CN106611275A - Production scheduling algorithm for solving job shop production problem - Google Patents
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Abstract
The invention provides a production scheduling algorithm for solving a job shop production problem. The algorithm not only solves a problem existing in reasonable resource utilization and scheduling, but also considers constraint condition of an order cycle, so that the algorithm is more accurate and practical. An inventory problem existing in an actual production process is solved, and current inventory limitation is calculated and measured based on average volumes of workpieces, so that the algorithm is relatively practical, high in real-time property, simple and efficient; a calculation way of calculating discovering probability of a foreign bird egg in a cuckoo search algorithm is determined, so that the algorithm is accurate and efficient, and the algorithm is more applicable to an actual production environment; and one of three assumed conditions of the cuckoo search algorithm is broken through: the number of bird nests is unchanged. By considering a condition of increasing number of the bird nests, a processing way of urgency order inserting is set.
Description
Art
The present invention relates to solving job shop scheduling problem technical field.
Background technology
Job-shop scheduling problem (Job-shop Scheduling Problem) is many actual production scheduling problems
Simplified model, has a wide range of applications background, for example the manufacturing, traffic rules, post and telecommunications, VLSI Design
The problems such as.The assignment problem that task configuration and sequence constraint are required is met as a class, JSP has proved to be one typically
NP_hard problems, its solution difficulty are far longer than fluvial incision.Algorithm for solving job-shop scheduling problem
The important topic that always academia and engineering circles are paid close attention to jointly.
Manufacturing competition, enterprise is just towards the polymorphic type for having different completion dates and product requirement, small quantities of
Amount, large batch of production model.How existing resource is utilized, meet various constraints needed for processing tasks, all tasks is use up
Amount is timely completed, i.e., how to efficiently solve JSP problems, becomes a very real and urgent problem.Efficient scheduling is calculated
Method cannot greatly improve production efficiency and resource utilization, and so as to strengthen the competitiveness of enterprise, therefore the research to JSP has
Very important theoretical and realistic meaning.
Existing many algorithms are suggested, and for solving job-shop scheduling problem, but only solve the work of the bottom
Industry Job-Shop problem, does not account for rush order disposition present in actual production process, and with regard to solving workpiece
The scheduling algorithm of (workpiece stock) problem is placed in room still to be optimized.
The content of the invention
For deficiencies of the prior art, the technical problem to be solved in the present invention is to provide a kind of new based on cloth
The scheduling algorithm of paddy bird search, to solve rush order process problem and optimized algorithm performance so that being more applicable for workshop reality
Border production environment.
The technical solution adopted in the present invention is：The step of scheduling algorithm of problem, the algorithm are produced for job shop
It is as follows：
Step 1：Coding：Encoded using the coding rule based on operation；
Step 2：Workpiece priority exponent number La is set；
Step 3：Workpiece priority sequence P (which workpiece belongs to which priority) is set；
Step 4：If the piece count of a certain priority is not sky, scheduling algorithm at the same level, otherwise priority+1 are performed；Its
Improved scheduling algorithm steps at the same level are as follows：
Step 4.1 selects initial optimal solution：Initial optimal solution is selected according to cuckoo searching algorithm is improved；
Step 4.2 judges whether current optimal solution meets trial assembly condition, if meeting, performs trial assembly operation；Otherwise turn step
Rapid 4.3；
Whether step 4.3 has space to place the workpiece, is to go to step 4.4, otherwise goes to step 4.1；
Step 4.4 judges whether the operation that currently selected workpiece (current optimal solution) will be performed meets the sufficient bar of resource
Part, if meeting, goes to step 4.5, otherwise goes to step 4.1；
Step 4.5 determines optimal solution, exports optimal solution, performs process operation；
Step 4.6 is circulated, until meeting end condition.
The invention has the beneficial effects as follows：
1st, not only solve resource rational utilization scheduling problem, it is also contemplated that order monocyclic constraints, make algorithm solution
More accurately, with practicality.
2nd, inventory problem present in actual production process is solved, is calculated by using the average external volume of workpiece and is weighed
Current inventory limitation is measured, practical, real-time is good, it is simple efficient.
3rd, determine the calculation of the probability that exotic bird eggs in cuckoo algorithm are found, it is accurate efficiently, make algorithm more
Plus suitable for actual production environment.
4th, one of three assumed conditions of cuckoo algorithm are breached：Bird's nest quantity is constant.The present invention considers bird's nest number
The situation that amount increases, is provided with the processing mode of rush order insertion.
Description of the drawings
The detail flowchart of Fig. 1 this algorithm
The improved scheduling algorithm flow charts at the same level of Fig. 2
A kind of basic flow sheets for improving cuckoo searching algorithm of Fig. 3
Fig. 4 represents trial assembly process embodiments
Fig. 5 represents complicated workpiece combinatorial problem embodiment
Specific embodiment
Below in conjunction with accompanying drawing 1 to 5, to present invention detailed description.
First, in the actual production process, trial assembly process combines Fig. 4 embodiments, is described as follows：Several little labor cost trial assemblies
Into one than larger labor cost, this big workpiece just carries out its working procedure processing, when processing (does not complete its to a certain extent
All process steps), needs take it apart, and its little parts workpiece continues back to process the operation that the labor cost is not also processed, and waits to reach
To after certain condition, labor cost is assembled again, then proceed to process subsequent handling needed for the workpiece.Reason circulate operation successively, directly
To meeting end condition.Embodiment is as follows with reference to Fig. 4：Workpiece 3 is assembled by workpiece 1 and labor cost 2, and workpiece 1 has 5 operations
Processing, labor cost 2 is needed there are 9 operations to need processing.Workpiece 1 is processed first to the 5th operation, and processing workpiece 2 is to the 4th work
Sequence, assembles (the referred to as trial assembly during machinery production of this process) workpiece 1 and workpiece 2 and obtains workpiece 3；Then process work
Part 3 splits workpiece 3 to the 2nd operation；6th, the 7th operation of following processing workpiece 1, the 5th, the 6th of processing workpiece 2 the, the
7 operations, after completing, and assemble workpiece 1 and workpiece 2 and obtain workpiece 3；Then the 3rd, the 4th of workpiece 3 is processed,
5th procedure, after completing, splits；1 all process steps of workpiece have been completed, and at this moment process the 8th, the 9th procedure of workpiece 2,
After completing, workpiece 1 and workpiece are assembled and obtains workpiece 3.At this moment whole process is completed.
2nd, the complicated workpiece combinatorial problem combines Fig. 5 embodiments, is described as follows：In actual production process, exist many
Individual unit construction forms new part, and this new part 1 may also can be combined into new part 2 with other workpiece again, new
Part 2 may need processing again, then be assembled into a workpiece with new part 3, so circulate.
3rd, the step 1 is described in detail below：Encoded using the coding rule based on operation, i.e., chromosome is by w × n
× m genomic constitution, they represent the arrangement of an operation, and in this array of procedures, each workpiece number at most occurs m time, its
Chromosome is represented by two-dimensional space point (x, y), i.e. y-th workpiece of x-th order.For example, 3 × 4 × 3 (order ×
Exponent number × workpiece × machine) example, chromosome sequence for (1,1) (1,2) (2,1) (1,1) (3,1) (3,1) (3,3) (3,2)
(1,2)(1,2)(1,1)(1,4).So, its corresponding work pieces process sequence is：
(J1,1,1, J1,2,1, J2,1,1, J1,1,2, J3,1,1, J3,1,2, J3,1,1, J3,2,1, J1,2,1, J1,2,2, J1,1,3, JIsosorbide-5-Nitrae, 1)
Wherein, JT, i, jThe jth procedure of i-th workpiece of t-th order is represented, j represents the number of times that workpiece i occurs.Cause
This, the chromosome sequence expression of previous example means that first processing sequence is：1st road work of the 1st workpiece of the 1st order
Sequence, processes the 1st procedure of the 2nd workpiece of the 1st order, in the 1st procedure of processing the 1st workpiece of the 2nd order, processing
2nd procedure of the 1st workpiece of the 1st order, by that analogy, finally processes the 1st procedure of the 4th workpiece of the 1st order.
Therefore can be just a scheduling scheme according to the appearance sequential conversions of workpiece in decoding.
4th, the execution of the step 4.2 trial assembly operation is as follows：
Trial assembly is performed, if succeeded in assembling, needs return processing subsequent handling, be returned directly to need the follow-up of processing to add
Work operation point；If trial assembly is unsuccessful, by artificial judgment, returning needs the operation point of processing to be processed.If trial assembly into
The workpiece that work(is combined is needed with other workpiece trial assemblies, with regard to trial assembly, carries out following process until meeting splitting condition and splitting again.
5th, the step 4.3 whether have space place workpiece determination methods be：
Assumed condition：Assume that each order is not delayed the situation of picking.
Concrete steps：
Step 4.3.1：Initialization finished product inventory limitation C.
Step 4.3.2：Calculate workpiece average external volume：
Step 4.3.3：Full stock's alert consitions are set：If meeting following formula, full stock's alarm is sent：(f+k)·Vave
>=C, wherein, f is completed piece count, and k is a definite value, takes k=1 here.
6th, the step 4.4 judges that whether sufficient workpiece resource requirement decision rule be as follows：Resource stock is set
Pond：
Decision rule：
(there is the Suo Xushebei ＆＆ stocks number of devices in stock pond to If>There is institute in=required She Beishuoliang ＆＆ stocks pond
Need the Gong Ju ＆＆ stocks number of tools>There is required work post Gong Ren ＆＆ stocks workman's number in=required Gong Jushuoliang ＆＆ stocks pond
Amount>=required number of workers) meet resource sufficiency；
Else is unsatisfactory for resource sufficiency.
7th, the improved cuckoo searching algorithm of the step 4.1：
Step 4.1.1：Initialization algorithm basic parameter：Bird's nest number (piece count) N is set, and host has found exotic bird eggs
Probability P a (probability is seized in operation), and maximum iteration time MaxT or search precision ε：
Wherein, n is Bird's Nest (workpiece) quantity of L priority；
Step 4.1.2：Initialization bird's nest position (work pieces process deadline)：It is in rising trend according to length process time
Arrangement.
Step 4.1.3：Calculating target function value：Bird's nest position (deadline) is converted to into operation row according to coding rule
Row, calculate the corresponding target function value in each bird's nest position, and obtain current optimum bird's nest position, be implemented as：
Object function：
F (T)=min max1≤o≤w{max1≤k≤m{max1≤i≤nToik}} (1)
Constraints：
Toik-poik+M(1-aoihk)≥Toih
(o=1,2 ..., w；I=1,2 ..., n；H, k=1,2 ..., m) (2)
Tojk-Toik+M(1-xoijk)≥poik
(i, j=1,2 ... n；O=1,2 ..., w；K=1,2 ..., m) (3)
Toik>=0 (o=1,2 ..., w；I=1,2 ..., n；K=1,2 ..., m) (4)
xoijk=0 or 1 (i, j=1,2 ..., n；O=1,2 ..., w；K=1,2 ..., m) (5)
maxi{Toi}≤To (6)
Wherein, formula (1) represents object function, i.e. deadline (Makespan)；Formula (2) represents that process constraints are determined
Each workpiece operation sequencing；Formula (3) represents the sequencing of every machine for processing each workpiece；Formula (4) table
Show completion date variable bound condition；Formula (5) represents the possible value size of variable.Involved symbol definition in above-mentioned formula
Implication is as follows：ToikAnd poikDeadline point of i-th workpiece in respectively o-th order (or exponent number) on machine k and
Process time length；M is a sufficiently large integer；aoihkAnd xoijkCoefficient and indicator variable are indicated respectively, its implication is：
Formula (6) represents that all workpiece longest finishing times of o-th order are less than order cycle ToTime-constrain.
Step 4.1.4：Update bird's nest position：
(1) a kind of situation：If (bird's nest quantity does not increase (does not have going out for new order not to have new bird's nest to occur
It is existing))：Start iteration, reservation previous generation's optimum bird's nest position is constant, updates bird's nest position (i.e. global search), so as to randomly generate
Bird's nest of future generation, and the target function value of each bird's nest after location updating is assessed, the current optimum bird's nest position of record.It is embodied as
Shown in the following mathematical formulae of scheme：
Wherein,Represent that i-th cuckoo (uses C in Job-Shop problem in the bird's nest position in t generationsoikRepresent), α
It is step sizes parameter, typically takes α=0.1.Parameter S is the step-length of random walk, and computing formula is as follows：
S=u+ α σ (10)
Wherein,
Each bird's nest position is according to condition updated in Local Search：Sent out as bird's nest owner with random number R a
The probability of existing exotic bird eggs is simultaneously compared with Pa, if Ra>Pa, then change bird's nest position at random, otherwise keep origin-location not
Become, and calculate the target function value of each bird's nest after the movement of position, the current optimum bird's nest position of record.With following one-zero programming mould
Type is represented：
(2) another kind of situation：If new bird's nest occurs (have new order to occur), bird's nest quantity increases, i.e.,：N+H,
H is newly-increased bird's nest quantity, meanwhile, determine whether rush order：If it is, doing rush order processes operation, the order
The priority of operation processed for needed for of workpiece setting；If not rush order, then emergent management is not done.
It is as follows that its rush order processes operation：Urgency factor is calculated, the bigger order urgency level of urgency factor is bigger, more
Need to obtain priority treatment, urgency factor is calculated as follows：
Wherein, max { TopreFor the estimated time to completion of order o, estimate to obtain here by artificial experience, To is order
The delivery cycle of o.
Step 4.1.5：Update optimal function value：Compare the optimal value of current iteration and last iteration bird's nest position, such as
Really new optimal value then gives new optimal value the target function value of current optimum bird's nest position less than former optimal value.
Step 4.1.6：Step 4.1.7 is proceeded to when maximum search number of times is reached or meet search precision, otherwise, is gone to step
4.1.3 searched for next time.
Step 4.1.7：Output optimal scheduling value and corresponding scheduling scheme (chromosome sequence).
Claims (5)
1. the scheduling algorithm of problem is produced for job shop, and the algorithm is related to solving job shop scheduling problem technical field, it is characterized in that：
The step of algorithm, is as follows：
Step 1：Coding：Encoded using the coding rule based on operation；
Step 2：Workpiece priority exponent number La is set；
Step 3：Workpiece priority sequence P is set（Which workpiece belongs to which priority）；
Step 4：If the piece count of a certain priority is not sky, performs and improve scheduling algorithm at the same level；Otherwise priority+1, its
Improved scheduling algorithm steps at the same level are as follows：
Step 4.1 selects initial optimal solution：Initial optimal solution is selected according to cuckoo searching algorithm is improved；
Step 4.2 judges whether current optimal solution meets trial assembly condition, if meeting, performs trial assembly operation；Otherwise go to step
4.3；
Whether step 4.3 has space to place the workpiece, is to go to step 4.4, otherwise goes to step 4.1；
Step 4.4 judges currently selected workpiece（Current optimal solution）Whether the operation that will be performed meets the sufficient condition of resource,
If meeting, 4.5 are gone to step, 4.1 are otherwise gone to step；
Step 4.5 determines optimal solution, exports optimal solution, performs process operation；
Step 4.6 is circulated, until meeting end condition.
2. the scheduling algorithm that problem is produced for job shop according to claim 1, is characterized in that：The step 4.2
The execution of trial assembly operation is as follows：Trial assembly is performed, if succeeded in assembling, is needed to return processing subsequent handling, is returned directly to needs
The subsequent processing operations point of processing；If trial assembly is unsuccessful, by artificial judgment, returning needs the operation point of processing to carry out adding
Work；If the workpiece for combining that succeeds in assembling is needed with other workpiece trial assemblies, with regard to trial assembly, split until meeting splitting condition again
Carry out following process.
3. the scheduling algorithm that problem is produced for job shop according to claim 1, is characterized in that：The step 4.3
Whether have space place workpiece determination methods be：
Assumed condition：Assume that each order is not delayed the situation of picking
Concrete steps：
Step 4.3.1：Initialization finished product inventory limitation C；
Step 4.3.2：Calculate workpiece average external volume：；
Step 4.3.3：Full stock's alert consitions are set：If meeting following formula, full stock's alarm is sent：,
Wherein, f is completed piece count, and k is a definite value, takes k=1 here.
4. the scheduling algorithm that problem is produced for job shop according to claim 1, is characterized in that：The step 4.1
Improved cuckoo searching algorithm step is as follows：
Step 4.1.1：Initialization algorithm basic parameter：Bird's nest number is set（Piece count）N, host have found the general of exotic bird eggs
Rate Pa（Probability is seized in operation）, and maximum iteration time MaxT or search precision：
Wherein, n is the Bird's Nest of L priority（Workpiece）Quantity；
Step 4.1.2：Initialization bird's nest position（The work pieces process deadline）：According to length process time row in rising trend
Row；
Step 4.1.3：Calculating target function value：According to coding rule by bird's nest position（Deadline）Be converted to array of procedures,
The corresponding target function value in each bird's nest position is calculated, and obtains current optimum bird's nest position, be implemented as：
Object function：
（1）
Constraints：
（2）
（3）
（4）
（5）
（6）
Wherein, formula（1）Represent object function, i.e. deadline（Makespan）；Formula（2）Represent that process constraints are determined every
The sequencing of the operation of individual workpiece；Formula（3）Represent the sequencing of every machine for processing each workpiece；Formula（4）Represent
Work time variable constraints；Formula（5）The possible value size of variable is represented, involved symbol definition implication in above-mentioned formula
It is as follows：Respectively o-th order（Or exponent number）In deadline point of i-th workpiece on machine k and plus
Work time span；M is a sufficiently large integer；Coefficient and indicator variable, its implication are indicated respectively
For：
Formula（6）Represent that all workpiece longest finishing times of o-th order are less than the order cycleTime-constrain；
Step 4.1.4：Update bird's nest position：
（1）A kind of situation：If not having new bird's nest to occur（Bird's nest quantity does not increase（Appearance without new order））：Open
Beginning iteration, reservation previous generation's optimum bird's nest position are constant, update bird's nest position（That is global search）, so as to randomly generate bird of future generation
Nest, and the target function value of each bird's nest after location updating is assessed, the current optimum bird's nest position of record, specific embodiment are as follows
Shown in mathematical formulae：
（9）
Wherein,Represent i-th cuckoo in the bird's nest position in t generations（Use in Job-Shop problemRepresent）,It is step
Long size parameter, typically takes, parameter S is the step-length of random walk, and computing formula is as follows：
（10）
Wherein,
（11）
（12）
Each bird's nest position is according to condition updated in Local Search：Found as bird's nest owner with random number R a outer
Carry out the probability of bird egg and be compared with Pa, if Ra>Pa, then change bird's nest position at random, otherwise keeps origin-location constant, and
Calculate the target function value of each bird's nest after position is moved, the current optimum bird's nest position of record, with following one-zero programming model table
Show：
（13）
（2）Another kind of situation：If new bird's nest occurs（There is new order to occur）, bird's nest quantity
Increase, i.e.,：N+H, H are newly-increased bird's nest quantity, meanwhile, determine whether rush order：
If it is, doing rush order processes operation, the operation processed for needed for by the workpiece setting of the order
Priority；If not rush order, then emergent management is not done；
It is as follows that its rush order processes operation：Calculate urgency factor, the urgent journey of the bigger order of urgency factor
Degree is bigger, more need to obtain priority treatment, and urgency factor is calculated as follows：
Wherein,For the estimated time to completion of order o, estimate to obtain here by artificial experience, To is order o
Delivery cycle；
Step 4.1.5：Update optimal function value：Compare the optimal value of current iteration and last iteration bird's nest position, if newly
Optimal value less than former optimal value, then new optimal value is given the target function value of current optimum bird's nest position；
Step 4.1.6：Step 4.1.7 is proceeded to when maximum search number of times is reached or meet search precision, otherwise, is gone to step
4.1.3 searched for next time；
Step 4.1.7：Output optimal scheduling value and corresponding scheduling scheme（Chromosome sequence）.
5. the scheduling algorithm that problem is produced for job shop according to claim 1, is characterized in that：This algorithm is breached
One of three assumed conditions of cuckoo algorithm：Bird's nest quantity is constant, it is contemplated that the situation that bird's nest quantity increases, and is provided with urgent
The processing mode of order insertion.
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