CN106611220A - Novel mixed algorithm for solving flexible job shop scheduling problem - Google Patents
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Abstract
The invention provides a novel mixed algorithm for solving a flexible job shop scheduling problem. A culture algorithm is combined with a genetic algorithm; the culture algorithm consists of two parts including a main population space and a belief space, useful knowledge is obtained from a population and stored in the belief space, a search process is guided by utilizing the knowledge, and the culture algorithm is a knowledge multi-evolution process-based global optimization search algorithm, so that the knowledge guidance-based genetic algorithm is proposed; and the genetic algorithm is adopted as the main population space, feature knowledge of a solution is extracted by utilizing the optimization mechanism of the culture algorithm in an iteration process to guide the selection operation of the genetic algorithm, so that a two-layer evolution structure is formed. The similarity selection operation is executed by adopting a k-nearest neighbor method, and the performance of the algorithm is enhanced by adopting a two-point crossing mode and a self-learning neighborhood search mutation method. Therefore, the convergence rate and the solving quality of the algorithm are better improved.
Description
Art
The present invention relates to solving job shop scheduling problem technical field, more particularly to being asked with Algorithm for Solving flexible job shop scheduling
Topic.
Background technology
Flexible Job-shop Scheduling Problems (FJSP) are the extensions of classical job-shop scheduling problem (JSP).In JSP
In, only consider that workpiece has a case that well-determined machining process route.And in FJSP, can be in multiple stage machine per procedure
Process on device, workpiece has selectable processing route, and the time needed for processing on different machines is different, therefore
FJSP, closer to actual manufacturing environment, is a class scheduling problem of urgent need to resolve in actual production than JSP.
FJSP is not only it needs to be determined which platform machining is the processing sequence of workpiece, be also predefined certain procedure by.Therefore,
FJSP is the problem more increasingly complex than JSP.Existing research method is broadly divided into exact algorithm, heuristic rule and meta-heuristic
Algorithm (such as simulated annealing, genetic algorithm).Wherein exact algorithm cannot effectively be solved to large-scale F JSP；Heuristic rule
Then solving speed is fast, but gained is second-rate；The features such as genetic algorithm has versatility, robustness, implict parallelism, in production
The application in scheduling field widely, but its iterative process be do not instruct and completely random natural selection with heredity behaviour
Make, ignore important function of the characteristic information of problem in Solve problems.
The content of the invention
For above-mentioned deficiency, the present invention is combined Cultural Algorithm with genetic algorithm, and Cultural Algorithm is by main group space and letter
Face upward space two parts composition, be it is a kind of useful knowledge obtained from population be stored in belief space, and using these knowledge
Guidance search process, is a kind of global optimization search of many evolutionary process of Knowledge based engineering.Spy of the present invention for FJSP
Point, proposes the genetic algorithm that knowledge based is instructed, and using genetic algorithm as main group space, the algorithm is sharp in an iterative process
The feature knowledge of solution is extracted with the optimizing mechanism of Cultural Algorithm, the selection operation of genetic algorithm is instructed, a kind of two level evolution is formed
Structure.
The purpose of the present invention is：Improve convergence of algorithm speed and solve quality.
For achieving the above object, the technical scheme for being adopted is the present invention：A kind of new hybrid algorithm solves flexible job
Job-Shop problem.The technical scheme is comprised the following steps：
Step 1：Make Swarm Evolution iterations t=0, renewal frequency record number of times f=0, and initialization algorithm is various
Parameter, main group space, belief space A and belief space B；
Step 2：Algorithm terminates if t >=Maxlter (maximum iteration time), otherwise goes to next step；
Step 3：According to renewal frequency f0, decide whether to update belief space, if f=f0, update；Otherwise go to step 5；
Step 4：Using k nearest neighbour methods, instructed using the knowledge of belief space B, perform the operation of similitude selection opertor；
Step 5：Crossover operation is carried out by the way of two-point crossover；
Step 6：Self study neighborhood search makes a variation, and the chromosome for entering row variation is entered with optimum chromosome in belief space A
Row compares, and according to the different quantity of gene value the mode of mutation operation is determined；
Step 7：Population of new generation is generated, makes t=t+1, f=f+1, return to step 2 repeat this program.
The invention has the beneficial effects as follows：The characteristics of present invention based on Cultural Algorithm there is knowledge to instruct, proposes there is knowledge
The genetic algorithm of guidance, extracts the feature knowledge of solution using the optimizing mechanism of Cultural Algorithm in an iterative process, instructs heredity to calculate
The selection operation of method, forms double-deck genetic structure, makes individuality that convergence rate is accelerated in search space, it is to avoid to occur in that precocity
And converge on locally optimal solution.Meanwhile, instruct selection operation to guarantee that excellent individual is entered by calculating index of similarity next
The subspace of secondary iteration；Self study neighborhood operation variation is carried out by the change point in specified range, it is ensured that individuality is in iteration mistake
The excellent characteristic of parent is effectively inherited in journey, so as to acceleration search process is constantly to optimum direction approximation.
Description of the drawings：
Fig. 1 represents the detail flowchart of this algorithm
Fig. 2 represents that the coded system exemplary plot of workpiece number is replaced in the repetition of this algorithm
Specific embodiment：
The present invention proposes a kind of new hybrid algorithm and solves Flexible Job-shop Scheduling Problems, and the algorithm is based on culture calculation
The characteristics of there is method knowledge to instruct, proposes the genetic algorithm instructed with knowledge, in an iterative process seeking using Cultural Algorithm
Excellent mechanism extracts the feature knowledge of solution, instructs the selection operation of genetic algorithm, forms double-deck genetic structure.
Below in conjunction with the accompanying drawings, to further description of the present invention：
First, Flexible Job-shop Scheduling Problems
Flexible job shop scheduling is described as follows：One system of processing has the different machine M={ M of m platformsj| j=1,2 ...
M } to process n workpiece J={ Ji| i=1,2 ... n }.FJSP includes two subproblems：(1) it is every procedure OikCorresponding
Available machines used set MikIt is middle to select suitable machine Mj, i.e. machine loading problem.
(2) it is that selected machine collection M arranges the alignment process of n workpiece collection J, and is meeting certain constraints
Optimize one or more given performance indications, i.e. Job Scheduling problem simultaneously.
2nd, the key content explanation of algorithm
1st, coded system, with reference to Fig. 2
The present invention is using the coded system for repeating to replace workpiece number.I.e. to a scale for the solving job shop scheduling problem of n × m
Speech, item chromosome has n × m gene, one workpiece number of each gene representation, the position table that workpiece number occurs in chromosome
Show its corresponding operation, as shown in Figure 2.The advantage of this coded system is not need repair mechanism, because its heredity for carrying out
Operation does not produce infeasible solution.
With reference to Fig. 2, the rectangle frame in figure represents the gene on chromosome, one workpiece number of each gene representation,
322112313 corresponding operations are J31、J21、J22、J11、J12、J23、J32、J13、J33.Workpiece number in first gene position is 3,
And the workpiece number occurs for the first time, then corresponding operation is the first procedure of the 3rd workpiece, as J31, foundation below
Such method, the like.
2nd, decoding process
Because the scheduling scheme that activity scheduling algorithm is generated necessarily includes optimal value, so the decoding of this algorithm is using work
The method of dynamic scheduling.
3rd, belief space is designed
(1) composition of belief space
The belief space of this algorithm is made up of A and B two parts, respectively by receiving function accept1() and accept2() comes
Determine.Assume to have L bar chromosomes in main group space, make chmlRepresent the l article chromosome, chm in main group spacelIt is suitable
Answer angle value FlFor the Maximal Makespan C of all workpiece of its correspondence scheduling schememax, then belief space A be：
accept1()：A=[chm*]
F*=minFl, (1≤l≤L)
Belief space A is made up of optimum chromosome, belief space B is：
accept2()：B=[chm1, chm2..., chmx]
The size of the fitness value of chromosome is first according to, is arranged in order as F1＜ F2＜ ... ＜ Fx＜ Fl, then take front x
Individuality is stored in belief space B.That is, select given amount for x part optimum genome into belief space B.
(2) renewal of belief space
After per the set number of times of iteration, belief space is updated, make belief space persistently preserve current best knowledge information.
Therefore, this algorithm using current The cream of the crop scheduling scheme as learning object, by belief space is adjacent update twice between
Algorithm iteration number of times be referred to as renewal frequency, remember f0。
4th, crossover operation
Using having ability of searching optimum, the two-point crossover operator of convergence with probability 1 performs the intersection of this algorithm to the present invention
Operation.
5th, mutation operation
The present invention is made a variation using neighborhood search, mutation operation is searched with broader under the guidance of knowledge in belief space A
Rope region is iterated, and implements process as follows：
(1) range of choice of definitive variation point, according to mutation probability PmItem chromosome is randomly choosed in subspace, with
Optimum chromosome compares, and records the different chromosome position pos of gene value and number q (q is even number)；
(2) different mutation operations are carried out according to the size of q：
A kind of mutation operation：When q≤2, change point is randomly choosed, carry out neighborhood search variation.
Another kind of mutation operation：When q >=4, then one is first produced by 1 random sequence constituted to the integer q
P, makes u represent the gene number for carrying out neighborhood search variation, and v represents cycle-index, and w represents maximum cycle, and w is q/u
Round downwards, i.e. w=[q/u], generally, u=3, detailed process is as follows：1) v=1 is made；2) from left to right take successively with
3 element P [uv-2], P [uv-1], P [uv] in machine sequence P are come the gene location that determines to carry out neighborhood search variation on pos；
3) neighborhood search variation is carried out；4) by v ← v+1, go to if v≤w 2), otherwise algorithm terminates.
There it can be seen that the numerical value of q is bigger, illustrate by the gene value between mutated chromosome and optimum chromosome not
Same position is more；Conversely, then fewer.The characteristics of variation mode has self study, its time complexity is O (q), wherein q etc.
In in current chromosome and belief space A between chromosome gene location value dissimilarity number, its false code is as follows：
6th, selection operation
The present invention adopts k-nearest neighbor, and using the knowledge in belief space B selection operation is instructed, and detailed process is as follows：
(1) initial sub-population space is generated using the selection mode based on roulette；
(2) given amount is selected in sub-group space for the defect individual set of k, it is according to k nearest neighbour methods that these are individual
Index of similarity calculating is carried out with the chromosome in belief space B；
(3) the maximum individualities of k index of similarity Sd are searched, and these individualities are inserted in current sub-population space,
K worst individuality is eliminated simultaneously.Its index of similarity computing formula is as follows:
If the value of correspondence gene location is identical in two chromosomes,Return value is 1, no
It is then 0, its computing formula is as follows：
Wherein, chm1And chm2Two chromosomes are represented respectively, and i represents gene location in chromosome, and y represents dye
The length of colour solid, typically its size is y=nm in scale is for the job-shop scheduling problem of n × m.
The index of similarity Sd of this algorithm represents the Hamming distances between two chromosome codings, because between two solutions
Difference is almost directly proportional to the Hamming distances between chromosome coding, so can release two solutions by calculating index of similarity
Between close degree, if the value of index of similarity Sd is bigger, two chromosomes are more close, and vice versa.
Above-mentioned combination accompanying drawing is description to the algorithm, therefore limits the present invention, protection scope of the present invention according to
Determine according to the content of claims.
Claims (7)
1. a kind of new hybrid algorithm solves Flexible Job-shop Scheduling Problems, and the algorithm is related to solving job shop scheduling problem technology neck
Domain, more particularly to Algorithm for Solving Flexible Job-shop Scheduling Problems are used, is characterized in that：The specific implementation step of the algorithm is such as
Under：
Step 1：Make Swarm Evolution iterations t=0, renewal frequency record number of times f=0, and various parameters, the master of initialization algorithm
Group space, belief space A and belief space B；
Step 2：If tThen algorithm terminates Maxlter (maximum iteration time), otherwise goes to next step；
Step 3：According to renewal frequency f0, decide whether to update belief space, if f=is f0, update；Otherwise go to step 5；
Step 4：Using k nearest neighbour methods, instructed using the knowledge of belief space B, perform the operation of similitude selection opertor；
Step 5：Crossover operation is carried out by the way of two-point crossover；
Step 6：Self study neighborhood search makes a variation, and the chromosome for entering row variation is compared with optimum chromosome in belief space A
Compared with according to the mode of the different quantity decision mutation operation of gene value；
Step 7：Population of new generation is generated, makes t=t+1, f=f+1, return to step 2 repeat this program.
2. a kind of new hybrid algorithm according to claim 1 solves Flexible Job-shop Scheduling Problems, it is characterized in that：This
Invention is using the coded system for repeating to replace workpiece number, i.e., for a scale is for the solving job shop scheduling problem of n × m, a dye
Colour solid has n × m gene, one workpiece number of each gene representation, the positional representation that workpiece number occurs in chromosome its correspondence
Operation, the advantage of this coded system is not need repair mechanism, because the genetic manipulation that it is carried out does not produce infeasible solution.
3. a kind of new hybrid algorithm according to claim 1 solves Flexible Job-shop Scheduling Problems, it is characterized in that：This
The method that the decoding of algorithm adopts activity scheduling, the scheduling scheme that it is generated necessarily includes optimal value.
4. a kind of new hybrid algorithm according to claim 1 solves Flexible Job-shop Scheduling Problems, it is characterized in that：This
The belief space of algorithm is made up of A and B two parts, respectively by receiving function（）With determining, it is assumed that main group body is empty
Between in have L bar chromosomes, orderRepresent in main group spaceBar chromosome,Fitness valueFor it
The Maximal Makespan of all workpiece of correspondence scheduling scheme, then belief space A be：
（）：A=
,
Belief space A is made up of optimum chromosome, belief space B is：
QUOTE ：B=
Be first according to the size of the fitness value of chromosome, be arranged in order for, then
Take front x individuality to be stored in belief space B, i.e. select given amount for x part optimum genome into belief space B.
5. a kind of new hybrid algorithm according to claim 1 solves Flexible Job-shop Scheduling Problems, it is characterized in that：This
The update method of the belief space of algorithm is：After per the set number of times of iteration, belief space is updated, belief space is persistently preserved
Current best knowledge information, therefore, this algorithm, as learning object, will look up to sky using current The cream of the crop scheduling scheme
Between it is adjacent twice update between algorithm iteration number of times be referred to as renewal frequency, remember f0.
6. a kind of new hybrid algorithm according to claim 1 solves Flexible Job-shop Scheduling Problems, it is characterized in that：This
Invention is made a variation using neighborhood search, mutation operation is carried out with broader region of search under the guidance of knowledge in belief space A
Iteration, implements process as follows：
（1）The range of choice of definitive variation point, according to mutation probabilityItem chromosome is randomly choosed in subspace, and most
Excellent chromosome compares, and records the different chromosome position pos of gene value and number q（Q is even number）；（2）According to the size of q
Carry out different mutation operations：
A kind of mutation operation：Work as qWhen 2, change point is randomly choosed, carry out neighborhood search variation；
Another kind of mutation operation：Work as qWhen 4, then one is first produced by 1 random sequence P constituted to the integer q, make u
Expression carries out the gene number of neighborhood search variation, and v represents cycle-index, and w represents maximum cycle, and w takes downwards for q/u
It is whole, i.e. w=, generally, u=3, detailed process is as follows：1）Make v=1；2）From left to right take successively in random sequence P
3 element P、P、PCome the gene location for determining to carry out neighborhood search variation on pos；3）
Carry out neighborhood search variation；4）WillIf, vW then goes to 2）, otherwise algorithm terminates；
There it can be seen that the numerical value of q is bigger, illustrate different by the gene value between mutated chromosome and optimum chromosome
Position is more；Conversely, then fewer, the characteristics of the variation mode has self study, its time complexity is O (q), and wherein q is equal to and works as
In prochromosome and belief space A between chromosome gene location value dissimilarity number, its false code is as follows：
。
7. a kind of new hybrid algorithm according to claim 1 solves Flexible Job-shop Scheduling Problems, it is characterized in that：This
Invention adopts k-nearest neighbor, and using the knowledge in belief space B selection operation is instructed, and detailed process is as follows：
（1）Initial sub-population space is generated using the selection mode based on roulette；
（2）Given amount is selected in sub-group space for the defect individual set of k, according to k nearest neighbour methods are by these individualities and believe
The chromosome faced upward in space B carries out index of similarity calculating；
（3）The maximum individualities of k index of similarity Sd are searched, and these individualities are inserted in current sub-population space, while
K worst individuality is eliminated, its index of similarity computing formula is as follows:
（1）
If the value of correspondence gene location is identical in two chromosomes,Return value is 1, no
It is then 0, its computing formula is as follows：
Wherein,WithTwo chromosomes are represented respectively,Gene location in chromosome is represented, y represents dye
The length of colour solid, typically its size is y=nm in scale is for the job-shop scheduling problem of n × m；
This algorithm can release the close degree between two solutions by calculating Sd index of similarity, if index of similarity Sd
Value is bigger, then two chromosomes are more close, and vice versa.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109816262A (en) * | 2019-01-31 | 2019-05-28 | 贵州大学 | Using the flexible job shop scheduling method of improvement immune genetic algorithm |
| CN110738365A (en) * | 2019-10-09 | 2020-01-31 | 湖北工业大学 | flexible job shop production scheduling method based on particle swarm optimization |
| CN113344383A (en) * | 2021-06-04 | 2021-09-03 | 兰州理工大学 | Energy-saving workshop scheduling system for distributed heterogeneous factory |
| CN115145235A (en) * | 2022-08-30 | 2022-10-04 | 武汉理工大学 | Multi-target intelligent scheduling method for casting whole process |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109816262A (en) * | 2019-01-31 | 2019-05-28 | 贵州大学 | Using the flexible job shop scheduling method of improvement immune genetic algorithm |
| CN109816262B (en) * | 2019-01-31 | 2023-04-28 | 贵州大学 | Flexible job shop scheduling method adopting improved immune genetic algorithm |
| CN110738365A (en) * | 2019-10-09 | 2020-01-31 | 湖北工业大学 | flexible job shop production scheduling method based on particle swarm optimization |
| CN110738365B (en) * | 2019-10-09 | 2022-07-19 | 湖北工业大学 | Flexible job shop production scheduling method based on particle swarm algorithm |
| CN113344383A (en) * | 2021-06-04 | 2021-09-03 | 兰州理工大学 | Energy-saving workshop scheduling system for distributed heterogeneous factory |
| CN115145235A (en) * | 2022-08-30 | 2022-10-04 | 武汉理工大学 | Multi-target intelligent scheduling method for casting whole process |
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Application publication date: 20170503 |