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 PDFInfo
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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、Set U of internal and external intersections of backward search boundaryn B、The set of the two-way boundary intersections is MnUpper and lower bounds of travel timeT; 3. updating set U of internal and external intersections of set forward and backward search boundaryn F、Un B、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 madeAnd (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
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 anddijrepresenting 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
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 ofAnd 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
Step 3.2: defining forward search parameters:
defining the forward search boundary internal intersection set of the nth iteration asDefining the forward search boundary external intersection set of the nth iteration asDefining forward search expansion boundary intersection set as
Step 3.3: defining a backward search parameter:
defining the set of internal intersections of the backward search boundary of the nth iteration asDefining the set of backward search boundary external intersections of the nth iteration asDefining a backward search expansion boundary intersection set as
Step 3.4: defining the set of bidirectional boundary intersections of the nth iteration asDefining a boundary internal intersection for the nth iteration
Step 3.5: initializing parameters:
and 4, step 4: updating the forward search boundary internal intersection set of the nth iterationForward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 4.1: updating the forward search boundary internal intersection set of the nth iterationAnd assembling to search for intersections outside the boundary
Will satisfy ask=(vs,vk) The kth intersection v of epsilon AkAs a neighbor intersection; and traversing the s-th intersection vsAll neighbors of, ifIf it is true, thenIs assigned toWill be the kthV. intersectionkJoining extended boundary intersection setsOtherwise, it willIs assigned toWherein,indicates the s-th intersection vsAnd the k-th intersection vkThe distance vector between the road segment vector and the road segment vector,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 iterationAnd backward searching boundary external intersection set
Will satisfy alt=(vl,vt) The ith intersection v of E AlAs a neighbor intersection; traversing the t-th intersection vtAll neighbors of, ifIf it is true, thenIs assigned toThe first crossing vlJoining extended boundary intersection setsCombination of Chinese herbsOtherwise, it willIs assigned toWherein,indicates the t-th intersection vtAnd the l-th intersection vlThe distance vector between the road segment vector and the road segment vector,indicates the t-th intersection vtAnd the s-th intersection vsA road segment vector in between;
and 5: if the boundary intersection set is expandedStep 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 5.2Forward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 5.1: continuously updating the forward search boundary internal intersection set of the nth iterationAnd n iteration of forward search boundary outer intersection set
Step 5.1.2: will satisfy aij=(vi,vj) J th intersection v of epsilon AjAs a neighbor intersection, and
traversing the ith intersection viAll neighbors of, ifIf it is true, thenIs assigned toThe ith intersection viExpanding set of boundary intersections from forward searchIs deleted, willIs assigned toAnd executing step 5.1.3; wherein,indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between; otherwise, it willIs assigned toThe ith intersection viExpanding set of boundary intersections from forward searchDeleting; and judging a forward search extended boundary intersection set according to the process of the step 5.1.2The next intersection in;
step 5.1.3: judging forward search expansion boundary intersection set according to the process of step 5.1.2J-th intersection v in (1)j;
Step 5.2: continuously updating the set of backward search boundary internal intersections of the nth iterationAnd n iteration backward search boundary external intersection set
traversing the m-th intersection vmAll neighbors of, ifThen will beIs assigned toThe m-th intersection vmExpanding set of boundary intersections by backward searchIs deleted, willIs assigned toAnd step 5.2.3 is executed; wherein,represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between; otherwise, it willIs assigned toThe m-th intersection vmExpanding set of boundary intersections by backward searchDeleting; and judging and then searching and expanding the boundary intersection set according to the process of the step 5.2.2The next intersection in;
step 5.2.3: searching and expanding the boundary intersection set after judging according to the process of the step 5.2.2At 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 iterationThe 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 iterationThe 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
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 ofIs updated toBoundary intersection is expanded by forward and backward searchTurning to step 7;
and 7: based on travel time upper boundContinuously updating the forward search boundary internal intersection set of the nth iterationForward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 7.1: based on travel time upper boundContinuously updating the forward search boundary internal intersection set of the nth iterationAnd forward search boundary external intersection set
Forward search boundary outer intersection set for nth iterationAt 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 isWherein 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 notThen will beIs assigned toThe ith intersection viAdding intoForward search extended boundary intersection setThe ith intersection viSearching boundary external intersection set from forward directionDeleting to obtain updated forward search boundary external intersection setOtherwise, the ith intersection v is usediSearching boundary external intersection set from forward directionDeleting to obtain updated forward boundary external intersection set
Step 7.2: based on travel time upper boundContinuously updating the set of backward search boundary internal intersections of the nth iterationAnd backward searching boundary external intersection set
Set of backward search boundary external intersections for nth iterationM 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 isWherein 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 notThen will beIs assigned toThe ith intersection viAdding backward search to expand boundary intersection setThe ith intersection viSearching boundary external intersection set from backward directionDeleting to obtain updated backward search boundary external intersection setOtherwise, the ith intersection v is usediSearching boundary external intersection set from backward directionDeleting to obtain an updated backward boundary external intersection set
And 8: based on travel time upper boundContinuously updating the forward search boundary internal intersection set of the (n + 1) th iterationForward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 8.1: based on travel time upper boundContinuously updating the forward search boundary internal intersection set of the (n + 1) th iterationAnd forward search boundary external intersection set
Sequential judgment of forward search expansion boundary intersection setMiddle 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,And isJ th intersection vjIf, ifAnd isThe ith intersection viExpanding set of boundary intersections from forward searchIs deleted, willIs assigned toOtherwise, the ith intersection v is usediExpanding set of boundary intersections from forward searchIs deleted, willIs assigned toWherein,indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between;
step 8.2: based on travel time upper boundContinuously updating the backward search boundary internal intersection set of the (n + 1) th iterationSearching in harmony directionCable boundary external intersection set
Sequential judgment backward search expansion boundary intersection setMiddle 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,And isN th intersection vnIf, ifAnd isThe m-th intersection vmExpanding set of boundary intersections by backward searchIs deleted, willIs assigned toOtherwise, the m-th intersection vmExpanding set of boundary intersections by backward searchIs deleted, willIs assigned toWherein,represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between;
And step 9: judge Un+1=UnIf yes, executing step 10; otherwise, assigning n +1 to n, and turning to step 6;
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 anddijrepresenting 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
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 ofAnd 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
Step 3.2: defining forward search parameters:
defining the forward search boundary internal intersection set of the nth iteration asDefining the forward search boundary external intersection set of the nth iteration asDefining forward search expansion boundary intersection set as
Step 3.3: defining a backward search parameter:
defining the set of internal intersections of the backward search boundary of the nth iteration asDefinition of nThe backward search boundary external intersection set of the sub-iteration isDefining a backward search expansion boundary intersection set as
Step 3.4: defining the set of bidirectional boundary intersections of the nth iteration asDefining a boundary internal intersection for the nth iteration
Step 3.5: initializing parameters:
the initialization n is equal to 1 and the initialization is carried out,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 iterationForward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
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 setOtherwise, adding the intersection set to the forward search boundary external intersection set of the nth iterationThe t-th intersection v meeting the angle limiting conditiontThe neighbor intersection is added into the n iteration forward search boundary internal intersection setOtherwise, adding the intersection set to the forward search boundary external intersection set of the nth iteration
Step 4.1: updating the forward search boundary internal intersection set of the nth iterationAnd assembling to search for intersections outside the boundary
Will satisfy ask=(vs,vk) The kth intersection v of epsilon AkAs a neighbor intersection; and traversing the s-th intersection vsAll neighbors of, ifIf it is true, thenIs assigned toWill be the kthV. intersectionkJoining extended boundary intersection setsOtherwise, it willIs assigned toWherein,indicates the s-th intersection vsAnd the k-th intersection vkThe distance vector between the road segment vector and the road segment vector,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 iterationAnd backward searching boundary external intersection set
Will satisfy alt=(vl,vt) The ith intersection v of E AlAs a neighbor intersection; traversing the t-th intersection vtAll neighbors of, ifIf it is true, thenIs assigned toThe first crossing vlJoining extended boundary intersection setsCombination of Chinese herbsOtherwise, it willIs assigned toWherein,indicates the t-th intersection vtAnd the l-th intersection vlThe distance vector between the road segment vector and the road segment vector,indicates the t-th intersection vtAnd the s-th intersection vsA road segment vector in between;
and 5: if the boundary intersection set is expandedStep 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 5.2Forward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 5.1: continuously updating the forward search boundary internal intersection set of the nth iterationAnd n iteration of forward search boundary outer intersection set
Step 5.1.2: will satisfy aij=(vi,vj) J th intersection v of epsilon AjAs a neighbor intersection, and
traversing the ith intersection viAll neighbors of, ifIf it is true, thenIs assigned toThe ith intersection viExpanding set of boundary intersections from forward searchIs deleted, willIs assigned toAnd executing step 5.1.3; wherein,indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between; otherwise, it willIs assigned toThe ith intersection viExpanding set of boundary intersections from forward searchDeleting; and judging a forward search extended boundary intersection set according to the process of the step 5.1.2The next intersection in;
step 5.1.3: judging forward search expansion boundary intersection set according to the process of step 5.1.2J-th intersection v in (1)j;
Step 5.2: continuously updating the set of backward search boundary internal intersections of the nth iterationAnd n iteration backward search boundary external intersection set
traversing the m-th intersection vmAll neighbors of, ifThen will beIs assigned toThe m-th intersection vmExpanding set of boundary intersections by backward searchIs deleted, willIs assigned toAnd step 5.2.3 is executed; wherein,represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between; otherwise, it willIs assigned toWill m beV. of each intersectionmExpanding set of boundary intersections by backward searchDeleting; and judging and then searching and expanding the boundary intersection set according to the process of the step 5.2.2The next intersection in;
step 5.2.3: searching and expanding the boundary intersection set after judging according to the process of the step 5.2.2At 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 iterationThe 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 iterationThe 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
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 ofIs updated toBoundary intersection is expanded by forward and backward searchTurning to step 7;
and 7: as shown in fig. 7, based on the upper bound of travel timeContinuously updating the forward search boundary internal intersection set of the nth iterationForward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 7.1: based on travel time upper boundContinuously updating the forward search boundary internal intersection set of the nth iterationAnd forward search boundary external intersection set
Forward search boundary outer intersection set for nth iterationAt 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 isWherein 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 notThen will beIs assigned toThe ith intersection viAdding forward search expansion boundary intersection setThe ith intersection viSearching boundary external intersection set from forward directionDeleting to obtain updated forward search boundary external intersection setOtherwise, the ith intersection v is usediSearching boundary external intersection set from forward directionDeleting to obtain updated forward boundary external intersection set
Step 7.2: based on travel time upper boundContinuously updating the set of backward search boundary internal intersections of the nth iterationAnd backward searching boundary external intersection set
Set of backward search boundary external intersections for nth iterationM 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 isWherein 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 notThen will beIs assigned toThe ith intersection viAdding backward search to expand boundary intersection setThe ith intersection viSearching boundary external intersection set from backward directionDeleting to obtain updated backward search boundary external intersection setOtherwise, the ith intersection v is usediSearching boundary external intersection set from backward directionDeleting to obtain an updated backward boundary external intersection set
And 8: as shown in fig. 7, based on the upper bound of travel timeContinuously updating the forward search boundary internal intersection set of the (n + 1) th iterationForward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 8.1: based on travel time upper boundContinuously updating the forward search boundary internal intersection set of the (n + 1) th iterationAnd forward search boundary external intersection set
Sequential judgment of forward search expansion boundary intersection setMiddle 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,And isJ th intersection vjIf, ifAnd isThe ith intersection viExpanding set of boundary intersections from forward searchIs deleted, willIs assigned toOtherwise, the ith intersection v is usediExpanding set of boundary intersections from forward searchIs deleted, willIs assigned toWherein,indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between;
step 8.2: based on travel time upper boundContinuously updating the backward search boundary internal intersection set of the (n + 1) th iterationAnd backward searching boundary external intersection set
Sequential judgment backward search expansion boundary intersection setMiddle 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,And isN th intersection vnIf, ifAnd isThe m-th intersection vmExpanding set of boundary intersections by backward searchIs deleted, willIs assigned toOtherwise, the m-th intersection vmBoundary intersection extended by backward searchCollectionIs deleted, willIs assigned toWherein,represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between;
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),
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 anddijrepresenting 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
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 ofAnd 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
Step 3.2: defining forward search parameters:
defining the forward search boundary internal intersection set of the nth iteration asDefining the forward search boundary external intersection set of the nth iteration asDefining forward search expansion boundary intersection set as
Step 3.3: defining a backward search parameter:
defining a set of backward search boundary internal intersections for the nth iterationAre synthesized intoDefining the set of backward search boundary external intersections of the nth iteration asDefining a backward search expansion boundary intersection set as
Step 3.4: defining the set of bidirectional boundary intersections of the nth iteration asDefining a boundary internal intersection for the nth iteration
Step 3.5: initializing parameters:
and 4, step 4: updating the forward search boundary internal intersection set of the nth iterationForward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 4.1: updating the forward search boundary internal intersection set of the nth iterationAnd assembling to search for intersections outside the boundary
Will satisfy ask=(vs,vk) The kth intersection v of epsilon AkAs a neighbor intersection; and traversing the s-th intersection vsAll neighbors of, ifIf it is true, thenIs assigned toThe k-th intersection vkJoining extended boundary intersection setsOtherwise, it willIs assigned toWherein,indicates the s-th intersection vsAnd the k-th intersection vkThe distance vector between the road segment vector and the road segment vector,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 iterationAnd backward searching boundary external intersection set
Will satisfy alt=(vl,vt) The ith intersection v of E AlAs a neighbor intersection; traversing the t-th intersection vtAll neighbors of, ifIf it is true, thenIs assigned toThe first crossing vlJoining extended boundary intersection setsOtherwise, it willIs assigned toWherein,indicates the t-th intersection vtAnd the l-th intersection vlThe distance vector between the road segment vector and the road segment vector,indicates the t-th intersection vtAnd the s-th intersection vsA road segment vector in between;
and 5: if the boundary intersection set is expandedStep 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 5.2Forward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 5.1: continuously updating the forward search boundary internal intersection set of the nth iterationAnd n iteration of forward search boundary outer intersection set
Step 5.1.2: will satisfy aij=(vi,vj) J th intersection v of epsilon AjAs a neighbor intersection, and
traversing the ith intersection viAll neighbors of, ifIf it is true, thenIs assigned toThe ith intersection viExpanding set of boundary intersections from forward searchIs deleted, willIs assigned toAnd executing step 5.1.3; wherein,indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,indicates the ith intersection viAnd the t-th intersection vtA road segment vector in between; otherwise, it willIs assigned toThe ith intersection viExpanding set of boundary intersections from forward searchDeleting; and judging a forward search extended boundary intersection set according to the process of the step 5.1.2The next intersection in;
step 5.1.3: judging forward search expansion boundary intersection set according to the process of step 5.1.2J-th intersection v in (1)j;
Step 5.2: continuously updating the set of backward search boundary internal intersections of the nth iterationAnd n iteration backward search boundary external intersection set
traversing the m-th intersection vmAll neighbors of, ifThen will beIs assigned toThe m-th intersection vmExpanding set of boundary intersections by backward searchIs deleted, willIs assigned toAnd step 5.2.3 is executed; wherein,represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between; otherwise, it willIs assigned toThe m-th intersection vmExpanding set of boundary intersections by backward searchDeleting; and judging and then searching and expanding the boundary intersection set according to the process of the step 5.2.2The next intersection in;
step 5.2.3: searching and expanding the boundary intersection set after judging according to the process of the step 5.2.2At 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 iterationThe 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 iterationThe 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
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 ofIs updated toBoundary intersection is expanded by forward and backward searchTurning to step 7;
and 7: based on travel time upper boundContinuously updating the forward search boundary internal intersection set of the nth iterationForward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 7.1: based on travel time upper boundContinuously updating the forward search boundary internal intersection set of the nth iterationAnd forward search boundary external intersection set
Forward search boundary outer intersection set for nth iterationAt 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 isWherein 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 notThen will beIs assigned toThe ith intersection viAdding forward searchExpanding set of boundary intersectionsThe ith intersection viSearching boundary external intersection set from forward directionDeleting to obtain updated forward search boundary external intersection setOtherwise, the ith intersection v is usediSearching boundary external intersection set from forward directionDeleting to obtain updated forward boundary external intersection set
Step 7.2: based on travel time upper boundContinuously updating the set of backward search boundary internal intersections of the nth iterationAnd backward searching boundary external intersection set
Set of backward search boundary external intersections for nth iterationM 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 isWherein 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 notThen will beIs assigned toThe ith intersection viAdding backward search to expand boundary intersection setThe ith intersection viSearching boundary external intersection set from backward directionDeleting to obtain updated backward search boundary external intersection setOtherwise, the ith intersection v is usediSearching boundary external intersection set from backward directionDeleting to obtain an updated backward boundary external intersection set
And 8: based on travelUpper bound of timeContinuously updating the forward search boundary internal intersection set of the (n + 1) th iterationForward search boundary external intersection setBackward search boundary internal intersection setBackward search boundary external intersection set
Step 8.1: based on travel time upper boundContinuously updating the forward search boundary internal intersection set of the (n + 1) th iterationAnd forward search boundary external intersection set
Sequential judgment of forward search expansion boundary intersection setMiddle 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,And isJ th intersection vjIf, ifAnd isThe ith intersection viExpanding set of boundary intersections from forward searchIs deleted, willIs assigned toOtherwise, the ith intersection v is usediExpanding set of boundary intersections from forward searchIs deleted, willIs assigned toWherein,indicates the ith intersection viAnd j-th intersection vjThe distance vector between the road segment vector and the road segment vector,indicates the ith intersection viAnd tV. of each intersectiontA road segment vector in between;
step 8.2: based on travel time upper boundContinuously updating the backward search boundary internal intersection set of the (n + 1) th iterationAnd backward searching boundary external intersection set
Sequential judgment backward search expansion boundary intersection setMiddle 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,And isN th intersection vnIf, ifAnd isThe m-th intersection vmExpanding set of boundary intersections by backward searchIs deleted, willIs assigned toOtherwise, the m-th intersection vmExpanding set of boundary intersections by backward searchIs deleted, willIs assigned toWherein,represents the m-th intersection vmAnd the nth intersection vnThe distance vector between the road segment vector and the road segment vector,represents the m-th intersection vmAnd the s-th intersection vsA road segment vector in between;
And step 9: judge Un+1=UnIf yes, executing step 10; otherwise, assigning n +1 to n, and turning to step 6;
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