CN106776053A - A kind of solving job shop scheduling problem Deadlock Detection and restorative procedure based on matrix - Google Patents
A kind of solving job shop scheduling problem Deadlock Detection and restorative procedure based on matrix Download PDFInfo
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- CN106776053A CN106776053A CN201611206622.5A CN201611206622A CN106776053A CN 106776053 A CN106776053 A CN 106776053A CN 201611206622 A CN201611206622 A CN 201611206622A CN 106776053 A CN106776053 A CN 106776053A
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- G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
- G06F9/46—Multiprogramming arrangements
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Abstract
The invention discloses a kind of solving job shop scheduling problem Deadlock Detection based on matrix and restorative procedure, its feature comprises the following steps：（1）According to the corresponding graph model of extracting of scheduling resultGBuild adjacency matrixA；（2）According to adjacency matrixA, calculate reachability matrixM；（3）Deadlock Detection, if it find that deadlock is then found and being caused the matrix element of deadlock and being marked, otherwise, terminates；（4）According to deadlock information, with reference to the domain knowledge of JSP problems, splitting off causes the directed circuit of deadlock, breaks deadlock；（5）According to step（4）The modified result of middle modification is extracted graph modelG, return to step 1.The present invention is from matrix angle research solving job shop scheduling problem Deadlock, there is provided a kind of new Research Thinking, quick detection can be realized and repaired by deadlock caused by operation movement, it is feasible solution not only to repair, and it is the more preferable feasible solution of target function value to repair as far as possible.
Description
Technical field
The present invention relates to production scheduling technical field, and in particular to a kind of solving job shop scheduling problem Deadlock Detection based on matrix
With restorative procedure.
Background technology
Job-shop scheduling problem（Job Shop Scheduling Problem, JSP）It is manufacturing execution system research
One of core and emphasis, its research have important theory significance and application value.At present, calculated with genetic algorithm, differential evolution
Method, tabu search algorithm, artificial bee colony algorithm etc. have obtained successful Application for the intelligent algorithm of representative in JSP problems are solved.
Research finds that a common ground of various high efficiency smart algorithms is always to incorporate the neighbor search techniques based on neighbour structure, because
For neighbour structure can embody problem feature domain knowledge in itself, the characteristics of with reference to problem in itself, can effectively instruct to search
Suo Fangxiang.But, in the critical process moving process based on neighbour structure, it is infeasible to may result in existing feasible solution, i.e.,
Deadlock state.Deadlock be vie each other resource affairs between mutually wait, the resource request of each things is in existing con current control
A kind of dead state being not being met forever under mechanism.It is reflected in JSP problems, is that the machining sequence constraint of workpiece operation is closed
System is not being met.And then machine process is caused from being smoothed out, or even cause the new machine process can not to start, therefore,
It is necessary to study Deadlock.
At present, solving JSP Deadlocks has three kinds of strategies：Deadlock prevention, dead time revision, Deadlock Detection and reparation.Wherein,
For Deadlock Detection with repair, it is theoretical that most research is all based on graph model, more particularly to one kind is extracted graph model, i.e. structure
The graph model of extracting that can describe problem characteristic is made, if it find that there is directed circuit in the model, then deadlock occurs.Deadlock is repaired
It is critical only that and split off directed circuit, be met the machining sequence constraint relation of each workpiece operation.It is each in current document
Correcting strategy is planted, it is a feasible solution simply to be repaired, the present invention intends realizing a kind of more advanced correcting strategy, is obtaining
On the premise of feasible solution, it is the more excellent feasible solution of target function value to repair as far as possible.
The content of the invention
The purpose of the present invention is that the adjacency matrix in mathematics and reachability matrix are introduced the research of job-shop scheduling problem
In, and then related theoretical research is carried out from math matrix computing and the angle of property, propose a kind of Operation Van based on matrix
Between dispatch Deadlock Detection and restorative procedure, to pass through mathematical logic computing energy quick detection go out by operation movement trigger it is dead
Lock, and when providing deadlock, cause the information of deadlock.Then in conjunction with the domain knowledge of JSP problems, according to operation type information, tear open
It is disconnected to cause the directed circuit of deadlock, more advanced reparation is realized, it is feasible solution not only to repair, and it is target to repair as far as possible
The more preferable feasible solution of functional value, and then cause the various high efficiency smart algorithms based on neighbour structure search when JSP problems are solved
It is more efficiently feasible.
The purpose of the present invention adopts the following technical scheme that realization.
A kind of solving job shop scheduling problem Deadlock Detection and restorative procedure based on matrix, it is characterised in that comprise the following steps：
Step 1：According to the corresponding graph model of extracting of scheduling resultGBuild adjacency matrixA；
Step 2：According to adjacency matrixA, calculate reachability matrixM；
Step 3：Deadlock Detection, if it find that deadlock is then found causes the matrix element of deadlock, and marks, and otherwise, terminates；
Step 4：According to deadlock information, with reference to the domain knowledge of JSP problems, splitting off causes the directed circuit of deadlock, breaks deadlock；
Step 5：Modified result according to being changed in step 4 is extracted graph modelG, return to step 1.
Extracted described in step 1 graph modelG=<V,E>, wherein：VIt is node set,V={v 1,v 2...,v n , including one
Virtual start nodeSThe end node virtual with oneF；EIt is the set of directed edge；VIn remove nodeSAnd nodeFIn addition
Node represents operation；EIncluding connection arc and arc of extracting, connection arc represents the binary crelation of workpiece operation, and arc of extracting represents machine
The binary crelation of device operation.
Adjacency matrix described in step 1AIt isnRank square formation,A=(a ij ) n×n ,a ij Value by following formula determine：
The element of matrix Far Left and the top represents operation number, wheniIt is equal tojWhen,x i Withy j Represent same processes.
Reachability matrix described in step 2MIt is the adjacency matrix according to constructed byAIt is calculated,MIt is also n rank 0-1 square formations,
And meeting boolean calculation rule, its computing formula is：, whereinIBe withAWith the unit square of order
Battle array, reflection element itself is reached, maximum delivered number of times（Road is long）rDetermined according to following formula：
。
Deadlock Detection described in step 3 is in the reachability matrix being calculatedMOn the basis of, detect with matrix leading diagonal
For the symmetric position of line of symmetry whether there is equal two-by-two and equal to 1 element, i.e.,：M ij =M ji =1.If it does not, explanation exists
Extract graph modelGIt is middle without directed circuit, then this scheduling result is feasible.If it does, explanation is in graph model of extractingGIn must there are
To loop, this scheduling result is infeasible, is judged to deadlock, and mark causes the matrix element of deadlock.
According to deadlock information described in step 4, with reference to the domain knowledge of JSP problems, splitting off causes the directed circuit of deadlock,
Principle is as follows：Deadlock information includes the binary crelation for causing between the element of deadlock and element, be reflected in JSP problems be operation and
The binary crelation of inter process, because same workpiece inter process binary crelation is unalterable, so to split off directed circuit need to change
Become with machine inter process binary crelation.By the last completion date of solving job shop scheduling problem is true by the length institute of critical path
It is fixed, therefore, priority service is carried out to the critical process in same machine operation, change its binary crelation, break deadlock.It is specifically walked
It is rapid as follows：
Step 4.1：Resulting deadlock information is divided into two classes：With workpiece inter process binary crelation and with machine inter process binary
Relation；
Step 4.2：Whether according to it is that critical process is also divided into two classes to same machine operation, prioritizing selection critical process changes
Its binary crelation, breaks deadlock.
The present invention has advantages below and beneficial effect.
（1）Be introduced into adjacency matrix and reachability matrix in mathematics in the research of JSP problems by the present invention, and then from mathematics square
Battle array computing carries out related theoretical research to the angle of property, there is provided a kind of new research solving job shop scheduling problem Deadlock
Thinking.
（2）The present invention can go out the deadlock triggered by operation movement with quick detection, and be given when there is deadlock, cause deadlock
Information, according to deadlock information, more advanced reparation is realized with reference to the domain knowledge of JSP problems, it is feasible solution not only to repair,
And it is the more preferable feasible solution of target function value to repair as far as possible, and then cause the various high efficiency smarts based on neighbour structure search
Algorithm is more efficiently feasible when JSP problems are solved.
Brief description of the drawings
Fig. 1 is implementation flow chart of the present invention.
Fig. 2 is solving job shop scheduling problem Gantt chart feasible known to.
Fig. 3 is the Gantt chart of the new presence deadlock that a mobile operation is obtained on the basis of Fig. 2.
Fig. 4 is the corresponding graph models of extracting of Fig. 3.
Fig. 5 is the corresponding adjacency matrix of Fig. 4A。
Fig. 6 is according to adjacency matrixAThe reachability matrix being calculatedM。
Fig. 7 is based on reachability matrixMDetect the result of deadlock.
Fig. 8 is the presence of the Gantt chart after deadlock Gantt chart is repaired to Fig. 3.
Below in conjunction with the accompanying drawings and embodiment the present invention is further illustrated.
A kind of solving job shop scheduling problem Deadlock Detection based on matrix is as shown in Figure 1 with restorative procedure flow chart.
Feasible solving job shop scheduling problem Gantt chart as known to Fig. 2 is one, the Gantt chart is shown with 3 workpiece, each workpiece
There are 3 procedures, the arrangement of operating sequence on 3 machines.Transverse axis represents process time, and the longitudinal axis represents processing machine, filler
The rectangular block of word represents workpiece operation, for example：（3,1）The 3rd the first procedure of workpiece is represented,（1,2）Represent the 1st workpiece
Second operation work.The operation coupled together with arrow in figure represents critical process, and all critical processes constitute a critical path
Footpath, Maximal Makespan is 19.
Now the operation in critical path is moved, operation on the basis of the Gantt chart of Fig. 2（1,2）According to guiding arrow
Head moves to operation（2,1）Before, a new scheduling Gantt chart is obtained, as shown in Figure 3.Comparison diagram 2 and Fig. 3, have found to close
Key path changes, and Maximal Makespan shorten to 18, is once beneficial movement.But whether the Gantt chart after being moved through
It is feasible, it is necessary to carry out Deadlock Detection, detection process is as follows.
1. according to given extracting figureGBuild adjacency matrixA
Its corresponding extracting figure is drawn according to Fig. 3G, as shown in Figure 4.Wherein dummy nodeSWithFBeginning and end is represented respectively,
NodeO i,j RepresentiThe of individual workpiecejProcedure.Adjacency matrix is built according to Fig. 4A, as shown in Figure 5.
2. reachability matrix is calculatedM
According to the adjacency matrix for buildingACalculate reachability matrixM, by reachability matrixMThe elements in a main diagonal is marked, result of calculation
As shown in Figure 6.
3. Deadlock Detection
In reachability matrixMOn the basis of detect whether existM ij =M ji =1, as a result as shown in Figure 7.From result,M 23=M 32=1,M 25=M 52=1,M 26=M 62=1,M 35=M 53=1,M 36=M 63=1,M 65=M 56=1, i.e., there is directed circuit in fig. 4
(O 1,1→O 1,2→O 2,1→O 2,2→O 1,1), this solution is infeasible, is judged to deadlock.To cause the matrix element of deadlock and its
Binary crelation is marked, as shown in Figure 7.
4. repair
From the figure 3, it may be seen that critical process for (O 1,1,O 1,2,O 2,1,O 2,2,O 3,3), the deadlock information the inside for being given is comprising operation（O 1,1,O 1,2,O 2,1,O 2,2）, so this four procedure is the object for considering, its binary crelation has four groups：O 1,1→O 1,2,O 1,2→O 2,1,O 2,1→O 2,2,O 2,2→O 1,1。O 1,1→O 1,2WithO 2,1→O 2,2Belong to same machine inter process binary crelation, do not consider, in order to tear open
Disconnected directed circuit,O 1,2→O 2,1WithO 2,2→O 1,1One group of binary crelation of middle random selection, such as selectsO 2,2→O 1,1, it is changed toO 1,1→O 2,2, realization split off directed circuit (O 1,1→O 1,2→O 2,1→O 2,2→O 1,1) purpose, break deadlock.
5. detect again
Extracted graph model by amended modified resultG, return to step 1, discovery does not exist deadlock after detection, obtains a feasible tune
Degree result, its Gantt chart is as shown in Figure 8.
Claims (6)
1. a kind of solving job shop scheduling problem Deadlock Detection and restorative procedure based on matrix, it is characterised in that comprise the following steps：
Step 1：According to the corresponding graph model of extracting of scheduling resultGBuild adjacency matrixA；
Step 2：According to adjacency matrixA, calculate reachability matrixM；
Step 3：Deadlock Detection, if it find that deadlock is then found causes the matrix element of deadlock, and marks, and otherwise, terminates；
Step 4：According to deadlock information, with reference to the domain knowledge of JSP problems, splitting off causes the directed circuit of deadlock, breaks deadlock；
Step 5：Modified result according to being changed in step 4 is extracted graph modelG, return to step 1.
2. a kind of solving job shop scheduling problem Deadlock Detection and restorative procedure based on matrix according to claim 1, its feature
It is the graph model of extractingG=<V,E>, wherein：VIt is node set,V={v 1,v 2...,v n , including a virtual beginning
NodeSThe end node virtual with oneF；EIt is the set of directed edge；VIn remove nodeSAnd nodeFNode in addition is represented
Operation；EIncluding connection arc and arc of extracting, connection arc represents the binary crelation of workpiece operation, and arc of extracting represents the two of machine operation
First relation.
3. a kind of solving job shop scheduling problem Deadlock Detection and restorative procedure based on matrix according to claim 1, its feature
It is the adjacency matrixAIt isnRank square formation,A=(a ij ) n×n ,a ij Value by following formula determine：
The element of matrix Far Left and the top represents operation number, wheniIt is equal tojWhen,x i Withy j Represent same processes.
4. a kind of solving job shop scheduling problem Deadlock Detection and restorative procedure based on matrix according to claim 1, its feature
It is the reachability matrixMIt is the adjacency matrix according to constructed byAIt is calculated,MIt is also n rank 0-1 square formations, and meets boolean's generation
Algorithm is counted, its computing formula is：, whereinIBe withAWith the unit matrix of order, reflection element itself is arrived
Reach, maximum delivered number of times（Road is long）rDetermined according to following formula：
。
5. a kind of solving job shop scheduling problem Deadlock Detection and restorative procedure based on matrix according to claim 1, its feature
It is that the Deadlock Detection is in the reachability matrix being calculatedMOn the basis of, detect with matrix leading diagonal as line of symmetry
Symmetric position whether there is equal two-by-two and equal to 1 element, i.e.,：M ij =M ji =1, if it does not, explanation is in graph model of extractingGIt is middle without directed circuit, then this scheduling result is feasible；If it does, explanation is in graph model of extractingGIn must there is directed circuit, this
Scheduling result is infeasible, is judged to deadlock, and mark causes the matrix element of deadlock.
6. a kind of solving job shop scheduling problem Deadlock Detection and restorative procedure based on matrix according to claim 1, its feature
It is that described splitting off causes the principle of the directed circuit of deadlock to be：Deadlock information includes causing two between the element of deadlock and element
First relation, be reflected in job-shop scheduling problem be operation and inter process binary crelation, due to same workpiece inter process binary
Relation is unalterable, so to split off directed circuit need to change same machine inter process binary crelation, because job shop is adjusted
The last completion date of degree is determined by the length of critical path, therefore, the critical process in same machine operation is carried out excellent
First operate, change its binary crelation, break deadlock, it is comprised the following steps that：
Step 6.1：Resulting deadlock information is divided into two classes：With workpiece inter process binary crelation and with machine inter process binary
Relation；
Step 6.2：Whether according to it is that critical process is also divided into two classes to same machine operation, prioritizing selection critical process changes
Its binary crelation, breaks deadlock.
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