the t iteration
Figure BDA00033616752800000431
And is
Figure BDA00033616752800000432
Does not belong to the intersection v 'with the k source point under the previous t iterations'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000433
Namely, it is
Figure BDA00033616752800000434
If it is not
Figure BDA00033616752800000435
Then the kth source point is intersected by v'kThe ith in the intersection set VminIndividual intersection
Figure BDA00033616752800000436
Upper bound of weight of shortest path of
Figure BDA00033616752800000437
Assigning to k source point intersection v'kThe ith in the intersection set VminIndividual intersection
Figure BDA0003361675280000051
Weight of shortest path of
Figure BDA0003361675280000052
And will be the ithminIndividual intersection
Figure BDA0003361675280000053
Adding the source point intersection V ' to the kth source point intersection V ' in the source point intersection set V 'kThe first in the intersection set V
Figure BDA0003361675280000054
Individual intersection
Figure BDA0003361675280000055
Shortest path intersection set
Figure BDA0003361675280000056
Thereby obtaining the kth source point intersection V 'in the source point intersection set V'kThe ith in the intersection set VminIndividual intersection
Figure BDA0003361675280000057
Shortest path intersection set
Figure BDA0003361675280000058
Namely, it is
Figure BDA0003361675280000059
And will be the ithminIndividual intersection
Figure BDA00033616752800000510
Join to a collection
Figure BDA00033616752800000511
Intersection set
Figure BDA00033616752800000512
And 5: backtracking kth source point intersection v 'under the tth iteration'kSet of intersections
Figure BDA00033616752800000513
Shortest path at intersection (iii):
step 5.1: recording the intersection v 'with the k source point in the t iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000514
The number of intersections in (1) is MtAnd taking out the m-th intersection as
Figure BDA00033616752800000515
And the m-th intersection
Figure BDA00033616752800000516
The serial number in the intersection set V is
Figure BDA00033616752800000517
Namely, it is
Figure BDA00033616752800000518
Step 5.2: initializing m to 1;
step 5.3: recording k source point intersection v'kThe first in the intersection set V
Figure BDA00033616752800000519
Individual intersection
Figure BDA00033616752800000520
Set of shortest path points of
Figure BDA00033616752800000521
The number of each intermediate crossing is EmAnd the serial number of the epsilon middle crossing in the crossing set V is recorded as rhoε；
Step 5.3.1: initializing epsilon to be 1;
step 5.3.2: if it is not
Figure BDA00033616752800000522
Then assume that
Figure BDA00033616752800000523
Simultaneously, the source point intersection V ' at the k ' th source point intersection in the source point intersection set V 'k′I.e. by
Figure BDA00033616752800000524
Then take the shortest path point set
Figure BDA00033616752800000525
Middle epsilon intersection
Figure BDA00033616752800000526
To Em+2 crossings
Figure BDA00033616752800000527
All intersections are used as k 'source point intersections v'k′The first in the intersection set V
Figure BDA00033616752800000528
Individual intersection
Figure BDA00033616752800000529
Shortest path intersection set
Figure BDA00033616752800000530
And will be
Figure BDA00033616752800000531
Is assigned to
Figure BDA00033616752800000532
If k' > k, then
Figure BDA00033616752800000533
Individual intersection
Figure BDA00033616752800000534
Add to t-1 previous iterations to intersect v ' at the k ' th source point 'k′Set of weights to get shortest path for source point
Figure BDA00033616752800000535
And the kth ' source point intersection v ' in the t-1 iterations 'k′Intersection set for obtaining weight of shortest path for source
Figure BDA00033616752800000536
Otherwise, it will be
Figure BDA00033616752800000537
Individual intersection
Figure BDA00033616752800000538
Add to k ' th Source Point intersection v ' of the previous t iterations 'k′Set of weights to get shortest path for source point
Figure BDA00033616752800000539
And intersecting v ' with the k ' source point in the t iteration 'k′Intersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000540
Step 5.3.3: judging E ═ EmIf yes, turning to step 5.4, otherwise, assigning epsilon +1 to epsilon, and turning to step 5.3.2;
step 5.4: judging M as MtIf yes, turning to step 6, otherwise, assigning m +1 to m, and turning to step 5.3;
step 6: judging whether K is true or not, if so, turning to a step 7, otherwise, assigning K +1 to K, and turning to a step 4.2;
and 7: and if the shortest path search with all the source point intersections as source points in the source point intersection set V 'under the previous t iterations is finished, indicating that the shortest path from each source point intersection in the source point intersection set V' to any one intersection in the intersection set V is obtained, otherwise, assigning t +1 to t, and turning to the step 4.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention provides a method for generating partial source shortest paths between a single-source shortest path algorithm and a full-source shortest path algorithm, and provides that in the process of calculating the multisource shortest path, the shortest path weights of all source points can be calculated in a shared mode, and finally the weights of the shortest paths are obtained through ideas such as shared calculation and the like on the basis of a dijkstra algorithm, so that the calculation efficiency is further improved, a large-scale road network graph is processed more efficiently, the efficiency is guaranteed while resources are saved, the current situation of actual navigation application requirements is combined, unnecessary time loss is avoided, a smart multisource shortest path optimization method is provided for the problem of complexity in calculation of the large-scale road network, the calculation efficiency and the solution quality are substantially improved, the calculation burden of navigation planning can be relieved, and the actual application is more fit.
2. In the existing full-source shortest-path algorithm, due to the essential characteristics, the calculation efficiency is not high when a complex large-scale graph is handled, and traversal search needs to be performed on all intersection source points in the large-scale road network graph, so that the efficiency is greatly reduced. The invention considers that only the source point with the user search path requirement is selected to expand the shortest path search calculation, and the source point search calculation without the user initiated path search is omitted, thereby carrying out a multisource shortest path algorithm with higher efficiency under the condition of avoiding the parallel calculation of the full-source expanded path search or the single-source shortest path algorithm, and providing a new solution for the navigation system to simultaneously provide the customized shortest path for a plurality of users.
3. Based on the theorem that the sub-path of one shortest path is always the shortest sub-path, after the shortest path from a source intersection to a certain intersection is obtained, the shortest paths from other source intersections to the intersection which may exist in the shortest path can be traced back. The invention skillfully utilizes the point and records the weight of the shortest path of backtracking, avoids independent calculation of each source point intersection, facilitates the utilization of subsequent iterative update and reduces repeated calculation to carry out cooperative operation, and forms a unique common calculation idea. The common calculation idea complements with a method for acquiring the shortest path of multiple sources, and is used as one of new ways for acquiring the weight of the shortest path, so that the calculation workload is reduced.
4. The invention researches a directional traffic network, namely, the bidirectional traffic transportation condition difference of roads is considered in practical application, and the invention is more accurately fit with the reality. Meanwhile, the invention finds that if all the predecessor adjacent intersections of a certain intersection have searched for the shortest path with the intersection of the same source point as the starting point, the weight of the shortest path from the source point intersection to the intersection can be directly calculated and obtained compared with the upper bound of the weight of the shortest path updated by continuing the dijkstra algorithm. With this, the present invention adds another way to get the shortest path, substantially improving computational efficiency and computational quality. Meanwhile, the shortest path obtained by backtracking of the common calculation idea can be effectively utilized under certain conditions, so that the steps in the invention can interact, the work calculation amount is greatly reduced, and the shortest path search of the large-scale road network graph is facilitated.
5. According to the invention, under each iteration, after the suitable path for obtaining the shortest path is judged and selected, the calculation of the two paths for obtaining the shortest path can be carried out simultaneously, and according to the characteristics, the invention provides possibility for parallel calculation under the condition of multithreading, lays a foundation for fusing parallel multi-source search in the subsequent urban road network navigation planning work, is convenient to be matched with a graph division technology and parallel search, and further speeds up the multi-user path planning.
Drawings
FIG. 1 is an overall flow chart of the present invention;
FIG. 2 is a flow chart of the present invention for obtaining shortest paths in multiple paths;
FIG. 3 is a schematic diagram of the main idea of point 4 (adjacent intersection can directly calculate the right to obtain the shortest path) in the summary of the invention;
FIG. 4 is a simple city road network graph and weight table (containing initial parameter values) of the present invention;
FIG. 5 shows source point intersection v 'at iteration 3 of the invention'1An upper bound table and a path graph of the weight of the shortest path to each intersection;
FIG. 6 shows source point intersection v 'at iteration 3 of the invention'2An upper bound table and a path graph of the weight of the shortest path to each intersection;
fig. 7 is an upper bound table and a path diagram of the weight from each source intersection to the shortest path of each intersection in the 6 th iteration of the present invention.
Detailed Description
In this embodiment, starting from an idea of solving a multisource shortest path between a single source and a full source, a method for obtaining a multisource shortest path of an urban road network based on common computation and dijkstra algorithm is provided, and specific process steps are shown in fig. 1, a main body thought framework is shown in fig. 2, and main processes a, b, c, and d in fig. 1 and fig. 2 correspond to one another and are performed according to the following steps:
step 1: constructing an urban road network, defining parameters and initializing;
the real-time road network data is acquired to obtain an urban road network G ═ (V, a, W), and in the following, taking the simple road network graph in fig. 4 as an example, V denotes an intersection set, and V ═ V1,v2,v3,…,vi,…,vR}，viDenotes the ith intersection, i is 1,2,3, …, R is the total number of intersections in the urban road network G, a denotes the set of links between intersections, and a is { (v)i,vj)|i,j＝1,2,3,…,R}，(vi,vj) Indicates the ith intersection viTo the jth intersection vjW represents a set of weights for links between intersections, W ═ ωi,j|i,j＝1,2,3,…,R}，ωi,jAs directed links (v)i,vj) If the ith intersection viTo the jth intersection vjThere is a directed road section (v) in betweeni,vj) Then the jth intersection vjIs the ith intersection viAdjacent intersection, i-th intersection viFor the jth intersection vjAt a front-drive intersection of, and ωi,jNot less than 0; if the ith intersection viTo the jth intersection vjThere is no directed link (v) betweeni,vj) Then let ω bei,jInfinity, +,; defining the current iteration times as t;
step 2: acquiring a source point intersection set:
k source point intersections are selected and a source point intersection set V ' ═ V ' is formed 'k1,2, …, K, where v'kRepresenting the kth source point intersection in the source point intersection set V ', and enabling the kth source point intersection V'kThe serial number in the intersection set V is skI.e. by
Figure BDA0003361675280000081
Figure BDA0003361675280000082
Represents the s th in the intersection set VkK is more than 1 and less than or equal to R at each intersection, as shown by a V' set in the figure 4 and the intersections corresponding to black italic fonts in the simple road network diagram in the figures 4 to 7;
and step 3: initializing the weights from the source point intersection to each intersection of the t iteration:
defining the kth source point intersection V ' in the source point intersection set V ' at the t iteration 'kThe ith intersection V in the intersection set ViThe upper bound of the weight of the shortest path of (1) is
Figure BDA0003361675280000083
And initialize
Figure BDA0003361675280000084
Is + ∞;
defining the kth source point intersection V 'in the source point intersection set V'kThe ith intersection V in the intersection set ViWeight of the shortest path of Pk(vi) And initializes Pk(vi) Is + ∞;
initializing t ═ 1;
initializing kth source point intersection v 'under the t iteration'kTo skIndividual intersection
Figure BDA0003361675280000085
The upper bound of the weight of the shortest path of (1) is
Figure BDA0003361675280000086
The kth source point intersection V ' in the source point intersection set V ' at the t iteration 'kTo skIndividual intersection
Figure BDA0003361675280000087
Has the weight of the shortest path of
Figure BDA0003361675280000088
And will bekIndividual intersection
Figure BDA0003361675280000089
Add to t-1 iterations before crossing v 'with the kth Source Point'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000810
And intersecting v 'with the k source point in the t-1 iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000811
Such as S in fig. 43,S5,ΔS3,ΔS5Shown;
definition of Lk,iRepresenting the kth source point intersection V 'in the source point intersection set V'kThe ith intersection V in the intersection set ViAnd initializing intersection sets of shortest paths
Figure BDA00033616752800000812
And 4, step 4: intersecting v 'with k source point in t-1 iterations'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000813
All intersections in (1) perform forward search and update the weight of the shortest path:
step 4.1: initializing k to 1;
step 4.2: if it is beforet-1 iterations through the k-th source point intersection v'kIntersection set for obtaining weight of shortest path for source point
Figure BDA0003361675280000091
If the intersection set V contains all the intersections in the intersection set V, the kth source point intersection V ' in the source point intersection set V ' is subjected to intersection treatment 'kThe shortest search for the source point is ended and the process goes to step 6, which takes fig. 7 as an example, S3V ', stopping the source point intersection V'kSearching for the shortest path of the source point, otherwise, turning to the step 4.3;
step 4.3: initializing intersection v 'with k source point in t iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA0003361675280000092
Recording the k source point intersection v 'in the t-1 iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA0003361675280000093
The number of intersections in (1) is Mt-1(ii) a Taking out the m-th intersection and marking as
Figure BDA0003361675280000094
Order the m-th intersection
Figure BDA0003361675280000095
The serial number in the intersection set V is
Figure BDA0003361675280000096
Namely, it is
Figure BDA0003361675280000097
Step 4.3.1: initializing m to 1;
step 4.3.2: traverse the m-th intersection
Figure BDA0003361675280000098
And selecting all the adjacent intersections from the intersection set which does not belong to
Figure BDA0003361675280000099
And join into an adjacency set
Figure BDA00033616752800000910
Step 4.3.2.1: fetching contiguous collections
Figure BDA00033616752800000911
At the q-th intersection in (1), recording the adjacency set
Figure BDA00033616752800000912
Middle q intersection
Figure BDA00033616752800000913
The set of the front driving intersections is
Figure BDA00033616752800000914
Make the adjacent set
Figure BDA00033616752800000915
Middle q intersection
Figure BDA00033616752800000916
The serial number in the intersection set V is rqI.e. by
Figure BDA00033616752800000917
Step 4.3.2.2: initializing q to be 1;
step 4.3.2.3: traversing precursor intersection set
Figure BDA00033616752800000918
If all the intersections in (1) are set in the front-driving intersection
Figure BDA00033616752800000919
All the intersections in (1) belong toCrossing v 'with the kth source point at the previous t-1 iterations'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800000920
Go to step 4.4 otherwise go to step 4.5 as shown in fig. 5, v1Adjacent intersection v of2Front-drive intersection v1，v5Have all obtained the shortest path, i.e.
Figure BDA00033616752800000921
And v is1Is adjacent to the other intersection v6Front-drive intersection v8The shortest path is not obtained, so v1Go to step 4.4, v6And (5) transferring to the step 4.5.
Step 4.4: acquiring v 'from k-th source point intersection'kObtaining a k source point intersection v 'from all the precursor intersections'kThe shortest path weight of the intersection, which is the weight of the shortest path of the source point, i.e. flow a in fig. 2, the overall idea and steps are shown in fig. 3:
step 4.4.1: precursor-memory intersection set
Figure BDA0003361675280000101
The number of the intersections in the tree is B, and a precursor intersection set is taken out
Figure BDA0003361675280000102
The b-th intersection in (1)
Figure BDA0003361675280000103
The serial number of the intersection in the intersection set V is nbI.e. by
Figure BDA0003361675280000104
Step 4.4.2: initializing b to be 1;
step 4.4.3: if it is
Figure BDA0003361675280000105
Then will be
Figure BDA0003361675280000106
Is assigned to
Figure BDA0003361675280000107
And memory forerunner intersection
Figure BDA0003361675280000108
Sequence number n of intersection set VbAssigning to the r-th in the intersection set VqIndividual intersection
Figure BDA0003361675280000109
Number n of temporary predecessor intersectionb,min(ii) a Wherein the content of the first and second substances,
Figure BDA00033616752800001010
represents the kth source point intersection v'kN-th in intersection set VbThe weight of the shortest path of each intersection,
Figure BDA00033616752800001011
represents the n-th in the intersection set VbIndividual intersection
Figure BDA00033616752800001012
To the r < th > rqIndividual intersection
Figure BDA00033616752800001013
The weight of (a) is determined,
Figure BDA00033616752800001014
represents the kth source point intersection v'kR-th in intersection set VqIndividual intersection
Figure BDA00033616752800001015
The weight of the shortest path of (1);
step 4.4.4: b +1 is assigned to B, the step 4.4.3 is carried out until B is equal to B, and therefore the k source point intersection v 'is output'kR-th in intersection set VqIndividual intersection
Figure BDA00033616752800001016
Weight of shortest path of
Figure BDA00033616752800001017
And number nb,minAnd will r beqIndividual intersection
Figure BDA00033616752800001018
Adding the source point intersection V ' to the kth source point intersection V ' in the source point intersection set V 'kN-th in intersection set Vb,minIndividual intersection
Figure BDA00033616752800001019
Intersection set of shortest paths of
Figure BDA00033616752800001020
Thereby obtaining the kth source point intersection V 'in the source point intersection set V'kR-th in intersection set VqIndividual intersection
Figure BDA00033616752800001021
Intersection set of shortest paths of
Figure BDA00033616752800001022
Namely, it is
Figure BDA00033616752800001023
Will r toqIndividual intersection
Figure BDA00033616752800001024
To k source point intersection v'kSet of weights to get the shortest path for a source point
Figure BDA00033616752800001025
And intersecting v 'with the k source point in the t iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800001026
Go to step 4.6, v in FIG. 51Adjacent intersection v of2For example, calculate intersection v from the origin3Starting respectively through v2Front-drive intersection v1、v5Reaches v2And the weight of the shortest path selected as the minimum is updated to v3To v2Weight of the shortest path of (1), P3(v2)＝min{P3(v1)+ω1，2，P3(v5)+ω5，215 and record the predecessor node at this time as v5I.e. λ3，2＝v5V is to be2Is added to L3(v5) In (b) to obtain L3(v2)＝L3(v5)∪{v2}＝{v3,v4,v5,v2V, simultaneously2Join into set S3And
Figure BDA00033616752800001027
in, i.e. S3＝S3∪{v2}，
Figure BDA00033616752800001028
Step 4.5: if it is not
Figure BDA00033616752800001029
Then will be
Figure BDA00033616752800001030
Is assigned to
Figure BDA00033616752800001031
Otherwise, go to step 4.6, using v in FIG. 41Is adjacent to the intersection v6For example, P3(v5)+ω5,6＝14＜T3 3(v6) Thus updating T3 3(v6)＝P3(v5)+ω 5,614, i.e. corresponding to the scheme b in fig. 2;
step 4.6: if Q is not equal to Q, thenAssigning q +1 to q, and turning to step 4.3.2.3, otherwise, assigning M +1 to M, and judging that M is larger than Mt-1If yes, executing step 4.7; otherwise, turning to the step 4.3.2;
step 4.7: selecting an intersection with the minimum upper bound of the weight of the shortest path from the intersection set V under the t iteration
Figure BDA0003361675280000111
And is
Figure BDA0003361675280000112
Does not belong to the intersection v 'with the k source point under the previous t iterations'kIntersection set for obtaining weight of shortest path for source point
Figure BDA0003361675280000113
Namely, it is
Figure BDA0003361675280000114
If it is not
Figure BDA0003361675280000115
Then the kth source point is intersected by v'kThe ith in the intersection set VminIndividual intersection
Figure BDA0003361675280000116
Upper bound of weight of shortest path of
Figure BDA0003361675280000117
Assigning to k source point intersection v'kThe ith in the intersection set VminIndividual intersection
Figure BDA0003361675280000118
Weight of shortest path of
Figure BDA0003361675280000119
And will be the ithminIndividual intersection
Figure BDA00033616752800001110
Is added toK source point intersection V 'in source point intersection set V'kThe first in the intersection set V
Figure BDA00033616752800001111
Individual intersection
Figure BDA00033616752800001112
Shortest path intersection set
Figure BDA00033616752800001113
Thereby obtaining the kth source point intersection V 'in the source point intersection set V'kThe ith in the intersection set VminIndividual intersection
Figure BDA00033616752800001114
Shortest path intersection set
Figure BDA00033616752800001115
Namely, it is
Figure BDA00033616752800001116
And will be the ithminIndividual intersection
Figure BDA00033616752800001117
Join to a collection
Figure BDA00033616752800001118
Intersection set
Figure BDA00033616752800001119
Corresponding to the flow shown in FIG. 2, according to FIG. 4 with respect to the source point v3Selecting the upper bound of the shortest path right to each intersection, which does not belong to S3The intersection v corresponding to the minimum upper bound value6，
Figure BDA00033616752800001120
At the same time v6Join into set S3And
Figure BDA00033616752800001121
in, i.e. S3＝S3∪{v6}，
Figure BDA00033616752800001122
To obtain v3To v6Shortest path of (L)3(v6)；
And 5: backtracking kth source point intersection v 'under the tth iteration'kSet of intersections
Figure BDA00033616752800001123
The shortest path at the intersection in (1), i.e. the step thought of the flow d in fig. 1:
step 5.1: recording the intersection v 'with the k source point in the t iteration'kIntersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800001124
The number of intersections in (1) is MtAnd taking out the m-th intersection as
Figure BDA00033616752800001125
And the m-th intersection
Figure BDA00033616752800001126
The serial number in the intersection set V is
Figure BDA00033616752800001127
Namely, it is
Figure BDA00033616752800001128
Step 5.2: initializing m to 1;
step 5.3: recording k source point intersection v'kThe first in the intersection set V
Figure BDA00033616752800001129
Individual intersection
Figure BDA00033616752800001130
Set of shortest path pointsCombination of Chinese herbs
Figure BDA00033616752800001131
The number of each intermediate crossing is EmAnd the serial number of the epsilon middle crossing in the crossing set V is recorded as rhoε；
Step 5.3.1: initializing epsilon to be 1;
step 5.3.2: if it is not
Figure BDA0003361675280000121
Then assume that
Figure BDA0003361675280000122
Simultaneously, the source point intersection V ' at the k ' th source point intersection in the source point intersection set V 'k′I.e. by
Figure BDA0003361675280000123
Then take the shortest path point set
Figure BDA0003361675280000124
Middle epsilon intersection
Figure BDA0003361675280000125
To Em+2 crossings
Figure BDA0003361675280000126
All intersections are used as k 'source point intersections v'k′The first in the intersection set V
Figure BDA0003361675280000127
Individual intersection
Figure BDA0003361675280000128
Shortest path intersection set
Figure BDA0003361675280000129
And will be
Figure BDA00033616752800001210
Is assigned to
Figure BDA00033616752800001211
If k' > k, then
Figure BDA00033616752800001212
Individual intersection
Figure BDA00033616752800001213
Add to t-1 previous iterations to intersect v ' at the k ' th source point 'k′Set of weights to get shortest path for source point
Figure BDA00033616752800001214
And the kth ' source point intersection v ' in the t-1 iterations 'k′Intersection set for obtaining weight of shortest path for source
Figure BDA00033616752800001215
Namely, it is
Figure BDA00033616752800001216
Figure BDA00033616752800001217
Otherwise, it will be
Figure BDA00033616752800001218
Individual intersection
Figure BDA00033616752800001219
Add to k ' th Source Point intersection v ' of the previous t iterations 'k′Set of weights to get shortest path for source point
Figure BDA00033616752800001220
And intersecting v ' with the k ' source point in the t iteration 'k′Intersection set for obtaining weight of shortest path for source point
Figure BDA00033616752800001221
Instant game
Figure BDA00033616752800001222
V in FIG. 52For example, L3(v2)＝{v3,v4,v5,v2The 2 nd intermediate crossing (excluding v)3And v2)v5Belongs to a source point intersection set V', and
Figure BDA00033616752800001223
then v will be taken5To v2All intersections in between add to L5(v2) In (b) to obtain L5(v2)＝{v5,v2}，P5(v2)＝P3(v2)-P3(v5) At the same time v2Is added to5As a set S of source points5And
Figure BDA00033616752800001224
in, i.e. S5＝S5∪{v2}，
Figure BDA00033616752800001225
As shown in fig. 6;
step 5.3.3: judging E ═ EmIf yes, turning to step 5.4, otherwise, assigning epsilon +1 to epsilon, and turning to step 5.3.2;
step 5.4: judging M as MtIf yes, turning to step 6, otherwise, assigning m +1 to m, and turning to step 5.3;
step 6: judging whether K is true or not, if so, turning to a step 7, otherwise, assigning K +1 to K, and turning to a step 4.2;
and 7: if the shortest path search with all source point intersections as source points in the source point intersection set V 'is finished under the previous t iterations, the shortest path from each source point intersection in the source point intersection set V' to any intersection in the intersection set V is obtained, if the shortest path search from all source point intersections to all intersections is finished under the 6 th iteration in FIG. 7, the shortest path values (such as table 1) from all source point intersections to all intersections and the corresponding shortest paths (such as table 2) are output; otherwise, assigning t +1 to t, and going to step 4.
The shortest path values from each source point to each intersection point obtained in this example are shown in table 1:
table 1 shortest path value from each source point to each intersection according to the present invention
Figure BDA0003361675280000131
The shortest path from each source point to each intersection point obtained in this embodiment is shown in table 2:
table 2 shortest path acquisition result of the present invention
L v1 v2 v3 v4 v5 v6 v7 v8 v9
v3 v3，v4， v1 v3，v4， v5，v2 v3 v3，v4 v3，v4，v5 v3，v4， v5，v6 v3，v4， v7 v3，v4， v7，v8 v3，v4，v5，v6，v9
v5 v5，v4， v1 v5，v2 v5，v4， v3 v5，v4 v5 v5，v6 v5，v4， v7 v5，v6， v9，v8 v5，v6，v9
As can be seen from tables 1 and 2, at this time, the shortest path to each intersection in the road network has been searched for at each source intersection, and the efficiency is obviously improved after the calculation is finished.

Claims (1)

1. A method for obtaining multisource shortest paths of an urban road network based on common calculation and dijkstra algorithm is characterized by comprising the following steps:
step 1: constructing an urban road network, defining parameters and initializing;
acquiring real-time road network data and obtaining an urban road network G ═ (V, A, W), V represents an intersection set, and V ═ V1,v2,v3,…,vi,…,vR}，viDenotes the ith intersection, i is 1,2,3, …, R is the total number of intersections in the urban road network G, a denotes the set of links between intersections, and a is { (v)i,vj)|i,j＝1,2,3,…,R}，(vi,vj) Indicates the ith intersection viTo the jth intersection vjW represents a set of weights for links between intersections, W ═ ωi,j|i,j＝1,2,3,…,R}，ωi,jAs directed links (v)i,vj) If the ith intersection viTo the jth intersection vjThere is a directed road section (v) in betweeni,vj) Then the jth intersection vjIs the ith intersection viAdjacent intersection, i-th intersection viFor the jth intersection vjAt a front-drive intersection of, and ωi,jNot less than 0; if the ith intersection viTo the jth intersection vjThere is no directed link (v) betweeni,vj) Then let ω bei,jInfinity, +,; defining the current iteration times as t;
step 2: acquiring a source point intersection set:
k source point intersections are selected and a source point intersection set V ' ═ V ' is formed 'k1,2, …, K, where v'kRepresenting the kth source point intersection in the source point intersection set V ', and enabling the kth source point intersection V'kThe serial number in the intersection set V is skI.e. by
Figure FDA0003361675270000011
Figure FDA0003361675270000012
Represents the s th in the intersection set VkAt each intersection, K is more than 1 and less than or equal to R;
and step 3: initializing the weights from the source point intersection to each intersection of the t iteration:
defining the kth source point intersection V ' in the source point intersection set V ' at the t iteration 'kThe ith intersection V in the intersection set ViThe upper bound of the weight of the shortest path of (1) is
Figure FDA0003361675270000013
And initialize
Figure FDA0003361675270000014
Is + ∞;
defining the kth source point intersection V 'in the source point intersection set V'kThe ith intersection V in the intersection set ViWeight of the shortest path of Pk(vi) And initializes Pk(vi) Is + ∞;
initializing t ═ 1;
initializing kth source point intersection v 'under the t iteration'kTo skIndividual intersection
Figure FDA0003361675270000015
The upper bound of the weight of the shortest path of (1) is
Figure FDA0003361675270000016
The kth source point intersection V ' in the source point intersection set V ' at the t iteration 'kTo skIndividual intersection
Figure FDA0003361675270000017
Has the weight of the shortest path of
Figure FDA0003361675270000018
And will bekIndividual intersection
Figure FDA0003361675270000019
Add to t-1 iterations before crossing v 'with the kth Source Point'kIntersection set for obtaining weight of shortest path for source point
Figure FDA0003361675270000021
And intersecting v 'with the k source point in the t-1 iteration'kIntersection set for obtaining weight of shortest path for source point
Figure FDA0003361675270000022
Definition of Lk,iRepresenting the kth source point intersection V 'in the source point intersection set V'kThe ith intersection V in the intersection set ViAnd initializing intersection sets of shortest paths
Figure FDA0003361675270000023
And 4, step 4: intersecting v 'with k source point in t-1 iterations'kIntersection set for obtaining weight of shortest path for source point
Figure FDA0003361675270000024
All intersections in (1) perform forward search and update the weight of the shortest path:
step 4.1: initializing k to 1;
step 4.2: crossing v 'with the kth source point if t-1 iterations ahead'kIntersection set for obtaining weight of shortest path for source point
Figure FDA0003361675270000025
In the intersection set VFor all the intersections in the source point intersection set V ', the kth source point intersection V ' is used 'kEnding the shortest path search of the source point, and turning to the step 6, otherwise, turning to the step 4.3;
step 4.3: initializing intersection v 'with k source point in t iteration'kIntersection set for obtaining weight of shortest path for source point
Figure FDA0003361675270000026
Recording the k source point intersection v 'in the t-1 iteration'kIntersection set for obtaining weight of shortest path for source point
Figure FDA0003361675270000027
The number of intersections in (1) is Mt-1(ii) a Taking out the m-th intersection and marking as
Figure FDA0003361675270000028
Order the m-th intersection
Figure FDA0003361675270000029
The serial number in the intersection set V is
Figure FDA00033616752700000210
Namely, it is
Figure FDA00033616752700000211
Step 4.3.1: initializing m to 1;
step 4.3.2: traverse the m-th intersection
Figure FDA00033616752700000212
And selecting all the adjacent intersections from the intersection set which does not belong to
Figure FDA00033616752700000213
And join into an adjacency set
Figure FDA00033616752700000214
Step 4.3.2.1: fetching contiguous collections
Figure FDA00033616752700000215
At the q-th intersection in (1), recording the adjacency set
Figure FDA00033616752700000216
Middle q intersection
Figure FDA00033616752700000217
The set of the front driving intersections is
Figure FDA00033616752700000218
Make the adjacent set
Figure FDA00033616752700000219
Middle q intersection
Figure FDA00033616752700000220
The serial number in the intersection set V is rqI.e. by
Figure FDA00033616752700000221
Step 4.3.2.2: initializing q to be 1;
step 4.3.2.3: traversing precursor intersection set
Figure FDA00033616752700000222
If all the intersections in (1) are set in the front-driving intersection
Figure FDA0003361675270000031
All intersections in (1) belong to the intersection v 'of the kth source point under the first t-1 iterations'kIntersection set for obtaining weight of shortest path for source point
Figure FDA0003361675270000032
Then step 4.4 is carried out, otherwise step 4.5 is carried out;
step 4.4: acquiring v 'from k-th source point intersection'kObtaining a k source point intersection v 'from all the precursor intersections'kThe shortest path weight of the intersection which is the weight of the shortest path of the source point:
step 4.4.1: precursor-memory intersection set
Figure FDA0003361675270000033
The number of the intersections in the tree is B, and a precursor intersection set is taken out
Figure FDA0003361675270000034
The b-th intersection in (1)
Figure FDA0003361675270000035
The serial number of the intersection in the intersection set V is nbI.e. by
Figure FDA0003361675270000036
Step 4.4.2: initializing b to be 1;
step 4.4.3: if it is
Figure FDA0003361675270000037
Then will be
Figure FDA0003361675270000038
Is assigned to
Figure FDA0003361675270000039
And memory forerunner intersection
Figure FDA00033616752700000310
Sequence number n of intersection set VbAssigning to the r-th in the intersection set VqIndividual intersection
Figure FDA00033616752700000311
Number n of temporary predecessor intersectionb,min(ii) a Wherein the content of the first and second substances,
Figure FDA00033616752700000312
represents the kth source point intersection v'kN-th in intersection set VbThe weight of the shortest path of each intersection,
Figure FDA00033616752700000313
represents the n-th in the intersection set VbIndividual intersection
Figure FDA00033616752700000314
To the r < th > rqIndividual intersection
Figure FDA00033616752700000315
The weight of (a) is determined,
Figure FDA00033616752700000316
represents the kth source point intersection v'kR-th in intersection set VqIndividual intersection
Figure FDA00033616752700000317
The weight of the shortest path of (1);
step 4.4.4: b +1 is assigned to B, the step 4.4.3 is carried out until B is equal to B, and therefore the k source point intersection v 'is output'kR-th in intersection set VqIndividual intersection
Figure FDA00033616752700000318
Weight of shortest path of
Figure FDA00033616752700000319
And number nb,minAnd will r beqIndividual intersection
Figure FDA00033616752700000320
Adding the source point intersection V ' to the kth source point intersection V ' in the source point intersection set V 'kN-th in intersection set Vb,minIndividual intersection
Figure FDA00033616752700000321
Intersection set of shortest paths of
Figure FDA00033616752700000322
Thereby obtaining the kth source point intersection V 'in the source point intersection set V'kR-th in intersection set VqIndividual intersection
Figure FDA00033616752700000323
Intersection set of shortest paths of
Figure FDA00033616752700000324
Namely, it is
Figure FDA00033616752700000325
Will r toqIndividual intersection
Figure FDA00033616752700000326
To k source point intersection v'kSet of weights to get the shortest path for a source point
Figure FDA00033616752700000327
And intersecting v 'with the k source point in the t iteration'kIntersection set for obtaining weight of shortest path for source point
Figure FDA00033616752700000328
Namely, it is
Figure FDA00033616752700000329
Figure FDA00033616752700000330
Turning to step 4.6;
step 4.5: if it is not
Figure FDA00033616752700000331
Then will be
Figure FDA00033616752700000332
Is assigned to
Figure FDA00033616752700000333
Otherwise, turning to step 4.6;
step 4.6: if Q is not equal to Q, assigning Q +1 to Q, and turning to step 4.3.2.3, otherwise, assigning M +1 to M, and judging that M is larger than Mt -1If yes, executing step 4.7; otherwise, turning to the step 4.3.2;
step 4.7: selecting an intersection with the minimum upper bound of the weight of the shortest path from the intersection set V under the t iteration
Figure FDA0003361675270000041
And is
Figure FDA0003361675270000042
Does not belong to the intersection v 'with the k source point under the previous t iterations'kIntersection set for obtaining weight of shortest path for source point
Figure FDA0003361675270000043
Namely, it is
Figure FDA0003361675270000044
If it is not
Figure FDA0003361675270000045
Then the kth source point is intersected by v'kThe ith in the intersection set VminIndividual intersection
Figure FDA0003361675270000046
Upper bound of weight of shortest path of
Figure FDA0003361675270000047
Assigning to k source point intersection v'kThe ith in the intersection set VminIndividual intersection
Figure FDA0003361675270000048
Weight of shortest path of
Figure FDA0003361675270000049
And will be the ithminIndividual intersection
Figure FDA00033616752700000410
Adding the source point intersection V ' to the kth source point intersection V ' in the source point intersection set V 'kThe first in the intersection set V
Figure FDA00033616752700000411
Individual intersection
Figure FDA00033616752700000412
Shortest path intersection set
Figure FDA00033616752700000413
Thereby obtaining the kth source point intersection V 'in the source point intersection set V'kThe ith in the intersection set VminIndividual intersection
Figure FDA00033616752700000414
Shortest path intersection set
Figure FDA00033616752700000415
Namely, it is
Figure FDA00033616752700000416
And will be the ithminIndividual intersection
Figure FDA00033616752700000417
Join to a collection
Figure FDA00033616752700000418
Intersection set
Figure FDA00033616752700000419
And 5: backtracking kth source point intersection v 'under the tth iteration'kSet of intersections
Figure FDA00033616752700000420
Shortest path at intersection (iii):
step 5.1: recording the intersection v 'with the k source point in the t iteration'kIntersection set for obtaining weight of shortest path for source point
Figure FDA00033616752700000421
The number of intersections in (1) is MtAnd taking out the m-th intersection as
Figure FDA00033616752700000422
And the m-th intersection
Figure FDA00033616752700000423
The serial number in the intersection set V is
Figure FDA00033616752700000424
Namely, it is
Figure FDA00033616752700000425
Step 5.2: initializing m to 1;
step 5.3: recording k source point intersection v'kThe first in the intersection set V
Figure FDA00033616752700000426
Individual intersection
Figure FDA00033616752700000427
Set of shortest path points of
Figure FDA00033616752700000428
The number of each intermediate crossing is EmAnd the serial number of the epsilon middle crossing in the crossing set V is recorded as rhoε；
Step 5.3.1: initializing epsilon to be 1;
step 5.3.2: if it is not
Figure FDA00033616752700000429
Then assume that
Figure FDA00033616752700000430
Simultaneously, the source point intersection V ' at the k ' th source point intersection in the source point intersection set V 'k′I.e. by
Figure FDA00033616752700000431
Then take the shortest path point set
Figure FDA00033616752700000432
Middle epsilon intersection
Figure FDA00033616752700000433
To Em+2 crossings
Figure FDA00033616752700000434
All intersections are used as k 'source point intersections v'k′The first in the intersection set V
Figure FDA00033616752700000435
Individual intersection
Figure FDA00033616752700000436
Shortest path intersection set
Figure FDA00033616752700000437
And will be
Figure FDA00033616752700000438
Is assigned to
Figure FDA00033616752700000439
If k' > k, then
Figure FDA00033616752700000440
Individual intersection
Figure FDA00033616752700000441
Add to t-1 previous iterations to intersect v ' at the k ' th source point 'k′Set of weights to get shortest path for source point
Figure FDA00033616752700000442
And the kth ' source point intersection v ' in the t-1 iterations 'k′Intersection set for obtaining weight of shortest path for source
Figure FDA00033616752700000443
Otherwise, it will be
Figure FDA00033616752700000444
Individual intersection
Figure FDA00033616752700000445
Add to k ' th Source Point intersection v ' of the previous t iterations 'k′Set of weights to get shortest path for source point
Figure FDA0003361675270000051
And intersecting v ' with the k ' source point in the t iteration 'k′Intersection set for obtaining weight of shortest path for source point
Figure FDA0003361675270000052
Step 5.3.3: judging E ═ EmIf yes, turning to step 5.4, otherwise, assigning epsilon +1 to epsilon, and turning to step 5.3.2;
step 5.4: judging M as MtIf yes, turning to step 6, otherwise, assigning m +1 to m, and turning to step 5.3;
step 6: judging whether K is true or not, if so, turning to a step 7, otherwise, assigning K +1 to K, and turning to a step 4.2;
and 7: and if the shortest path search with all the source point intersections as source points in the source point intersection set V 'under the previous t iterations is finished, indicating that the shortest path from each source point intersection in the source point intersection set V' to any one intersection in the intersection set V is obtained, otherwise, assigning t +1 to t, and turning to the step 4.
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