CN106503789A - Loop-free shortest path searching method based on Di Jiesitela and minimax ant colony - Google Patents
Loop-free shortest path searching method based on Di Jiesitela and minimax ant colony Download PDFInfo
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Abstract
The invention discloses a kind of loop-free shortest path searching method based on Di Jiesitela and minimax ant colony, mainly solves the problems, such as that prior art time complexity height, routine weight value are not excellent enough.Implementation step is：1) construction meets the weighted and directed graph G of path relation, rejects unwanted node using beta pruning and directed edge obtains the weighted and directed graph G1 after beta pruning；2) by beta pruning after weighted and directed graph G1 be reduced to only comprising source node, Dominator collection, the simple graph G2 of destination node；3) the minimax ant colony method with reference to Dijkstra's algorithm used in simple graph G2 is found optimal path and is exported.The present invention compared with prior art, with solving speed fast, shortest path is excellent the characteristics of, can be used for Path selection in network route system, layout of roads scene in transportation.
Description
Technical field
The invention belongs to communication technical field, further relates to a kind of loop-free shortest path searching method, can be used for net
Layout of roads scene in Path selection in network route system, transportation.
Background technology
Shortest route problem is in given net figure, seeks source node to the routine weight value sum that passes through between destination node
Minimum path.Classical shortest-path method has Di Jiesite pulling methods and Freud's method, but both approaches are initial
Proposition be not applied for through specified Dominator.Shortest-path method master through specify Dominator is solved at present
Depth first traversal to be had, Di Jiesite pulling methods, genetic method, traditional ant colony method.Depth-first traversal is to find out institute
There are the path for meeting condition, contrast to obtain most short path, although the shortest path for obtaining is optimum result, but the time is complicated
Degree is high, for complicated figure, generally can not be solved in effective time；Di Jiesite pulling methods are produced by the incremental order of weights
Shortest path of the source of students point to remaining Dominator, equally faces the high problem of time complexity；Genetic method and traditional ant colony
Method belongs to didactic intelligent method, has certain randomness, and surpasses more than 15, total node number in Dominator number
Cross 300 figure scale is big, the weights of solution that generally yield in baroque scene are not little enough.
Patent " a kind of crude oil tank farm dispatching method " (application number that Nanjing RichIsland Information Technology Co., Ltd. applies at which:
CN201410240939.5, publication number CN104008431A) disclosing a kind of acquisition must be through the shortest path on summit through n
Method.The method is mainly achieved in that the method for order between Dominator using fully intermeshing generates n！Individual combination,
For each combination is separately added into source node and destination node in head and the tail, the local optimum road between adjacent vertex is then solved
Local optimum combination of paths between adjacent node is obtained n by footpath！Bar fullpath, then select most from these fullpaths
Short paths are used as optimal solution.The weak point of the method is：Fully intermeshing combination first takes very much, causes solving speed
Slowly, secondly when using n！Individual combination obtains n！During paths, loop may be produced.
Patent " the topological diagram optimal path of a kind of Problem with Some Constrained Conditions that Wuhan flames of war Technology Service Co., Ltd applies at which
Method " (application number：201510589652.8, publication number 105141524A) disclose a kind of Problem with Some Constrained Conditions topological diagram optimum
Path Method.The method is mainly according to given Dominator order, sets up Dominator topology List, and real-time update is kept away
Node topology list is opened, until finding destination node.The weak point of the method is only to give Necessary Locations, finds
The probability of solution is less and the weights of solution that find are generally larger.
Pornographic books and magazines power, recklessly big kasaya, " shortest-path method of the set of intermediate nodes through specifying " that Jiang Yuming is proposed (《Calculate
Machine engineering and application》2015) source node is calculated to first Dominator, first Dominator by Dijkstra's algorithm
Sequentially pass through other Dominators and reach last Dominator, the shortest path of last Dominator to destination node
Footpath, after fully intermeshing obtains Dominator built-up sequence, seeks shortest-path method according to segmentation, obtains shortest path.The party
Method has the disadvantage that fully intermeshing method time complexity is high, for the more complex web figure of Dominator in effective time is difficult to find
Solution.
Wu W, Ruan Q " A hierarchical approach for the shortest in its paper that delivers
path problem with obligatory intermediate nodes”(《Signal Processing》2006) propose
Shortest path through Dominator collection is solved using genetic method, it is adaptable to solve network of the Dominator number less than 20
Figure, it is likely that through duplicate node, constituting has endless path.
Xu Qingzheng, Ke Xizheng " must be ground through a shortest route problem model and corresponding genetic method in its paper that delivers
Study carefully " (《System engineering and electronic technology》2009) genetic method for generating loop-free shortest path is proposed, by constructing unique fitting
Response function, enable preferentially to be chosen to enter comprising more chromosome that must be through putting of future generation, but for more than node number
Network is difficult to be solved.
To sum up, for the more large complicated figure of solution node number, time complexity is high, in effective time for existing method
The routine weight value for inside obtaining is big, is not suitable for reality.
Content of the invention
The deficiency that the present invention is present for above-mentioned prior art, proposes one kind based on Di Jiesitela and minimax ant colony
Loop-free shortest path searching method, to reduce time complexity, improve routine weight value.
The present invention realize technical scheme be：Deep search is carried out to original graph by using source node as search starting point
Traversal and figure screening, reject useless point and useless side；By using Di Jiesite pulling methods calculate source node in figure, must warp knuckle
Beeline in point set, destination node two-by-two between node, the complicated figure comprising auxiliary node is converted into not comprising auxiliary
The simple graph of node；By minimax ant colony method find simple graph like shortest path, then by Di Jiesite pulling methods, will
Simple graph expands into the acyclic like shortest path of original graph like shortest path, and selects from the acyclic set like shortest path of original graph
The minimum paths of weights are exported as optimal path.Implementation step includes as follows：
(1) weighted and directed graph is constructed：
With G (V, E) for original graph, construction meets source node s, destination node t, Dominator collection V' and auxiliary node collection X
The weighted and directed graph G of mutual relation, wherein, V is node set, and E is line set of having the right；
(2) initialize：
One is set up like shortest path set W, and is initialized as sky, the structure according to weighted and directed graph G sets up going out for p node
Degree set OpWith in-degree set Ip, wherein p ∈ V；
(3) beta pruning is carried out to weighted and directed graph G, obtains the weighted and directed graph G1 after beta pruning：
(3.1) weighted and directed graph G is searched for by depth-first search traversal method, can not be reached in deletion weighted and directed graph G
Node；
(3.2) the out-degree set O of decision node set V interior joint ppBe whether empty, if it is empty, then deletion of node p and and p
Related directed edge, wherein p ≠ s and p ≠ t；
(3.3) access flag of all nodes in Dominator collection V' and auxiliary node collection X is initialized as 0, if visiting
Ask that flag bit is represented for 0 not being accessed, access flag is that 1 expression is accessed；
(3.4) take in Dominator collection V' one and be not accessed for node p, its access flag is set to 1, decision node
The in-degree set I of ppWhether size is 1：If 1, then only retain predecessor node to p directed edge, delete the predecessor node its
Its out-degree side, executes (3.5), otherwise, directly executes (3.5)；
(3.5) the out-degree set O of decision node ppWhether size is 1, if 1, then only retain p to the oriented of descendant node
Side, deletes other in-degree sides of the descendant node, executes (3.6), otherwise, directly executes (3.6)；
(3.6) whether the access flag of all Dominators is judged all for 1, if being all 1, execute (3.7), otherwise,
Return (3.4)；
(3.7) take in auxiliary node collection X one and be not accessed for node p1, its access flag is set to 1, decision node
The in-degree set I of p1p1Whether size is 1：If 1, then only retain predecessor node to the directed edge of p1, p1 is deleted to its forerunner's section
The directed edge of point, executes (3.8), otherwise, directly executes (3.8)；
(3.8) the out-degree set O of decision node p1p1Whether size is 1, if 1, then only retain p1 having to descendant node
Xiang Bian, deletes descendant node to the directed edge of p1, executes (3.9), otherwise, directly executes (3.9)；
(3.9) whether the access flag of all auxiliary nodes is judged all for 1, if being all 1, obtaining having the right after beta pruning has
To figure G1, execute (4), otherwise, return (3.7).
(4) the weighted and directed graph G1 after Di Jiesite pulling methods are by beta pruning is only reduced to comprising source node s, purpose section
Point t, the weighted and directed graph G2 of Dominator collection V' mutual relation；
(5) the minimax ant colony method with reference to Di Jiesitela used in simplified weighted and directed graph G2 obtains optimum
Path：
(5.1) initiation parameter：Formica fusca number is m, arranges maximum iteration time F, puts the initial weight of globally optimal solution
For infinity, iterationses are 0；
(5.2) the taboo list Tabu for depositing the node that passes through of Formica fusca and path is configured tok, k=1,2 ..., m, and initially
Turn to sky；
(5.3) whole Formica fuscas are placed on source node s, source node s and destination node t is added to taboo list Tabuk,
K=1,2 ..., m, the initial weight for putting current iteration optimal solution are infinity；
(5.4) a Formica fusca k is taken, its path P is calculatedk；
(5.5) the walked path Ps of current Formica fusca k are calculatedkWeights, empty the corresponding taboo list Tabu of the Formica fuscak；
(5.6) judge whether whole Formica fuscas complete pathfinding, if so, execute (5.7)；Otherwise, (5.4) are returned；
(5.7) path P to all Formica fuscas1, P2... Pk..., PmSorted according to weights from small to large, and according to sequence according to
The path P of secondary selection Formica fusca kk, judge its path PkWeights whether be less than current iteration optimal solution, if so, then by G2 each
The access flag of node is set to 0, executes (5.8), otherwise, jumps to (5.12)；
(5.8) path P current Formica fusca k obtained using positive Di Jiesite pulling methodskRevert to positive Actual path
P′k, judge positive Actual path P 'kWeights whether be less than current iteration optimal solution, if so, then update current iteration optimal solution,
Execute (5.9), otherwise, execute (5.10)；
(5.9) judge positive Actual path P 'kWeights whether be less than globally optimal solution, if so, then update global optimum
Solution, and will be positive Actual path P ' like the path replacement in shortest path set Wk, execute (5.10), otherwise, directly execute
(5.10)；
(5.10) all node visit flag bits are set to 0 again, using reverse Di Jiesite pulling methods by path PkRecover
For reverse Actual path P "k, judge reverse Actual path P "kWeights whether less than current iteration optimal solution, if so, then update
Current iteration optimal solution, executes (5.11), otherwise, executes (5.12)；
(5.11) judge reverse Actual path P "kWeights whether be less than globally optimal solution, if so, then update global optimum
Solution, and will be reverse Actual path P like the path replacement in shortest path set W "k, execute (5.12), otherwise, directly execute
(5.12)；
(5.12) minimax pheromone is calculated, and updates routing information element；
(5.13) iterationses add 1, judge whether to reach predetermined iterationses F, if so, then will be like shortest path set W
The path of middle preservation is exported as optimal path, otherwise, is returned (5.3).
The present invention compared with prior art, with advantages below：
First：The present invention using beta pruning and simplification, by originally complicated Large Graph be changed into only comprising source node, must warp knuckle
Point, the simple graph of destination node, are substantially reduced the scale of figure, overcome multiple in its time when complexity is schemed that processes in prior art
The high shortcoming of miscellaneous degree.
Second：Present invention employs this heuristic of minimax ant colony, Di Jiesite used in solution procedure
Pulling method carries out forward and reverse Actual path recovery, in effective time, can obtain than traditional ant group algorithm and genetic algorithm more
Excellent solution.
Description of the drawings
Fig. 1 be the present invention realize general flow chart.
Fig. 2 is the sub-process figure for obtaining optimal path in the present invention.
Fig. 3 is the routine weight value broken line graph 5 test cases solutions obtained for 30 times with the present invention.
Fig. 4 is the comparison diagram in front and back sample topology simplified with the present invention.
Specific embodiment
Below in conjunction with the accompanying drawings the present invention is described in further detail.
Referring to the drawings 1, step is described in further detail to be realized to of the invention.
Step 1, constructs weighted and directed graph：
With G (V, E) for original graph, construction meets source node s, destination node t, Dominator collection V' and auxiliary node collection X
The weighted and directed graph G of mutual relation, wherein V are node set, and E is line set of having the right.
Step 2, initialization：
One is set up like shortest path set W, and is initialized as sky, the structure according to weighted and directed graph G sets up going out for p node
Degree set OpWith in-degree set Ip, wherein p ∈ V.
Step 3, carries out beta pruning to weighted and directed graph G, obtains the weighted and directed graph G1 after beta pruning.
(3.1) weighted and directed graph G is searched for by depth-first search traversal method, can not be reached in deletion weighted and directed graph G
Node；
(3.2) the out-degree set O of decision node set V interior joint ppBe whether empty, if it is empty, then deletion of node p and and p
Related directed edge, wherein p ≠ s and p ≠ t；
(3.3) access flag of all nodes in Dominator collection V' and auxiliary node collection X is initialized as 0, if visiting
Ask that flag bit is represented for 0 not being accessed, access flag is that 1 expression is accessed；
(3.4) take in Dominator collection V' one and be not accessed for node p, its access flag is set to 1, decision node
The in-degree set I of ppWhether size is 1：If 1, then only retain predecessor node to p directed edge, delete the predecessor node its
Its out-degree side, executes (3.5), otherwise, directly executes (3.5)；
(3.5) the out-degree set O of decision node ppWhether size is 1, if 1, then only retain p to the oriented of descendant node
Side, deletes other in-degree sides of the descendant node, executes (3.6), otherwise, directly executes (3.6)；
(3.6) whether the access flag of all Dominators is judged all for 1, if being all 1, execute (3.7), otherwise,
Return (3.4)；
(3.7) take in auxiliary node collection X one and be not accessed for node p1, its access flag is set to 1, decision node
The in-degree set I of p1p1Whether size is 1：If 1, then only retain predecessor node to the directed edge of p1, p1 is deleted to its forerunner's section
The directed edge of point, executes (3.8), otherwise, directly executes (3.8)；
(3.8) the out-degree set O of decision node p1p1Whether size is 1, if 1, then only retain p1 having to descendant node
Xiang Bian, deletes descendant node to the directed edge of p1, executes (3.9), otherwise, directly executes (3.9)；
(3.9) whether the access flag of all auxiliary nodes is judged all for 1, if being all 1, obtaining having the right after beta pruning has
To figure G1, execute (4), otherwise, return (3.7).
Step 4, the weighted and directed graph G1 after Di Jiesite pulling methods are by beta pruning are only reduced to comprising source node s, mesh
Node t, the weighted and directed graph G2 of Dominator collection V' mutual relation.
(4.1) source node weight matrix U is defined, for preserving source node s to the routine weight value between each Dominator,
If from source node s to one there is no path in a Dominator, or have to pass through other Dominators get to this must warp knuckle
Point, then preserve the routine weight value for infinity, if in the presence of having mulitpath between source node s a to Dominator, protecting
Deposit that most short paths weights；
(4.2) Dominator weight matrix E is defined, for preserving routine weight value two-by-two between Dominator；
(4.3) destination node weight matrix D is defined, for preserving each Dominator to the routine weight value of destination node；
(4.4) only wrapped according to source node weight matrix U, Dominator weight matrix E, destination node weight matrix D
The simplified weighted and directed graph G2 of s containing source node, destination node t and Dominator collection V' mutual relation.
Step 5, the minimax ant colony method with reference to Di Jiesitela used in simplified weighted and directed graph G2 are obtained
Optimal path.
With reference to Fig. 2, this step is implemented as follows：
(5.1) initiation parameter：Formica fusca number is m, arranges maximum iteration time F, puts the initial weight of globally optimal solution
For infinity, iterationses are 0；
(5.2) the taboo list Tabu for depositing the node that passes through of Formica fusca and path is configured tok, k=1,2 ..., m, and initially
Turn to sky；
(5.3) whole Formica fuscas are placed on source node s, source node s and destination node t is added to taboo list Tabuk,
K=1,2 ..., m, the initial weight for putting current iteration optimal solution are infinity；
(5.4) kth Formica fusca is taken, its path P is calculatedk：
(5.4a) set of paths P of kth Formica fusca is initializedkFor sky, calculate the current a moment, from source node s to all not
It is accessed for the transition probability of Dominator p
Wherein, τspA () represents current time, the pheromone on node s to node p paths, ηsp(a) represent from node s to
The visibility of node p, value are inverses of the node s to the distance of node p, and weighted values of the α for pheromone, β are adding for visibility
Weights；
(5.4b) pass through transition probabilityDetermine subsequent time accessed node, which is conducted interviews, and by source node s
Set of paths P is added to the corresponding directed edge of the nodekIn, update taboo list Tabuk；
(5.4c) current accessed node i is calculated to the transition probability of next addressable Dominator j
τijA () represents the pheromone on current time, node i to node j paths, ηijA () is represented from node i to section
The visibility of point j, value are inverse of the node i to node j distances；
(5.4d) transition probability drawn by (5.4c)Determine next accessed node, which is conducted interviews, and more
New route set PkWith taboo list Tabuk；
(5.4e) judge whether all Dominators are all accessed, if so, by last Dominator to purpose section
The directed edge of point t adds set of paths Pk, otherwise, return (5.4c).
(5.5) the walked path Ps of current Formica fusca k are calculatedkWeights, empty the corresponding taboo list Tabu of the Formica fuscak；
(5.6) judge whether whole Formica fuscas complete pathfinding, if so, execute (5.7)；Otherwise, (5.4) are returned；
(5.7) path (P to all Formica fuscas1, P2... Pk..., Pm) sorted according to weights from small to large, and according to sequence
The path P of Formica fusca k is chosen successivelyk, judge its path PkWeights whether be less than current iteration optimal solution, if so, then will in G2 per
The access flag of individual node is set to 0, executes (5.8), otherwise, jumps to (5.14)；
(5.8) path P current Formica fusca k obtained using positive Di Jiesite pulling methodskRevert to positive Actual path
P′k：
(5.8a) positive Actual path P ' is constructedk, be initialized as sky, by beta pruning after weighted and directed graph G1 in all nodes
Access flag sets to 0；
(5.8b) in the weighted and directed graph G1 after beta pruning, according to path PkForward sequence, from source node s, seek
The Dominator for looking for the next one not access, and update positive Actual path P 'k；
(5.8c) Dominator that the next one is not accessed is found, updates positive Actual path P 'k；
(5.8d) judge positive Actual path P 'kDestination node t whether is reached, positive Actual path P ' is if so, obtainedk, no
Then, (5.8c) is returned；
(5.9) judge positive Actual path P 'kWeights whether less than current iteration optimal solution, if so, then update this
Iteration optimal solution, executes (5.10), otherwise, executes (5.11)；
(5.10) judge positive Actual path P 'kWeights whether be less than globally optimal solution, if so, then update global optimum
Solution, and will be positive Actual path P ' like the path replacement in shortest path set Wk, execute (5.11), otherwise, directly execute
(5.11)；
(5.11) all node visit flag bits are set to 0 again, using reverse Di Jiesite pulling methods by path PkRecover
For reverse Actual path P "k：
(5.11a) reverse Actual path P is constructed "k, be initialized as sky, by beta pruning after weighted and directed graph G1 in all sections
Point access flag sets to 0；
(5.11b) in the weighted and directed graph G1 after beta pruning, according to current path PkReverse sequence, from destination node t
Set out, find the Dominator that the next one is not accessed, and update reverse Actual path P "k；
(5.11c) Dominator that the next one is not accessed is found, updates reverse Actual path P "k；
(5.11d) judge reverse Actual path P "kSource node s whether is reached, reverse Actual path P is if so, obtained "k, no
Then, (5.11c) is returned；
(5.12) judge reverse Actual path P "kWeights whether less than current iteration optimal solution, if so, then update this
Iteration optimal solution, executes (5.13), otherwise, executes (5.14)；
(5.13) judge reverse Actual path P "kWeights whether be less than globally optimal solution, if so, then update global optimum
Solution, and will be reverse Actual path P like the path replacement in shortest path set W "k, execute (5.14), otherwise, directly execute
(5.14)；
(5.14) maximum information element τ is calculatedmaxWith minimal information element τmin：
Wherein, ρ represents the residual coefficients of pheromone, and L is the path that optimum Formica fusca is passed by, and n is for having the right after simplifying
Node number in figure G2, avg=n/2, PbestRepresent that Formica fusca once searches for the probability for finding optimal solution；
(5.15) routing information element τ is updatedij(a+1), and meet τmin≤τij(a+1)≤τmax：
Wherein,Optimum Formica fusca is represented at (a, a+1) in the time, the pheromone increment of path i to j,
Q is constant, represents the pheromone total amount that single Formica fusca discharges in the paths；
(5.16) iterationses add 1, judge whether to reach predetermined iterationses F, if so, then will be like shortest path set W
The path of middle preservation is exported as optimal path, otherwise, is returned (5.3).
The effect of the present invention is further illustrated by following experiment：
1. experiment condition：
Test environment is Ubuntu, and single core processor inside saves as 2048MB.Programming language is c++.
Minimax ant colony method major parameter is set in the present invention for α=1, β=2, ρ=0.96, Q=100, Pbest=
0.05, maximum iteration time F is according to different Dominator number dynamic adjustment.
The present invention chooses 5 test cases：The total node numbers of test case Case1 are 20, and Dominator number is 6；
The total node numbers of Case2 are 50, and Dominator number is 10；The total node numbers of Case3 are 300, and Dominator number is 20；
The total node numbers of Case4 are 500, and Dominator number is 22；The total node numbers of Case5 are 500, and Dominator number is 42.
2. experiment content and interpretation of result：
Experiment 1, with the present invention and existing Depth Priority Searching, Di Jiesite pulling methods, genetic method to above-mentioned 5
Individual test case carries out 30 tests, obtains optimal path weights and search time such as table 1, wherein, did not still have more than 20 minutes
Obtaining solution then thinks the method to this example without solution (NA).
1 four kinds of method test results of table
Following result as can be seen from Table 1：
In 30 tests, depth-first traversal and Di Jiesite are pulled in effective time, for simple graph can find
One optimal solution, but for the more complicated figure of Dominator, the probability for finding solution is less, such as in table Case3, Case4 and
Case5 does not find a near-optimum solution, and not there is feasibility in actual applications.Analysis reason is：Depth-first traversal
Each node in figure is scanned for traveling through, is difficult to find a path comprising all Dominators in effective time；Enlightening
Jie Site pulling methods are increased rapidly, are difficult in effective time with the increase of Dominator number, the time complexity of fully intermeshing
Find solution.
In 30 tests, genetic method can solve Case1, Case2, Case3, Case4, but the weights of near-optimum solution compared with
Greatly, and time-consuming many, and for Case5, genetic method is not met for through must be through summit like shortest path.
In 30 tests, the present invention after node simplifies greatly reduces data volume, can quickly find optimal solution.
For Case1, Case2, four kinds of methods are obtained for optimal solution, and the present invention is time-consuming less；For Case3 and Case5, although this
Invention does not obtain theoretical optimal solution, but obtained one with theoretical optimal solution very close to suboptimal solution, better than other three kinds of sides
Method.
In order to test the average behavior of the present invention, table 2 counts the average weights of 30 tests of the present invention, average time-consuming with
And error rate, wherein, error rate=(average weight-theory optimal solution)/theory optimal solution.
Average weight and the error rate of 30 times tested by table 2 for 5 use-cases
| Example | Theoretical optimal solution | Average weight | Averagely time-consuming (ms) | Error rate |
| Case1 | 71 | 71 | 7.7 | 0.0 |
| Case2 | 99 | 99 | 51.8 | 0.0 |
| Case3 | 375 | 398.1 | 8154.1 | 0.061 |
| Case4 | 447 | 447 | 4171.9 | 0.0 |
| Case5 | 444 | 469.7 | 8496.47 | 0.057 |
From table 2 it can be seen that for Case1, Case2 and Case4, the present invention can obtain optimum in the short period every time
Solution, its error rate are 0.For Case3 and Case5, the present invention can find the excellent path of relative proximity, error in effective time
Rate is respectively 0.061 and 0.057.Although Case3 Dominators number is less than Case4, the out-degree of its Dominator is more, deposits
Actual path more, so as to be similar to Case3 this part figure cannot get optimal solution.Case5 relative to other figures,
Total node and all must compare many through points, the path that Formica fusca walks is relatively more, obtains the probability minimizing of optimal solution.
Broken line graph drafting is carried out to the optimal path weights change of 30 tests of the present invention, as a result such as Fig. 3.
As can be seen from Figure 3：Case1, Case2 and Case4 obtain optimal solution, the road of Case3 in 30 tests all the time
Footpath weights rise and fall between 385 to 420, and the routine weight value of Case5 rises and falls between 446 to 512, with certain stability.
Experiment 2, is simplified to sample topology with the present invention, as a result such as Fig. 4.Wherein：
Fig. 4 (a) represents not simplified complicated figure：S is source node, and t is purpose node, and k1, k2, k3, k4 are must warp knuckle
Point, remaining node (a, b, c, d, e, f, g) be auxiliary node, the digitized representation weight in each edge.According to Di Jiesitela side
Method, the beeline that s to k1 is obtained are 2, and respective path is s → a → k1；In the same manner, obtain source node to other Dominators,
Two-by-two between Dominator and arbitrary Dominator to destination node beeline.
Fig. 4 (b) is the simple graph after simplification.Some routing informations in complicated figure are concealed in simple graph, extensive
During multiple original path, the situation for iterating through same auxiliary node is can be potentially encountered, for example：Assume finally to obtain from simple graph
To the path order from s to t it is：S → k1 → k2 → k3 → k4 → t, the then path for recovering s to k1 correspond to original path for s
→ a → k1, k1 to k2 correspond to k1 → a → k2, and k2 to k3 corresponds to k2 → d → k3, and k3 to k4 corresponds to k3 → k4, and k4 is to mesh
Node t routing informations correspond to k4 → t, complete original path information is s → a → k1 → a → k2 → d → k3 → k4 → t,
It can be seen that, a nodes are iterated through in original path.Therefore, after figure simplifies, the node number of original complicated figure reduces, significantly
Complexity is reduced, solving speed is improved, but if not carrying out Actual path recovery, it is likely that generating has endless path, and this is just
It is subsequently used in using minimax ant colony method the reason for forward and reverse Di Jiesitela.
In sum, the present invention has on solving speed relative to Depth Priority Searching, Di Jiesite pulling methods
Very big lifting, compared with genetic method, all has very big advantage in solving result quality and solving speed.
Claims (7)
1. a kind of loop-free shortest path searching method based on Di Jiesitela and minimax ant colony, comprises the following steps：
(1) weighted and directed graph is constructed：
With G (V, E) for original graph, it is mutual that construction meets source node s, destination node t, Dominator collection V' and auxiliary node collection X
The weighted and directed graph G of relation, wherein, V is node set, and E is line set of having the right；
(2) initialize：
One is set up like shortest path set W, and is initialized as sky, the structure according to weighted and directed graph G sets up the out-degree collection of p node
Close OpWith in-degree set Ip, wherein p ∈ V；
(3) beta pruning is carried out to weighted and directed graph G, obtains the weighted and directed graph G1 after beta pruning：
(3.1) weighted and directed graph G is searched for by depth-first search traversal method, deletes the node that can not be reached in weighted and directed graph G；
(3.2) the out-degree set O of decision node set V interior joint ppBe whether empty, if it is empty, then deletion of node p and related to p
Directed edge, wherein p ≠ s and p ≠ t；
(3.3) access flag of all nodes in Dominator collection V' and auxiliary node collection X is initialized as 0, if accessing mark
Will position is that 0 expression is not accessed, and access flag is that 1 expression is accessed；
(3.4) take in Dominator collection V' one and be not accessed for node p, its access flag is set to 1, decision node p
In-degree set IpWhether size is 1：If 1, then only retain predecessor node to p directed edge, delete the predecessor node other
Out-degree side, executes (3.5), otherwise, directly executes (3.5)；
(3.5) the out-degree set O of decision node ppWhether size is 1, if 1, then only retain p to the directed edge of descendant node, delete
Except other in-degree sides of the descendant node, execute (3.6), otherwise, directly execute (3.6)；
(3.6) whether the access flag of all Dominators is judged all for 1, if being all 1, executed (3.7), otherwise, return
(3.4)；
(3.7) take in auxiliary node collection X one and be not accessed for node p1, its access flag is set to 1, decision node p1
In-degree set Ip1Whether size is 1：If 1, then only retain predecessor node to the directed edge of p1, p1 is deleted to its predecessor node
Directed edge, executes (3.8), otherwise, directly executes (3.8)；
(3.8) the out-degree set O of decision node p1p1Whether size is 1, if 1, then only retain p1 to the oriented of descendant node
Side, deletes descendant node to the directed edge of p1, executes (3.9), otherwise, directly executes (3.9)；
(3.9) judge that the access flag of all auxiliary nodes, whether all for 1, if being all 1, obtains the weighted and directed graph after beta pruning
G1, executes (4), otherwise, returns (3.7).
(4) the weighted and directed graph G1 after Di Jiesite pulling methods are by beta pruning be reduced to only comprising source node s, destination node t,
The weighted and directed graph G2 of Dominator collection V' mutual relation；
(5) the minimax ant colony method with reference to Di Jiesitela used in simplified weighted and directed graph G2 obtains optimum road
Footpath：
(5.1) initiation parameter：Formica fusca number is m, arranges maximum iteration time F, and the initial weight for putting globally optimal solution is nothing
Poor big, iterationses are 0；
(5.2) the taboo list Tabu for depositing the node that passes through of Formica fusca and path is configured tok, k=1,2 ..., m, and be initialized as
Empty；
(5.3) whole Formica fuscas are placed on source node s, source node s and destination node t is added to taboo list Tabuk, k=1,
2 ..., m, the initial weight for putting current iteration optimal solution are infinity；
(5.4) a Formica fusca k is taken, its path P is calculatedk；
(5.5) the walked path Ps of current Formica fusca k are calculatedkWeights, empty the corresponding taboo list Tabu of the Formica fuscak；
(5.6) judge whether whole Formica fuscas complete pathfinding, if so, execute (5.7)；Otherwise, (5.4) are returned；
(5.7) path P to all Formica fuscas1, P2... Pk..., PmSorted according to weights from small to large, and selected according to sequence successively
Take the path P of Formica fusca kk, judge its path PkWeights whether be less than current iteration optimal solution, if so, then by each node in G2
Access flag be set to 0, execute (5.8), otherwise, jump to (5.12)；
(5.8) path P current Formica fusca k obtained using positive Di Jiesite pulling methodskRevert to positive Actual path P 'k, sentence
Disconnected forward direction Actual path P 'kWeights whether be less than current iteration optimal solution, if so, then update current iteration optimal solution, execute
(5.9), otherwise, (5.10) are executed；
(5.9) judge positive Actual path P 'kWeights whether be less than globally optimal solution, if so, then update globally optimal solution, and
To be positive Actual path P ' like the path replacement in shortest path set Wk, execute (5.10), otherwise, directly execute (5.10)；
(5.10) all node visit flag bits are set to 0 again, using reverse Di Jiesite pulling methods by path PkRevert to reversely
Actual path P "k, judge reverse Actual path P "kWeights whether less than current iteration optimal solution, if so, then update this and change
For optimal solution, execute (5.11), otherwise, execute (5.12)；
(5.11) judge reverse Actual path P "kWeights whether be less than globally optimal solution, if so, then update globally optimal solution, and
To be reverse Actual path P like the path replacement in shortest path set W "k, execute (5.12), otherwise, directly execute (5.12)；
(5.12) minimax pheromone is calculated, and updates routing information element；
(5.13) iterationses add 1, judge whether to reach predetermined iterationses F, if so, then will protect like in shortest path set W
The path that deposits is exported as optimal path, otherwise, is returned (5.3).
2. method according to claim 1, wherein having the right after Di Jiesite pulling methods are to beta pruning in step (4)
Simplified to figure G1, carried out as follows：
(4.1) source node weight matrix U is defined, for preserving source node s to the routine weight value between each Dominator, if from
There is no path in source node s a to Dominator, or have to pass through other Dominators and get to the Dominator, then
The routine weight value is preserved for infinity, if in the presence of having mulitpath between source node s a to Dominator, preserving most short
That paths weights；
(4.2) Dominator weight matrix E is defined, for preserving routine weight value two-by-two between Dominator；
(4.3) destination node weight matrix D is defined, for preserving each Dominator to the routine weight value of destination node；
(4.4) only obtained comprising source according to source node weight matrix U, Dominator weight matrix E, destination node weight matrix D
The simplified weighted and directed graph G2 of node s, destination node t and Dominator collection V' mutual relation.
3. method according to claim 1, wherein calculates the path P of a Formica fusca k in step (5.4)k, as follows
Carry out：
(5.4a) set of paths P of kth Formica fusca is initializedkFor sky, the current a moment is calculated, from source node s to all not interviewed
The transition probability of the Dominator p for asking
τspA () represents current time, the pheromone on node s to node p paths, ηspA () is represented from node s to the energy of node p
Degree of opinion, value are inverses of the node s to the distance of node p, and weighted values of the α for pheromone, β are the weighted value of visibility；
(5.4b) pass through transition probabilityDetermine subsequent time accessed node, access the node, and by source node s to the section
The corresponding directed edge of point is added to set of paths PkIn, update taboo list Tabuk；
(5.4c) current accessed node i is calculated to the transition probability of next addressable Dominator j
τijA () represents the pheromone on current time, node i to node j paths, ηijA () is represented from node i to node j's
Visibility, value are inverse of the node i to node j distances；
(5.4d) transition probability drawn by (5.4c)Determine next accessed node, access the node, and more new route
Set PkWith taboo list Tabuk；
(5.4e) judge whether all Dominators are all accessed, if so, by last Dominator to destination node t
Directed edge adds set of paths Pk, otherwise, return (5.4c).
4. method according to claim 1, wherein used in step (5.8), forward direction Di Jiesite pulling methods are by current Formica fusca
The path P that k is obtainedkRevert to positive Actual path P 'k, carry out as follows：
(5.8a) positive Actual path P is constructedk', be initialized as sky, by beta pruning after weighted and directed graph G1 in all node visits
Mark position 0；
(5.8b) in the weighted and directed graph G1 after beta pruning, according to path PkForward sequence, from source node s, find next
The individual Dominator not accessed, and update positive Actual path P 'k；
(5.8c) Dominator that the next one is not accessed is found, updates positive Actual path P 'k；
(5.8d) judge whether to reach destination node t, if so, obtain positive Actual path P 'k, otherwise, return (5.8c).
5. method according to claim 1, wherein used in step (5.10), reverse Di Jiesite pulling methods are by current ant
The path P that ant k is obtainedkRevert to reverse Actual path P "k, carry out as follows：
(5.10a) reverse Actual path P is constructed "k, be initialized as sky, by beta pruning after weighted and directed graph G1 in all node visits
Mark position 0；
(5.10b) in the weighted and directed graph G1 after beta pruning, according to current path PkReverse sequence, from destination node t,
The Dominator that the next one is not accessed is found, and updates reverse Actual path P "k；
(5.10c) Dominator that the next one is not accessed is found, updates reverse Actual path P "k；
(5.10d) judge whether to reach source node s, if so, obtain reverse Actual path P "k, otherwise, return (5.10c).
6. method according to claim 1, wherein calculates minimax pheromone in step (5.12), by below equation
Carry out：
Wherein, τmaxFor maximum information element, ρ represents the residual coefficients of pheromone, and L is the path that optimum Formica fusca is passed by, τmin
For minimal information element, n be simplify after node number in weighted and directed graph G2, avg=n/2, PbestRepresent that Formica fusca is once searched for
Find the probability of optimal solution.
7. method according to claim 1, wherein in step (5.12), fresh information element, is carried out by below equation：
Wherein,Optimum Formica fusca is represented at (a, a+1) in the time, the pheromone increment of path i to j；
Q is constant, represents the pheromone total amount that single Formica fusca discharges in the paths.
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