CN112991800B - Urban road network shortest path acquisition method based on angle limitation and bidirectional search - Google Patents

Urban road network shortest path acquisition method based on angle limitation and bidirectional search Download PDF

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CN112991800B
CN112991800B CN202110235456.6A CN202110235456A CN112991800B CN 112991800 B CN112991800 B CN 112991800B CN 202110235456 A CN202110235456 A CN 202110235456A CN 112991800 B CN112991800 B CN 112991800B
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intersection
boundary
search
backward
ith
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CN112991800A (en
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丁建勋
冯战雨
江宇鹏
周润东
丁卫东
满忠运
查菲菲
夏力
徐小明
龙建成
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Hefei University of Technology
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/09—Arrangements for giving variable traffic instructions
    • G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
    • G08G1/0968—Systems involving transmission of navigation instructions to the vehicle
    • G08G1/096805—Systems involving transmission of navigation instructions to the vehicle where the transmitted instructions are used to compute a route
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/09—Arrangements for giving variable traffic instructions
    • G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
    • G08G1/0968—Systems involving transmission of navigation instructions to the vehicle
    • G08G1/096833—Systems involving transmission of navigation instructions to the vehicle where different aspects are considered when computing the route

Abstract

The invention discloses a method for acquiring the shortest path of an urban road network based on angle limitation and bidirectional search, which comprises the following steps: 1. constructing an urban network by real-time road condition information; 2. introducing a forward search boundary internal and external intersection set Un F、
Figure DDA0002959834240000011
Set U of internal and external intersections of backward search boundaryn B、
Figure DDA0002959834240000012
The set of the two-way boundary intersections is MnUpper and lower bounds of travel time
Figure DDA0002959834240000013
T; 3. updating set U of internal and external intersections of set forward and backward search boundaryn F、
Figure DDA0002959834240000014
Un B、
Figure DDA0002959834240000015
4. Obtaining a set M of a starting point passing through a bidirectional boundary intersection by a label correction methodnThe shortest path from the intersection to the destination point; 5. shortest path travel time equal to lower bound of travel timeTOr searching the internal intersection set U of the boundary in the forward and backward directionsn F、Un BNo more updates are made, the shortest path is obtained, otherwise updates are made
Figure DDA0002959834240000016
And (6) turning to the step 3. The invention considers adding angle limitation and bidirectional search in the navigation of the urban road network, thereby effectively reducing the search range, improving the navigation efficiency and providing a faster and efficient driving path.

Description

Urban road network shortest path acquisition method based on angle limitation and bidirectional search
Technical Field
The invention belongs to the field of navigation optimization of the existing urban road network, and particularly relates to an urban road network shortest path acquisition method based on angle limitation and bidirectional search.
Background
With the development of society, the traffic navigation based on the internet brings more and more convenience to users, and the users can input own departure place and destination at the navigation starting stage, so that the automatically planned path of the navigation product can be obtained. However, as the quantity of retained urban automobiles gradually rises, the road network construction is relatively lagged, the traffic resources are wasted, and the traveling efficiency is low, so that inconvenience is brought to the traveling of urban residents, the urban operation efficiency is greatly reduced, and certain loss is caused to the economic development. Therefore, a path navigation method for improving the trip level and the urban road network utilization rate is required to be researched. With the development of the GPS, the network technology, and the computer technology, the conditions established by the vehicle navigation system have matured, and whether the road navigation of the vehicle can be realized within the urban road network range, so that the vehicle can quickly and smoothly reach the destination has become the target of the current research.
In the urban road network at the present stage, roads (express roads, main roads, secondary roads and branch roads) at various levels are crossed and mixed, road level factors seriously affect various aspects of navigation travel, navigation products at the present stage often cannot effectively utilize the factors in the navigation process so as to improve the timeliness of the navigation process, and the travel experience of drivers and the utilization efficiency of the urban road network are seriously affected. Furthermore; in a route searching stage in a specific navigation process, the existing route searching method is often used for performing route searching in a single direction from a starting point to an end point in a global scope according to real-time road network information, the traveling directionality of a driver in the navigation process is not considered in the route searching method, and the timeliness of the route searching in the navigation process and the matching degree with the travel intention of the driver are reduced.
Disclosure of Invention
The invention aims to solve the defects of the prior art and provides an urban road network shortest path acquisition method based on angle limitation and bidirectional search, so that directional induction and angle limitation can be added in urban road network navigation to reduce the search range, and the path search efficiency is improved through bidirectional search, so that the navigation efficiency can be improved, a more humanized and efficient shortest path is provided for a driver, and the driving process is more efficient.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a method for acquiring the shortest path of an urban road network based on angle limitation and bidirectional search, which is characterized by comprising the following steps of:
step 1: constructing an urban road network and acquiring plane coordinates of any intersection;
acquiring real-time road network data and obtaining an urban road network G ═ (V, A), wherein V represents an intersection set, and V ═ V1,v2,…,vq,…,vQ}，vqRepresents the Q-th intersection, Q is 1,2, …, Q; q denotes the total number of intersections, a denotes the set of links between intersections, and a ═ aij＝(vi,vj)|i,j＝1,2,...Q}，aijIndicates the ith intersection viAt the j intersection vjA road section in between, and aij∈{A1,A2,A3,A4In which A is1Denotes the expressway, A2Denotes the main road, A3Denotes the secondary artery, A4Representing a branch; let road section aijHas a time weight attribute of tijAnd is and
Figure GDA0003365319500000021
dijrepresenting a road section aijLength of (v)ijRepresenting a road section aijExpected traffic speed of the vehicle; if the ith intersection viAt the j intersection vjIf there is no road section in between, let tij＝+∞；
Obtaining the ith intersection v in the urban road according to the real-time road network dataiHas a plane coordinate of (x)i,yi) And j-th intersection vjHas a plane coordinate of (x)j,yj) Then the ith intersection viAt the j intersection vjThe road section vector between
Figure GDA0003365319500000022
Step 2: suppose that the starting point of the driver is the s-th intersection and the destination point is the t-th intersection vtTaking the driving direction from the starting point to the destination point as a forward searching direction, taking the driving direction from the destination point to the starting point as a backward searching direction, and setting the limited angle of the path search to be alpha, wherein the alpha is more than or equal to 0 and less than or equal to pi;
and step 3: defining parameters and initializing;
step 3.1: defining basic parameters:
defining n as the current iteration number, the s-th intersection v of the n-th iterationsTo the jth intersection vjThe shortest travel time of Tn(vs,vj) (ii) a Defining the s-th intersection vsV at the t-th intersectiontIs recorded as the Euclidean distance of lstDefinition of vmaxDefining the s-th intersection v for the maximum speed of travel in all road section typessTo the t-th intersection vtThe theoretical minimum travel time of
Figure GDA0003365319500000023
And is used as the lower bound of travel time; defining an intersection v of the starting point of the nth iterationsCrossing with destination pointMouth vtThe shortest travel time therebetween is Tn(vs,vt) And as an upper bound on travel time
Figure GDA00033653195000000212
Step 3.2: defining forward search parameters:
defining the forward search boundary internal intersection set of the nth iteration as
Figure GDA0003365319500000024
Defining the forward search boundary external intersection set of the nth iteration as
Figure GDA0003365319500000025
Defining forward search expansion boundary intersection set as
Figure GDA0003365319500000026
Step 3.3: defining a backward search parameter:
defining the set of internal intersections of the backward search boundary of the nth iteration as
Figure GDA0003365319500000027
Defining the set of backward search boundary external intersections of the nth iteration as
Figure GDA0003365319500000028
Defining a backward search expansion boundary intersection set as
Figure GDA0003365319500000029
Step 3.4: defining the set of bidirectional boundary intersections of the nth iteration as
Figure GDA00033653195000000210
Defining a boundary internal intersection for the nth iteration
Figure GDA00033653195000000211
Step 3.5: initializing parameters:
the initialization n is equal to 1 and the initialization is carried out,
Figure GDA0003365319500000031
and 4, step 4: updating the forward search boundary internal intersection set of the nth iteration
Figure GDA0003365319500000032
Forward search boundary external intersection set
Figure GDA0003365319500000033
Backward search boundary internal intersection set
Figure GDA0003365319500000034
Backward search boundary external intersection set
Figure GDA0003365319500000035
Step 4.1: updating the forward search boundary internal intersection set of the nth iteration
Figure GDA0003365319500000036
And assembling to search for intersections outside the boundary
Figure GDA0003365319500000037
Will satisfy ask＝(vs,vk) The kth intersection v of epsilon AkAs a neighbor intersection; and traversing the s-th intersection vsAll neighbors of, if
Figure GDA0003365319500000038
If it is true, then
Figure GDA0003365319500000039
Is assigned to
Figure GDA00033653195000000310
Will be the kthV. intersectionkJoining extended boundary intersection sets
Figure GDA00033653195000000311
Otherwise, it will
Figure GDA00033653195000000312
Is assigned to
Figure GDA00033653195000000313
Wherein the content of the first and second substances,
Figure GDA00033653195000000314
indicates the s-th intersection vsAnd the k-th intersection vkThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000000315
indicates the s-th intersection vsAnd the t-th intersection vtA road segment vector in between;
step 4.2: updating the set of backward search boundary internal intersections of the nth iteration
Figure GDA00033653195000000316
And backward searching boundary external intersection set
Figure GDA00033653195000000317
Will satisfy alt＝(vl,vt) The ith intersection v of E AlAs a neighbor intersection; traversing the t-th intersection vtAll neighbors of, if
Figure GDA00033653195000000318
If it is true, then
Figure GDA00033653195000000319
Is assigned to
Figure GDA00033653195000000320
The first crossing vlJoining extended boundary intersection setsCombination of Chinese herbs
Figure GDA00033653195000000321
Otherwise, it will
Figure GDA00033653195000000322
Is assigned to
Figure GDA00033653195000000323
Wherein the content of the first and second substances,
Figure GDA00033653195000000324
indicates the t-th intersection vtAnd the l-th intersection vlThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000000325
indicates the t-th intersection vtAnd the s-th intersection vsA road segment vector in between;
and 5: if the boundary intersection set is expanded
Figure GDA00033653195000000326
Step 6 is carried out, otherwise, the forward search boundary internal intersection set of the nth iteration is continuously updated according to step 5.1 and step 5.2
Figure GDA00033653195000000327
Forward search boundary external intersection set
Figure GDA00033653195000000328
Backward search boundary internal intersection set
Figure GDA00033653195000000329
Backward search boundary external intersection set
Figure GDA00033653195000000330
Step 5.1: continuously updating the forward search boundary internal intersection set of the nth iteration
Figure GDA00033653195000000331
And n iteration of forward search boundary outer intersection set
Figure GDA00033653195000000332
Step 5.1.1: judging forward search expansion boundary intersection set
Figure GDA00033653195000000333
Middle ith intersection vi：
Step 5.1.2: will satisfy aij＝(vi,vj) J th intersection v of epsilon AjAs a neighbor intersection, and
Figure GDA00033653195000000334
traversing the ith intersection viAll neighbors of, if
Figure GDA0003365319500000041
If it is true, then
Figure GDA0003365319500000042
Is assigned to
Figure GDA0003365319500000043
The ith intersection viExpanding set of boundary intersections from forward search
Figure GDA0003365319500000044
Is deleted, will
Figure GDA0003365319500000045
Is assigned to
Figure GDA0003365319500000046
And executing step 5.1.3; wherein the content of the first and second substances,
Figure GDA0003365319500000047
indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,
Figure GDA0003365319500000048
indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between; otherwise, it will
Figure GDA0003365319500000049
Is assigned to
Figure GDA00033653195000000410
The ith intersection viExpanding set of boundary intersections from forward search
Figure GDA00033653195000000411
Deleting; and judging a forward search extended boundary intersection set according to the process of the step 5.1.2
Figure GDA00033653195000000412
The next intersection in;
step 5.1.3: judging forward search expansion boundary intersection set according to the process of step 5.1.2
Figure GDA00033653195000000413
J-th intersection v in (1)j；
Step 5.2: continuously updating the set of backward search boundary internal intersections of the nth iteration
Figure GDA00033653195000000414
And n iteration backward search boundary external intersection set
Figure GDA00033653195000000415
Step 5.2.1: judging backward search expansion boundary intersection set
Figure GDA00033653195000000416
Middle m crossing vm：
Step 5.2.2: will satisfy amn＝(vm,vn) N-th intersection v of E AnAs a neighbor intersection, and
Figure GDA00033653195000000417
traversing the m-th intersection vmAll neighbors of, if
Figure GDA00033653195000000418
Then will be
Figure GDA00033653195000000419
Is assigned to
Figure GDA00033653195000000420
The m-th intersection vmExpanding set of boundary intersections by backward search
Figure GDA00033653195000000421
Is deleted, will
Figure GDA00033653195000000422
Is assigned to
Figure GDA00033653195000000423
And step 5.2.3 is executed; wherein the content of the first and second substances,
Figure GDA00033653195000000424
represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000000425
represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between; otherwise, it will
Figure GDA00033653195000000426
Is assigned to
Figure GDA00033653195000000427
The m-th intersection vmExpanding set of boundary intersections by backward search
Figure GDA00033653195000000428
Deleting; and judging and then searching and expanding the boundary intersection set according to the process of the step 5.2.2
Figure GDA00033653195000000429
The next intersection in;
step 5.2.3: searching and expanding the boundary intersection set after judging according to the process of the step 5.2.2
Figure GDA00033653195000000430
At the n-th intersection vn；
Step 6: updating the set M of the bidirectional boundary intersection of the nth iterationnAnd obtaining a bidirectional boundary intersection set M subjected to nth iterationnThe shortest travel time of the inner intersection;
step 6.1: intersection v for obtaining departure point by label correction methodsForward search boundary internal intersection set up to nth iteration
Figure GDA0003365319500000051
The shortest travel time and the shortest path of any intersection, wherein the intersection v of the starting pointsSet M of bidirectional boundary intersections for the nth iterationnThe kth intersection vkThe shortest travel time of Tn(vs,vk)；
Step 6.2: intersection v of destination point obtained by label correction methodtBackward search boundary internal intersection set for nth iteration
Figure GDA0003365319500000052
The shortest travel time and the shortest path of any intersection, wherein the intersection v of the destination pointtSet M of bidirectional boundary intersections for the nth iterationnThe kth intersection vkThe shortest travel time of Tn(vt,vk)；
Step 6.3: traversing nth iteration bidirectional boundary intersection set MnInner k-th intersection vkThen the intersection v of the departure pointsIntersection v to destination pointtMinimum travel time of
Figure GDA0003365319500000053
Step 6.4: determining travel time optimality and updating an upper travel time bound
Figure GDA0003365319500000054
Step 6.4.1: if T isn(vs,vt) If T, the step is carried out, and step 12 is carried out; otherwise, go to step 6.4.2;
step 6.4.2: the s th intersection vsTo the t-th intersection vtUpper time bound of
Figure GDA00033653195000000526
Is updated to
Figure GDA0003365319500000055
Boundary intersection is expanded by forward and backward search
Figure GDA0003365319500000056
Turning to step 7;
and 7: based on travel time upper bound
Figure GDA00033653195000000525
Continuously updating the forward search boundary internal intersection set of the nth iteration
Figure GDA0003365319500000057
Forward search boundary external intersection set
Figure GDA0003365319500000058
Backward search boundary internal intersection set
Figure GDA0003365319500000059
Backward search boundary external intersection set
Figure GDA00033653195000000510
Step 7.1: based on travel time upper bound
Figure GDA00033653195000000511
Continuously updating the forward search boundary internal intersection set of the nth iteration
Figure GDA00033653195000000512
And forward search boundary external intersection set
Figure GDA00033653195000000513
Forward search boundary outer intersection set for nth iteration
Figure GDA00033653195000000514
At the ith intersection viFrom the intersection v of the departure pointsTo the ith intersection viI th intersection viIntersection v to destination pointtThe sum of the theoretical shortest travel time of the two is
Figure GDA00033653195000000515
Wherein lsiIndicates the s-th intersection vsV at the ith intersectioniOf Euclidean distance,/, ofitIndicates the ith intersection viV at the t-th intersectiontThe Euclidean distance of (c); if it is not
Figure GDA00033653195000000527
Then will be
Figure GDA00033653195000000516
Is assigned to
Figure GDA00033653195000000517
The ith intersection viAdding intoForward search extended boundary intersection set
Figure GDA00033653195000000518
The ith intersection viSearching boundary external intersection set from forward direction
Figure GDA00033653195000000519
Deleting to obtain updated forward search boundary external intersection set
Figure GDA00033653195000000520
Otherwise, the ith intersection v is usediSearching boundary external intersection set from forward direction
Figure GDA00033653195000000521
Deleting to obtain updated forward boundary external intersection set
Figure GDA00033653195000000522
Step 7.2: based on travel time upper bound
Figure GDA00033653195000000523
Continuously updating the set of backward search boundary internal intersections of the nth iteration
Figure GDA00033653195000000524
And backward searching boundary external intersection set
Figure GDA0003365319500000061
Set of backward search boundary external intersections for nth iteration
Figure GDA0003365319500000062
M th intersection v in (1)mFrom the intersection v of the departure pointsTo the m-th intersection vmAnd the m-th intersection vmIntersection v to destination pointtThe sum of the theoretical shortest travel time of the two is
Figure GDA0003365319500000063
Wherein lsmIndicates the s-th intersection vsV at the m-th intersectionmOf Euclidean distance,/, ofmtRepresents the m-th intersection vmV at the t-th intersectiontThe Euclidean distance of (c); if it is not
Figure GDA0003365319500000064
Then will be
Figure GDA0003365319500000065
Is assigned to
Figure GDA0003365319500000066
The ith intersection viAdding backward search to expand boundary intersection set
Figure GDA0003365319500000067
The ith intersection viSearching boundary external intersection set from backward direction
Figure GDA0003365319500000068
Deleting to obtain updated backward search boundary external intersection set
Figure GDA0003365319500000069
Otherwise, the ith intersection v is usediSearching boundary external intersection set from backward direction
Figure GDA00033653195000000610
Deleting to obtain an updated backward boundary external intersection set
Figure GDA00033653195000000611
And 8: based on travel time upper bound
Figure GDA00033653195000000612
Continuously updating the forward search boundary internal intersection set of the (n + 1) th iteration
Figure GDA00033653195000000613
Forward search boundary external intersection set
Figure GDA00033653195000000614
Backward search boundary internal intersection set
Figure GDA00033653195000000615
Backward search boundary external intersection set
Figure GDA00033653195000000616
Step 8.1: based on travel time upper bound
Figure GDA00033653195000000617
Continuously updating the forward search boundary internal intersection set of the (n + 1) th iteration
Figure GDA00033653195000000618
And forward search boundary external intersection set
Figure GDA00033653195000000619
Sequential judgment of forward search expansion boundary intersection set
Figure GDA00033653195000000620
Middle ith intersection viGo through the ith intersection viAt a neighboring intersection, i.e. satisfy aij＝(vi,vj) The j crossing v of the epsilon Aj，
Figure GDA00033653195000000621
And is
Figure GDA00033653195000000622
J th intersection vjIf, if
Figure GDA00033653195000000623
And is
Figure GDA00033653195000000624
The ith intersection viExpanding set of boundary intersections from forward search
Figure GDA00033653195000000625
Is deleted, will
Figure GDA00033653195000000626
Is assigned to
Figure GDA00033653195000000627
Otherwise, the ith intersection v is usediExpanding set of boundary intersections from forward search
Figure GDA00033653195000000628
Is deleted, will
Figure GDA00033653195000000629
Is assigned to
Figure GDA00033653195000000630
Wherein the content of the first and second substances,
Figure GDA00033653195000000631
indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000000632
indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between;
step 8.2: based on travel time upper bound
Figure GDA00033653195000000633
Continuously updating the backward search boundary internal intersection set of the (n + 1) th iteration
Figure GDA00033653195000000634
Searching in harmony directionCable boundary external intersection set
Figure GDA00033653195000000635
Sequential judgment backward search expansion boundary intersection set
Figure GDA00033653195000000636
Middle m crossing vmGo through the m-th intersection vmAt a neighboring intersection, i.e. satisfy amn＝(vm,vn) The mth intersection v belonging to the group Am，
Figure GDA00033653195000000637
And is
Figure GDA00033653195000000638
N th intersection vnIf, if
Figure GDA0003365319500000071
And is
Figure GDA0003365319500000072
The m-th intersection vmExpanding set of boundary intersections by backward search
Figure GDA0003365319500000073
Is deleted, will
Figure GDA0003365319500000074
Is assigned to
Figure GDA0003365319500000075
Otherwise, the m-th intersection vmExpanding set of boundary intersections by backward search
Figure GDA0003365319500000076
Is deleted, will
Figure GDA0003365319500000077
Is assigned to
Figure GDA0003365319500000078
Wherein the content of the first and second substances,
Figure GDA0003365319500000079
represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000000710
represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between;
step 8.3: updating the n +1 th iteration bidirectional boundary intersection set
Figure GDA00033653195000000711
And step 9: judge Un+1＝UnIf yes, executing step 10; otherwise, assigning n +1 to n, and turning to step 6;
step 10: if n is 1, the final shortest travel time is T*＝TAnd if not, the step (B),
Figure GDA00033653195000000712
compared with the prior art, the invention has the beneficial effects that:
1. the method can effectively combine the characteristics of the urban road network at the present stage, traverse the intersection and road section information in the urban road network at the initial navigation stage, and integrate the road section grade, the road section length and the intersection information into the navigation path searching stage, thereby providing an optimal path planning scheme for the user, saving the travel time of the user and improving the utilization efficiency of the urban road network.
2. The search range of the current common method for seeking the shortest path, such as Dijkstra, is global, and for an urban road network, the search range becomes very large when the distance from the departure point to the destination point is large, and a driver may take many return paths or curved paths. The invention considers that the directional induction is added in the urban road network navigation to reduce the search range and the bidirectional search is respectively carried out by the departure point and the destination point, thereby improving the navigation efficiency, providing a more humanized and comfortable shortest path for the driver and leading the driving process to be more efficient.
3. The method for acquiring the shortest path of the urban road network is carried out in a certain range, the search range is defined as a boundary internal intersection set, a boundary external intersection set is defined at the same time, intersections which are to be added into the boundary internal intersection set are included in the boundary external intersection set, the two sets are continuously updated by meeting angle limiting conditions and being smaller than the upper limit of travel time, intersections in the boundary internal intersection set form a similar semielliptical area, the semielliptical area is gradually enlarged, and when the semielliptical area is not enlarged, the algorithm is stopped, so that the efficiency of path search can be greatly improved, and the navigation process is more efficient and faster.
4. The invention overcomes the problems that the timeliness of the route search and the matching degree with the intention of the driver are not considered in the route search stage of the existing navigation method, in the route search stage, the adjustable advancing direction angle alpha is limited as one of the constraint conditions for screening the road sections, and the bidirectional search of the road sections is carried out; the path search angle limit α may be divided into directional search angles αFAngle alpha with the backward searchBCarrying out analysis; current forward search angle alphaFAngle alpha with the backward searchBWhen not equal, when αF＝π，α B0, the algorithm degenerates to the standard unidirectional Dijkstra algorithm (forward); when alpha isF＝0，αBPi, the algorithm degenerates to the standard unidirectional Dijkstra algorithm (inverse); current forward search angle limit alphaFWith backward search angle limit alphaBAre equal, αF＝π，αBPi, the algorithm degenerates to the standard bidirectional Dijkstra algorithm, and the driver can select the shortest path according to own will by selecting the search angle alpha, so that the timeliness of path search can be improved, and the use experience of the driver is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of an assembly of internal and external intersections of a search boundary before and after initialization according to the present invention;
FIG. 3 is a set of expanded views of internal and external intersections of a bi-directional starting boundary for a departure point intersection and a destination point intersection, respectively, in accordance with the present invention;
FIG. 4 is a schematic view of the stepwise expansion of the set of internal and external intersections within the forward and backward search boundaries in accordance with the present invention;
FIG. 5 is a schematic diagram of an nth iteration bidirectional boundary intersection set preliminarily formed in accordance with the present invention;
FIG. 6 is a schematic diagram of the shortest travel path of a preliminarily formed boundary intersection set resembling two semi-ellipses according to the present invention;
FIG. 7 is a schematic diagram of a set of external intersections and a set of bidirectional boundary intersections within a forward and backward search boundary for an nth iteration based on an upper bound of travel time;
FIG. 8 is a schematic diagram of the shortest travel path of a set of two boundary internal intersections similar to semiellipses finally formed by the present invention;
FIG. 9 is a schematic diagram illustrating the path search range of the currently commonly used forward Dijkstra algorithm;
FIG. 10 is a schematic diagram illustrating a path search range of a conventional reverse Dijkstra algorithm;
FIG. 11 is a schematic diagram of the path search range of the bi-directional Dijkstra algorithm of the present invention;
fig. 12 is a schematic diagram of the path search range of the bidirectional E-algorithm proposed in the present invention.
Detailed Description
In this embodiment, since the shortest path obtaining method of the present invention always searches for paths from front to back in two local regions having similar semi-elliptical (Half-Ellipse) boundaries, the shortest path obtaining method of the present invention may be referred to as a bidirectional E algorithm for short. Specifically, as shown in fig. 1, a method for obtaining the shortest path of an urban road network based on angle limitation and bidirectional search is performed according to the following steps:
step 1: constructing an urban road network and acquiring plane coordinates of any intersection;
acquiring real-time road network data and obtaining an urban road network G ═ (V, A), wherein V represents an intersection set, and V ═ V1,v2,…,vq,…,vQ}，vqRepresents the Q-th intersection, Q is 1,2, …, Q; q denotes the total number of intersections, a denotes the set of links between intersections, and a ═ aij＝(vi,vj)|i,j＝1,2,...Q}，aijIndicates the ith intersection viAt the j intersection vjA road section in between, and aij∈{A1,A2,A3,A4In which A is1Denotes the expressway, A2Denotes the main road, A3Denotes the secondary artery, A4Representing a branch; let road section aijHas a time weight attribute of tijAnd is and
Figure GDA0003365319500000091
dijrepresenting a road section aijLength of (v)ijRepresenting a road section aijExpected traffic speed of the vehicle; if the ith intersection viAt the j intersection vjIf there is no road section in between, let tij＝+∞；
Obtaining the ith intersection v in the urban road according to the real-time road network dataiHas a plane coordinate of (x)i,yi) And j-th intersection vjHas a plane coordinate of (x)j,yj) Then the ith intersection viAt the j intersection vjThe road section vector between
Figure GDA0003365319500000092
Step 2: suppose that the starting point of the driver is the s-th intersection and the destination point is the t-th intersection vtTaking the driving direction from the starting point to the destination point as a forward searching direction, taking the driving direction from the destination point to the starting point as a backward searching direction, and setting the limited angle of the path search to be alpha, wherein the alpha is more than or equal to 0 and less than or equal to pi;
and step 3: defining parameters and initializing;
step 3.1: defining basic parameters:
defining n as the current iteration number, the s-th intersection v of the n-th iterationsTo the jth intersection vjThe shortest travel time of Tn(vs,vj) (ii) a Defining the s-th intersection vsV at the t-th intersectiontIs recorded as the Euclidean distance of lstDefinition of vmaxDefining the s-th intersection v for the maximum speed of travel in all road section typessTo the t-th intersection vtThe theoretical minimum travel time of
Figure GDA0003365319500000093
And is used as the lower bound of travel time; defining an intersection v of the starting point of the nth iterationsAnd a destination pointtThe shortest travel time therebetween is Tn(vs,vt) And as an upper bound on travel time
Figure GDA0003365319500000094
Step 3.2: defining forward search parameters:
defining the forward search boundary internal intersection set of the nth iteration as
Figure GDA0003365319500000095
Defining the forward search boundary external intersection set of the nth iteration as
Figure GDA0003365319500000096
Defining forward search expansion boundary intersection set as
Figure GDA0003365319500000097
Step 3.3: defining a backward search parameter:
defining the set of internal intersections of the backward search boundary of the nth iteration as
Figure GDA0003365319500000098
Definition of nThe backward search boundary external intersection set of the sub-iteration is
Figure GDA0003365319500000099
Defining a backward search expansion boundary intersection set as
Figure GDA00033653195000000910
Step 3.4: defining the set of bidirectional boundary intersections of the nth iteration as
Figure GDA00033653195000000911
Defining a boundary internal intersection for the nth iteration
Figure GDA00033653195000000912
Step 3.5: initializing parameters:
the initialization n is equal to 1 and the initialization is carried out,
Figure GDA0003365319500000101
as shown in fig. 2, a circle represents a general intersection, a square represents a forward search boundary internal intersection, and a diamond represents a backward search boundary internal intersection;
and 4, step 4: updating the forward search boundary internal intersection set of the nth iteration
Figure GDA0003365319500000102
Forward search boundary external intersection set
Figure GDA0003365319500000103
Backward search boundary internal intersection set
Figure GDA0003365319500000104
Backward search boundary external intersection set
Figure GDA0003365319500000105
As shown in FIG. 3, the hexagons represent the intersection outside the forward search boundary and the parallelograms representBackward searching boundary external intersection, and enabling the s-th intersection v meeting the angle limiting conditionsThe neighbor intersection is added into the n iteration forward search boundary internal intersection set
Figure GDA0003365319500000106
Otherwise, adding the intersection set to the forward search boundary external intersection set of the nth iteration
Figure GDA0003365319500000107
The t-th intersection v meeting the angle limiting conditiontThe neighbor intersection is added into the n iteration forward search boundary internal intersection set
Figure GDA0003365319500000108
Otherwise, adding the intersection set to the forward search boundary external intersection set of the nth iteration
Figure GDA0003365319500000109
Step 4.1: updating the forward search boundary internal intersection set of the nth iteration
Figure GDA00033653195000001010
And assembling to search for intersections outside the boundary
Figure GDA00033653195000001011
Will satisfy ask＝(vs,vk) The kth intersection v of epsilon AkAs a neighbor intersection; and traversing the s-th intersection vsAll neighbors of, if
Figure GDA00033653195000001012
If it is true, then
Figure GDA00033653195000001013
Is assigned to
Figure GDA00033653195000001014
Will be the kthV. intersectionkJoining extended boundary intersection sets
Figure GDA00033653195000001015
Otherwise, it will
Figure GDA00033653195000001016
Is assigned to
Figure GDA00033653195000001017
Wherein the content of the first and second substances,
Figure GDA00033653195000001018
indicates the s-th intersection vsAnd the k-th intersection vkThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000001019
indicates the s-th intersection vsAnd the t-th intersection vtA road segment vector in between;
step 4.2: updating the set of backward search boundary internal intersections of the nth iteration
Figure GDA00033653195000001020
And backward searching boundary external intersection set
Figure GDA00033653195000001021
Will satisfy alt＝(vl,vt) The ith intersection v of E AlAs a neighbor intersection; traversing the t-th intersection vtAll neighbors of, if
Figure GDA00033653195000001022
If it is true, then
Figure GDA00033653195000001023
Is assigned to
Figure GDA00033653195000001024
The first crossing vlJoining extended boundary intersection setsCombination of Chinese herbs
Figure GDA00033653195000001025
Otherwise, it will
Figure GDA00033653195000001026
Is assigned to
Figure GDA00033653195000001027
Wherein the content of the first and second substances,
Figure GDA00033653195000001028
indicates the t-th intersection vtAnd the l-th intersection vlThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000001029
indicates the t-th intersection vtAnd the s-th intersection vsA road segment vector in between;
and 5: if the boundary intersection set is expanded
Figure GDA00033653195000001030
Step 6 is carried out, otherwise, as shown in fig. 4, the set of internal intersections of the forward search boundary of the nth iteration is continuously updated according to step 5.1 and step 5.2
Figure GDA0003365319500000111
Forward search boundary external intersection set
Figure GDA0003365319500000112
Backward search boundary internal intersection set
Figure GDA0003365319500000113
Backward search boundary external intersection set
Figure GDA0003365319500000114
Step 5.1: continuously updating the forward search boundary internal intersection set of the nth iteration
Figure GDA0003365319500000115
And n iteration of forward search boundary outer intersection set
Figure GDA0003365319500000116
Step 5.1.1: judging forward search expansion boundary intersection set
Figure GDA0003365319500000117
Middle ith intersection vi：
Step 5.1.2: will satisfy aij＝(vi,vj) J th intersection v of epsilon AjAs a neighbor intersection, and
Figure GDA0003365319500000118
traversing the ith intersection viAll neighbors of, if
Figure GDA0003365319500000119
If it is true, then
Figure GDA00033653195000001110
Is assigned to
Figure GDA00033653195000001111
The ith intersection viExpanding set of boundary intersections from forward search
Figure GDA00033653195000001112
Is deleted, will
Figure GDA00033653195000001113
Is assigned to
Figure GDA00033653195000001114
And executing step 5.1.3; wherein the content of the first and second substances,
Figure GDA00033653195000001115
indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000001116
indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between; otherwise, it will
Figure GDA00033653195000001117
Is assigned to
Figure GDA00033653195000001118
The ith intersection viExpanding set of boundary intersections from forward search
Figure GDA00033653195000001119
Deleting; and judging a forward search extended boundary intersection set according to the process of the step 5.1.2
Figure GDA00033653195000001120
The next intersection in;
step 5.1.3: judging forward search expansion boundary intersection set according to the process of step 5.1.2
Figure GDA00033653195000001121
J-th intersection v in (1)j；
Step 5.2: continuously updating the set of backward search boundary internal intersections of the nth iteration
Figure GDA00033653195000001134
And n iteration backward search boundary external intersection set
Figure GDA00033653195000001122
Step 5.2.1: judging backward search expansion boundary intersection set
Figure GDA00033653195000001123
Middle m crossing vm：
Step 5.2.2: will satisfy amn＝(vm,vn) N-th intersection v of E AnAs a neighbor intersection, and
Figure GDA00033653195000001124
traversing the m-th intersection vmAll neighbors of, if
Figure GDA00033653195000001125
Then will be
Figure GDA00033653195000001126
Is assigned to
Figure GDA00033653195000001127
The m-th intersection vmExpanding set of boundary intersections by backward search
Figure GDA00033653195000001128
Is deleted, will
Figure GDA00033653195000001129
Is assigned to
Figure GDA00033653195000001130
And step 5.2.3 is executed; wherein the content of the first and second substances,
Figure GDA00033653195000001131
represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000001132
represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between; otherwise, it will
Figure GDA00033653195000001133
Is assigned to
Figure GDA0003365319500000121
Will m beV. of each intersectionmExpanding set of boundary intersections by backward search
Figure GDA0003365319500000122
Deleting; and judging and then searching and expanding the boundary intersection set according to the process of the step 5.2.2
Figure GDA0003365319500000123
The next intersection in;
step 5.2.3: searching and expanding the boundary intersection set after judging according to the process of the step 5.2.2
Figure GDA0003365319500000124
At the n-th intersection vn(ii) a As shown in fig. 5, the arrowhead shape represents a bidirectional boundary intersection, and an nth iteration bidirectional boundary intersection set M is formed preliminarilyn；
Step 6: updating the set M of the bidirectional boundary intersection of the nth iterationnAnd obtaining a bidirectional boundary intersection set M subjected to nth iterationnThe shortest travel time of the inner intersection;
step 6.1: intersection v for obtaining departure point by label correction methodsForward search boundary internal intersection set up to nth iteration
Figure GDA0003365319500000125
The shortest travel time and the shortest path of any intersection, wherein the intersection v of the starting pointsSet M of bidirectional boundary intersections for the nth iterationnThe kth intersection vkThe shortest travel time of Tn(vs,vk)；
Step 6.2: intersection v of destination point obtained by label correction methodtBackward search boundary internal intersection set for nth iteration
Figure GDA0003365319500000126
The shortest travel time and the shortest path of any intersection, wherein the intersection v of the destination pointtTo the nth iterationBidirectional boundary intersection set MnThe kth intersection vkThe shortest travel time of Tn(vt,vk)；
Step 6.3: as shown in fig. 6, the black squares represent intersections in the optimal path, the shortest travel path of the intersection set inside the boundary of two similar semiellipses is obtained preliminarily, and the bidirectional boundary intersection set M of the nth iteration is traversednInner k-th intersection vkThen the intersection v of the departure pointsIntersection v to destination pointtMinimum travel time of
Figure GDA0003365319500000127
Step 6.4: determining travel time optimality and updating an upper travel time bound
Figure GDA0003365319500000128
Step 6.4.1: if T isn(vs,vt)＝TThen go to step 12; otherwise, go to step 6.4.2;
step 6.4.2: the s th intersection vsTo the t-th intersection vtUpper time bound of
Figure GDA0003365319500000129
Is updated to
Figure GDA00033653195000001210
Boundary intersection is expanded by forward and backward search
Figure GDA00033653195000001211
Turning to step 7;
and 7: as shown in fig. 7, based on the upper bound of travel time
Figure GDA00033653195000001212
Continuously updating the forward search boundary internal intersection set of the nth iteration
Figure GDA00033653195000001213
Forward search boundary external intersection set
Figure GDA00033653195000001214
Backward search boundary internal intersection set
Figure GDA00033653195000001215
Backward search boundary external intersection set
Figure GDA00033653195000001216
Step 7.1: based on travel time upper bound
Figure GDA00033653195000001217
Continuously updating the forward search boundary internal intersection set of the nth iteration
Figure GDA00033653195000001218
And forward search boundary external intersection set
Figure GDA00033653195000001219
Forward search boundary outer intersection set for nth iteration
Figure GDA0003365319500000131
At the ith intersection viFrom the intersection v of the departure pointsTo the ith intersection viI th intersection viIntersection v to destination pointtThe sum of the theoretical shortest travel time of the two is
Figure GDA0003365319500000132
Wherein lsiIndicates the s-th intersection vsV at the ith intersectioniOf Euclidean distance,/, ofitIndicates the ith intersection viV at the t-th intersectiontThe Euclidean distance of (c); if it is not
Figure GDA0003365319500000133
Then will be
Figure GDA0003365319500000134
Is assigned to
Figure GDA0003365319500000135
The ith intersection viAdding forward search expansion boundary intersection set
Figure GDA0003365319500000136
The ith intersection viSearching boundary external intersection set from forward direction
Figure GDA0003365319500000137
Deleting to obtain updated forward search boundary external intersection set
Figure GDA0003365319500000138
Otherwise, the ith intersection v is usediSearching boundary external intersection set from forward direction
Figure GDA0003365319500000139
Deleting to obtain updated forward boundary external intersection set
Figure GDA00033653195000001310
Step 7.2: based on travel time upper bound
Figure GDA00033653195000001311
Continuously updating the set of backward search boundary internal intersections of the nth iteration
Figure GDA00033653195000001312
And backward searching boundary external intersection set
Figure GDA00033653195000001313
Set of backward search boundary external intersections for nth iteration
Figure GDA00033653195000001314
M th intersection v in (1)mFrom the intersection v of the departure pointsTo the m-th intersection vmAnd the m-th intersection vmIntersection v to destination pointtThe sum of the theoretical shortest travel time of the two is
Figure GDA00033653195000001315
Wherein lsmIndicates the s-th intersection vsV at the m-th intersectionmOf Euclidean distance,/, ofmtRepresents the m-th intersection vmV at the t-th intersectiontThe Euclidean distance of (c); if it is not
Figure GDA00033653195000001316
Then will be
Figure GDA00033653195000001317
Is assigned to
Figure GDA00033653195000001318
The ith intersection viAdding backward search to expand boundary intersection set
Figure GDA00033653195000001319
The ith intersection viSearching boundary external intersection set from backward direction
Figure GDA00033653195000001320
Deleting to obtain updated backward search boundary external intersection set
Figure GDA00033653195000001321
Otherwise, the ith intersection v is usediSearching boundary external intersection set from backward direction
Figure GDA00033653195000001322
Deleting to obtain an updated backward boundary external intersection set
Figure GDA00033653195000001323
And 8: as shown in fig. 7, based on the upper bound of travel time
Figure GDA00033653195000001324
Continuously updating the forward search boundary internal intersection set of the (n + 1) th iteration
Figure GDA00033653195000001325
Forward search boundary external intersection set
Figure GDA00033653195000001326
Backward search boundary internal intersection set
Figure GDA00033653195000001327
Backward search boundary external intersection set
Figure GDA00033653195000001328
Step 8.1: based on travel time upper bound
Figure GDA00033653195000001329
Continuously updating the forward search boundary internal intersection set of the (n + 1) th iteration
Figure GDA00033653195000001330
And forward search boundary external intersection set
Figure GDA00033653195000001331
Sequential judgment of forward search expansion boundary intersection set
Figure GDA00033653195000001332
Middle ith intersection viGo through the ith intersection viAt a neighboring intersection, i.e. satisfy aij＝(vi,vj) The j crossing v of the epsilon Aj，
Figure GDA00033653195000001430
And is
Figure GDA0003365319500000141
J th intersection vjIf, if
Figure GDA0003365319500000142
And is
Figure GDA0003365319500000143
The ith intersection viExpanding set of boundary intersections from forward search
Figure GDA0003365319500000144
Is deleted, will
Figure GDA0003365319500000145
Is assigned to
Figure GDA0003365319500000146
Otherwise, the ith intersection v is usediExpanding set of boundary intersections from forward search
Figure GDA0003365319500000147
Is deleted, will
Figure GDA0003365319500000148
Is assigned to
Figure GDA0003365319500000149
Wherein the content of the first and second substances,
Figure GDA00033653195000001410
indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000001411
indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between;
step 8.2: based on travel time upper bound
Figure GDA00033653195000001412
Continuously updating the backward search boundary internal intersection set of the (n + 1) th iteration
Figure GDA00033653195000001413
And backward searching boundary external intersection set
Figure GDA00033653195000001414
Sequential judgment backward search expansion boundary intersection set
Figure GDA00033653195000001415
Middle m crossing vmGo through the m-th intersection vmAt a neighboring intersection, i.e. satisfy amn＝(vm,vn) The mth intersection v belonging to the group Am，
Figure GDA00033653195000001416
And is
Figure GDA00033653195000001417
N th intersection vnIf, if
Figure GDA00033653195000001418
And is
Figure GDA00033653195000001419
The m-th intersection vmExpanding set of boundary intersections by backward search
Figure GDA00033653195000001420
Is deleted, will
Figure GDA00033653195000001421
Is assigned to
Figure GDA00033653195000001422
Otherwise, the m-th intersection vmBoundary intersection extended by backward searchCollection
Figure GDA00033653195000001423
Is deleted, will
Figure GDA00033653195000001424
Is assigned to
Figure GDA00033653195000001425
Wherein the content of the first and second substances,
Figure GDA00033653195000001426
represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,
Figure GDA00033653195000001427
represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between;
step 8.3: updating the n +1 th iteration bidirectional boundary intersection set
Figure GDA00033653195000001428
And step 9: judge Un+1＝UnIf yes, executing step 10; otherwise, assigning n +1 to n, and turning to step 6;
step 10: as shown in fig. 8, the shortest travel route of the finally formed two boundary internal intersection sets similar to the semi-ellipse is obtained, the shortest travel route obtained by the label correction method is output, and if n is 1, the final shortest travel time is T*＝TAnd if not, the step (B),
Figure GDA00033653195000001429
as shown in fig. 9, a currently commonly used algorithm for finding the shortest path, such as Dijkstra algorithm, performs the path search in a global scope, and performs the shortest path search in an area with a similar circular boundary; dividing the path search angle limit alpha provided by the invention into directional search angles alphaFAnd afterSearch angle alphaBCarrying out analysis; current forward search angle alphaFAngle alpha with the backward searchBWhen not equal, i.e. alphaF＝π，αBThe algorithm degenerates to the standard unidirectional Dijkstra algorithm (forward) with a path search range as shown in fig. 9.
As shown in fig. 10, as can be obtained in fig. 9, when αF＝0，αBPi, the algorithm degenerates to the standard unidirectional Dijkstra algorithm (inverse); the path search range is shown in the figure.
As shown in fig. 11, the bidirectional Dijkstra algorithm performs bidirectional global search with a starting point and a destination point respectively, and performs shortest path search in two areas with similar circular boundaries, and compared with the current commonly used algorithm for finding shortest paths, the efficiency of the bidirectional Dijkstra algorithm is improved to a certain extent in the path search process, but the optimality of the obtained shortest paths cannot be determined, and the obtained optimal paths are not necessarily time-consuming and shortest. Dividing the path search angle limit alpha provided by the invention into directional search angles alphaFAngle alpha with the backward searchBPerforming analysis, limiting the angle alpha by the current searchFWith backward search angle limit alphaBAre equal, αF＝π，αBThe pi algorithm degenerates to the standard bi-directional Dijkstra algorithm, whose path search range is shown in fig. 11.
As shown in fig. 12, the bidirectional E-algorithm proposed by the present invention performs bidirectional search within a certain range and with a starting point and a destination point respectively, always performs the shortest path search in two local areas having similar semi-elliptical boundaries, and adjusts the range of filtering the path search to ensure the optimality of the obtained path. Compared with the commonly used algorithms for seeking the shortest path such as Dijkstra algorithm and bidirectional Dijkstra algorithm, the bidirectional E-star algorithm has higher efficiency and accuracy in the path searching process.

Claims (1)

1. A method for obtaining the shortest path of an urban road network based on angle limitation and bidirectional search is characterized by comprising the following steps:
step 1: constructing an urban road network and acquiring plane coordinates of any intersection;
acquiring real-time road network data and obtaining an urban road network G ═ (V, A), wherein V represents an intersection set, and V ═ V1,v2,…,vq,…,vQ}，vqRepresents the Q-th intersection, Q is 1,2, …, Q; q denotes the total number of intersections, a denotes the set of links between intersections, and a ═ aij＝(vi,vj)|i,j＝1,2,...Q}，aijIndicates the ith intersection viAt the j intersection vjA road section in between, and aij∈{A1,A2,A3,A4In which A is1Denotes the expressway, A2Denotes the main road, A3Denotes the secondary artery, A4Representing a branch; let road section aijHas a time weight attribute of tijAnd is and
Figure FDA0003365319490000011
dijrepresenting a road section aijLength of (v)ijRepresenting a road section aijExpected traffic speed of the vehicle; if the ith intersection viAt the j intersection vjIf there is no road section in between, let tij＝+∞；
Obtaining the ith intersection v in the urban road according to the real-time road network dataiHas a plane coordinate of (x)i,yi) And j-th intersection vjHas a plane coordinate of (x)j,yj) Then the ith intersection viAt the j intersection vjThe road section vector between
Figure FDA0003365319490000012
Step 2: suppose that the starting point of the driver is the s-th intersection and the destination point is the t-th intersection vtTaking the driving direction from the starting point to the destination point as a forward searching direction, taking the driving direction from the destination point to the starting point as a backward searching direction, and giving a limited angle of path searching asAlpha is more than or equal to 0 and less than or equal to pi;
and step 3: defining parameters and initializing;
step 3.1: defining basic parameters:
defining n as the current iteration number, the s-th intersection v of the n-th iterationsTo the jth intersection vjThe shortest travel time of Tn(vs,vj) (ii) a Defining the s-th intersection vsV at the t-th intersectiontIs recorded as the Euclidean distance of lstDefinition of vmaxDefining the s-th intersection v for the maximum speed of travel in all road section typessTo the t-th intersection vtThe theoretical minimum travel time of
Figure FDA0003365319490000013
And is used as the lower bound of travel time; defining an intersection v of the starting point of the nth iterationsAnd a destination pointtThe shortest travel time therebetween is Tn(vs,vt) And as an upper bound on travel time
Figure FDA0003365319490000014
Step 3.2: defining forward search parameters:
defining the forward search boundary internal intersection set of the nth iteration as
Figure FDA0003365319490000015
Defining the forward search boundary external intersection set of the nth iteration as
Figure FDA0003365319490000016
Defining forward search expansion boundary intersection set as
Figure FDA0003365319490000017
Step 3.3: defining a backward search parameter:
defining a set of backward search boundary internal intersections for the nth iterationAre synthesized into
Figure FDA0003365319490000018
Defining the set of backward search boundary external intersections of the nth iteration as
Figure FDA0003365319490000021
Defining a backward search expansion boundary intersection set as
Figure FDA0003365319490000022
Step 3.4: defining the set of bidirectional boundary intersections of the nth iteration as
Figure FDA0003365319490000023
Defining a boundary internal intersection for the nth iteration
Figure FDA0003365319490000024
Step 3.5: initializing parameters:
the initialization n is equal to 1 and the initialization is carried out,
Figure FDA0003365319490000025
and 4, step 4: updating the forward search boundary internal intersection set of the nth iteration
Figure FDA0003365319490000026
Forward search boundary external intersection set
Figure FDA0003365319490000027
Backward search boundary internal intersection set
Figure FDA0003365319490000028
Backward search boundary external intersection set
Figure FDA0003365319490000029
Step 4.1: updating the forward search boundary internal intersection set of the nth iteration
Figure FDA00033653194900000210
And assembling to search for intersections outside the boundary
Figure FDA00033653194900000211
Will satisfy ask＝(vs,vk) The kth intersection v of epsilon AkAs a neighbor intersection; and traversing the s-th intersection vsAll neighbors of, if
Figure FDA00033653194900000212
If it is true, then
Figure FDA00033653194900000213
Is assigned to
Figure FDA00033653194900000214
The k-th intersection vkJoining extended boundary intersection sets
Figure FDA00033653194900000215
Otherwise, it will
Figure FDA00033653194900000216
Is assigned to
Figure FDA00033653194900000217
Wherein the content of the first and second substances,
Figure FDA00033653194900000218
indicates the s-th intersection vsAnd the k-th intersection vkThe distance vector between the road segment vector and the road segment vector,
Figure FDA00033653194900000219
represents the s-th crossMouth vsAnd the t-th intersection vtA road segment vector in between;
step 4.2: updating the set of backward search boundary internal intersections of the nth iteration
Figure FDA00033653194900000220
And backward searching boundary external intersection set
Figure FDA00033653194900000221
Will satisfy alt＝(vl,vt) The ith intersection v of E AlAs a neighbor intersection; traversing the t-th intersection vtAll neighbors of, if
Figure FDA00033653194900000222
If it is true, then
Figure FDA00033653194900000223
Is assigned to
Figure FDA00033653194900000224
The first crossing vlJoining extended boundary intersection sets
Figure FDA00033653194900000225
Otherwise, it will
Figure FDA00033653194900000226
Is assigned to
Figure FDA00033653194900000227
Wherein the content of the first and second substances,
Figure FDA00033653194900000228
indicates the t-th intersection vtAnd the l-th intersection vlThe distance vector between the road segment vector and the road segment vector,
Figure FDA00033653194900000229
indicates the t-th intersection vtAnd the s-th intersection vsA road segment vector in between;
and 5: if the boundary intersection set is expanded
Figure FDA00033653194900000230
Step 6 is carried out, otherwise, the forward search boundary internal intersection set of the nth iteration is continuously updated according to step 5.1 and step 5.2
Figure FDA00033653194900000231
Forward search boundary external intersection set
Figure FDA00033653194900000232
Backward search boundary internal intersection set
Figure FDA00033653194900000233
Backward search boundary external intersection set
Figure FDA00033653194900000234
Step 5.1: continuously updating the forward search boundary internal intersection set of the nth iteration
Figure FDA0003365319490000031
And n iteration of forward search boundary outer intersection set
Figure FDA0003365319490000032
Step 5.1.1: judging forward search expansion boundary intersection set
Figure FDA0003365319490000033
Middle ith intersection vi：
Step 5.1.2: will satisfy aij＝(vi,vj) J th intersection v of epsilon AjAs a neighbor intersection, and
Figure FDA0003365319490000034
traversing the ith intersection viAll neighbors of, if
Figure FDA0003365319490000035
If it is true, then
Figure FDA0003365319490000036
Is assigned to
Figure FDA0003365319490000037
The ith intersection viExpanding set of boundary intersections from forward search
Figure FDA0003365319490000038
Is deleted, will
Figure FDA0003365319490000039
Is assigned to
Figure FDA00033653194900000310
And executing step 5.1.3; wherein the content of the first and second substances,
Figure FDA00033653194900000311
indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,
Figure FDA00033653194900000312
indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between; otherwise, it will
Figure FDA00033653194900000313
Is assigned to
Figure FDA00033653194900000314
The ith intersection viExpanding set of boundary intersections from forward search
Figure FDA00033653194900000315
Deleting; and judging a forward search extended boundary intersection set according to the process of the step 5.1.2
Figure FDA00033653194900000316
The next intersection in;
step 5.1.3: judging forward search expansion boundary intersection set according to the process of step 5.1.2
Figure FDA00033653194900000317
J-th intersection v in (1)j；
Step 5.2: continuously updating the set of backward search boundary internal intersections of the nth iteration
Figure FDA00033653194900000318
And n iteration backward search boundary external intersection set
Figure FDA00033653194900000319
Step 5.2.1: judging backward search expansion boundary intersection set
Figure FDA00033653194900000320
Middle m crossing vm：
Step 5.2.2: will satisfy amn＝(vm,vn) N-th intersection v of E AnAs a neighbor intersection, and
Figure FDA00033653194900000321
traversing the m-th intersection vmAll neighbors of, if
Figure FDA00033653194900000322
Then will be
Figure FDA00033653194900000323
Is assigned to
Figure FDA00033653194900000324
The m-th intersection vmExpanding set of boundary intersections by backward search
Figure FDA00033653194900000325
Is deleted, will
Figure FDA00033653194900000326
Is assigned to
Figure FDA00033653194900000327
And step 5.2.3 is executed; wherein the content of the first and second substances,
Figure FDA00033653194900000328
represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,
Figure FDA00033653194900000329
represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between; otherwise, it will
Figure FDA00033653194900000330
Is assigned to
Figure FDA00033653194900000331
The m-th intersection vmExpanding set of boundary intersections by backward search
Figure FDA00033653194900000332
Deleting; and judging and then searching and expanding the boundary intersection set according to the process of the step 5.2.2
Figure FDA00033653194900000333
The next intersection in;
step 5.2.3: searching and expanding the boundary intersection set after judging according to the process of the step 5.2.2
Figure FDA0003365319490000041
At the n-th intersection vn；
Step 6: updating the set M of the bidirectional boundary intersection of the nth iterationnAnd obtaining a bidirectional boundary intersection set M subjected to nth iterationnThe shortest travel time of the inner intersection;
step 6.1: intersection v for obtaining departure point by label correction methodsForward search boundary internal intersection set up to nth iteration
Figure FDA0003365319490000042
The shortest travel time and the shortest path of any intersection, wherein the intersection v of the starting pointsSet M of bidirectional boundary intersections for the nth iterationnThe kth intersection vkThe shortest travel time of Tn(vs,vk)；
Step 6.2: intersection v of destination point obtained by label correction methodtBackward search boundary internal intersection set for nth iteration
Figure FDA0003365319490000043
The shortest travel time and the shortest path of any intersection, wherein the intersection v of the destination pointtSet M of bidirectional boundary intersections for the nth iterationnThe kth intersection vkThe shortest travel time of Tn(vt,vk)；
Step 6.3: traversing nth iteration bidirectional boundary intersection set MnInner k-th intersection vkThen the intersection v of the departure pointsIntersection v to destination pointtMinimum travel time of
Figure FDA0003365319490000044
Step 6.4: determining travel time optimality and updating an upper travel time bound
Figure FDA0003365319490000045
Step 6.4.1: if T isn(vs,vt) If T, the step is carried out, and step 12 is carried out; otherwise, go to step 6.4.2;
step 6.4.2: the s th intersection vsTo the t-th intersection vtUpper time bound of
Figure FDA0003365319490000046
Is updated to
Figure FDA0003365319490000047
Boundary intersection is expanded by forward and backward search
Figure FDA0003365319490000048
Turning to step 7;
and 7: based on travel time upper bound
Figure FDA0003365319490000049
Continuously updating the forward search boundary internal intersection set of the nth iteration
Figure FDA00033653194900000410
Forward search boundary external intersection set
Figure FDA00033653194900000411
Backward search boundary internal intersection set
Figure FDA00033653194900000412
Backward search boundary external intersection set
Figure FDA00033653194900000413
Step 7.1: based on travel time upper bound
Figure FDA00033653194900000414
Continuously updating the forward search boundary internal intersection set of the nth iteration
Figure FDA00033653194900000415
And forward search boundary external intersection set
Figure FDA00033653194900000416
Forward search boundary outer intersection set for nth iteration
Figure FDA00033653194900000417
At the ith intersection viFrom the intersection v of the departure pointsTo the ith intersection viI th intersection viIntersection v to destination pointtThe sum of the theoretical shortest travel time of the two is
Figure FDA0003365319490000051
Wherein lsiIndicates the s-th intersection vsV at the ith intersectioniOf Euclidean distance,/, ofitIndicates the ith intersection viV at the t-th intersectiontThe Euclidean distance of (c); if it is not
Figure FDA0003365319490000052
Then will be
Figure FDA0003365319490000053
Is assigned to
Figure FDA0003365319490000054
The ith intersection viAdding forward searchExpanding set of boundary intersections
Figure FDA0003365319490000055
The ith intersection viSearching boundary external intersection set from forward direction
Figure FDA0003365319490000056
Deleting to obtain updated forward search boundary external intersection set
Figure FDA0003365319490000057
Otherwise, the ith intersection v is usediSearching boundary external intersection set from forward direction
Figure FDA0003365319490000058
Deleting to obtain updated forward boundary external intersection set
Figure FDA0003365319490000059
Step 7.2: based on travel time upper bound
Figure FDA00033653194900000510
Continuously updating the set of backward search boundary internal intersections of the nth iteration
Figure FDA00033653194900000511
And backward searching boundary external intersection set
Figure FDA00033653194900000512
Set of backward search boundary external intersections for nth iteration
Figure FDA00033653194900000513
M th intersection v in (1)mFrom the intersection v of the departure pointsTo the m-th intersection vmAnd the m-th intersection vmTo the eyesV of pointstThe sum of the theoretical shortest travel time of the two is
Figure FDA00033653194900000514
Wherein lsmIndicates the s-th intersection vsV at the m-th intersectionmOf Euclidean distance,/, ofmtRepresents the m-th intersection vmV at the t-th intersectiontThe Euclidean distance of (c); if it is not
Figure FDA00033653194900000515
Then will be
Figure FDA00033653194900000516
Is assigned to
Figure FDA00033653194900000517
The ith intersection viAdding backward search to expand boundary intersection set
Figure FDA00033653194900000518
The ith intersection viSearching boundary external intersection set from backward direction
Figure FDA00033653194900000519
Deleting to obtain updated backward search boundary external intersection set
Figure FDA00033653194900000520
Otherwise, the ith intersection v is usediSearching boundary external intersection set from backward direction
Figure FDA00033653194900000521
Deleting to obtain an updated backward boundary external intersection set
Figure FDA00033653194900000522
And 8: based on travelUpper bound of time
Figure FDA00033653194900000523
Continuously updating the forward search boundary internal intersection set of the (n + 1) th iteration
Figure FDA00033653194900000524
Forward search boundary external intersection set
Figure FDA00033653194900000525
Backward search boundary internal intersection set
Figure FDA00033653194900000526
Backward search boundary external intersection set
Figure FDA00033653194900000527
Step 8.1: based on travel time upper bound
Figure FDA00033653194900000528
Continuously updating the forward search boundary internal intersection set of the (n + 1) th iteration
Figure FDA00033653194900000529
And forward search boundary external intersection set
Figure FDA00033653194900000530
Sequential judgment of forward search expansion boundary intersection set
Figure FDA00033653194900000531
Middle ith intersection viGo through the ith intersection viAt a neighboring intersection, i.e. satisfy aij＝(vi,vj) The j crossing v of the epsilon Aj，
Figure FDA0003365319490000061
And is
Figure FDA0003365319490000062
J th intersection vjIf, if
Figure FDA0003365319490000063
And is
Figure FDA0003365319490000064
The ith intersection viExpanding set of boundary intersections from forward search
Figure FDA0003365319490000065
Is deleted, will
Figure FDA0003365319490000066
Is assigned to
Figure FDA0003365319490000067
Otherwise, the ith intersection v is usediExpanding set of boundary intersections from forward search
Figure FDA0003365319490000068
Is deleted, will
Figure FDA0003365319490000069
Is assigned to
Figure FDA00033653194900000610
Wherein the content of the first and second substances,
Figure FDA00033653194900000611
indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,
Figure FDA00033653194900000612
indicates the ith intersection viAnd tV. of each intersectiontA road segment vector in between;
step 8.2: based on travel time upper bound
Figure FDA00033653194900000613
Continuously updating the backward search boundary internal intersection set of the (n + 1) th iteration
Figure FDA00033653194900000614
And backward searching boundary external intersection set
Figure FDA00033653194900000615
Sequential judgment backward search expansion boundary intersection set
Figure FDA00033653194900000616
Middle m crossing vmGo through the m-th intersection vmAt a neighboring intersection, i.e. satisfy amn＝(vm,vn) The mth intersection v belonging to the group Am，
Figure FDA00033653194900000617
And is
Figure FDA00033653194900000618
N th intersection vnIf, if
Figure FDA00033653194900000619
And is
Figure FDA00033653194900000620
The m-th intersection vmExpanding set of boundary intersections by backward search
Figure FDA00033653194900000621
Is deleted, will
Figure FDA00033653194900000622
Is assigned to
Figure FDA00033653194900000623
Otherwise, the m-th intersection vmExpanding set of boundary intersections by backward search
Figure FDA00033653194900000624
Is deleted, will
Figure FDA00033653194900000625
Is assigned to
Figure FDA00033653194900000626
Wherein the content of the first and second substances,
Figure FDA00033653194900000627
represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,
Figure FDA00033653194900000628
represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between;
step 8.3: updating the n +1 th iteration bidirectional boundary intersection set
Figure FDA00033653194900000629
And step 9: judge Un+1＝UnIf yes, executing step 10; otherwise, assigning n +1 to n, and turning to step 6;
step 10: if n is 1, the final shortest travel time is T*＝TAnd if not, the step (B),
Figure FDA00033653194900000630
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