CN103049656B - Construction method of Euler diagram and method for optimizing test sequence based on method - Google Patents
Construction method of Euler diagram and method for optimizing test sequence based on method Download PDFInfo
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Abstract
The invention discloses a construction method of Euler diagram and a method for optimizing test sequence based on the method, wherein the construction method of Euler diagram comprises the following steps: judging whether out-degree and in-degree of each peak in the digraph are balanced, wherein arcs among all peaks in the diagraph have access directions, the out-degree is total number of arcs by using the current peak as a beginning point, and the in-degree is the total number of arcs by using the current peak as an ending point; if the difference between the out-degree and the in-degree of the peak A is W, searching W peaks mostly close to the peak A, respectively using W peaks as beginning points to construct repeated arcs by using the peak A as an ending point, or respectively using the peak A as the beginning point to respectively construct repeated arcs by using W peaks as ending points. Through the method disclosed by the invention, the use of auxiliary space is reduced, and the efficiency of Euler diagram construction is improved.
Description
Technical field
The present invention relates to Train operation control system, more particularly to a kind of Euler diagram building method and be based on the party
The method that method carries out test sequence optimization.
Background technology
Test cases is the verification and testing carried out to train-installed equipment certain functional character.Perform fc-specific test FC case
Requirement system must reach the original state needed for this test cases.These original states are only by performing particular system function
Can be only achieved, and these particular system functions are included in other test cases.
Cycle testss are test cases to be connected by certain method, can be with actual motion so as to form one
Test scene, and after guaranteeing that test terminates, all tested mistake of all of test cases is at least one times.Cycle testss are not arbitrarily to produce
Raw, but certain method is followed, some test cases are together in series in order, the orderly survey of a test scene formula is formed
Examination casebook.
Due to test cases substantial amounts, and mobile unit function is complicated, in cycle testss, reuses test case
The situation of example is more.In order to more easily be optimized to cycle testss, one group of cycle tests can be converted into directed graph, train
Summit of each mode of operation as directed graph, Test segment as the directed arc between summit, included in Test segment
Test cases quantity regard the expense of directed arc as.
By the construction of Euler diagram is carried out to directed graph optimizing directed arc in prior art, to reduce the weight of test cases
It is multiple to use.But when Euler diagram construction is carried out, aid in the addition number of arc more, additionally take certain memory headroom, shadow
The efficiency of Euler diagram construction has been rung, also, it is larger by the quantity of the posttectonic directed graph repetition arc of Euler diagram, cause to test sequence
The cost of row increases.
The content of the invention
It is an object of the invention to provide a kind of building method of Euler diagram and carrying out test sequence optimization based on the method
Method, reduces the use of auxiliary space, improves the efficiency of Euler diagram construction.
The purpose of the present invention is achieved through the following technical solutions：
A kind of building method of Euler diagram, the method include：
Whether the out-degree and in-degree for judging each summit in directed graph balances, wherein, in directed graph between all of summit
Arc there is any discrepancy direction, out-degree is the sum of the arc with current vertex as starting point, and in-degree is the arc with current vertex as terminal
Sum；
If the out-degree of summit A is W with the difference of in-degree, search apart from the W summit A nearest summit, respectively with institute
The repetition arc that W summit is stated for starting point structure with the summit A as terminal, or distinguish by starting point of the summit A respectively
Build the repetition arc with the W summit as terminal.
A kind of method of test sequence optimization, the method include：
Repeat, after arc, to carry out Europe to the directed graph that addition repeats after arc by Fleury Fleury algorithms for directed graph addition
Retract the calculating on road, obtain with a certain summit as starting point and the cycle testss by all arcs at least one times.
As seen from the above technical solution provided by the invention, by using greedy strategy, local optimum is made to reach entirely
Office is optimum, progressively constructs optimal solution, and reduces the use of auxiliary space, improves the efficiency of Euler diagram construction.
Description of the drawings
In order to be illustrated more clearly that the technical scheme of the embodiment of the present invention, below will be to using needed for embodiment description
Accompanying drawing be briefly described, it should be apparent that, drawings in the following description are only some embodiments of the present invention, for this
For the those of ordinary skill in field, on the premise of not paying creative work, can be obtaining other according to these accompanying drawings
Accompanying drawing.
Fig. 1 is a kind of flow chart of the building method of Euler diagram that the embodiment of the present invention one is provided；
Fig. 2 is the flow chart of the building method of another Euler diagram that the embodiment of the present invention two is provided；
Fig. 3 is a kind of schematic diagram of cycle testss directed graph that the embodiment of the present invention two is provided；
Fig. 4 repeats the schematic diagram of the directed graph after arc for a kind of construction that the embodiment of the present invention two is provided；
Fig. 5 is a kind of flow chart of the method for test sequence optimization that the embodiment of the present invention three is provided.
Specific embodiment
With reference to the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Ground description, it is clear that described embodiment is only a part of embodiment of the invention, rather than the embodiment of whole.Based on this
Inventive embodiment, the every other enforcement obtained under the premise of creative work is not made by those of ordinary skill in the art
Example, belongs to protection scope of the present invention.
Embodiment one
A kind of flow chart of the building method of Euler diagram that Fig. 1 is provided for the embodiment of the present invention one, the method mainly include
Following steps：
Step 101, judge whether the out-degree and in-degree on each summit in directed graph balance.Wherein, summit is each of train
Individual mode of operation, there is any discrepancy the direction of the arc in directed graph between all of summit, out-degree is the arc with current vertex as starting point
Sum, in-degree is the sum of the arc with current vertex as terminal, and the arc is the Test segment between mode of operation.
Judge whether directed graph is Euler diagram, mainly judge each summit in directed graph goes out whether in-degree balances, that is, sentence
Whether the disconnected arc number with current vertex as starting point is identical with the arc number with current vertex as terminal.
If the difference of step 102, the out-degree of summit A and in-degree is W, search apart from the W summit A nearest summit,
Build repetition arc with the summit A as terminal by starting point of the W summit respectively, or respectively with the summit A for
Initial point builds the repetition arc with the W summit as terminal respectively.
Show that current directed graph is not Euler diagram if in-degree imbalance is gone out, need addition to repeat arc.Using greedy plan
Slightly solve：Global optimum is reached by local optimum, i.e., an optimal decision is chosen in each stage, progressively construct optimal solution.
From the original state of problem, optimal value (or more excellent solution) is drawn by greedy selection several times.
For example, calculate each summit respectively goes out whether in-degree balances, when summit A go out in-degree it is uneven when, degree of obtaining with
The poor W of in-degree, when out-degree is more than in-degree, then searches apart from the W summit A nearest summit, respectively with the W summit
The repetition arc with the summit A as terminal is built for starting point；When in-degree be more than out-degree when, then respectively with the summit A for
Initial point builds the repetition arc with the W summit as terminal respectively.When by add repeat arc balance summit A go out in-degree after,
Go out the unbalanced summit addition of in-degree for other again and repeat arc, until the in-degree that goes out on all summits is balanced.
The embodiment of the present invention is made local optimum reach global optimum, progressively constructs optimal solution by using greedy strategy, and
The use of auxiliary space is reduced, the efficiency of Euler diagram construction is improve.
Embodiment two
In order to more specifically introduce the present invention, 2-4 is described further to the present invention below in conjunction with the accompanying drawings.As shown in Fig. 2
Comprise the following steps：
Step 201, judge whether the out-degree and in-degree on each summit in directed graph balance.Step is proceeded to if imbalance
202。
Wherein, each mode of operation of summit for train, there is any discrepancy the direction of the arc in directed graph between all of summit goes out
Degree is the sum of the arc with current vertex as starting point, and in-degree is the sum of the arc with current vertex as terminal, and the arc is work
Test segment between operation mode.
Show that current directed graph is not Euler diagram if in-degree imbalance is gone out, need addition to repeat arc to balance summit
Go out in-degree, now proceed to step 202.
Step 202, the distance matrix and route matrix that calculate directed graph.Current directed graph is not Euler diagram, needs addition
That repeats arc to balance fixed point goes out in-degree.And need before this to calculate the distance matrix and route matrix of the directed graph, can
Calculate with using Freud Floyd algorithms, its calculation process is：Adjoin from the cum rights of the distance of any 2 summit i to j
Matrix（I is connected with j）Start, every time one summit k of insertion, then by the known shortest path between i to j and to insert summit k
Compare as the path distance of intermediate vertex, it is new distance matrix to take smaller value.And with this loop iteration, construct successively
N matrix D (1), D (2) ... ... D (n).
For example, to the result of directed graph computed range matrix as shown in Figure 3 it is：
Wherein, summit order is：NP、SB、SH、OS、PT、TR、CO、FS.The i row j column elements of matrix D (n) are No. i tops
Shortest path length of the point to j summits, for example, shortest path of the distance " 1 " that the 1st row the 2nd is arranged for summit NP to summit SB
Length；Shortest path length of the distance " 1 " of the row of the 3rd row the 2nd for summit SH to summit SB.
One descendant node matrix path can be introduced according to calculated distance matrix（Route matrix）To record at 2 points
Between shortest path.For example, learnt in conjunction with the distance matrix of Fig. 3 according to Fig. 3, D（TR, SH）=PT, then it represents that summit TR is to top
Point SH have passed through summit PT, for another example, D（SB, CO）=CO, then it represents that summit SB and CO is joined directly together.
Step 203, Euler diagram construction is carried out to the directed graph.Carry out Euler diagram to construct so that directed graph is each to directed graph
The in-degree that goes out on individual summit reaches balance.And the present invention is causing going out on the basis of in-degree is balanced for each summit of directed graph to need to guarantee
Total cost is minimum.The total cost of one directed graph is the cost metric according to original arc and repetition arc（Comprising test cases
Number）Calculating gets, and the cost metric of original arc of directed graph and arc will not change, therefore, directed graph is total to be taken
Decision variable is：Repeat arc quantity and repeat the cost metric of arc.
Following formula subrepresentation can be passed through：
Wherein, s.t. is constraints,For the out-degree of summit i,For the in-degree of summit i, biFor the confession of summit i
To amount,For the total cost of directed graph, ωijFor the cost metric of arc, xijIt is ω for expense in summit i to summit jij
Arc number, cijFor the permission maximum of arc number.
For solution object functionMinima, it is possible to use greedy strategy solve：Reached by local optimum
Global optimum, i.e., choose an optimal decision in each stage, progressively construct optimal solution.From the original state of problem, lead to
Optimal value (or more excellent solution) is drawn after greedy selection several times.
When the Euler diagram that said method is used for directed graph is constructed, it is represented by first making which for a certain summit addition repetition arc
After going out in-degree balance, then go out the unbalanced summit addition repetition arc of in-degree for other, until the in-degree that goes out on all summits is balanced.Example
Such as, when summit A goes out in-degree imbalance, the poor W of degree of obtaining and in-degree, when out-degree is more than in-degree, then according to described apart from square
Battle array is searched apart from the W summit A nearest summit with the route matrix, is built by starting point of the W summit respectively
Repetition arc with the summit A as terminal；When in-degree is more than out-degree, then built with the summit A respectively as starting point respectively
Repetition arc with the W summit as terminal.
Euler diagram construction is carried out for the directed graph in Fig. 3 according to the method described above, obtain a result for：Five repetitions need to be added
Arc, NP->SB；NP->CO；TR->CO；OS->FS；TR->FS.As shown in figure 4, thick arc portion point（b1-b5）For the repetition of addition
Arc.
The embodiment of the present invention is made local optimum reach global optimum, progressively constructs optimal solution by using greedy strategy, and
The use of auxiliary space is reduced, the efficiency of Euler diagram construction is improve.
Embodiment three
Euler diagram construction has been carried out to directed graph by the method for embodiment two（Addition repeats arc）, and on this basis may be used
To be optimized to cycle testss.As shown in figure 5, mainly comprising the steps：
Step 501, the calculating that Euler's circuit is carried out to Euler diagram, obtain cycle testss.
The calculating of Euler's circuit can be carried out by Fleury Fleury algorithms to the directed graph that addition repeats after arc, is obtained
Cycle testss with a certain summit as starting point and by all arcs at least one times.Specifically：
Appoint and take v0 ∈ V (G), make P0=v0；
If Pi=v0e1v1e2 ... ei vi have gone time, ei+1 is therefrom chosen by following method：
（a）Ei+1 is associated with vi；
（b）Unless be available for row time without other side, otherwise ei+1 should not be the bridge in Gi=G- { e1, e2 ..., ei }（Bridge is
One arc for making connected graph no longer connect after deleting）；
（c）When（b）When can not carry out again, algorithm stops.
Wherein, v represents summit, and e represents arc, and p represents path, and P0=v0 is represented with v0 as starting point, Gi=G- e1, e2 ...,
Ei } represent arc e1, the e2 in directed graph G ..., ei is deleted.
So that summit NP in Fig. 4 is as starting point as an example, the calculating of Euler's circuit is carried out, following cycle testss are obtained：
P1=NP b1 SB a16 CO a19 FS a18 CO a12 TR b4 CO a26 NP b2 CO a17 SB a15
FS a14SB a4 SH a3 SB a1 NP a2 SB a7 OS a13 SB a6 OS a5 SH a8 OS b3 FS a23 OS
a24 FS a20 TRb5 FS a21 TR a9 PT a10 OS a22 TR a11 PT a25 SH a27 NP。
Step 502, optimal inspection sequence.
For the directed graph for being originally used for Euler diagram, after Euler's circuit calculating is carried out, this step need not be carried out, directly can be turned
Entering step 503 carries out the calculating of total cost.
Last step carries out being calculated one group of cycle tests to Fig. 4, and the expense in cycle testss P1 is least cost,
But due to the repetition arc included in sequence P1（b1-b5）It is arteface for the ease of calculating cycle testss, in reality
There is no above-mentioned repetition arc in operation, i.e., the above-mentioned arc that repeats does not have actual meaning in cycle testss, accordingly, it would be desirable to logical
Cross original arc and be replaced arc is repeated.For example, for the summit NP in sequence P1 connects summit SB by " arc b1 ", then need
" arc b1 " is replaced with original arc.And the foundation replaced is the route matrix of the directed graph that step 202 is calculated（To record point-to-point transmission
Shortest path）.
Optimal path can be solved by backtracking method：Known route matrix path, solves summit i with top using backtracking method
The shortest path of point j, if Pij=k1, then start backtracking from summit i and summit j respectively.
1）Start backtracking from point i
Pik1=k2,Pik2=k3, Pik3=k4 ..., Pikr=kr+1.
2）Start backtracking from point j
Pk1j=q1, Pq1j=q2, Pq2j=q3 ..., Pikr=j.
It is calculated from point i to the shortest path of point and is：I, kr, kr-1 ..., k2, k1, q1, q2 ..., qm, j.
By said method in Fig. 4 with repeat arc（b1-b5）Related summit is recalled, and obtains three route letters
Breath：TR->PT->SH->SB->CO、NP->SB->CO、TR->PT->OS->FS.
The repetition arc in cycle testss P1 is replaced with above-mentioned routing iinformation, the cycle testss after being optimized：
P2=NP a2 SB a16 CO a19 FS a18 CO a12 TR a9 PT a10 OS a24 FS a18 CO
a26 NP a2 SBa16 COa 17 SB a15 FS a14 SB a4 SH a3 SB a1 NP a2 SB a7 OS a13 SB
a6 OS a5 SH a8 OSa24 FS a23 OS a24 FS a20 TR a9 PT a10 OS a24 FS a21 TR a9 PT
a10 OS a22 TR a11 PT a25SH a27 NP。
Step 503, the total cost for calculating cycle testss.
The total cost of cycle testss is all arc expenses（The number of test cases）Summation.Assume institute in cycle testss P2
The number for having the test cases that arc includes is 1, then sum of the total cost for arc（38）, staff can be directly used for live
Adjust joint-trial and can quickly calculate cycle testss total cost.
Repetition arc in cycle testss result is replaced by the embodiment of the present invention by being optimized to cycle testss result
For original arc set so that cycle testss more conform to the requirement of on-the-spot test and can quickly calculate cycle testss total cost.
Through the above description of the embodiments, those skilled in the art can be understood that above-described embodiment can
To be realized by software, it is also possible to by software plus necessary general hardware platform mode realizing.Based on such understanding,
The technical scheme of above-described embodiment can be embodied in the form of software product, the software product can be stored in one it is non-easily
The property lost storage medium（Can be CD-ROM, USB flash disk, portable hard drive etc.）In, use so that a computer sets including some instructions
It is standby（Can be personal computer, server, or network equipment etc.）Perform the method described in each embodiment of the invention.
The above, the only present invention preferably specific embodiment, but protection scope of the present invention is not limited thereto,
Any those familiar with the art in the technical scope of present disclosure, the change or replacement that can be readily occurred in,
Should all be included within the scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of claims
Enclose and be defined.
Claims (4)
1. a kind of building method of Euler diagram, it is characterised in that the method includes：
Whether the out-degree and in-degree for judging each summit in directed graph balances, wherein, the arc in directed graph between all of summit is equal
There is any discrepancy direction, out-degree is the sum of the arc with current vertex as starting point, and in-degree is the total of the arc with current vertex as terminal
Number；
If the out-degree of summit A is W with the difference of in-degree, search apart from the W summit A nearest summit, respectively with the W
Summit is that starting point builds repetition arc with the summit A as terminal, or respectively with the summit A as starting point build respectively with
Repetition arc of the W summit for terminal；
The distance matrix and route matrix of the directed graph are calculated according to Freud Floyd algorithms, and according to described apart from square
Battle array is searched apart from the W summit A nearest summit with the route matrix；
Wherein, the distance matrix represents the length of two summit shortest paths, and the route matrix represents the company on each summit
Connect path；From the beginning of the weighted adjacency matrix of the distance of any 2 summit i to j, a summit k is inserted every time, then by i to j
Between known shortest path with using insert summit k as compared with the path distance of intermediate vertex, it is new distance to take smaller value
Matrix；Introduce a route matrix to record the shortest path of point-to-point transmission according to calculated distance matrix；
Optimal path is solved by backtracking method, it is known that route matrix path, fixed point i and fixed point j is solved most using backtracking method
Short path, if Pij=k1, then start backtracking from summit i and summit j respectively；From fixed point i to the path for pinpointing j, k1 is represented most Pij
Short path；
When the minimum number for repeating arc in the directed graph, and during the cost metric minimum of each repetition arc, the repetition arc
Total cost is minimum, wherein repeatedly the cost metric of arc is the number for repeating the test cases that arc is included；
Its expression formula is：
Wherein, z represents directed graph total cost, and s.t. is constraints,For the out-degree of summit i,For entering for summit i
Degree, biFor the quantity delivered of summit i,For the total cost of directed graph, ωijFor the cost metric of arc, xijArrive for summit i
In the j of summit, expense is ωijArc number, cijFor the permission maximum of arc number；
Object function is solved using greedy strategyMinima：Global optimum is reached by local optimum, i.e., every
The individual stage chooses an optimal decision, progressively constructs optimal solution, from the original state of problem, by greediness choosing several times
Select and draw optimal value.
2. a kind of method of test sequence optimization, it is characterised in that the method includes：Based on the method described in claim 1 it is
Directed graph addition repeats arc；
The calculating of Euler's circuit is carried out by Fleury Fleury algorithms to the directed graph that addition repeats after arc, is obtained with a certain top
Point is starting point the cycle testss by all arcs at least one times.
3. method according to claim 2, it is characterised in that the method also includes：
The route matrix of the directed graph is recalled by backtracking method, obtain the most short of all two vertex correspondences for repeating arc
Path；
The repetition arc in the cycle testss is replaced using the shortest path of two vertex correspondences for repeating arc.
4. method according to claim 3, it is characterised in that described using the most short of two vertex correspondences for repeating arc
Also include after repetition arc in cycle testss described in path replacement：
The cost metric of all arcs in cycle testss is added the total cost for obtaining cycle testss；The total cost is represented and completes this
Expense needed for cycle testss, when the total cost for repeating arc is minimum, the total cost of cycle testss is minimum.
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| CN107179993A (en) * | 2017-06-01 | 2017-09-19 | 中国铁道科学研究院通信信号研究所 | Method for creating test sequence applied to train control system |
| CN111444534A (en) * | 2020-03-12 | 2020-07-24 | 中国建设银行股份有限公司 | Method, device, equipment and computer readable medium for monitoring user operation |
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