CN108053152A - The method that improved adaptive GA-IAGA based on polychromatic sets solves dynamic job shop scheduling - Google Patents
The method that improved adaptive GA-IAGA based on polychromatic sets solves dynamic job shop scheduling Download PDFInfo
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Abstract
The invention discloses a kind of methods that improved adaptive GA-IAGA based on polychromatic sets solves dynamic job shop scheduling,It the method achieve the method that genetic algorithm is combined the Dynamic Job-shop job scheduling of solution with polychromatic sets theory,Specifically genetic algorithm is applied to the innovatory algorithm that polychromatic sets theory is combined in dynamic flexible Job Shop Scheduling,Purpose makes the activity duration most short to provide a kind of suitable algorithm to dynamic flexible job-shop scheduling problem,The dynamic weight scheduling problem in the case of two kinds of machine tool damage and urgent key insertion can be solved simultaneously,Both process time and cost can be reduced,The dynamic change of Job-Shop environment can be tackled again,The improved adaptive GA-IAGA of the present invention,It can be by only changing circuit matrix,Into Mobile state readjustment degree in the case of without changing scheduler program in itself,Its solving speed is very fast,Solving precision is higher.
Description
Technical field
The invention belongs to Flexible workshop schedulings to arrange technical field, is related to a kind of improved adaptive GA-IAGA based on polychromatic sets
The method for solving dynamic job shop scheduling.
Background technology
Traditional work Job-Shop the name of the game is exactly the relation rationally, scientifically arranged between task and resource, and
Predefine processing sequence, machining tool and the process time of every process.Flexible Job-shop Scheduling Problems can be expressed as：
When multiple workpiece on multiple lathes when being processed, process route cannot determine completely before reprocessing, i.e., each workpiece
Processing route may have several, and the choice situation of every route need to be determined according to the idle condition of lathe.Because FJSP is added
The uncertainty of lathe expands and understands domain, the difficulty of problem optimization process added, so being that more complicated NP-hard is asked
Topic, i.e. problems have higher algorithm complexity, but are existing scheduling class problems since it more meets actual production status
Research terminal.
All kinds of JSSP are solved using traditional genetic algorithm, its main feature is that simply, it is easy to implement, and one can be acquired rapidly
A more excellent solution illustrates potentiality and validity of the GA in scheduling problem is solved.Problem solving is improved by the coding for improving GA
Efficiency, be GA coding time and space complexity substantially reduce, but its research scheduling situation it is excessively single, do not hold
Production flexibility.With reference to the characteristics of JFSP, chromosome coding mode, crossover operator and mutation operator are properly improved, is simplified
The repair process of chromosome improves solution efficiency, but the space complexity of its chromosome is still higher.It can thus be seen that it adopts
Coding, intersection and the variation mode for improving chromosome with GA the key of FJSP to be solved the problems, such as to be, so as to improve efficiency of algorithm.
Because the optimization process of GA not directly applies to problem space in itself, but is searched again on corresponding code space
Rope, so good coding mode helps to improve the improvement of the small reconciliation of search of GA.Utilize enclosing in polychromatic sets theory
The concepts such as road matrix, same color, personal color have carried out retouching for mathematical form from Function Decomposition and constraints etc. are many-sided
It states and reasoning, and demonstrates the superiority that polychromatic sets are applied to model foundation, but it is still using double carrying out coding to GA
Layer coding form virtually adds the room and time complexity of algorithm.
Traditional genetic algorithm has very strong ability of searching optimum, from arbitrary initial population, finally can all find complete
Office.But when population quantity is excessive, due to there is the convergence problem of " precocity " in genetic algorithm, i.e., algorithm is due to converging to part most
The phenomenon that cannot regenerating performance in excellent solution or population and be more than the individual of parent, and no longer being evolved.
The content of the invention
The shortcomings that it is an object of the invention to overcome the above-mentioned prior art, provides a kind of improvement heredity based on polychromatic sets
The method of Algorithm for Solving dynamic job shop scheduling, this method are become by the constraint of circuit Boolean matrix and the intersection of recessive chromosomal
It is different, optimal new chromosome is obtained, finds the optimal case of static Job-Shop, on the basis of static Job-Shop, is being gone out
In the case of existing machine failure and the urgent part of insertion, the optimal case of dynamic job shop scheduling is found.
In order to achieve the above objectives, the present invention is achieved by the following scheme：
The method that improved adaptive GA-IAGA based on polychromatic sets solves dynamic job shop scheduling, comprises the following steps：
Step 1：Obtain the specifying information of processing tasks, equipment and process；
Step 2：It determines the specific constraint of static state Job-Shop, is represented with schedule constraints expression formula, represent that index becomes with " 1 "
Measure xihk, " 0 " represents index coefficient aihk；
Step 3：Processing tasks information table is drawn according to specific machining information, according to processing tasks information table, establishment is enclosed
To express scheduling constraint, process-lathe circuit Boolean matrix is obtained according to processing tasks information table for road matrix；
Step 4：According to process-lathe circuit Boolean matrix, generation process recessiveness polynucleotide；
Step 5：Recessive chromosomal is encoded under model constraint；
Step 6：Each process is obtained according to the recessive coding information of chromosome and corresponds to process time needed for lathe, substitutes into scheduling about
Beam expression formula draws the completion date of each process and the release time of lathe；So as to generate scheduling scheme；
Step 7：It is theoretical according to Flexible workshop scheduling, object function is created, which is oneself of improved adaptive GA-IAGA
Fitness function；The fitness value of each chromosome is calculated by auto-adaptive function, value reckling is the best individual of fitness value；
Step 8：Chromosome corresponding to the best individual of fitness value in previous generation populations is directly selected into next
For population, then two chromosomes chrom1 and chrom2 are selected from parent at random；
Step 9：Judge whether randomly selected two parent chromosome chrom1 and chrom2 need to intersect, if then into
Row next step, if it is not, then retaining original chromosome；Two parent chromosomes intersected after two child chromosomes of formation, point
Fitness value, which Dui Ying not carried out, to be compared, and be deposited excellent；Repeat this process, obtain optimal chromosome coding sequence；
Step 10：Variation under model constraint, controls mutation process using circuit Boolean matrix, finally obtains more preferably
New chromosome；
Step 11：Repeat to select, intersect with making a variation, until number of repetition reaches threshold value W, record current fitness
Value；If fitness value is restrained with iterations, if terminating genetic algorithm output scheduling as a result, not restraining, above-mentioned institute is repeated
There is step until convergence；
Step 12：Dynamic Job-shop readjustment degree based on improved adaptive GA-IAGA
After making static job-shop scheduling plan, if all kinds of schedulable conditions all possess, as Workshop Production according to
According to arranging production；If since disturbance factor causes processing tasks that cannot be carried out according to static scheduling scheme, it is necessary to be adjusted to static state
Degree plan is adjusted, optimizes and dispatches again, i.e. dynamically re-dispatching.
Further improve of the invention is：
Specifying information in step 2 is as follows：
2-1) Flexible Workshop static scheduling is described as：The processing of N kind workpiece, each workpiece J are arranged in M platform equipmentjBy nj
Procedure forms, and process constraint is satisfied by per procedure, and every procedure of workpiece is processed by the multiple devices in M platform equipment, used
MijRepresent the i-th procedure available machines used set of jth kind workpieceOijkRepresent the i-th of jth kind workpiece
Process available machines used K, PijkRepresent that the i-th procedure of jth kind workpiece is processed the time of needs in kth platform equipment, i.e. 1≤j≤
N, 1≤i≤nj, 1≤k≤M ignores doing over again of occurring in production process and reprocesses and scrap phenomenon；The task of scheduling is in M platforms
The processing tasks of N kind workpiece are arranged in equipment, while optimize set target, and are met it is assumed hereinafter that condition：
A. the Process Plans of all workpiece are changeless that is, the sequencing of process cannot be run counter to；
B. process time of the process on alternative machine has determined that；
When c. there is scheduling factor again, the process processed is unaffected to be continued to process, until this process is completed；
D. each workpiece can only be processed in fixed time in an equipment；
2-2) according to the description of FJSP problems, static Job-Shop is specifically constrained to：1) every procedure of workpiece must be by
It is processed according to process constraint；2) each process can only be constrained on the machine tool specified according to lathe and is processed；It is specific public
Formula is expressed as follows：
Cik-tik+M(1-aihk)≥Cih；I=1,2 ..., n；H, k=1,2 ..., m (1)
Cjk-Cik+M(1-xijk)≥Pik；I, j=1,2 ..., n；K=1,2 ..., m (2)
Cik≥0；I=1,2 ..., n；K=1,2 ..., m (3)
In above formula, formula (1) represents object function, that is, longest finishing time is required to minimize；Formula (2) represents technique about
The priority processing sequence that the various workpiece of beam conditional decision respectively operate, ensure each workpiece processing sequence meet it is preset
It is required that；Formula (3) represents that each workpiece process of processing processes the sequencing of each machine, ensures that every equipment can only once process
One workpiece, the t in above-mentioned expression formulaikAnd CikRepresent theoretical process times of the workpiece i on equipment k and actual completion date；
M is a sufficiently large positive number；xijkAnd aihkRepresent target variable and index coefficient, meaning is as follows：
In step 3, each row of circuit Boolean matrix represents the first procedure of process to a last procedure successively, and matrix is each
Row represent different lathes, if certain process belongs to certain part workpiece, corresponding ranks are identified as 1 and are otherwise denoted as 0；Each lathe circuit
Boolean matrix is referred to as the restricted model of processing relationship, for describing the process of same class workpiece and corresponding to the real-time of machining tool
State.
In step 4, by process recessiveness polynucleotide, the logic circuit matrix of generation technique-equipment and its real number circuit
Matrix, the row expression of the logic circuit matrix and its real number circuit matrix of technique-equipment, lathe coding, row represent coding：
Boolean 1 represents that this process can use this machine tooling, and 0 is on the contrary.
Step 5 is specific as follows：
5-1) for the production model of more than one piece multi items, first all work pieces process order are carried out with randomly ordered, generation
Dominant chromosome；
In conjunction with sequence-lathe circuit Boolean matrix, recessive chromosomal is generated；It, will be with i.e. on the basis of dominant chromosome
Machine sequence each workpiece selected at random in process-lathe circuit matrix according to process sequence be denoted as 1 lathe, be filled into
In corresponding procedure position, generation recessive chromosomal coding；
The process of more than one piece multi-item production schema creation recessive chromosomal coding 5-2) is repeated, generates w chromosome, w is
Odd number.
Chromosome is the coded sequence of the available lathe per procedure, i.e., the available lathe code of certain procedure is directly from enclosing
Road matrix obtains, and ensures that all chromosomes are the feasible solution of problem with this, and genetic manipulation purpose hereafter is simply in feasible solution
In, find optimal solution；For same part workpiece is avoided to occur deadlock situation, the code bit number and process of chromosome in process computing
Number is to arrange from small to large.
Object function is specific as follows in step 7：
In Markov chain, object function should meet process constraint and meet lathe constraint, and total processing
Time and lathe free time are most short, i.e., auto-adaptive function is：
F (x)=min (f1(x)+f2(x)) (6)
The f in above-mentioned formula1(x) for each process its correspond to lathe on process time and；f2(x) adding for each lathe
Free time during work and.
In step 9, the specific method for obtaining optimal chromosome coding sequence is as follows：
According to crossover probability pc, it is random in parent chromosome chrom1, chrom2 to select what is intersected
Two genetic fragments are intersected, and genetic fragment length=crossover probability pc× chromosome length；Its son generated after intersecting
Generation individual is chrom1 ', and chrom2 ' is concretely comprised the following steps：
A. it is e1, e2 to randomly generate 2 to intersect, if e1<e2；
B. two random numbers 1 are generated at random<e1<e2<N, N are chromogene number, and find out chrom1, chrom2,
Genetic fragment w1 [], w2 [] between e1, e2；
C. by positions of the genetic fragment w1 [] according to its original in chrom1, it is inserted into chrom2；Similarly by gene
Segment w2 [] is inserted into chrom2, so as to generate new chromosome chrom1 ', chrom2 '；
When carrying out crossover operation, the intersection between code bit corresponds；
Operation is decoded again, and intersection is repeated in two chromosomes for selecting parent best with fitness in filial generation
Operation, while the adaptive response functional value of chromosome best in select two is charged into genetic evolution curve, until losing
Coming into curve convergence reaches threshold value w；The best chromosome of fitness in final step result is subjected to mutation operation.
The specific method of step 10 is as follows：
A. determined to need the chromogene code bit i to make a variation according to aberration rate；
B. process-lathe circuit matrix is searched for, searches out the replaceable lathe coding of this code bit, while produces new dyeing
Body；
C. the object function Z ' of new chromosome, and new and old chromosome corresponding Z and Z ' are calculated, if Z is better than Z ',
It eliminates new chromosome and retains old chromosome, instead then eliminate old chromosome and retain new chromosome.
The method of dynamically re-dispatching is specific as follows in step 12：
12-1) the improvement GA of readjustment degree is operated under machine failure situation；
A. static workshop initial schedule；
The improvement GA operations under above-mentioned static Job-Shop are repeated, obtain static initial schedule result；According to static initial
Scheduling result, determines whether corresponding process-lathe arrangement meets process constraint and lathe constraint, and whether can realize process
The balanced tenancy rate of concentrated processing and lathe resource, the initial scheme that this scheduling scheme will be dispatched as subsequent dynamic；
B. more relevant circuit matrix is become；
At the t1 moment, lathe damage；The device attribute that the lathe will be used to be processed is changed to 0；
C. initial scheme is dispatched again；
First, finding out the equipment damage moment in pre-scheduling scheduling needs the process position of scheduling again, is denoted as Zi；Next, with
Circuit matrix is constraint after change, and the Zi code bits of chromosome are encoded again, other code bits remain unchanged, and produces new dyeing
Body；Finally, it is in optimized selection according to improved circuit matrix by GA, obtains optimal dispatching schedule scheme again；
12-2) the improvement GA of readjustment degree is operated under urgent part insertion situation；
The urgent part insertion at the t2 moment, new workpiece insertion；
A. related circuit matrix is added；
By step 12-1) in based on static initial schedule result, added in its workpiece-equipment circuit matrix it is urgent plus
The circuit matrix of the workpiece entered；
B. the schedule scheme of pre-scheduling is dispatched again；
First, new chromosome is produced under the constraint of circuit matrix；Secondly, find out in pre-scheduling scheme, before the t2 moment,
Chromosome coding corresponding to the coding of finished work；Again, the priority of subsequent workpiece is adjusted to highest, preferentially into
Row arranges；Finally, the coding of the corresponding position in new chromosome is replaced using old code, so as to generate new chromosome, and is carried out
Dispatch scheduling.
Compared with prior art, the invention has the advantages that：
The advantages of solving the method for static Job-Shop the present invention is based on the improved adaptive GA-IAGAs of polychromatic sets is, to pass
System set coats different colors, and as set imparts certain meaning with the element in set in itself.If set is regarded
For the coding in genetic algorithm, then coding is with regard to having certain meaning simultaneously can establish certain relation with other sequences.The present invention
The restricted model for giving set is introduced into genetic algorithm, is mainly had the following advantages：
1) insignificant solution or trivial solution are removed, so as to ensure the validity of gained solution
To limit the generation illegally solved, usually there are two types of modes：First, the specific chromosome coding of design or genetic operator
Ensure the validity of solution, the method cause genetic coding and genetic operator be designed to genetic algorithm apply bottleneck；Two
It is that illegal solution is eliminated using penalty, but when problem is more complicated, the efficiency of the method is too low.The present invention is based on polychromes
The improved adaptive GA-IAGA of set carries out under restricted model, i.e., the individual generated after all genetic manipulations represents one
A efficient scheduling scheme, and due to the introducing of restricted model, the design of genetic coding and genetic operator are obtained for certain
Simplify.
2) method that domain is solved by reducing reduces the possibility of Premature Convergence and improves convergence speed of the algorithm
When being solved the problems, such as using genetic algorithm, when one timing solution space of population invariable number is bigger, the sampled point covering of population
Rate is just smaller, and it is bigger to generate precocious probability；When solution space is very big, and the quantity effectively solved is relatively fewer, not only easily
It generates precocity or convergence rate is excessively slow, it is also likely to be illegal to obtain solution.If it conversely, reduces the space of solution or removes meaningless
Solution, can not only reduce the possibility of Premature Convergence, may also speed up convergence speed of the algorithm.
3) solution can be realized in the circuit matrix for starting constraint by change, without reprogramming code
The processing technology established herein using PS circuit matrixes has formal unification with the model that scheduling is integrated
Property, there is well adapting to property for the description of uncertain problem.Dynamic change (such as equipment fault, order in Real-Time Scheduling
Change etc.), it can be emerged from by changing the row and column of circuit matrix [A × A], and the overall structure of model is constant.Institute
With the validity of the genetic manipulations such as coding, decoding and variation in the heredity based on PS constraints will not be affected, also
It is to say, it is not necessary to modify program codes can be obtained by preferable effect of optimization.
Description of the drawings
The improved adaptive GA-IAGA flow chart that Fig. 1 is constrained based on circuit；
The process of each workpiece of Fig. 2-lathe polychrome figure；
Modeling procedure figures of the Fig. 3 based on circuit Boolean matrix；
The variation flow chart of Fig. 4 improved adaptive GA-IAGAs；
Fig. 5 dynamic dispatching flow charts；
Fig. 6 static scheduling genetic evolution curves；
Dynamically re-dispatching flow in the case of Fig. 7 machine failures；
Fig. 8 machine failure two times scheduling Gantt charts；
Dynamically re-dispatching flow in the case of the urgent part insertions of Fig. 9；
The urgent part insertion two times scheduling Gantt charts of Figure 10；
2 genetic evolution curve of Figure 11 Case Simulations；
2 scheduling result Gantt chart of Figure 12 Case Simulations；
Figure 13 dynamic job shop scheduling system flow charts.
Specific embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings：
Referring to Fig. 1, the present invention is based on the improved adaptive GA-IAGA method that solves dynamic job shop scheduling of polychromatic sets, including with
Lower step：
Step 1：The specifying information of processing tasks, equipment and process is obtained, specifying information is as follows：The present invention is with one 3 × 6
Exemplified by × 8 FJSP scheduling problems, there are 3 class workpiece, corresponding maximum process number is 6, is processed in 8 equipment, to describe
How to use and color sets theory is constrained to describe the technique in scheduler task suffered by process to be processed with lathe.
Step 2：It determines the specific constraint of static state Job-Shop, is represented with schedule constraints expression formula, with " 1 ", " 0 " difference table
Show target variable xihkWith index coefficient aihk, specifying information is as follows：
2-1) Flexible Workshop static scheduling can be described as：The processing of N kind workpiece, each workpiece J are arranged in M platform equipmentj
By njProcedure forms, and is satisfied by process constraint per procedure, every procedure of workpiece can be added by the multiple devices in M platform equipment
Work uses MijRepresent the i-th procedure available machines used set of jth kind workpieceOijkRepresent jth kind workpiece
I-th procedure available machines used K, PijkRepresent that the i-th procedure of jth kind workpiece is processed the time of needs in kth platform equipment, i.e., 1
≤ j≤N, 1≤i≤nj, 1≤k≤M ignores doing over again of occurring in production process and reprocesses and scrap phenomenon.The task of scheduling is
The processing tasks of N kind workpiece are arranged in M platform equipment, while optimize set target, and are met it is assumed hereinafter that condition：
A, the Process Plans of all workpiece are changeless that is, the sequencing of process cannot be run counter to；
B, process time of the process on alternative machine has determined that；
When c, there is scheduling factor again, the process processed is unaffected to be continued to process, until this process is completed；
D, each workpiece can only be processed in fixed time in an equipment.
2-2) according to the description of FJSP problems, static Job-Shop is specifically constrained to：1) every procedure of workpiece must
It must be processed according to certain process sequence, i.e. process constraint；2) each process can only be added on specific machine tool
Work, i.e. lathe constrain.Specific formula is expressed as follows：
Cik-tik+M(1-aihk)≥Cih；I=1,2 ..., n；H, k=1,2 ..., m (1)
Cjk-Cik+M(1-xijk)≥Pik；I, j=1,2 ..., n；K=1,2 ..., m (2)
Cik≥0；I=1,2 ..., n；K=1,2 ..., m (3)
In above formula, formula (1) represents object function, that is, longest finishing time is required to minimize；Formula (2) represents technique about
The priority processing sequence that the various workpiece of beam conditional decision respectively operate, ensure each workpiece processing sequence meet it is preset
It is required that；Formula (3) represents that each workpiece process of processing processes the sequencing of each machine, ensures that every equipment can only once process
One workpiece, the t in above-mentioned expression formulaikAnd CikRepresent theoretical process times of the workpiece i on equipment k and actual completion date；
M is a sufficiently large positive number；xijkAnd aihkRepresent target variable and index coefficient, meaning is as follows：
Step 3：Processing tasks information table is drawn according to specific machining information, according to processing tasks information table, establishment is enclosed
Road matrix, to express scheduling constraint, processing tasks information table 1 is as follows：
Table 1
Wherein：The outer data of table bracket represent the process time t of each processijk, data represent process capability index in bracket
qijk, the long-run cost rate c of equipment M1-M8k, respectively 20 yuan/hour, 33 yuan/hour, 60 yuan/hour, 72 yuan/hour,
45 yuan/hour, 100 yuan/hour, 126 yuan/hour, 179 yuan/hour.Process capability index：Represent that process capability produces design
The guaranteed extent of product specification, i.e. manufacturing process system meet the degree of processing technology requirement.
It is as follows that A, B, C lathe circuit Boolean matrix are obtained according to processing tasks information table：
The process of workpiece A-lathe circuit Boolean matrix
The process of workpiece B-lathe circuit Boolean matrix
The process of workpiece C-lathe circuit Boolean matrix
Each row of circuit Boolean matrix represents the first procedure of process to a last procedure successively, and matrix, which respectively arranges, to be represented not
Same lathe, if certain process belongs to certain part workpiece, corresponding ranks are identified as 1 and are otherwise denoted as 0.
Each lathe circuit Boolean matrix is referred to alternatively as the restricted model of processing relationship, for describing the process of same class workpiece
And the real-time status of corresponding machining tool；The workpiece of Fig. 2-lathe polychrome figure is used for the feasible processing of graph-based all process steps
Path.
Based on the modeling procedure of circuit Boolean matrix, as shown in Figure 3.
Step 4：According to process-lathe circuit Boolean matrix, generation process recessiveness polynucleotide, as shown in table 2：
Table 2
By process recessiveness polynucleotide, the logic circuit matrix [A × F (A)] and its real number circuit of generation technique-equipment
Matrix [A × A (F)], wherein F1--F9Represent the different processing technologys in machining：Rough turn, smart car, peripheral milling, face grinding, boring,
Drilling etc.；F10--F12Represent 3 kinds of workpiece types A, B, C；a1--a18Represent each road technology type of each workpiece；M1--M8It has represented
Into lathe used in various processes.
The logic circuit matrix [A × F (A)] of technique-equipment and its real number circuit matrix [A × A (F)] such as the following table 3 and table 4
It is shown：
Table 3
Wherein：Row represents that lathe coding, row represent coding：Boolean 1 represents that this process can be added using this lathe
Work, 0 is on the contrary；
Table 4
Step 5：Recessive chromosomal coding under model constraint, is as follows：
5-1) for the production model of more than one piece multi items, first all work pieces process order are carried out with randomly ordered, generation
Dominant chromosome.If any each 3 of A, B, C class workpiece, the dominant chromosome of generation is：
| A | C | A | A | B | C | B | B | C |
Wherein：The A occurred for the first time represents first of A class workpiece, and second of A occurred represents the second of A class workpiece
It is a, and so on.
In conjunction with sequence-lathe circuit Boolean matrix, recessive chromosomal is generated.It, will be with i.e. on the basis of dominant chromosome
Machine sequence each workpiece selected at random in process-lathe circuit matrix according to process sequence be denoted as 1 lathe, be filled into
In corresponding procedure position, generation recessive chromosomal coding：
| A11 | ... | A1m | C11 | ... | C1m | A21 | ... | A2m | ... | Ck1 | ... | Ckm |
Wherein：A, B, C be product category, A11For the first procedure of the unit one of A class products, and so on.
The process of more than one piece multi-item production schema creation recessive chromosomal coding 5-2) is repeated, generates w chromosome, w is
Odd number.
Chromosome in the present invention is the available lathe generation of the coded sequence, i.e. certain procedure of the available lathe per procedure
Code is directly obtained from circuit matrix, ensures that all chromosomes are the feasible solution of problem with this, and genetic manipulation purpose hereafter is only
It is in feasible solution, finds optimal solution.It is noted that for same part workpiece is avoided to occur deadlock situation in process computing, contaminate
The code bit number of colour solid and process number are to arrange from small to large.
By taking above-mentioned 3 × 6 × 8 single-piece scheduling problem as an example, according to the chromosome coding that circuit matrix generates, following institute
Show.
| 1 | 4 | 6 | 7 | 4 | 0 | 2 | 3 | 4 | 2 | 8 | 7 | 1 | 3 | 5 | 1 | 7 | 3 |
1-6 code bits imply position for the process of workpiece 1, and machining tool is：1、4、6、7、4、0
7-12 code bits imply position for the process of workpiece 2, and machining tool is：2、3、4、2、8、7
13-18 code bits imply position for the process of workpiece 3, and machining tool is：1、3、5、1、7、3
Due to the maximum process numerical digit 6 of workpiece A, B, C, chromosome is then using 6 as one unit.I.e. every 6 recessiveness
Code bit represents all process steps that some workpiece is included, and needs to meet process constraint, corresponding dyeing in its process
Body surface shows the lathe coding completed needed for this procedure.If certain chromosome coding represents for 0：1st, this recessive code bit is completion
Position, i.e., this procedure is not present；2nd, the lathe for processing this procedure is in damaged condition, it is impossible to use.
By taking above-mentioned 3 × 6 × 8 more than one piece scheduling problem as an example, according to the chromosome coding that circuit matrix generates, following institute
Show.
| A | C | A | A | B | C | B | B | C |
Workpiece classification in chromosome searches for corresponding process-lathe circuit matrix, it can be processed successively by finding out
Lathe information, generation recessive chromosomal coding.
Step 6：Each process, which is obtained, according to the recessive coding information of chromosome corresponds to process time needed for lathe, substitution formula (1),
(2) schedule constraints expression formula draws the completion date of each process and the release time of lathe.So as to generate scheduling scheme, with
The item chromosome that upper 3 × 6 × 8 single-piece scheduling problem is generated is as follows：
| 1 | 4 | 6 | 7 | 4 | 0 | 2 | 3 | 4 | 2 | 8 | 7 | 1 | 3 | 5 | 1 | 7 | 3 |
Step 7：It is theoretical according to Flexible workshop scheduling, object function is created, objectives function is as follows：
In Markov chain, object function should meet process constraint and meet lathe constraint, and total processing
Time and lathe free time are most short, i.e., auto-adaptive function is：
F (x)=min (f1(x)+f2(x)) (6)
The f in above-mentioned formula1(x) for each process its correspond to lathe on process time and；f2(x) adding for each lathe
Free time during work and.This function is the auto-adaptive function of improved adaptive GA-IAGA.
The fitness value of each chromosome is calculated by auto-adaptive function, value reckling is the best individual of fitness value.
Step 8：Chromosome corresponding to the best individual of fitness value in previous generation populations is directly selected into next
For population, then two chromosomes chrom1 and chrom2 are selected from parent at random；
Step 9：Judge whether randomly selected two parent chromosome chrom1 and chrom2 need to intersect, if then into
Row next step, if it is not, then retaining original chromosome.Two parent chromosomes intersected after two child chromosomes of formation, point
Fitness value, which Dui Ying not carried out, to be compared, and be deposited excellent.Repeat this process, obtain optimal chromosome coding sequence.Specifically such as
Under：
According to crossover probability pc, it is random in parent chromosome chrom1, chrom2 to select what is intersected
Two genetic fragments are intersected, and genetic fragment length=crossover probability pc× chromosome length.Its son generated after intersecting
Generation individual is chrom1 ', and chrom2 ' is concretely comprised the following steps：
A. 2 are randomly generated to intersect for (e1, e2, if e1<e2).
B. two random numbers 1 are generated at random<e1<e2<N (N is chromogene number), and chrom1, chrom2 are found out,
Genetic fragment w1 [] between e1, e2, w2 []
C. by positions of the genetic fragment w1 [] according to its original in chrom1, it is inserted into chrom2；Similarly by gene
Segment w2 [] is inserted into chrom2, so as to generate new chromosome chrom1 ', chrom2 '.
For example, parent chromosome is：
Chrom1
| 1 | 4 | 6 | 7 | 4 | 3 | 2 | 3 | 4 | 2 | 8 | 7 | 1 | 3 | 5 | 1 | 7 | 3 |
Chrom2
| 2 | 3 | 4 | 2 | 4 | 0 | 6 | 7 | 4 | 8 | 2 | 3 | 6 | 1 | 4 | 6 | 7 | 4 |
Then child chromosome is：
Chrom1’
| 1 | 4 | 6 | 7 | 4 | 0 | 6 | 7 | 4 | 8 | 8 | 7 | 1 | 3 | 5 | 1 | 7 | 3 |
Chrom2’
| 2 | 3 | 4 | 2 | 4 | 3 | 2 | 3 | 4 | 2 | 2 | 3 | 6 | 1 | 4 | 6 | 7 | 4 |
Each chromosome location has implication during due to coding, so when carrying out crossover operation, the friendship between code bit
Fork must correspond.
Operation is decoded again, and intersection is repeated in two chromosomes for selecting parent best with fitness in filial generation
Operation, while the adaptive response functional value of chromosome best in select two is charged into genetic evolution curve, until losing
Coming into curve convergence reaches threshold value w.The best chromosome of fitness in final step result is subjected to mutation operation；
Step 10：Variation under model constraint, controls mutation process using circuit Boolean matrix, finally obtains more preferably
New chromosome.Detailed process is as follows：
A. determined to need the chromogene code bit i to make a variation according to aberration rate.
B. process-lathe circuit matrix is searched for, searches out the replaceable lathe coding of this code bit, while produces new dyeing
Body.
C. the object function Z ' of new chromosome, and new and old chromosome corresponding Z and Z ' are calculated, if Z is better than Z ',
It eliminates new chromosome and retains old chromosome, instead then eliminate old chromosome and retain new chromosome.Such as：
Old chromosome is：
| 1 | 4 | 6 | 7 | 4 | 3 | 2 | 3 | 4 | 2 | 8 | 7 | 1 | 3 | 5 | 1 | 7 | 3 |
Then new chromosome is：
| 1 | 3 | 6 | 7 | 4 | 3 | 1 | 3 | 4 | 1 | 8 | 7 | 1 | 4 | 5 | 1 | 7 | 4 |
Code bit of determining need to make a variation is：2,7,10,14,18, search process-lathe circuit matrix is returned, it can using other
Being replaced with lathe needs the lathe for becoming dystopy coding in old chromosome, so as to generate new chromosome.Make a variation flow chart such as Fig. 4 institutes
Show.
Step 11：Repeat to select, intersect with making a variation, until number of repetition reaches threshold value W, record current fitness
Value.If fitness value is restrained with iterations, if terminating genetic algorithm output scheduling as a result, not restraining, above-mentioned institute is repeated
There is step until convergence.
Step 12：Dynamic Job-shop readjustment degree based on improved adaptive GA-IAGA
It makes after static job-shop scheduling plan, it is necessary to the further feasibility of verification plan, if all kinds of schedulable conditions are all
Possess, then arrange production as the foundation of Workshop Production.However, there is imprevision in plant produced process
Disturbance factor, such as equipment fault, hot job, these factors cause processing tasks cannot according to static scheduling scheme into
Row is, it is necessary to be adjusted static scheduling plan, optimize and dispatch again, i.e. dynamically re-dispatching.The system of dynamic job shop scheduling is whole
Body flow chart is as shown in figure 13.Still based on 3 × 6 scheduling problem in table 3-1, appropriate is with the addition of partial dynamic change
It moves, two class of damage of insertion and lathe including urgent part, carries out emulation experiment.Parameter setting, Population Size 50, crossing-over rate
For 0.6, aberration rate 0.08, maximum is evolved band number 100.Idiographic flow is as shown in Figure 5.
12-1) the improvement GA of readjustment degree is operated under machine failure situation
A. static workshop initial schedule
Based on 3 × 6 scheduling problem in table 1, the improvement GA operations under above-mentioned static Job-Shop are repeated, are obtained
The results are shown in Figure 6 for static initial schedule, according to result, improved adaptive GA-IAGA at 8 generation, minimum completion time from
86.5min converges to 73min quickly, and corresponding process-lathe arrangement not only meets process constraint and constrained with lathe, and can be real
The concentrated processing of existing process and the balanced tenancy rate of lathe resource, the initial side that this scheduling scheme will be dispatched as subsequent dynamic
Case.
B. more relevant circuit matrix is become
In t=15min, lathe 3 damages regulation in this problem.The equipment category that lathe 3 will be used to be processed
Property is changed to 0, by taking workpiece A circuit Boolean matrix as an example.
Former A matrixes are as follows：
A matrixes are as follows after change：
C. initial scheme is dispatched again
First, finding out the equipment damage moment in pre-scheduling scheduling needs the process position of scheduling again, is denoted as Zi；Next, with
Circuit matrix is constraint after change, and the Zi code bits of chromosome are encoded again, other code bits remain unchanged, and produces new dyeing
Body；Finally, it is in optimized selection according to improved circuit matrix by GA, obtains optimal dispatching schedule scheme again.Specifically
Shown in steps flow chart Fig. 7.
After program operation, obtain that the results are shown in Figure 8.According to result above, at 9 generation, Maximal Makespan is obtained
For 90min.
12-2) the improvement GA of readjustment degree is operated under urgent part insertion situation
Based on 3 × 6 scheduling problem in table 1, it is specified that when urgent part is inserted in t=35min, new workpiece 4 and new
Workpiece 5 is inserted into, and machining information is as shown in table 5：
5 new processing tasks information table of table
A. related circuit matrix is added
By 12-1) in based on static initial schedule result, add what is promptly added in its workpiece-equipment circuit matrix
The circuit matrix of two workpiece, concrete matrix are as follows：
The circuit Boolean matrix of workpiece 4.
The circuit Boolean matrix of workpiece 5.
B. the schedule scheme of pre-scheduling is dispatched again
First, new chromosome is produced under the constraint of circuit matrix；Secondly, find out in pre-scheduling scheme, before 35min,
Chromosome coding corresponding to the coding of finished work.Again, the priority of D, E are adjusted to highest, are preferentially pacified
Row.Finally, the coding of the corresponding position in new chromosome is replaced using old code, so as to generate new chromosome, and is scheduled
Scheduling.
The flow chart of specific steps is as shown in figure 9, according to result, and at 13 generation, obtaining Maximal Makespan is
94min, two times scheduling Gantt chart concrete outcome are as shown in Figure 10.
Embodiment：
Using the processing tasks of table 1 as basic task information, optimization aim only considers that the total elapsed time that task is completed is most short.
Order setting workpiece A, B, C respectively have 3, and genetic parameter is set as follows：Population Size is 50, crossing-over rate 0.6, aberration rate
For 0.08, maximum is evolved band number 140, obtains optimal solution as 121minute (most short process time).It is bent by the genetic evolution of Figure 11
Line understands that this Revised genetic algorithum can converge to 121 quickly, corresponding process-lathe row at 41 generation from 145
Cloth not only meets constraint (process constraint, lathe constraint), and can realize process concentrated processing and lathe resource it is equal
Weigh occupancy.Figure 12 is scheduling result Gantt chart.
Note：Homochromy coding in figure belongs to same workpiece species, and number represents such workpiece in chromosome above
Code bit sequence number and process number.(example：Represent certain class workpiece in chromosome in the 3rd code bit, 3-5 tables
Show that the 5th of such workpiece arrives process.)
More than content is merely illustrative of the invention's technical idea, it is impossible to protection scope of the present invention is limited with this, it is every to press
According to technological thought proposed by the present invention, any change done on the basis of technical solution each falls within claims of the present invention
Protection domain within.
Claims (10)
1. the method that the improved adaptive GA-IAGA based on polychromatic sets solves dynamic job shop scheduling, which is characterized in that including following step
Suddenly：
Step 1：Obtain the specifying information of processing tasks, equipment and process；
Step 2：It determines the specific constraint of static state Job-Shop, is represented with schedule constraints expression formula, target variable is represented with " 1 "
xihk, " 0 " represents index coefficient aihk；
Step 3：Processing tasks information table is drawn according to specific machining information, according to processing tasks information table, creates circuit square
Battle array, to express scheduling constraint, process-lathe circuit Boolean matrix is obtained according to processing tasks information table；
Step 4：According to process-lathe circuit Boolean matrix, generation process recessiveness polynucleotide；
Step 5：Recessive chromosomal is encoded under model constraint；
Step 6：Each process is obtained according to the recessive coding information of chromosome and corresponds to process time needed for lathe, substitutes into formula (1), (2)
Schedule constraints expression formula, draw the completion date of each process and the release time of lathe；So as to generate scheduling scheme；
Step 7：It is theoretical according to Flexible workshop scheduling, object function is created, the object function is adaptive for improved adaptive GA-IAGA
Function；The fitness value of each chromosome is calculated by auto-adaptive function, value reckling is the best individual of fitness value；
Step 8：Chromosome corresponding to the best individual of fitness value in previous generation populations is directly selected into next-generation kind
Group, then at random two chromosomes chrom1 and chrom2 are selected from parent；
Step 9：Judge whether randomly selected two parent chromosome chrom1 and chrom2 need to intersect, if then carrying out down
One step, if it is not, then retaining original chromosome；Two parent chromosomes intersected after two child chromosomes of formation, it is right respectively
Should carry out fitness value must compare, and deposit excellent；Repeat this process, obtain optimal chromosome coding sequence；
Step 10：Variation under model constraint, mutation process is controlled using circuit Boolean matrix, finally obtains more preferably new dye
Colour solid；
Step 11：Repeat to select, intersect with making a variation, until number of repetition reaches threshold value W, record current fitness value；If
Fitness value is restrained with iterations, if then terminating genetic algorithm output scheduling as a result, not restraining, repeats above-mentioned all steps
Until convergence；
Step 12：Dynamic Job-shop readjustment degree based on improved adaptive GA-IAGA
After making static job-shop scheduling plan, if all kinds of schedulable conditions all possess, come as the foundation of Workshop Production
It arranges production；If since disturbance factor causes processing tasks that cannot be carried out according to static scheduling scheme, it is necessary to static scheduling meter
It draws and is adjusted, optimizes and dispatches again, is i.e. dynamically re-dispatching.
2. the method that the improved adaptive GA-IAGA according to claim 1 based on polychromatic sets solves dynamic job shop scheduling,
It is characterized in that, the specifying information in step 2 is as follows：
2-1) Flexible Workshop static scheduling is described as：The processing of N kind workpiece, each workpiece J are arranged in M platform equipmentjBy njRoad work
Sequence forms, and process constraint is satisfied by per procedure, and every procedure of workpiece is processed by the multiple devices in M platform equipment, uses MijTable
Show the i-th procedure available machines used set of jth kind workpieceOijkRepresent the i-th procedure of jth kind workpiece
Available machines used K, PijkRepresent that the i-th procedure of jth kind workpiece is processed the time of needs in kth platform equipment, i.e. 1≤j≤N, 1
≤i≤nj, 1≤k≤M ignores doing over again of occurring in production process and reprocesses and scrap phenomenon；The task of scheduling is set in M platforms
The processing tasks of standby upper arrangement N kind workpiece, while set target is optimized, and meet it is assumed hereinafter that condition：
A. the Process Plans of all workpiece are changeless that is, the sequencing of process cannot be run counter to；
B. process time of the process on alternative machine has determined that；
When c. there is scheduling factor again, the process processed is unaffected to be continued to process, until this process is completed；
D. each workpiece can only be processed in fixed time in an equipment；
2-2) according to the description of FJSP problems, static Job-Shop is specifically constrained to：1) every procedure of workpiece must be according to work
Skill constraint is processed；2) each process can only be constrained on the machine tool specified according to lathe and is processed；Specific formula table
Up to as follows：
Cik-tik+M(1-aihk)≥Cih；I=1,2 ..., n；H, k=1,2 ..., m (1)
Cjk-Cik+M(1-xijk)≥Pik；I, j=1,2 ..., n；K=1,2 ..., m (2)
Cik≥0；I=1,2 ..., n；K=1,2 ..., m (3)
In above formula, formula (1) represents object function, that is, longest finishing time is required to minimize；Formula (2) represents process constraint item
The priority processing sequence that the various workpiece that part determines respectively operate ensures that the processing sequence of each workpiece meets preset want
It asks；Formula (3) represents that each workpiece process of processing processes the sequencing of each machine, ensures that every equipment can only once process one
A workpiece, the t in above-mentioned expression formulaikAnd CikRepresent theoretical process times of the workpiece i on equipment k and actual completion date；M
For a sufficiently large positive number；xijkAnd aihkRepresent target variable and index coefficient, meaning is as follows：
3. the method that the improved adaptive GA-IAGA according to claim 1 based on polychromatic sets solves dynamic job shop scheduling,
It is characterized in that, in step 3, each row of circuit Boolean matrix represents the first procedure of process to a last procedure, matrix successively
Each row represent different lathes, if certain process belongs to certain part workpiece, corresponding ranks are identified as 1 and are otherwise denoted as 0；Each lathe encloses
Road Boolean matrix is referred to as the restricted model of processing relationship, for describing the reality of the process of same class workpiece and corresponding machining tool
When state.
4. the method that the improved adaptive GA-IAGA according to claim 1 based on polychromatic sets solves dynamic job shop scheduling,
It is characterized in that, in step 4, by process recessiveness polynucleotide, the logic circuit matrix of generation technique-equipment and its real number circuit
Matrix, the row expression of the logic circuit matrix and its real number circuit matrix of technique-equipment, lathe coding, row represent coding：
Boolean 1 represents that this process can use this machine tooling, and 0 is on the contrary.
5. the method that the improved adaptive GA-IAGA according to claim 1 based on polychromatic sets solves dynamic job shop scheduling,
It is characterized in that, step 5 is specific as follows：
5-1) for the production model of more than one piece multi items, randomly ordered to the progress of all work pieces process order first, generation is dominant
Chromosome；
In conjunction with sequence-lathe circuit Boolean matrix, recessive chromosomal is generated；I.e. on the basis of dominant chromosome, it will arrange at random
Each workpiece of sequence selected at random in process-lathe circuit matrix according to process sequence be denoted as 1 lathe, be filled into correspondence
In procedure position, generation recessive chromosomal coding；
The process of more than one piece multi-item production schema creation recessive chromosomal coding 5-2) is repeated, generates w chromosome, w is odd number.
6. the method that the improved adaptive GA-IAGA according to claim 5 based on polychromatic sets solves dynamic job shop scheduling,
Be characterized in that, chromosome be per procedure available lathe coded sequence, i.e., the available lathe code of certain procedure directly from
Circuit matrix obtains, and ensures that all chromosomes are the feasible solution of problem with this, and genetic manipulation purpose hereafter is simply feasible
Xie Zhong finds optimal solution；For same part workpiece is avoided to occur deadlock situation, the code bit number and work of chromosome in process computing
Sequence number is to arrange from small to large.
7. the method that the improved adaptive GA-IAGA according to claim 1 based on polychromatic sets solves dynamic job shop scheduling,
It is characterized in that, object function is specific as follows in step 7：
In Markov chain, object function should meet process constraint and meet lathe constraint, and total process time
Most short with lathe free time, i.e., auto-adaptive function is：
F (x)=min (f1(x)+f2(x)) (6)
The f in above-mentioned formula1(x) for each process its correspond to lathe on process time and；f2(x) for each lathe processed
Free time in journey and.
8. the method that the improved adaptive GA-IAGA according to claim 1 based on polychromatic sets solves dynamic job shop scheduling,
It is characterized in that, in step 9, the specific method for obtaining optimal chromosome coding sequence is as follows：
According to crossover probability pc, it is random in parent chromosome chrom1, chrom2 to select two bases intersected
Because segment is intersected, and genetic fragment length=crossover probability pc× chromosome length；Its offspring individual generated after intersecting
It is concretely comprised the following steps for chrom1 ', chrom2 '：
A. it is e1, e2 to randomly generate 2 to intersect, if e1<e2；
B. two random numbers 1 are generated at random<e1<e2<N, N are chromogene number, and find out chrom1, chrom2, in e1, e2
Between genetic fragment w1 [], w2 []；
C. by positions of the genetic fragment w1 [] according to its original in chrom1, it is inserted into chrom2；Similarly by genetic fragment
W2 [] is inserted into chrom2, so as to generate new chromosome chrom1 ', chrom2 '；
When carrying out crossover operation, the intersection between code bit corresponds；
Operation is decoded again, crossover operation is repeated in two chromosomes for selecting parent best with fitness in filial generation,
The adaptive response functional value of chromosome best in select two is charged into genetic evolution curve simultaneously, until genetic evolution
Curve convergence reaches threshold value w；The best chromosome of fitness in final step result is subjected to mutation operation.
9. the method that the improved adaptive GA-IAGA according to claim 1 based on polychromatic sets solves dynamic job shop scheduling,
It is characterized in that, the specific method of step 10 is as follows：
A. determined to need the chromogene code bit i to make a variation according to aberration rate；
B. process-lathe circuit matrix is searched for, searches out the replaceable lathe coding of this code bit, while produces new chromosome；
C. the object function Z ' of new chromosome, and new and old chromosome corresponding Z and Z ' are calculated, if Z is better than Z ', is eliminated
New chromosome retains old chromosome, instead then eliminates old chromosome and retains new chromosome.
10. the method that the improved adaptive GA-IAGA according to claim 1 based on polychromatic sets solves dynamic job shop scheduling,
It is characterized in that, the method for dynamically re-dispatching is specific as follows in step 12：
12-1) the improvement GA of readjustment degree is operated under machine failure situation；
A. static workshop initial schedule；
The improvement GA operations under above-mentioned static Job-Shop are repeated, obtain static initial schedule result；According to static initial schedule
As a result, determining whether corresponding process-lathe arrangement meets process constraint and lathe constraint, and whether can realize the concentration of process
Processing and the balanced tenancy rate of lathe resource, the initial scheme that this scheduling scheme will be dispatched as subsequent dynamic；
B. more relevant circuit matrix is become；
At the t1 moment, lathe damage；The device attribute that the lathe will be used to be processed is changed to 0；
C. initial scheme is dispatched again；
First, finding out the equipment damage moment in pre-scheduling scheduling needs the process position of scheduling again, is denoted as Zi；Secondly, with change
Circuit matrix is constraint afterwards, the Zi code bits of chromosome is encoded again, other code bits remain unchanged, and produce new chromosome；
Finally, it is in optimized selection according to improved circuit matrix by GA, obtains optimal dispatching schedule scheme again；
12-2) the improvement GA of readjustment degree is operated under urgent part insertion situation；
The urgent part insertion at the t2 moment, new workpiece insertion；
A. related circuit matrix is added；
By step 12-1) in based on static initial schedule result, add what is promptly added in its workpiece-equipment circuit matrix
The circuit matrix of workpiece；
B. the schedule scheme of pre-scheduling is dispatched again；
First, new chromosome is produced under the constraint of circuit matrix；Secondly, find out in pre-scheduling scheme, before the t2 moment, added
Chromosome coding corresponding to the coding of work workpiece；Again, the priority of subsequent workpiece is adjusted to highest, is preferentially pacified
Row；Finally, the coding of the corresponding position in new chromosome is replaced using old code, so as to generate new chromosome, and is scheduled
Scheduling.
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| CN109214090A (en) * | 2018-09-07 | 2019-01-15 | 哈尔滨工业大学 | Digital microcurrent-controlled failure of chip restorative procedure based on improved adaptive GA-IAGA |
| CN109214090B (en) * | 2018-09-07 | 2022-08-30 | 哈尔滨工业大学 | Digital microfluidic chip fault repairing method based on improved genetic algorithm |
| CN109409774A (en) * | 2018-11-14 | 2019-03-01 | 合肥工业大学智能制造技术研究院 | Dispatching method, system and storage medium for intelligence manufacture digitlization workshop |
| CN110597218A (en) * | 2019-10-18 | 2019-12-20 | 天津开发区精诺瀚海数据科技有限公司 | Scheduling optimization method based on flexible scheduling |
| CN111144710A (en) * | 2019-12-06 | 2020-05-12 | 重庆大学 | Construction and dynamic scheduling method of sustainable hybrid flow shop |
| CN111144710B (en) * | 2019-12-06 | 2023-04-07 | 重庆大学 | Construction and dynamic scheduling method of sustainable hybrid flow shop |
| CN111985841A (en) * | 2020-08-31 | 2020-11-24 | 华中科技大学 | Injection molding workshop scheduling method and system based on improved genetic algorithm |
| CN111985841B (en) * | 2020-08-31 | 2023-10-24 | 华中科技大学 | Injection workshop scheduling method and system based on improved genetic algorithm |
| CN116993135A (en) * | 2023-09-27 | 2023-11-03 | 中南大学 | Multi-stage sequencing and reservation scheduling method and device based on waiting time constraint |
| CN116993135B (en) * | 2023-09-27 | 2024-02-02 | 中南大学 | Multi-stage sequencing and reservation scheduling method and device based on waiting time constraint |
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