CN106779251A - A kind of heuristic search of the shortest route problem based on position study efficacy - Google Patents
A kind of heuristic search of the shortest route problem based on position study efficacy Download PDFInfo
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Abstract
The heuristic search of the accurate solution of the shortest route problem of position study efficacy, more particularly to a kind of robot path planning method are based on the present invention relates to a kind of band.Robot is during shortest path is found, interacted with environment by intensified learning, acquisition experience, it is meant that robot can with smaller cost by same paths, therefore shortest path in this case from without study efficacy when shortest path be likely to different.In order to solve this problem, external environmental information is obtained in robot, after determining study efficacy function according to priori, by heuristic information, the cut operator that meets the problem needs and filter operation is designed to exclude determine to be not in part path on shortest paths in advance, so as to acceleration search process so that robot searches out an accurate overall situation shortest path within the reasonable effective time, and then for guidance machine people traveling.
Description
Technical field
The present invention relates to a kind of method for precisely solving with the shortest route problem based on position study efficacy, belong to people
Work smart field, more particularly to a kind of robot path planning method.
Background technology
Shortest route problem is widely used in the field of practice, such as：Logistics, communications and transportation, robot path planning, car
Route etc..Shortest route problem is exactly to find a shortest path from origin-to-destination in one drawing.As a rule, away from
Traversal expense from, time or every arc is referred to as cost, it is generally the case that have the path of many bar origin-to-destinations in figure,
Shortest path is exactly the path with minimum total cost.If the cost of every arc shifts to an earlier date, it is known that the problem is static shortest path
Footpath problem.If every the cost of arc can change according to some factors (e.g., traffic, learning experience), this class is asked
Topic belongs to shortest path problem in dynamic networks.
In practice, the cost of arc would generally change with study efficacy in figure." study efficacy " is carried first by Wright
Go out, there are many researchs all relevant with study efficacy at present.Such as：In robot soccer game, robot space exploration and complicated ring
In the scenes such as the rescuing robot under border, robot is interacted by intensified learning with environment, obtains experience, and is more passed through
Testing means that robot can pass through same paths with smaller cost.Therefore, the robot shortest path with learning ability
Footpath problem is a shortest route problem with study efficacy.Under normal circumstances, study efficacy model has three kinds：Based on position
Put, based on total processing time and based on experience.In the method, it is considered to which location-based study efficacy, i.e. robot often pass through
One arc, will rule of thumb update, adjust various parameters, more adapt to environment, so that certain cost of arc is with it
Position in the paths and change.
In the method for known solution shortest route problem, A* algorithms are that the most frequently used, effective one kind is opened in all algorithms
Hairdo searching algorithm, is proposed, this algorithm is expanded by dijkstra's algorithm by Hart etc., and heuristic information is A* algorithm timeliness
The key of energy.To shortest route problem, A* algorithms are typically superior to other traditional exact algorithms.In spite of much on solving dynamic
The A* algorithms of shortest path, but these problems major part is all the cost change at random of arc, and in the shortest path with study efficacy
In the problem of footpath, the cost of arc is that the two is differed as place sequence location rule changes.Under normal circumstances, imitated without study
Shortest path that should be in figure is different from the shortest path in study efficacy figure.Therefore, traditional A* algorithms and Dijkstra
The mutation of algorithm and A* algorithms is not suitable for solving the shortest route problem with study efficacy and learned, it is necessary to find one and solve to carry
Practise the new method of the shortest route problem of effect.
[1]A.Konar,I.G.Chakraborty,S.J.Singh,L.C.Jain,and A.K.Nagar,“A
deterministic improved q-learning for path planning of a mobile robot,”
Systems,Man,and Cybernetics:Systems,IEEE Transactions on,vol.43,no.5,pp.1141–
1153,2013.
[2]P.E.Hart,N.J.Nilsson,and B.Raphael,“A formal basis for the
heuristic determination of minimum cost paths,”Systems Science and
Cybernetics,IEEE Transactions on,vol.4,no.2,pp.100–107,1968.
[3]P.E.Hart,N.J.Nilsson,and B.Raphael,“A formal basis for the
heuristic determination of minimum cost paths,”Systems Science and
Cybernetics,IEEE Transactions on,vol.4,no.2,pp.100–107,1968.
The content of the invention
Goal of the invention：The present invention proposes a kind of accurate solution with the shortest route problem based on position study efficacy
Heuristic search, to solve with the robot shortest route problem based on position study efficacy.
Technical scheme；Heuristic search side with the shortest route problem based on position study efficacy of the present invention
Method, comprises the following steps：
Step 1：Searching map information, obtains digraph G=＜ N, A, c ＞, wherein, N represents the collection of all nodes in figure G
Close, A represents the set of all arcs in figure G, then | N | represents nodal point number in figure, | A | represents the number of arc in figure, c (n, n*) represent
Node n is to n*Between arc cost；
Step 2：Study efficacy function is determined according to the priori that robot path is travelled：According to digraph G, nothing is designed
Estimation function h (n) during study efficacy, h (n) represents node n to the estimate of the path cost of terminal；Then imitated according to study
Function and estimation function h (n) are answered, estimation function h during with study efficacy is obtainedl(n)；
Step 3：Using heuristic search algorithm shortest path is found in the digraph G for considering study efficacy：
Step 31：It is stored in by the information of the estimate f reached home by the path P for only including starting point and by the path
In treating extensions path set OPEN；And path P is charged to the search graph SG formed in search procedure；
Step 32：The minimum part path conducts of origin-to-destination estimate f are selected from extensions path set OPEN is treated
The path of shortest path is most possibly expanded at present；
Step 33：If path P is reached home, judgement treats whether extensions path set OPEN is empty；If it is empty, then perform
Step 37；If not empty, then step 34 is performed；
Step 34：The successor node of the part path of selection is extended successively, specially：Successor node is added into part path
New part path is constituted, according to the estimation function with study efficacy, the node to the estimate of destination node is calculated；By band
The actual value for having the new portion path of study efficacy is added with the estimate of the node to destination node, used as by the part road
Footpath reaches the estimate of destination node；Target is reached by new part path, the quantity of its arc for including and by respective path
The estimate of node is put into treats extensions path set OPEN；Extensions path is charged into search graph SG；
Step 35：By the part path that shortest path can not possibly be expanded in beta pruning, filter operation Delete Search figure SG；
Step 36：Judgement treats whether extensions path set OPEN is empty；If it is empty, then step 37 is performed；If not empty, then
Perform step 34；
Step 37：The shortest path of origin-to-destination is obtained according to search graph SG.
Study efficacy function described in step 2 is L (r), and wherein r is certain arc position in the paths.
The only path P comprising starting point and the estimate f reached home by the path is specifically calculated such as described in step 31
Under：
According to the estimation function with study efficacy, the estimate h of zequin to terminall(n0)=h (n0) × L (ρ),
The actual cost value of path P is gl(n0, 0)=0, then the estimate reached home by path P is fl(n0, 0) and=gl(n0,0)+
hl(n0)；Gop(n0) it is starting point to node n0Treat extensions path set, Gcl(n0) it is starting point to node n0Extensions path collection
Close, thenGcl(n)=φ, and by vectorIt is placed on band extensions path set
In OPEN, path P is charged into search graph SG.
Treat to select the minimum part paths of origin-to-destination estimate f specific such as in extensions path set OPEN in step 32
Under：From extensions path set OPEN is treated, estimate f is selectedlMinimum path P, as the part path being extended, from
Vector is deleted in OPENWherein, n represents that the path reaches summit n by starting point；The path for reaching summit n by starting point includes r bar arcs, and its actual cost is gl(n, r), ρ-r
Expression reaches home γ by the path at most will also be by ρ-r bar arcs；fl(n, r)=gl(n,r)+hlN () represents and passes through the road
Footpath is reached home the estimate cost of γ；Simultaneously by vectorFrom set GopN () moves on to set GclN (), wherein r are path P
Comprising arc quantity；GopWhat n () represented is starting point to current not yet extension in all paths of summit n and is likely to become most short
The part path in path；GclWhat n () represented is starting point to the current path for having propagated through in the path of summit n.
The estimate that part path in step 3 by extending reaches destination node is calculated as follows：According to study efficacy, position
C (n, m, r+1)=c (n, m) × L (r+1) is changed into by c (n, m) in the cost of the arc (n, m) of r+1 positions, so path P '
Cost is gl(m, r+1)=gl(n,r)+c(n,m)×(r+1)α；Calculate node m to the estimate h of terminall(m)=h (m) × L
(ρ), then, the estimate f reached home by the pathl(m, r+1)=gl(m,r+1)+hl(m)。
The beta pruning, filter operation are specific as follows：
Step 351：Delete Gop(m)UGclQuilt in (m)The vector of domination, and delete correspondence in SG and OPEN
Information, if Gop(m)U GclThere is domination in (m)Vector, then mark Prune be true, otherwise mark
Prune is false；
Step 352：Carry out filter operation：If fl＞ C, flag F ilter are true, and otherwise, flag F ilter is false；Such as
Fruit fl＜ C, delete f in OPENlThe vector of ＜ C, and delete GopCorrespondence vector, corresponding path in Delete Search figure SG in (m)；
Step 353：If during cut operator and filter operation, path P ' be not all deleted, i.e. Prune and
Filter is false, then by vectorIt is put into OPEN, willIt is stored in GopIn (m),
And by path P ' charge to search graph SG.
Beneficial effect
Present invention contemplates that with the robot path planning based on position learning ability, how by heuristic search
Method finds the accurate global shortest path of origin-to-destination in digraph, instructs the robot row with learning ability
Sail.
Brief description of the drawings
Fig. 1 is robot path planning's flow chart in the inventive method
Fig. 2 is heuristic search flow chart in the inventive method
Fig. 3 is the flow chart of path extended method in the inventive method
Fig. 4 is case diagram.
Fig. 5 is the search graph that step (2) is obtained.
Fig. 6 is the search graph that step (3) is obtained.
Fig. 7 is the search graph that step (4) is obtained.
Fig. 8 is the search graph that step (5) is obtained.
Fig. 9 is the search graph that step (6) is obtained.
Figure 10 is the shortest path of case diagram.
Table 1 is the heuristic function value of each node in case diagram.
Specific embodiment
Technical scheme is described in detail below in conjunction with the accompanying drawings：
In the scenes such as the rescuing robot under robot soccer game, robot space exploration and complex environment, carry
The robot of learning ability needs to find from a certain position fastest to the path up to target location, that is, a minimum cost road
Footpath.A kind of heuristic search of accurate solution with the shortest route problem based on position study efficacy of the invention,
As shown in figure 1, comprising the following steps：
Step s101：Cartographic information is collected, digraph G=＜ N, A, c ＞ are obtained, wherein, N represents all nodes in figure G
Set, A represents the set of all arcs in figure G, then | N | represents nodal point number in figure, and | A | represents the number of arc in figure, c (n, n*)
Represent node n to n*Between arc cost；
Step s102：Study efficacy function is determined according to the priori that robot path is travelled；Study efficacy function is
Estimate what is obtained in advance according to priori, be a nonincreasing function；The priori travelled according to robot path determines
Study efficacy function L (r), wherein r are certain arc positions in the paths, and r is bigger, and the value of L (r) is smaller.According to digraph G,
Estimation function h (n) during without study efficacy is designed, node n to the estimate of the path cost of terminal is represented, then according to study
Effect function and estimation function h (n), obtain estimation function h during with study efficacyl(n)=h (n) × L (ρ), wherein, ρ=
Min { | N | -1, | A | }, represents the maximal possible length of shortest path；
Step s103：Heuristic search algorithm is initialized, and treats that extensions path set OPEN is initialized as sky, has been found at present
Shortest path cost C be initialized as infinity；
Step s104：The shortest path for considering study efficacy is found in digraph G using heuristic search algorithm；
Step s105：Guidance machine people travels according to the shortest path for searching out.
The heuristic search algorithm of shortest path is found as shown in Fig. 2 comprising the steps of：
Step s201:Deposited by the information of the estimate f reached home by the path P for only including starting point and by the path
In entering to treat extensions path set OPEN；And path P is charged to the search graph SG formed in search procedure；
Step s202：If treating that extensions path set OPEN is sky, step s206 is performed；
Step s203:The minimum part path P of origin-to-destination estimate f are selected from OPEN, can as most having at present
The path of shortest path can be expanded to；
Step s204：If path P is reached home, step s202 is performed；
Step s205：The successor node of the part path selected is extended successively, and is deleted not by beta pruning, filter operation
The part path of shortest path may be expanded to, extensions path is charged into search graph SG, perform step s202；
Step s206：If having searched terminal, then according to the search graph SG that search procedure is formed, obtain starting point
To the shortest path of terminal, C is exactly the cost of shortest path；Otherwise, the path in the absence of origin-to-destination is illustrated.
Extension starting point n in Fig. 20Process：For only containing starting point n0Path P, according to the estimation letter with study efficacy
Number, the estimate h of zequin to terminall(n0)=h (n0) × L (ρ), the actual cost value of path P is gl(n0, 0) and=0, bag
The information for containing arc quantity containing path and path is stored in vectorThen pass through
The estimate that path P is reached home is fl(n0, 0) and=gl(n0,0)+hl(n0), Gop(n0) it is starting point to node n0Road to be extended
Footpath is gathered, Gcl(n0) it is starting point to node n0Extensions path set, thenGcl(n)=φ, and
By vectorIt is placed in OPEN, P is charged into search graph SG.
Selection path process in Fig. 2：From extensions path set OPEN is treated, estimate f is selectedlMinimum path P, makees
It is the part path being extended, vector is deleted from OPENWherein, n represent the path by starting point to
Up to summit n；The path for reaching summit n by starting point includes r bar arcs, and its actual cost is gl
(n, r), ρ-r represent reach home γ by the path at most will also be by ρ-r bar arcs；fl(n, r)=gl(n,r)+hl(n) table
Show the estimate cost of the γ that reached home by the path.Simultaneously by vectorFrom set GopN () moves on to set Gcl(n), its
The quantity of the arc that middle r is included for path P；GopWhat n () represented is that starting point again can to current not yet extension in all paths of summit n
The part path of shortest path can be turned into；GclWhat n () represented is starting point to the current road for having propagated through in the path of summit n
Footpath.
Extensions path process in Fig. 2：As shown in figure 3, extending the successor node of the part path selected successively.By after
New part path P is constituted after node join part path, according to the estimation function with study efficacy, the node to mesh is calculated
Mark the estimate of node.By the estimate h of the actual value g of new portion path P and the node to destination nodelIt is added, as logical
Cross the estimate f that the part path reaches destination node.The quantity of the arc that path P and path P are included, path P are corresponding to be estimated
Evaluation f is put into and treats extensions path set OPEN, and can not possibly turn into the part of shortest path by beta pruning and filter operation deletion
Path, comprises the following steps that：
Step s301：Assuming that it is the path P from starting point to node n to select path to be extended, P includes r bar arcs, will scheme
All successor nodes of node n are placed in set S in G；
Step s302：If set S is sky, terminate, if not being sky, perform step s303；
Step s303：A node m in taking-up S, addition path P, the new path P of formation '；
Step s304：Because study efficacy, the cost positioned at the arc (n, m) of r+1 positions is changed into c (n, m, r by c (n, m)
+ 1)=c (n, m) × L (r+1), so, path P ' cost be gl(m, r+1)=gl(n,r)+c(n,m)×(r+1)α；Calculate
Estimate hs of the node m to terminallM ()=h (m) × L (ρ), when calculating actual cost, study efficacy functional value can be with below
Arc can become with the increase of position under, but, because m to the quantity of the arc of terminal, nothing cannot be known a priori by
Method is estimated with accurate, herein with the worst situation as estimate；VectorThat
, the estimate f reached home by the pathl(m, r+1)=gl(m,r+1)+hl(m)；
Step s305：If node m is terminal, and gl(m,r+1)<C performs step s306, otherwise performs step
s307；
Step s306：Update the shortest path cost C=g for finding at presentl；
Step s307：Carry out cut operator：Delete Gop(m)UGclQuilt in (m)The vector of domination, and delete SG
Information corresponding with OPEN, if Gop(m)UGclThere is domination in (m)Vector, then mark Prune be it is true,
Otherwise mark Prune is false；
Step s308：Carry out filter operation：If fl＞ C, flag F ilter are true, and otherwise, flag F ilter is false；Such as
Fruit fl＜ C, delete f in OPENlThe vector of ＜ C, and delete GopCorrespondence vector, corresponding path in Delete Search figure SG in (m)；
Step s309：If during cut operator and filter operation, path P ' be not all deleted, i.e. Prune and
Filter is false, then by vectorIt is put into OPEN, willIt is stored in GopIn (m),
And by path P ' charge to search graph SG；
We explain in detail the method with legend below, and Fig. 4 is oriented mark figure, wherein, n0It is starting point, γ is unique
Destination node.Assuming that study efficacy function is L (r)=rα, wherein r represents the position on path where arc.Figure includes 8 tops
Point and 14 arcs, because from starting point n0There is no ring, therefore ρ=min { 8-1,14 }=7 to the path of γ, study efficacy factor-alpha takes
Value -0.2.C is initialized as+∞, and when there is arc (n, γ) in scheming G, then c (n, γ) is the cost of arc (n, γ), otherwise value
For+∞.In the figure G with study efficacy, we use heuristic function hl(n)=ρα× h (n) (in this example, hl(n)=7-0.2×
H (n)) estimate summit n to the value of terminal γ It is actual value；hlN () isEstimate.Each summit
H and hlValue is given in Table 1.
| n | n0 | n1 | n2 | n3 | n4 | n5 | n6 | γ |
| h(n) | 3 | 5 | 2 | 4 | 5 | 3 | 5 | 0 |
| hl(n) | 2.033 | 3.338 | 1.355 | 2.710 | 3.388 | 2.033 | 3.388 | 0 |
Table 1
(1) by n0Root node is initialized as, and is only node in search graph SG.Therefore, gl(n0, 0) and=0, ρ=
7, Gop(n0) ← { (0,7) }, Gcl(n0)=φ, fl=gl(n0,0)+hl(n0)=0+2.033=2.033.OPEN←{(n0,(0,
7),2.033)}。
(2) unique path in selection OPEN tables, its four extension point n1、n2、n3And n4It is added to search graph SG neutralizations
In OPEN tables.Corresponding four arcs are located at first position in the searching route for each producing.Generation of the study efficacy to them
Valency does not influence.Therefore gl(n1, 1)=6, from node n1At most there was only 6 arcs to destination node γ, thenfl
(n1, 1) and=gl(n1,1)+hl(n1)=6+3.338=9.338, Gop(n1) ← { (6,6) }, while tuple (n1,(6,6),
9.338) it is added in OPEN tables.Similar treatment is carried out to others extension, the search graph SG for obtaining is as shown in Figure 5.
(3) due to node n3There is minimum estimate cost value in OPEN tables, therefore be selected as extending.Node n1
It is node n3Unique follow-up child node.Arc (n3,n1) it is located at the 2nd position of new route.Due to the influence of study efficacy, arc
Cost c (n3,n1, 2) and it is 2 × 2-0.2=1.741.By cut operator PRUNE, arc (n1,n0) removed from SG, tuple (n1,
(6,6), 9.338) deleted from OPEN tables,From Gop(n1) delete, similarly, to arc (n1,n3) carry out similar place
Reason, finally, node n3Expansion process it is as shown in Figure 6.
(4) due to node n1There is minimum estimate cost value in OPEN tables, therefore be selected as extending.Node n1
There are two immediate successors, n4And n6.Due to arc (n1,n4) the 3rd position in path is located at, so cost c (n1,n4, 3) and it is 3
×3-0.2=2.408.Therefore, gl(n4, 3) and=gl(n1,2)+c(n1,n4, 3)=5.149, Have at present
Two paths reach node n4, two single sub paths are all added in SG, i.e. arc (n4,n1) be added in figure SG, tuple (n4,
(5.149,4), 8.537) it is inserted into OPEN tables, vectorIt is added to Gop(n4), for node n6Enter
The similar operation of row, is calculated：fl(n6, 3) and=gl(n6,3)+hl(n6)=7.557+3.388=
10.945.Finally, node n1Expansion process it is as shown in Figure 7.
(5) due in OPEN tables, node n4FlValue it is minimum, therefore, extend node n6And γ.To destination node γ
The cost of new route be 9.353, less than C values, therefore C values are updated to 9.353. because of fl(n2, 1) and=gl(n2,1)+hl(n2)
=8+1.355=9.355>C, then to node n2Path by operation FILTER filtering.Due to fl(n6, 3)=10.945>C, because
This is also filtered.From γ to n4Path be added in SG, tuple (γ, (9.353,5), 9.353) is inserted into OPEN tables.To
AmountIt is added to Gop(γ).As for node n6, arc (n4,n6) cost be now c (n4,n6,2)
=4 × 2-0.2=3.482.gl(n6, 2) and=8.482.fl(n6, 2) and=gl(n6,2)+hl(n6)=12.860.Therefore, because fl
(n6,2)>C, is operated, to node n by FILTER6Path be removed.Finally, node n1Expansion process it is as shown in Figure 8.
(6) next, choosing node n4The 2nd paths because in OPEN tables, it has the f of minimumlValue.n4Two
Individual immediate successor n6It is checked again with γ.Arc (n4, γ) and it is located at the 4th position in new generation path, therefore cost c (n4,γ,
4)=5 × 4-0.2=3.789. therefore, fl(γ, 4)=gl(γ, 4)=gl(n4,3)+c(n4, γ, 4) and=8.938. its value is less than
C=9.353. therefore C values are updated to 8.938. and produce the extension for arriving γ.Arc (n4,n6) cost be changed into c (n4,n6, 4)=4 × 4-0.2=3.031.gl(n6, 4) and=8.180.fl(n6, 4) and=gl(n6,4)+hl(n6)=11.568.Therefore to node n6Sub- road
Filtered in footpath.Final SG figures are as shown in Figure 9.
(7) at present, selectable tuple (γ, (8.938,3), 8.938) is there remains in OPEN tables, therefore select the tuple
And remove it OPEN tables.Therefore, OPEN tables are empty, and algorithm recalls acquired SG from γ, obtains the road that cost is 8.938
Footpath.As shown in Figure 10.
Claims (6)
1. a kind of heuristic search of the shortest route problem based on position study efficacy, it is characterised in that including following
Step：
Step 1：Searching map information, obtains digraph G=＜ N, A, c ＞, wherein, N represents the set of all nodes in figure G, A
The set of all arcs in figure G is represented, then | N | represents nodal point number in figure, | A | represents the number of arc in figure, c (n, n*) represent node
N to n*Between arc cost；
Step 2：Study efficacy function is determined according to the priori that robot path is travelled：According to digraph G, design without study
Estimation function h (n) during effect, h (n) represents node n to the estimate of the path cost of terminal；Then according to study efficacy letter
Number and estimation function h (n), obtain estimation function h during with study efficacyl(n)；
Step 3：Using heuristic search algorithm shortest path is found in the digraph G for considering study efficacy：
Step 31：It is stored in by the information of the estimate f reached home by the path P for only including starting point and by the path and waits to expand
In exhibition set of paths OPEN；And path P is charged to the search graph SG formed in search procedure；
Step 32：The minimum part paths of origin-to-destination estimate f are selected from extensions path set OPEN is treated as current
The most possible path for expanding to shortest path；
Step 33：If path P is reached home, judgement treats whether extensions path set OPEN is empty；If it is empty, then step is performed
37；If not empty, then step 34 is performed；
Step 34：The successor node of the part path of selection is extended successively, specially：Part path is added to constitute successor node
New part path, according to the estimation function with study efficacy, calculates the node to the estimate of destination node；Will be with
The actual value for practising the new portion path of effect is added with the estimate of the node to destination node, is arrived as by the part path
Up to the estimate of destination node；Destination node is reached by new part path, the quantity of its arc for including and by respective path
Estimate be put into and treat extensions path set OPEN；Extensions path is charged into search graph SG；
Step 35：By the part path that shortest path can not possibly be expanded in beta pruning, filter operation Delete Search figure SG；
Step 36：Judgement treats whether extensions path set OPEN is empty；If it is empty, then step 37 is performed；If not empty, then perform
Step 34；
Step 37：The shortest path of origin-to-destination is obtained according to search graph SG.
2. the heuristic search of shortest route problem according to claim 1, it is characterised in that：Described in step 2
Study efficacy function is L (r), and wherein r is certain arc position in the paths.
3. the heuristic search of shortest route problem according to claim 1, it is characterised in that：Described in step 31
The only path P comprising starting point and the estimate f reached home by the path is specifically calculated as follows：
According to the estimation function with study efficacy, the estimate h of zequin to terminall(n0)=h (n0) × L (ρ), path P
Actual cost value be gl(n0, 0)=0, then the estimate reached home by path P is fl(n0, 0) and=gl(n0,0)+hl
(n0)；Gop(n0) it is starting point to node n0Treat extensions path set, Gcl(n0) it is starting point to node n0Extensions path collection
Close, thenGcl(n)=φ, and by vectorIt is placed on band extensions path set
In OPEN, path P is charged into search graph SG.
4. the heuristic search of shortest route problem according to claim 1, it is characterised in that：Wait to expand in step 32
Select the minimum part paths of origin-to-destination estimate f specific as follows in exhibition set of paths OPEN：From treating extensions path set
In OPEN, estimate f is selectedlMinimum path P, as the part path being extended, deletes vector from OPENWherein, n represents that the path reaches summit n by starting point；By starting point to
Include r bar arcs up to the path of summit n, its actual cost is gl(n, r), ρ-r represent most by the path γ that reaches home
Will also be by ρ-r bar arcs；fl(n, r)=gl(n,r)+hlN () represents the estimate cost of the γ that reached home by the path；Simultaneously
By vectorFrom set GopN () moves on to set GclThe quantity of n arc that (), wherein r include for path P；GopN () represents
It is starting point to the current part path for not yet extending and being likely to become shortest path in all paths of summit n；GclN () represents
It is starting point to the current path for having propagated through in the path of summit n.
5. the heuristic search of shortest route problem according to claim 1, it is characterised in that：Pass through in step 3
The estimate that the part path of extension reaches destination node is calculated as follows：According to study efficacy, positioned at r+1 positions arc (n,
M) cost is changed into c (n, m, r+1)=c (n, m) × L (r+1) by c (n, m), so path P ' cost be gl(m, r+1)=gl
(n,r)+c(n,m)×(r+1)α；Calculate node m to the estimate h of terminall(m)=h (m) × L (ρ), then, by the path
The estimate f for reaching homel(m, r+1)=gl(m,r+1)+hl(m)。
6. the heuristic search of shortest route problem according to claim 1, it is characterised in that：The beta pruning, mistake
Filter operation is specific as follows：
Step 351：Delete Gop(m)UGclQuilt in (m)The vector of domination, and delete corresponding letter in SG and OPEN
Breath, if Gop(m)UGclThere is domination in (m)Vector, then mark Prune be it is true, otherwise mark Prune be
It is false；
Step 352：Carry out filter operation：If fl＞ C, flag F ilter are true, and otherwise, flag F ilter is false；If fl＜
C, deletes f in OPENlThe vector of ＜ C, and delete GopCorrespondence vector, corresponding path in Delete Search figure SG in (m)；
Step 353：If during cut operator and filter operation, path P ' be not all deleted, i.e. Prune and Filter are
It is false, then by vectorIt is put into OPEN, willIt is stored in GopIn (m), and by path
P' charges to search graph SG.
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