CN103729694A - Method for solving flexible job-shop scheduling problem with improved GA based on polychromatic set hierarchical structure - Google Patents
Method for solving flexible job-shop scheduling problem with improved GA based on polychromatic set hierarchical structure Download PDFInfo
- Publication number
- CN103729694A CN103729694A CN201310737478.8A CN201310737478A CN103729694A CN 103729694 A CN103729694 A CN 103729694A CN 201310737478 A CN201310737478 A CN 201310737478A CN 103729694 A CN103729694 A CN 103729694A
- Authority
- CN
- China
- Prior art keywords
- workpiece
- equipment
- benchmark
- egk
- lathe
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Abstract
The invention discloses a method for solving the flexible job-shop scheduling problem with an improved GA based on a polychromatic set hierarchical structure. According to the method, an original process-machine tool contour matrix is split into matrixes of relation of process-benchmark, benchmark-equipment model, equipment model-asset number by establishing equipment benchmarks and setting process constraint, equipment constraint, machine tool constraint and unique constraint, and the data size of a constraint model is effectively reduced; furthermore, by optimizing chromosome lengths reasonably and setting blending operation of batch benchmarks, the time and space complexity of chromosomes is effectively reduced, and then the solving speed and practicality of the algorithm can be greatly improved.
Description
Technical field
The invention belongs to Flexible Workshop dispatching technique field, relate to a kind of improved genetic algorithm, be specifically related to a kind of method that improvement GA based on polychromatic sets hierarchical structure solves Flexible Workshop scheduling.
Background technology
Flexible Workshop scheduling (Flexible Job-Shop Scheduling Problem, FJSP), its core concept is: multiple batches of multiple types parts can processing on generic polytypic equipment.Before formal processing, the technique of each parts is well-determined, but process route is indefinite, and every procedure has the selection of various processing equipment, be that each parts to be processed has many process routes to select, and equipment selection will be based on capacity of equipment balance.Compare traditional solve job shop scheduling problems, FJSP problem is more complicated NP-hard problem, solve problems and require algorithm to there is higher complicacy, but due to the actual conditions of its more approaching production, make it become the research emphasis at present inside and outside scheduling field.
In recent years, scholars dispatch and have also launched a large amount of research Flexible Workshop, in prior art, " Zhou Huiren, the big straightforward words of Zheng, An little Hui etc. the new method [J] based on genetic algorithm for solving Job Shop optimizing scheduling. Journal of System Simulation, 2009, 21 (11): 3295-3306 " and " Pezzella F.A genetic algorithm for the flexible Job-Shop scheduling problem[J] .Computers and Operations Research, 2007, 21 (9): 54-61 " in order to improve the search speed of GA, propose to improve coded system and optimized chromosomal method, the time and space complexity of GA algorithm is reduced greatly, but its scheduling situation too theorizes, fail to consider environmental change, tool is not flexible.
" Zhang Guohui; highlighted; Li Peigen etc. improved genetic algorithms method solves Flexible Job-shop Scheduling Problems [J]. mechanical engineering journal; 2009; 45 (7): 145-151 " in, in conjunction with FJSP problem feature, adopted suitable stragetic innovation chromosome coding mode, crossover operator and mutation operator, greatly improved Algorithm for Solving precision, but it solves speed and does not improve.
" Ji Shuxin; Qian Jixin; Sun Youxian. the coding study in Genetic Algorithms Applied To Job Shop Scheduling [J]. information and control; 1997; 26 (5): 393-400 " in, in order to eliminate GA, can only be applied to the limitation of group technology JSS, JSS linked gene compiling method has been proposed, although improved solution efficiency, its chromosomal space complexity is still higher.
" Pan Quanke, Zhu Jianying. the job shop optimization [J] based on Petri net and hybrid algorithm. computer integrated manufacturing system, 2007, 13 (3): 580-584 ", " Chen Weimin, Wang Bo, the applied research [J] of the genetic algorithm of defending beautiful Ke .Petri net in Job-Shop problem. Harbin University of Science and Technology's journal, 2008, 13 (1): 59-62 " and " Ju Quanyong, Zhu Jianying. the dynamic job shop scheduling systematic research [J] based on genetic algorithm. China Mechanical Engineering, 2007, 18 (1): 40-43 " in, model the timed transition Petri pessimistic concurrency control of JSP, then apply genetic algorithm (Genetic algorithm, GA), simulated annealing (Simulated Annealing, SA), particle group optimizing (Particle Swarm Optimization PSO) algorithm wherein a kind of or two kinds of algorithms of mixing addresses this problem, its derivation algorithm used still has very high Time & Space Complexity, could not effectively improve the speed that solves and the precision of algorithm simultaneously.
" Fu Weiping, Liu Dongmei, the next spring is, Wang Wen. the improved genetic algorithms method based on polychromatic sets solves the flexible scheduling problem [J] of many kinds. computer integrated manufacturing system, 2011, 17 (5): 1004-1011 " and " Liu Dongmei, Fu Wei equality. improved genetic algorithms method solves Markov chain [J]. Northwest University's journal, 2011, 41 (4): 611-616 " in, adopted the polychromatic sets theory of easier data of description logical relation, got rid of infeasible solution, greatly dwindle GA search and separated territory, proposed to represent the double constraints in scheduling problem by single layer coding mode simultaneously, reduced the Time & Space Complexity of algorithm.But described in the document, algorithm can only generate chromosome under simple scenario (operation corresponding device alternative), larger with practical application gap; And the segment encoding that chromosome adopts is to take maximum process number as base's generation, and this occurs the phenomenons such as chromosome is oversize, and invalid data is too much while just having caused algorithm to process in practice extensive multiple operation scheduling problem, requires further improvement.
Summary of the invention
The object of the invention is to overcome the shortcoming of above-mentioned prior art, provide a kind of improvement GA based on polychromatic sets hierarchical structure to solve the method for Flexible Workshop scheduling, the method has been introduced multi-level constraint specification method, by original huge circuit matrix cutting, reduce the redundant data amount of restricted model, increased the possibility of algorithm practical application; Improve in addition chromosomal coded system, removed a large amount of amorphs, from the further optimized algorithm of space complexity angle, improved speed of convergence.
For achieving the above object, the technical solution used in the present invention comprises the following steps:
1) set up the mathematical model of Markov chain;
2) set up the Job-Shop restricted model based on PST hierarchical structure;
3) according to operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, generating process-equipment real number circuit matrix, and then produce hereditary recessive code sequence list, the corresponding lathe coding of row mark, the corresponding recessive gene of rower position; Wherein, the process time that in table, content is operation, the operation numbering of the corresponding workpiece of recessive gene code bit, by searching for corresponding operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, thus find the lathe coding corresponding to certain working procedure, according to the availability aspect of lathe, select corresponding lathe coding as chromosomal dominant coding again.
In described step 1), the concrete grammar of setting up the mathematical model of Markov chain is:
FJSP can be described to, and supposes that M is the quantity of process equipment, and N is workpiece to be processed quantity, and P is process number, the set that I is all devices; I
egrepresent the available devices set of the g procedure of workpiece e,
j
eprocess number for workpiece e; X is the process sequence of all workpiece, S
egkthe start time that the g procedure of expression workpiece e is processed on equipment k; E
egkfor the g procedure of the workpiece e process finishing time on equipment k; T
egkfor the g procedure of workpiece e lasting process time on equipment k, and k ∈ I
egthere is E
egk=S
egk+ T
egk; E
pthe completion date that represents finishing operation; MS represents the last completion date of all workpiece;
When the j procedure of workpiece i and the g procedure of workpiece e are carried out on same equipment, if operation j adds man-hour prior to operation g, Q
ijeg=1, otherwise Q
ijeg=0; If the g procedure of workpiece e is processed on lathe k, X
egk=1, otherwise X
egk=0;
If certain FJSP has the possible processing sequence of S kind, require total the shortest Machining Sequencing of activity duration, first ask for each processing sequence x (x ∈ 1 ..., S}) the corresponding activity duration; Obviously, in order x, the i.e. last completion date of all workpiece of the completion date of last manufacturing procedure, has
MS=E
p （1）
Objective function F (x) is
F(x)=min(MS
x)=min（(E
p)
x） （2）
X=1，…，S
S.T.S
egk－E
e(g－1)n≥0
e=1，…，N;g=1，…，J
e;X
egk=1，X
e(g－1)n=1 （3）
S
egk－E
igk≥0
e=1，…，N;g=1，…，J
e;X
ijk=1，X
egk=1，Q
ijeg=1 （4）。
Described step 2), in, the restriction relation of Job-Shop restricted model is:
First equipment benchmark is set, several unit types that each equipment benchmark comprises process similarity, each unit type comprises again the concrete equipment of several this kind of models, every concrete equipment is corresponding with corresponding asset number again, and operation finally will complete processing on concrete equipment, therefore just can be by the restriction relation of operation and benchmark, the restriction relation of equipment benchmark and unit type, the restriction relation of unit type and asset number, indirectly set up the restriction relation of operation and concrete equipment, thereby realize huge operation lathe circuit matrix is divided into little relational matrix, to reduce scale and the data volume of matrix, improve the speed that solves of algorithm.
In described step 3), according to the availability aspect of lathe, select corresponding lathe coding to be specially as chromosomal dominant coding:
3.1) set up the restricted model based on hierarchical structure circuit Boolean matrix:
Use the hierarchical structure circuit Boolean matrix of benchmark and unit type, unit type and asset number, auto-correlation, process equipment, process equipment real number as restricted model, produce hereditary recessive code sequence list, the operation of GA is all carried out in the scope of restricted model;
3.2) chromosomal coding:
3.3) chromosomal decoding:
According to the corresponding information of chromosome the inside, search technique-equipment real number circuit matrix, determines parameter process time of all process steps on each lathe;
3.4) select operation:
The corresponding chromosome of individuality that fitness value in previous generation population is best is directly selected to enter population of future generation;
3.5) interlace operation:
Two parent chromosomes of random selection, two random number 0<a<b<N, wherein, N is chromogene number, finds out corresponding a on two parent chromosomes, the fragment between b exchanges each other;
3.6) variation.
The concrete grammar of described chromosome coding is:
First determine effective process number sum that chromosome length is each workpiece:
(a) when being the production model of the many kinds of single-piece:
Have each of n class workpiece, GA chromosome length is
l wherein
gprocess number for corresponding g part;
(b) when being the pattern of variety production more than many:
There is n class workpiece J part J=n altogether
1+ n
2+ ...+n
i+ ...+n
n, n wherein
1, n
2..., n
i..., n
nthe quantity i ∈ n that represents respectively i class workpiece, every class workpiece has p
iprocedure, needs first the process sequence of workpiece to be encoded, and workpiece process sequence is carried out randomly ordered, generates dominant chromosome;
When the quantity of part of the same race is less than 100, be merged into a task; Finally, according to benchmark and unit type, unit type and asset number circuit matrix, generate recessive chromosome;
When quantity employing over 100 of part of the same race strategy in batches, between the individual task body after in batches, be randomly ordered.
The concrete grammar of described variation is:
3.6.1) set aberration rate, determine the gene position that needs variation;
3.6.2) search benchmark and unit type, unit type and asset number circuit matrix, find this gene position can replace the coding of lathe, produces new chromosome;
3.6.3) calculate new chromosomal objective function, the target function value that new and old chromosome is corresponding, and then select preferably to enter the next generation.
Compared with prior art, the present invention has following beneficial effect:
The present invention is according to operation-benchmark, benchmark-device numbering, and device numbering-asset number circuit Boolean matrix, generating process-equipment real number circuit matrix, and then produce hereditary recessive code sequence list, the corresponding lathe coding of row mark, the corresponding recessive gene of rower position; Wherein, the process time that in table, content is operation, the operation numbering of the corresponding workpiece of recessive gene code bit, by searching for corresponding operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, thus find the lathe coding corresponding to certain working procedure, according to the availability aspect of lathe, select corresponding lathe coding as chromosomal dominant coding again.Improvement GA algorithm of the present invention is all at operation-benchmark in the random implementation of coding, decoding and variation, benchmark-device numbering, in device numbering-asset number circuit matrix restraint, carry out, random in a kind of controlled range, its role is to reduce the data volume of restricted model and removed invalid information and dwindled the hunting zone of solution space, finally having improved Algorithm for Solving precision and speed.
Further, chromogene of the present invention position coding method, has removed amorph position, has reduced space and the time complexity of algorithm, thereby improves the search efficiency of GA.
Accompanying drawing explanation
Fig. 1 is level restriction relation figure of the present invention;
Fig. 2 is that task of the present invention is distributed PS hierarchy Model figure;
Fig. 3 is the hereditary convergence curve figure of example 1 of the present invention;
Fig. 4 is the scheduling Gantt chart of example 1 of the present invention;
Fig. 5 is the hereditary convergence curve figure of example 2 of the present invention;
Fig. 6 is the scheduling result Gantt chart of example 2 of the present invention;
Fig. 7 is process flow diagram of the present invention.
Embodiment
Below in conjunction with drawings and Examples, the present invention is described in further detail:
Embodiment:
1) mathematical model of Markov chain
FJSP can be described to, and supposes that M is the quantity of process equipment, and N is workpiece to be processed quantity, and P is process number, the set that I is all devices; I
egrepresent the available devices set of the g procedure of workpiece e,
j
eprocess number for workpiece e; X is the process sequence of all workpiece, S
egkthe start time that the g procedure of expression workpiece e is processed on equipment k; E
egkfor the g procedure of the workpiece e process finishing time on equipment k; T
egkfor the g procedure of workpiece e lasting process time on equipment k, and k ∈ I
egthere is E
egk=S
egk+ T
egk; E
pthe completion date that represents finishing operation; MS represents the last completion date of all workpiece;
When the j procedure of workpiece i and the g procedure of workpiece e are carried out on same equipment, if operation j adds man-hour prior to operation g, Q
ijeg=1, otherwise Q
ijeg=0; If the g procedure of workpiece e is processed on lathe k, X
egk=1, otherwise X
egk=0;
If certain FJSP has the possible processing sequence of S kind, require total the shortest Machining Sequencing of activity duration, first ask for each processing sequence x (x ∈ 1 ..., S}) the corresponding activity duration; Obviously, in order x, the i.e. last completion date of all workpiece of the completion date of last manufacturing procedure, has
MS=E
p （1）
Objective function F (x) is
F(x)=min(MS
x)=min（(E
p)
x） （2）
X=1，…，S
S.T.S
egk－E
e(g－1)n≥0
e=1，…，N;g=1，…，J
e;X
egk=1，X
e(g－1)n=1 （3）
S
egk－E
igk≥0
e=1，…，N;g=1，…，J
e;X
ijk=1，X
egk=1，Q
ijeg=1 （4）
2) the FJSP restricted model based on PST hierarchical structure
2.1 polychromatic sets theory brief introductions
Polychromatic sets theory is the mathematical tool that a new systematic modeling theory and help information are processed, and this theory and method are in USSR (Union of Soviet Socialist Republics) and present Russian business circles after occurring, particularly Aero-Space enterprise has obtained propagation and employment widely.This theoretical core thought is in the different object of emulation (product, production system, design and processes process etc.) by identical the application of mathematical model, hierarchical structure between descriptive element and complex relationship, and at set layer and logical layer tissue and process information, in number of layers, process low layer data actual value problem.
2.2 workshop actual production constraint conditions are analyzed
For general manufacturing enterprise, actual production work meeting is subject to impact and the restriction of the factors such as a large amount of people, machine, material, method, ring, therefore the many factors that actual Job-Shop need of work is considered, with common PST, describe this restriction relation, can cause the circuit matrix of individual color, unified color and body all to there is larger data volume.How many-sided impact can be altered in the middle of the circuit matrix of descriptive element relation in time, be the important bottleneck that employing multicolor sets theory and intelligent algorithm solve scheduling problem.The hierarchy Model of PST is for the effective way that provides of this bottleneck is provided.
Practical experience analysis in conjunction with a large amount of Job-Shops is found, if relevant device benchmark and unit type are set to the equipment in workshop, can operation be carried out associated with equipment benchmark order, equipment benchmark carries out associated with device code, device code carries out associated with the asset number of the concrete equipment in workshop again, finally indirectly set up operation and equipment corresponding relation, and then bring convenience to equipment control and the Job-Shop work of enterprise.If with a single circuit matrix description operation and the corresponding relation of equipment, will certainly cause matrix excessive, and lack practicality.
2.3 Job-Shop restricted models based on PST hierarchical structure
Based on above-mentioned analysis, consider various influence factors in the actual production of workshop, the present invention is provided with four kinds of constraints in scheduling process: operation retrains and refers to according to actual processing technology, and operation must be carried out scheduling according to sequencing; Benchmark constraint refers to that a procedure can only process on the equipment of several benchmark types of appointment; Lathe constraint refers to the corresponding several fixing lathe models of each benchmark type; Unique constraint refers to that any operation of each workpiece can only process at fixed time on a machine.First its restriction relation for arranging equipment benchmark, several unit types that each equipment benchmark comprises process similarity, each unit type comprises again the concrete equipment of several this kind of models, every concrete equipment is corresponding with corresponding asset number again, and operation finally will complete processing on concrete equipment, therefore just can be by the restriction relation of operation and benchmark, the restriction relation of equipment benchmark and unit type, the restriction relation of unit type and asset number, indirectly set up the restriction relation of operation and concrete equipment, thereby realize huge operation lathe circuit matrix is divided into little relational matrix, to reduce scale and the data volume of matrix, improve the speed that solves of algorithm, its concrete hierarchical structure as shown in Figure 1.
In Fig. 1, upper left corner circuit matrix has reflected operation constraint and the reference device type constraint of part, and which reference device type each procedure can be processed by, can reflect by this matrix, without cannot processing of value.Upper right corner circuit matrix has reflected the lathe constraint of reference device type with concrete unit type.Wherein have 1, prove that this reference device type comprises this unit type.Below circuit matrix has reflected the corresponding relation of M workshop appliance model with concrete lathe, wherein the process time of the corresponding operation of numeric representation on this lathe.Can further draw its Task Assignment Model as shown in Figure 2 on this basis.
FJSP by 3 workpiece is introduced to the process of establishing of its PST hierarchical structure restricted model below, its processing tasks information table is as shown in table 1, wherein facility information is shown in list, line display workpiece process information, the capable corresponding operation of data representation in table is in the process time being listed as on corresponding lathe, relevant information and resemble process criterion for table 1 arrange equipment benchmark J1, J2, J3, unit type is S1, S2, S3, asset number M1, M2, M3, M4, M5, M6, be 6 equipment of this processing, its restriction relation is each other suc as formula (5), (6) shown in.
Table 1 processing tasks information table
C wherein
ijthis point of some bit representation unit type that laterally benchmark of representative comprises.From this matrix, can find the relation between benchmark and unit type.
C wherein
ijthe asset number of all devices in corresponding this workshop of unit type that=1 some bit representation laterally represents.
The autocorrelation matrix [F (a) * F (a)] that to sum up can obtain node set is as following table 2:
Table 2[F (a) * F (a)]
According to equipment benchmark corresponding to the workpiece of table 1 related data and setting and table 2[F (a) * F (a)] middle each internodal relation recording, can obtain circuit matrix [A * F (A)] and body circuit battle array [A * A (F)] as shown in Table 3 and Table 4.Wherein F1-F6 represents different technique title car, pincers, boring, boring, milling, plane; J1, J2, J3 represent respectively three kinds of different equipment benchmark.And corresponding one by one with operation in this example.A1-a15 represents the operation row of 3 workpiece; M1-M6 represents lathe to be processed.Wherein, C
ij=1 point represents that horizontal ordinate representative element and ordinate representative color contact directly.
Table 3 technique-equipment boolean circuit matrix [A * F (A)]
Table 4[A * A (F)] in real part matrix can be used as the foundation of further recessive chromosome coding.By this matrix, can obtain processing the equipment of each operation and add the needed time of cost order work at this equipment.
Table 4 technique-equipment real number circuit matrix [A * A (F)]
Generate based on this hereditary recessive code sequence list as shown in table 5, the corresponding lathe coding of row mark, the corresponding recessive gene of rower position, the process time that in table, content is operation, the operation numbering of the corresponding workpiece of recessive gene code bit, search for relative operation-benchmark, benchmark-device numbering, device numbering-asset number circuit matrix, thereby find the lathe coding corresponding to certain working procedure, according to the availability aspect of lathe (taking or the free time), select suitable lathe coding as chromosomal dominant coding again.
The hereditary recessive code sequence list of table 5
3) operation of the improvement GA under hierarchical structure restricted model
As shown in Figure 7, Fig. 7 is improved genetic algorithms method process flow diagram of the present invention;
3.1 restricted models based on hierarchical structure circuit Boolean matrix
The hierarchical structure circuit Boolean matrix of the improved GA use benchmark of the present invention and unit type, unit type and asset number, auto-correlation, process equipment, process equipment real number is as restricted model, the operation of GA is all carried out in the scope of restricted model, and concrete operations are as follows.
3.2 chromosomal codings
First determine effective process number sum that chromosome length is each workpiece
(a) when being the production model of the many kinds of single-piece: have each of n class workpiece, the present invention improves GA chromosome length and is
l wherein
gfor the process number of corresponding g part, the workpiece number that n is this batch of scheduling, with 3 * 6 separate room above, being scheduling to example, to generate chromosome as follows:
| 1 | 5 | 4 | 3 | 4 | 6 | 2 | 3 | 4 | 2 | 6 | 3 | 1 | 2 | 4 | 1 |
1-6 represents the machining tool information of workpiece 1; 7-11 represents the machining tool information of workpiece 2; 12-15 represents the machining tool information of workpiece 3.
(b) when being the pattern of variety production more than many:
When for many variety production pattern: have n class workpiece J part (J=n altogether
1+ n
2+ ...+n
i+ ...+n
n, n wherein
1, n
2..., n
i..., n
nthe quantity i ∈ n that represents respectively i class workpiece), every class workpiece has p
iprocedure, needs first the process sequence of workpiece to be encoded, and if any each 3 of A, B, C class workpiece, first workpiece process sequence is carried out randomly orderedly, generates dominant chromosome.
From learning curve theory, repetitive operation can increase the proficiency of employee's operation, shortens the process time of single part, so adopt in research of the present invention with kind part, closes batch production coding strategy.When the quantity of part of the same race is less than 100, be merged into a task.Above-mentioned example can encode as follows (A*3 represent its each operation process time all corresponding this coefficient that is multiplied by, i.e. this part number).
| A 11·3 | … | A 1m·3 | B 11·3 | … | B 1m·3 | C k1·3 | … | C km·3 |
Finally, according to benchmark and unit type, unit type and asset number circuit matrix, generate recessive chromosome.
If surpass 100, employing is strategy in batches, because if the quantity of a workpiece is too many, can affect the processing of subsequent parts after synthetic one batch.Because be different the delivery date of each batch of inner parts, so also can arrive and specify storehouse at the delivery date of regulation in order to meet other part, for example, get 100 conduct critical points in batches.If 150 of A workpiece, 211 of B workpiece, 50 of C workpiece:
| A·100 | C·50 | B·100 | B·11 | A·50 | B·100 |
Between the individual task body in batches, be randomly ordered.
3.3 chromosomal decodings
According to the corresponding information of chromosome the inside, the hereditary recessive code sequence list of search list 5, determines the parameters such as process time of all process steps on each lathe.
3.4 select operation
The corresponding chromosome of individuality that fitness value in previous generation population is best is directly selected to enter population of future generation.
3.5 interlace operation
Two parent chromosomes of random selection, two random number 0<a<b<N (N is chromogene number), find out corresponding a on two parent chromosomes, and the fragment between b exchanges each other.
3.6 variation
3.6.1 set aberration rate, determine the gene position that needs variation.
3.6.2 search for operation-benchmark, benchmark and unit type, unit type and asset number circuit matrix, find the coding of the replaceable lathe of this gene position, produce new chromosome.
3.6.3 calculate new chromosomal objective function, the target function value that new and old chromosome is corresponding, and then select preferably to enter the next generation.
According to operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, generating process-equipment real number circuit matrix, and then produce hereditary recessive code sequence list, the corresponding lathe coding of row mark, the corresponding recessive gene of rower position; Wherein, the process time that in table, content is operation, the operation numbering of the corresponding workpiece of recessive gene code bit, by searching for corresponding operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, thus find the lathe coding corresponding to certain working procedure, according to the availability aspect of lathe, select corresponding lathe coding as chromosomal dominant coding again.Improvement GA algorithm of the present invention is all at operation-benchmark in the random implementation of coding, decoding and variation, benchmark-device numbering, in device numbering-asset number circuit matrix restraint, carry out, random in a kind of controlled range, its role is to reduce the data volume of restricted model and removed invalid information and dwindled the hunting zone of solution space, finally having improved Algorithm for Solving precision and speed.Chromogene of the present invention position coding method, has removed amorph position, has reduced space and the time complexity of algorithm, thereby improves the search efficiency of GA, and concrete data can be drawn by table 3.
Principle of the present invention:
Genetic algorithm belongs to a kind of of evolution algorithm (Evolutionary Algorithms), by the heredity of natural imitation circle and the process of selection, finds optimum solution.Be applicable to solving of challenge, be now widely used in the middle of the research of every field.But from the angle of optimized algorithm and the angle of request for utilization, academia did not always all stop the improvement of this algorithm and optimization, reduce time and the space complexity of algorithm.
The optimization direction of algorithm
Single layer coding mode, can reduce the space complexity of genetic coding to a certain extent; When processing lot size scheduling problem, product type is carried out to binary encoding as one section of chromosome, each operation of product is to embody in circuit matrix with recessive chromosome segment simultaneously.
Although single layer coding mode has certain superiority, be conducive to scheduling and carry out, in chromosome, there is a large amount of amorph positions.Because it is defined as max (m by chromosome length
i) * n(max (m
i) the maximum process number that comprises for n class workpiece).So just make whole chromosomal length be decided by a great extent a workpiece of process number maximum in each batch of task.The long efficiency of genetic algorithm in iterative process that directly affected of chromosome, has increased the space complexity of algorithm.
The optimization of single layer coding
1) chromosome length optimization
Chromosome length of the present invention is
l wherein
gfor the process number of corresponding part, the workpiece number that n is this batch of scheduling.
Before improvement (with 3 parts, maximum process number is 6 for example):
| 1 | 4 | 6 | 7 | 0 | 0 | 2 | 3 | 4 | 0 | 0 | 0 | 1 | 3 | 5 | 1 | 7 | 3 |
After improvement:
| 1 | 4 | 6 | 7 | 2 | 3 | 4 | 1 | 3 | 5 | 1 | 7 | 3 |
From above, can find that only the chromosomal length of three workpiece has just had remarkable shortening.From algorithm optimization angle, when mass data, can reduce significantly the space complexity of algorithm.The present invention is improved to rear algorithm and its contrast is as shown in table 6.
The contrast of table 6 algorithm optimization
Wherein, G represents the genetic algebra of genetic algorithm; Initialized chromosome number in Z mating pond; m
iit is the process number that i class workpiece comprises; M is number of devices; J is reference device number (much smaller than physical device number).
2) close according to the actual requirements and criticize
During the scheduling of kind more than many: suppose that n class workpiece has j part (J=n
1+ n
2+ ...+n
i+ ...+n
n, n wherein
1, n
2..., n
i..., n
nrepresent respectively the quantity of i class workpiece, and i ∈ n), then establish every class workpiece and have p
iprocedure.
The mode of available technology adopting is as follows, if any each 3 of A, B, C class workpiece, workpiece process sequence is carried out randomly orderedly, generates dominant chromosome.
| A | C | A | A | B | C | B | B | C |
According to operation-lathe circuit matrix, generate recessive chromosome again.A wherein
11for the first operation of category-A product, by that analogy.As shown in the table.
| A 11 | … | A 1m | C 11 | … | C 1m | A 21 | … | A 2m | … | C k1 | … | C km |
From learning curve theory, repetitive operation can increase the proficiency of employee's operation, shortens the process time of single part, so adopt in the present invention with kind part, closes batch production coding strategy.When the quantity of part of the same race is less than 100, be merged into a task.The above-mentioned example following A*3 that can encode represents corresponding this coefficient that is multiplied by, i.e. this part number of its each operation process time.
| A·50 | B·11 | C·50 |
Finally, according to operation-lathe circuit matrix, generate recessive chromosome.
| A 11·3 | … | A 1m·3 | B 11·3 | … | B 1m·3 | C k1·3 | … | C km·3 |
If surpass 100, employing is strategy in batches, because if the quantity of a workpiece is too many, can affect the processing of subsequent parts after synthetic one batch.Because be different the delivery date of each batch of inner parts, so also can arrive and specify storehouse at the delivery date of regulation in order to meet other part, according to practical experience, get 100 conduct critical points in batches.If 150 of A workpiece, 211 of B workpiece, 50 of C workpiece:
| A·100 | C·50 | B·100 | B·11 | A·50 | B·100 |
Between the individual task body in batches, be randomly ordered.
Case Simulation
Example 1 emulation:
Example for table 1, the parameter that genetic algorithm is set is as follows: Population Size is 50, crossing-over rate is 0.6, aberration rate is 0.8, and maximum evolution is with severally 100, carries out emulation under MATILAB7.0 environment, obtain its GA evolution curve as shown in Figure 3, this improved GA algorithm can be when 70 generation as shown in Figure 3, converges to quickly 134 from 147, and its corresponding scheduling result Gantt chart as shown in Figure 4.
Example 2 emulation and comparison:
For further verification algorithm correctness, select example 2 to carry out emulation, 2 technological datums are set, 4 device numberings, 8 concrete equipment, obtaining optimum solution is 121 minutes.From the genetic evolution curve of Fig. 5, this improved genetic algorithm can be when 32 generation, converge to 121 from 130 soon, and its speed solving is obviously very fast, and its corresponding scheduling result Gantt chart as shown in Figure 6.
Example 3 emulation and comparison:
For comparing more all sidedly and verification algorithm effect.At CPU frequency 2.5G, inside save as on the computing machine of 512MB, take VB6.0 as development platform, 8 * 8 examples of choosing the Kacem benchmark problem the inside of job shop scheduling problem solve, and 2 technological datums are set, 4 device numberings, 8 concrete equipment, calculate 10 times.Table 7 is for algorithm of the present invention is by acquired results and the solving result contrast that is minimised as evolution algorithm (Approach by Localization & Controlled Genetic Algorithhm, AL+CGA), the MS master-slave genetic algorithm of apportion model, multistage genetic algorithm, ant group genetic algorithm with part.
Each method solving result contrast of table 7Kacem8 * 8 benchmark problem
For the larger deficiency of redundant data amount in the restricted model of traditional polychromatic sets theory improved genetic algorithms method and chromosome, the present invention further proposes to use polychromatic sets hierarchy Model to improve the restricted model of algorithm, by apparatus for establishing benchmark, operation constraint is set, facility constraints, lathe constraint, the mode of unique constraint, original operation-lathe circuit matrix is divided into benchmark and unit type, the relational matrix of unit type and asset number, greatly reduce the redundant data amount of restricted model, in addition by the reasonably optimizing of chromosome length with the batch operation that closes of benchmark is in batches set, effectively reduced chromosomal Time & Space Complexity, also improved the dynamic response of algorithm model simultaneously, the finally result comparison of the emulation by identical example, the improvement GA that has proved PST hierarchical structure is having raising compared with the improved GA of traditional PS T aspect solving precision and speed, simultaneously also by selecting the experiment of Kacem8 * 8 benchmark example on identical configuration computing machine, the various performances that proved algorithm of the present invention all more traditional various algorithms are improved, further proved that algorithm is in the practicality and the superiority that solve aspect Flexible Job-shop Scheduling Problems.
Above content is only explanation technological thought of the present invention; can not limit protection scope of the present invention with this; every technological thought proposing according to the present invention, any change of doing on technical scheme basis, within all falling into the protection domain of the claims in the present invention book.
Claims (6)
1. the improvement GA based on polychromatic sets hierarchical structure solves a method for Flexible Workshop scheduling, it is characterized in that, comprises the following steps:
1) set up the mathematical model of Markov chain;
2) set up the Job-Shop restricted model based on PST hierarchical structure;
3) according to operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, generating process-equipment real number circuit matrix, and then produce hereditary recessive code sequence list, the corresponding lathe coding of row mark, the corresponding recessive gene of rower position; Wherein, the process time that in table, content is operation, the operation numbering of the corresponding workpiece of recessive gene code bit, by searching for corresponding operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, thus find the lathe coding corresponding to certain working procedure, according to the availability aspect of lathe, select corresponding lathe coding as chromosomal dominant coding again.
2. the improvement GA based on polychromatic sets hierarchical structure according to claim 1 solves the method for Flexible Workshop scheduling, it is characterized in that: in described step 1), the concrete grammar of setting up the mathematical model of Markov chain is:
FJSP can be described to, and supposes that M is the quantity of process equipment, and N is workpiece to be processed quantity, and P is process number, the set that I is all devices; I
egrepresent the available devices set of the g procedure of workpiece e,
j
eprocess number for workpiece e; X is the process sequence of all workpiece, S
egkthe start time that the g procedure of expression workpiece e is processed on equipment k; E
egkfor the g procedure of the workpiece e process finishing time on equipment k; T
egkfor the g procedure of workpiece e lasting process time on equipment k, and k ∈ I
egthere is E
egk=S
egk+ T
egk; E
pthe completion date that represents finishing operation; MS represents the last completion date of all workpiece;
When the j procedure of workpiece i and the g procedure of workpiece e are carried out on same equipment, if operation j adds man-hour prior to operation g, Q
ijeg=1, otherwise Q
ijeg=0; If the g procedure of workpiece e is processed on lathe k, X
egk=1, otherwise X
egk=0;
If certain FJSP has the possible processing sequence of S kind, require total the shortest Machining Sequencing of activity duration, first ask for each processing sequence x (x ∈ 1 ..., S}) the corresponding activity duration; Obviously, in order x, the i.e. last completion date of all workpiece of the completion date of last manufacturing procedure, has
MS=E
p （1）
Objective function F (x) is
F(x)=min(MS
x)=min（(E
p)
x） （2）
X=1，…，S
S.T.S
egk－E
e(g－1)n≥0
e=1，…，N;g=1，…，J
e;X
egk=1，X
e(g－1)n=1 （3）
S
egk－E
igk≥0
e=1，…，N;g=1，…，J
e;X
ijk=1，X
egk=1，Q
ijeg=1 （4）。
3. the improvement GA based on polychromatic sets hierarchical structure according to claim 1 solves the method for Flexible Workshop scheduling, it is characterized in that: described step 2), the restriction relation of Job-Shop restricted model is:
First equipment benchmark is set, several unit types that each equipment benchmark comprises process similarity, each unit type comprises again the concrete equipment of several this kind of models, every concrete equipment is corresponding with corresponding asset number again, and operation finally will complete processing on concrete equipment, therefore just can be by the restriction relation of operation and benchmark, the restriction relation of equipment benchmark and unit type, the restriction relation of unit type and asset number, indirectly set up the restriction relation of operation and concrete equipment, thereby realize huge operation lathe circuit matrix is divided into little relational matrix, to reduce scale and the data volume of matrix, improve the speed that solves of algorithm.
4. the improvement GA based on polychromatic sets hierarchical structure according to claim 1 solves the method for Flexible Workshop scheduling, it is characterized in that: in described step 3), according to the availability aspect of lathe, select corresponding lathe coding to be specially as chromosomal dominant coding:
3.1) set up the restricted model based on hierarchical structure circuit Boolean matrix:
Use the hierarchical structure circuit Boolean matrix of benchmark and unit type, unit type and asset number, auto-correlation, process equipment, process equipment real number as restricted model, produce hereditary recessive code sequence list, the operation of GA is all carried out in the scope of restricted model;
3.2) chromosomal coding:
3.3) chromosomal decoding:
According to the corresponding information of chromosome the inside, search technique-equipment real number circuit matrix, determines parameter process time of all process steps on each lathe;
3.4) select operation:
The corresponding chromosome of individuality that fitness value in previous generation population is best is directly selected to enter population of future generation;
3.5) interlace operation:
Two parent chromosomes of random selection, two random number 0<a<b<N, wherein, N is chromogene number, finds out corresponding a on two parent chromosomes, the fragment between b exchanges each other;
3.6) variation.
5. the improvement GA based on polychromatic sets hierarchical structure according to claim 4 solves the method for Flexible Workshop scheduling, it is characterized in that, the concrete grammar of described chromosome coding is:
First determine effective process number sum that chromosome length is each workpiece:
(a) when being the production model of the many kinds of single-piece:
Have each of n class workpiece, GA chromosome length is
l wherein
gprocess number for corresponding g part;
(b) when being the pattern of variety production more than many:
There is n class workpiece J part J=n altogether
1+ n
2+ ...+n
i+ ...+n
n, n wherein
1, n
2..., n
i..., n
nthe quantity i ∈ n that represents respectively i class workpiece, every class workpiece has p
iprocedure, needs first the process sequence of workpiece to be encoded, and workpiece process sequence is carried out randomly ordered, generates dominant chromosome;
When the quantity of part of the same race is less than 100, be merged into a task; Finally, according to benchmark and unit type, unit type and asset number circuit matrix, generate recessive chromosome;
When quantity employing over 100 of part of the same race strategy in batches, between the individual task body after in batches, be randomly ordered.
6. the improvement GA based on polychromatic sets hierarchical structure according to claim 4 solves the method for Flexible Workshop scheduling, it is characterized in that, the concrete grammar of described variation is:
3.6.1) set aberration rate, determine the gene position that needs variation;
3.6.2) search benchmark and unit type, unit type and asset number circuit matrix, find this gene position can replace the coding of lathe, produces new chromosome;
3.6.3) calculate new chromosomal objective function, the target function value that new and old chromosome is corresponding, and then select preferably to enter the next generation.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310737478.8A CN103729694B (en) | 2013-12-26 | 2013-12-26 | The method that improvement GA based on polychromatic sets hierarchical structure solves Flexible workshop scheduling |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310737478.8A CN103729694B (en) | 2013-12-26 | 2013-12-26 | The method that improvement GA based on polychromatic sets hierarchical structure solves Flexible workshop scheduling |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN103729694A true CN103729694A (en) | 2014-04-16 |
| CN103729694B CN103729694B (en) | 2016-08-24 |
Family
ID=50453756
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201310737478.8A Active CN103729694B (en) | 2013-12-26 | 2013-12-26 | The method that improvement GA based on polychromatic sets hierarchical structure solves Flexible workshop scheduling |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN103729694B (en) |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105550825A (en) * | 2016-01-15 | 2016-05-04 | 中南民族大学 | Flexible factory work scheduling method based on MapReduce parallelization in cloud computing environment |
| CN106875094A (en) * | 2017-01-11 | 2017-06-20 | 陕西科技大学 | A kind of multiple target Job-Shop method based on polychromatic sets genetic algorithm |
| CN106933200A (en) * | 2015-12-31 | 2017-07-07 | 中国科学院沈阳计算技术研究所有限公司 | The control method of the solution Flexible Job-shop Scheduling Problems based on genetic algorithm |
| CN108053152A (en) * | 2018-01-30 | 2018-05-18 | 陕西科技大学 | The method that improved adaptive GA-IAGA based on polychromatic sets solves dynamic job shop scheduling |
| CN108364126A (en) * | 2018-01-30 | 2018-08-03 | 陕西科技大学 | The method that improved adaptive GA-IAGA based on polychromatic sets solves static Job-Shop |
| CN109034540A (en) * | 2018-06-29 | 2018-12-18 | 长安大学 | A kind of lathe serial arrangement dynamic prediction method based in article process stream |
| CN110796355A (en) * | 2019-10-22 | 2020-02-14 | 江苏金陵智造研究院有限公司 | Flexible job shop scheduling method based on dynamic decoding mechanism |
| CN111583055A (en) * | 2020-05-09 | 2020-08-25 | 电子科技大学 | Product grouping method under multiple process paths based on genetic algorithm |
| CN112631214A (en) * | 2020-11-27 | 2021-04-09 | 西南交通大学 | Flexible job shop batch scheduling method based on improved invasive weed optimization algorithm |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101944201A (en) * | 2010-07-27 | 2011-01-12 | 昆明理工大学 | Multi-agent-based steelmaking workshop crane scheduling simulation method |
| JP5255946B2 (en) * | 2008-08-06 | 2013-08-07 | 株式会社日立製作所 | Content scheduling device |
-
2013
- 2013-12-26 CN CN201310737478.8A patent/CN103729694B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP5255946B2 (en) * | 2008-08-06 | 2013-08-07 | 株式会社日立製作所 | Content scheduling device |
| CN101944201A (en) * | 2010-07-27 | 2011-01-12 | 昆明理工大学 | Multi-agent-based steelmaking workshop crane scheduling simulation method |
Non-Patent Citations (3)
| Title |
|---|
| 傅卫平等: "基于多色集合的改进遗传算法求解多品种柔性调度问题", 《计算机集成制造系统》 * |
| 唐自玉: "基于多色集合理论的柔性生产线及车间规划方法研究", 《中国博士学位论文全文数据库 工程科技II辑》 * |
| 葛凌志: "应用RFID的柔性混流式及时制造模式研究", 《中国优秀硕士学位论文全文数据库 工程科技II辑》 * |
Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106933200A (en) * | 2015-12-31 | 2017-07-07 | 中国科学院沈阳计算技术研究所有限公司 | The control method of the solution Flexible Job-shop Scheduling Problems based on genetic algorithm |
| CN105550825A (en) * | 2016-01-15 | 2016-05-04 | 中南民族大学 | Flexible factory work scheduling method based on MapReduce parallelization in cloud computing environment |
| CN105550825B (en) * | 2016-01-15 | 2021-07-02 | 中南民族大学 | Flexible factory job scheduling method based on MapReduce parallelization in cloud computing environment |
| CN106875094A (en) * | 2017-01-11 | 2017-06-20 | 陕西科技大学 | A kind of multiple target Job-Shop method based on polychromatic sets genetic algorithm |
| CN108053152A (en) * | 2018-01-30 | 2018-05-18 | 陕西科技大学 | The method that improved adaptive GA-IAGA based on polychromatic sets solves dynamic job shop scheduling |
| CN108364126A (en) * | 2018-01-30 | 2018-08-03 | 陕西科技大学 | The method that improved adaptive GA-IAGA based on polychromatic sets solves static Job-Shop |
| CN109034540A (en) * | 2018-06-29 | 2018-12-18 | 长安大学 | A kind of lathe serial arrangement dynamic prediction method based in article process stream |
| CN109034540B (en) * | 2018-06-29 | 2021-09-07 | 长安大学 | Machine tool sequence arrangement dynamic prediction method based on work-in-process flow |
| CN110796355A (en) * | 2019-10-22 | 2020-02-14 | 江苏金陵智造研究院有限公司 | Flexible job shop scheduling method based on dynamic decoding mechanism |
| CN111583055A (en) * | 2020-05-09 | 2020-08-25 | 电子科技大学 | Product grouping method under multiple process paths based on genetic algorithm |
| CN112631214A (en) * | 2020-11-27 | 2021-04-09 | 西南交通大学 | Flexible job shop batch scheduling method based on improved invasive weed optimization algorithm |
| CN112631214B (en) * | 2020-11-27 | 2022-03-18 | 西南交通大学 | Flexible job shop batch scheduling method based on improved invasive weed optimization algorithm |
Also Published As
| Publication number | Publication date |
|---|---|
| CN103729694B (en) | 2016-08-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN103729694A (en) | Method for solving flexible job-shop scheduling problem with improved GA based on polychromatic set hierarchical structure | |
| CN103020358A (en) | Construction method of adaptive dynamic design platform aiming at mechanical device | |
| Liu et al. | Mathematical modeling and a hybrid evolutionary algorithm for process planning | |
| Su et al. | Algorithms for solving assembly sequence planning problems | |
| CN103065207B (en) | Based on the engine cylinder-body process route optimization method of processing unit | |
| Yi et al. | Optimized tool path planning for five-axis flank milling of ruled surfaces using geometric decomposition strategy and multi-population harmony search algorithm | |
| CN107831740A (en) | A kind of Optimization Scheduling during the distributed manufacturing applied to notebook part | |
| CN110531716A (en) | The method for solving low-carbon Job-Shop problem based on discrete whale algorithm | |
| Cao et al. | Simulation optimization for a digital twin using a multi-fidelity framework | |
| Wang et al. | Application of hybrid artificial bee colony algorithm based on load balancing in aerospace composite material manufacturing | |
| CN105550825A (en) | Flexible factory work scheduling method based on MapReduce parallelization in cloud computing environment | |
| CN112101773A (en) | Task scheduling method and system for multi-agent system in process industry | |
| CN102222274A (en) | Immune clone selection job shop scheduling method based on scheduling coding | |
| Menzel et al. | Application of free form deformation techniques in evolutionary design optimisation | |
| CN108197186B (en) | Dynamic graph matching query method applied to social network | |
| Lou et al. | Improved hybrid immune clonal selection genetic algorithm and its application in hybrid shop scheduling | |
| CN108153254B (en) | A kind of part based on glowworm swarm algorithm is clustered to process route optimization method | |
| CN103246923A (en) | Self-adaptive genetic algorithm-based flexible workshop dispatching technology | |
| Ye | Optimization of resource scheduling based on genetic algorithm in cloud computing environment | |
| ZHANG et al. | MANUFACTURING FLOW SHOP SCHEDULING PROBLEM BASED ON SIMULATED ANNEALING ALGORITHM. | |
| Han et al. | Bus manufacturing workshop scheduling method with routing buffer | |
| Wang et al. | A hybrid technology for assembly sequence planning of reflector panels | |
| Yi et al. | The multi-objective optimization of the planet carrier in wind turbine gearbox | |
| CN113313283B (en) | Knowledge-driven method-based distributed assembly blocking flow workshop integrated scheduling method | |
| CN110532598A (en) | VR electric power training system electric power tool model standardization design method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| TR01 | Transfer of patent right | ||
| TR01 | Transfer of patent right |
Effective date of registration: 20230110 Address after: 230000 b-1018, Woye Garden commercial office building, 81 Ganquan Road, Shushan District, Hefei City, Anhui Province Patentee after: HEFEI WISDOM DRAGON MACHINERY DESIGN Co.,Ltd. Address before: No. 1, Weiyang District university garden, Xi'an, Shaanxi Province, Shaanxi Patentee before: SHAANXI University OF SCIENCE & TECHNOLOGY |
|
| TR01 | Transfer of patent right | ||
| TR01 | Transfer of patent right |
Effective date of registration: 20230613 Address after: No. 008, Hewan Road, Yuexi Economic Development Zone, Anqing City, Anhui Province 246600 Patentee after: RUILIN MECHANICS TECHNOLOGY Co.,Ltd. Address before: 230000 b-1018, Woye Garden commercial office building, 81 Ganquan Road, Shushan District, Hefei City, Anhui Province Patentee before: HEFEI WISDOM DRAGON MACHINERY DESIGN Co.,Ltd. |