CN106610651A - Hybrid genetic algorithm for solving multi-objective flexible job-shop scheduling problem - Google Patents
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- 230000002068 genetic effect Effects 0.000 title claims abstract description 27
- 239000011159 matrix material Substances 0.000 claims abstract description 27
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- 210000000349 chromosome Anatomy 0.000 claims abstract description 8
- 238000004519 manufacturing process Methods 0.000 claims abstract description 5
- 230000035772 mutation Effects 0.000 claims description 22
- 238000009434 installation Methods 0.000 claims description 6
- 238000001514 detection method Methods 0.000 claims description 5
- 238000010187 selection method Methods 0.000 claims description 2
- 230000000869 mutational effect Effects 0.000 claims 1
- 230000008569 process Effects 0.000 description 8
- 238000012545 processing Methods 0.000 description 4
- 238000011156 evaluation Methods 0.000 description 3
- 230000008901 benefit Effects 0.000 description 2
- 238000004043 dyeing Methods 0.000 description 2
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- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM]
- G05B19/41865—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM] characterised by job scheduling, process planning, material flow
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
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Abstract
The invention provides a hybrid genetic algorithm for solving a multi-objective flexible job-shop scheduling problem. The algorithm takes three objectives of the completion time, the production cost and the equipment utilization rate in flexible job-shop scheduling into consideration, and aims at the circumstances that algorithms at present are difficult in decoding and long in computation time because of possession of a complicated coding method and that the genetic algorithm is faced with problems of global near optimum and insufficient search capability in local search. In allusion to the problems, the invention provides a new matrix chromosome coding method which almost does not need to perform decoding. In addition, the algorithm provided by the invention combines the global search capability and local search of the genetic algorithm, the search capability of the algorithm is enhanced, and a feasible solution is found more easily. The hybrid algorithm is high in practicability, and can be well applied to flexible job-shop scheduling.
Description
Art
The present invention relates to solving job shop scheduling problem technical field, more particularly to Solving Multi-objective Flexible Job-shop Scheduling field.
Background technology
Flexible Job-shop Scheduling Problems (FJSP) are the scheduling that a kind of machine and operation have multiple selections.Generally, it is wrapped
Dispatch containing machine assignment and operation.For job-shop scheduling problem method be improve production work efficiency, motility and
The key method of reliability.Further investigation Flexible Job-shop Scheduling Problems simultaneously propose that efficient algorithm is with very big for it
Realistic meaning, especially for the enterprise in a keen competition environment.
Compared to traditional job-shop scheduling problem, Flexible Job-shop Scheduling Problems have less constraint, therefore can
The search space of row solution is bigger.Therefore, it is more difficult, is NP-hard problem.For the existing algorithm bag of this problem
Include heuritic approach, genetic algorithm and TABU search scheduling algorithm.
Genetic algorithm (Genetic Algorithm, GA), as a kind of Enlightened Search method, is based on " survival of the fittest "
The algorithm of Mechanism Design, its thought source is in Darwinian theory of evolution and Mendelian theory of heredity.GA is mainly by from changing
Enter the angle of crossover operation and mutation operation to be adapted to the solution of particular problem, but genetic algorithm may be produced after cross and variation
The infeasible solution of life, and genetic algorithm faces global nearly excellent problem.In this case genetic search and neighborhood search are combined
Genetic algorithm be suggested solution Flexible Job-shop Scheduling Problems, this combination makes algorithm be provided simultaneously with the overall situation to search
Suo Nengli and local search ability.
Even if many algorithms are suggested, but have the coded system of complexity so that decoding difficulties expend substantial amounts of calculating
Time.
The content of the invention
For deficiencies of the prior art, the problem to be solved in the present invention is to provide a kind of genetic algorithm solution
Certainly Solving Multi-objective Flexible Job-shop Scheduling problem.
The purpose of this algorithm is overcome present in prior art：Firstth, coded system is excessively complicated, causes decoding tired
Difficulty, calculates the time long；Secondth, feasible solution (scheduling scheme) may produce infeasible solution through intersecting, after mutation operation
(scheduling scheme)；3rd, genetic search has the overall situation near excellent, and Local Search may act on locally optimal solution；4th, with weighting
The weighted value of each object function is difficult to determine when method solves multi-objective problem；The neighborhood solution quantity of the five, solutions is very more, accounts for
Evaluation time of using tricks is excessive.
The technical scheme that adopted for achieving the above object of the present invention is：Flexible work is solved using a kind of genetic algorithm
Industry Job-Shop problem, the algorithm is comprised the following steps：
The parameter setting of the algorithm is as follows：Population scale N is set to 50, crossover probability PcIt is set as 0.5, mutation probability PmQuilt
It is set to 0.05；To each k neighborhood solution of current solution detection in Local Search；The end condition of algorithm iteration is：If optimum
Individuality can not be modified in continuous 20 generation, then algorithm is stopped.
Step 1：Initialization population N, using a kind of new coded system --- the matrix dyeing encoded based on Job Scheduling
Body；
Step 2：Update elite group；
Step 3：Each object function weighted value is obtained by the weights method of relative importance, by each object function of standardization
Determine fitness function value；
Step 4：Genetic search
Step 4.1：Random selection N/2 is individual；
Step 4.2：By probability PcTwo parents are selected, the single-point based on matrix is carried out and is intersected；
Step 4.3：By probability PmParent is selected, is carried out based on the mutation of matrix；
Step 5：Local Search is carried out to each solution；(carrying out simultaneously with step 4)
Step 6：It is individual using roulette method selection method random selection S；
Step 7：Iteration；
Step 8：Update elite group；
The invention has the beneficial effects as follows：
Firstth, using new coded system, cataloged procedure is simplified, while so that algorithm is hardly used in running
Decoded；Secondth, using the single-point crossover operator and mutation operator dedicated for this coded system, it is more easy to obtain feasible solution；
3rd, the ability of searching optimum of genetic algorithm is combined with Local Search, is strengthened search capability；4th, relative importance is adopted
Weighting method, make each object function weighted value more conform to practical condition.5th, the part for only randomly selecting current solution is adjacent
Domain solution is detected, it is to avoid Local Search takes excessive calculating time.
Description of the drawings
The detail flowchart of Fig. 1 this algorithm.
Fig. 2 represents the exemplary plot of flexible job shop scheduling.
Fig. 3 represents the coded system exemplary plot of the algorithm.
Fig. 4 .1 represent two parents for carrying out single-point intersection, and wherein thick line is reticule, only intersect two parent reticules
Task above.
Fig. 4 .2 represent the offspring after intersecting
Fig. 5 represented based on the mutation process example of matrix, and wherein thick line is mutation line, mutation only by exchange mutation line it
Between two row tasks.
Fig. 6 represents the relative importance of each target that expert's Evaluation Method draws.
Specific embodiment
In order that the objects, technical solutions and advantages of the present invention become more apparent, below in conjunction with drawings and Examples pair
The present invention is further described.It should be understood that specific embodiment described herein is used only for explaining that the present invention is not used to
Limit the present invention.Based on the embodiment in the present invention, those skilled in the art are obtained under the premise of creative work is not made
The every other embodiment for obtaining, belongs to the scope of protection of the invention.
The present invention does not account for multiobject flexible job shop scheduling for current some algorithms, and loses in prior art
Propagation algorithm has that global nearly excellent, decoding process is difficult.The invention proposes a kind of genetic algorithm and solves multiple target
Flexible Job-shop Scheduling Problems.Wherein time, cost and utilization rate of equipment and installations are used as object function.It is genetic algorithm
Ability of searching optimum in combination with the local search ability of neighborhood search operator.Based on operation dominance relation, matrix representation
It is devised.AHP analytic hierarchy process (AHP)s are taken to find the weighted value of each target.Each target is standardized to avoid inclining
To in some targets, also, by the linear of all object functions and, former problem is converted into single-object problem.
With reference to the accompanying drawings and examples, the present invention is described in detail.
In being located at Solving Multi-objective Flexible Job-shop Scheduling：N workpiece is expressed as：J1,J2... Jn；M platform machines are expressed as：
M1,M2,...Mm；Workpiece JiJth procedure be expressed as:Oij
Solving Multi-objective Flexible Job-shop Scheduling problem can find out that (" 0 " is represented on the machine without work in figure from Fig. 2 examples
Sequence is processed) there are m platforms machine and n workpiece in a production system.Each workpiece needs some steps to process, and
In each step, there are several machines to be chosen.The order of the step of each workpiece is predetermined.Each step can
It is performed with different costs on different machines.Problem is the program for how determining time started, end time and workpiece,
So that deadline, production cost and utilization rate of equipment and installations are optimised in the case where following condition is met：All of machine is in t
=0 moment can use；One machine is once merely capable of processing a workpiece；Processing of each operation sequence on related machine
Time is known；The step of each workpiece is sequential, is out-of-order the step of any two workpiece.
The mathematical model of Solving Multi-objective Flexible Job-shop Scheduling problem can be expressed as：Deadline is by all workpiece
Longest finishing time is evaluating.Cost is measured by the processing cost and inventory cost of product.Utilization rate of equipment and installations passes through machine
Total load measuring.They are used as object function.Therefore, the mathematical model of problem is as follows：
minf1=min (maxTi) (1)
It is constrained inXijk=1 or 0, (4)
I=1,2 ..., n, j=1,2 ..., ni, k=1,2 ..., m
Wherein TiThe deadline of i-th workpiece is represented, C represents wastage in bulk or weight, CijkRepresent i-th workpiece in kth platform machine
J-th operation in consumption,When representing the early start in j-th operation of i-th workpiece in kth platform machine
Between,End time of i-th workpiece in -1 operation of jth of kth platform machine is represented, it is, in -1 work of jth
The earliest time allowed in sequence.The stock for representing i-th workpiece during processing -1 operation of jth and j-th operation disappears
Consumption.TijkRepresent process time of i-th workpiece in j-th operation of kth platform machine.XijkDecision variable is represented, it is represented
Whether i-th workpiece can be processed on kth platform machine in j-th operation.If it is, XijkValue 1, otherwise, its value 0.
niIt is the process number of i-th workpiece.
The model of the problems referred to above for setting up, the implementation steps of the algorithm are as follows：
The parameter setting of the algorithm is as follows：Population scale N is set to 50, crossover probability PcIt is set as 0.5, mutation probability PmQuilt
It is set to 0.05；To each k neighborhood solution of current solution detection in Local Search；The end condition of algorithm iteration is：If optimum
Individuality can not be modified in continuous 20 generation, then algorithm is stopped.
Step 1：Initialization population N, using a kind of new coded system --- the matrix dyeing encoded based on Job Scheduling
Body；
One suitable encoding scheme is the first step of solving practical problems, by considering characteristic and flexible path structure,
One new matrix chromosome coding scheme encoded based on Job Scheduling is devised.This coded system be with i/j come
Represent i-th operation of j-th workpiece on kth platform machine.Using this encoding scheme to Flexible Job-shop Scheduling Problems
Speech is simpler, and hardly with being decoded.
The encoding scheme is described as follows with reference to Fig. 3:Invention research is 4 machines in flexible job shop, 2 works
Part, the scheduling of each procedure of workpiece 3, Fig. 3 represents j-th workpiece on kth platform machine in the element i/j of matrix row k
I-th operation, in figure 0 represent on kth platform machine without not be processed workpiece.For example, represent in the first row, 1/2
First operation of second workpiece on First machine, 0 represents and is processed without workpiece on First machine
Step 2：Update elite group；
Step 2.1：Non-domination solution in current population is copied into into elite group；
Step 2.2：Solution in detection elite group, will be deleted by the arranged solution of other solutions from elite group；
Step 3：Each object function weighted value is obtained by the weights method of relative importance, by each object function of standardization
Determine fitness function value；
Relatively important sexual intercourse such as Fig. 6 that step 3.1 is given according to expert's Evaluation Method, by formula (10), formula (11), formula
(12) weighted value of each object function is determined；
Step 3.2：The fitness function value of each solution is calculated by formula (7)；
Step 4：Genetic search
Step 4.1：Random selection N/2 is individual
Step 4.2：By probability PcTwo parents are selected, the single-point based on matrix is carried out and is intersected；
Probability p should be passed crosswise with reference to Fig. 4cAfter selecting two parents, one is referred to as reticule (thick line) in matrix
Horizontal line is selected randomly.Task above two parent exchange reticules obtains the result in two offsprings.If offspring
It is infeasible, then suitably adjust by carrying out to obtain two feasible offsprings.
Step 4.3：By probability PmParent is selected, is carried out based on the mutation of matrix；
The mutation with reference to Fig. 5 is by Probability pmSelect parent.For each selected individuality, it is referred to as dashing forward in matrix
Two horizontal lines of modified line (thick line) are selected randomly.Scheduling between these lines is randomly exchanged, but machine order is protected
Hold constant.There are two rows between mutation line, mutation is only carried out by exchanging this two row.
Step 5：Local Search is carried out to each solution (with step 4 while carrying out)；
Step 5.1：One neighborhood solution of the current solution of random selection, neighborhood solution is produced by the mutation operator in genetic search
It is raw:
Step 5.2：If neighborhood solution replaces former current solution using neighborhood solution better than current solution as current solution, step is returned
Rapid 5.1；Otherwise, next step is performed.
Step 5.3：If have detected k neighborhood solution of current solution, Local Search terminates, and current solution is local
The result of search；Otherwise, return to step 5.1
Step 6：Select random selection S individual using roulette method；
Step 6.1：:Calculate each individuality (xi) it is genetic to follow-on probability P (xi)：
Wherein S is the population scale for treating selected population
Step 6.2：Calculate each individuality (xi) accumulation probability qi：Step
Rapid 6.3：A random number r is produced between [0,1]
Step 6.4：If r<q1, then individuality x1It is chosen；If qk-1<r≤qk, then individuality x is selectedk
Step 6.5：N times are repeated to step 6.3,6.4, to choose individuality
Step 7：Iteration；
If algorithm iteration predetermined number of times, performs next step (updating elite group)；Otherwise, return to step 2.
Step 8:Update elite group
Step 8.1：Non-domination solution in current population is copied into into elite group；
Step 8.2：Solution in detection elite group, will be deleted by the arranged solution of other solutions from elite group；
The new coded system that the step 1 algorithm is used so that the algorithm hardly with decoding because decoding is one
Individual chromosome is converted into the process of the initiating structure of the solution of problem.It is, he is converted into scheduling scheme.The coded system
Each matrix can be expressed simply as very much a scheduling scheme, so hardly with being decoded.
The step 3 calculates fitness function value and is described in detail below：
This algorithm has three targets, and they are respectively the time, consume and utilization rate of equipment and installations.Because three targets have different
Tolerance, so they liberally can not directly be compared by quantitative target.Standardization each target is necessary.In order to do this
Individual, AHP analytic hierarchy process (AHP)s are taken to determine the weighted value of target.f1Express time, f2Represent utilization rate of equipment and installations, f3Expression disappears
Consumption.Weighting method solves (f1(x), f2(x) ..., fn(x)) problem when, fitness function is
F (x)=w1f1(x)+w2f2(x)+…+wnfn(x), (7)
Wherein
wi>=0, i=1,2 ..., n, (8)
w1+w2+…+wn=1. (9)
By taking the relative importance example of three object functions shown in Fig. 6 as an example, the determination method of weighted value is as follows：
1) relative importance table (Fig. 6) is converted into into matrix：
2) each row of the matrix to obtaining be standardized (a number is multiplied by respectively to each column, make each row and for 1)：
3) each row of the matrix after each row standardization is standardized (first will often go summation, then every row will be taken advantage of respectively
With a number, make each row and for 1)：
4) weighted value of three object functions, i.e. f are represented successively to the often row of the matrix after row standardization1、f2、f3Plus
Weights are respectively w1=0.578, w2=0.302, w3=0.120.
The step 6 is described as optimum individual and is directly remained to population of future generation, and other individualities are selected according to roulette
The method of selecting is selected, and in this way, poor individual organic can survive, and can avoid precocity.
Claims (4)
1. a kind of genetic algorithm solves Solving Multi-objective Flexible Job-shop Scheduling problem, and the algorithm is related to flexible job shop tune
Degree field, it is contemplated that the deadline, production cost and three targets of utilization rate of equipment and installations in flexible job shop scheduling, it is proposed that
Coded system and single-point based on matrix chromosome is intersected, mutation, be it is characterized in that：The implementation steps of the algorithm are as follows：
The parameter setting of the algorithm is as follows：Population scale N is set to 50, crossover probabilityIt is set as 0.5, mutation probabilityIt is set as
0.05；To each k neighborhood solution of current solution detection in Local Search；The end condition of algorithm iteration is：If the individuality of optimum
Can not be modified in continuous 20 generation, then algorithm is stopped：
Step 1：Initialization population N, using a kind of new coded system --- based on the matrix chromosome that Job Scheduling is encoded；
Step 2：Update elite group；
Step 3：Each object function weighted value is obtained by the weights method of relative importance, is determined by each object function of standardization
Fitness function value；
Step 4：Genetic search；
Step 4.1：Random selection N/2 is individual；
Step 4.2：By probabilityTwo parents are selected, the single-point based on matrix is carried out and is intersected；
Step 4.3：By probabilityParent is selected, is carried out based on the mutation of matrix；
Step 5：Local Search is carried out to each solution；（Carry out simultaneously with step 4）；
Step 6：It is individual using roulette method selection method random selection S；
Step 7：Iteration；
Step 8：Update elite group.
2. a kind of genetic algorithm according to claim 1 solves Flexible Job-shop Scheduling Problems, it is characterized in that：One
Individual suitable encoding scheme is the first step of solving practical problems, by considering characteristic and flexible path structure, a new base
It is devised in the matrix chromosome coding scheme of Job Scheduling coding, this coded system is that j-th work is represented with i/j
I-th operation of the part on kth platform machine, it is simpler for Flexible Job-shop Scheduling Problems using this encoding scheme,
And hardly with being decoded.
3. a kind of genetic algorithm according to claim 1 solves Flexible Job-shop Scheduling Problems, it is characterized in that：Adopt
Intersected with the single-point based on matrix chromosome, by Probability pcAfter selecting two parents, one is referred to as reticule in matrix
Horizontal line is selected randomly, and the task above two parent exchange reticules obtains the result in two offsprings, if offspring
It is infeasible, then suitably adjust by carrying out to obtain two feasible offsprings.
4. a kind of genetic algorithm according to claim 1 solves Flexible Job-shop Scheduling Problems, it is characterized in that：Adopt
With the mutational formats of matrix chromosome, the mutation is by Probability pmParent is selected, for each selected individuality, in matrix
It is referred to as mutation two horizontal lines of line to be selected randomly, the scheduling between these lines is randomly exchanged, but machine order
Keep constant, there are two rows between mutation line, mutation is only carried out by exchanging this two row.
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107704985A (en) * | 2017-08-11 | 2018-02-16 | 浙江工业大学 | A kind of differential evolution Flexible Workshop Optimization Scheduling of dynamic strategy |
| CN109522104A (en) * | 2018-10-15 | 2019-03-26 | 华南理工大学 | Utilize the method for differential evolution algorithm optimization two goal task of Iaas scheduling |
| CN110221583A (en) * | 2019-05-20 | 2019-09-10 | 清华大学 | A kind of Intelligent assembly shop-floor management method based on HoloLens |
| CN110501978A (en) * | 2018-05-18 | 2019-11-26 | 中国科学院沈阳自动化研究所 | A kind of robot product workshop scheduled production dispatching method |
| CN112580922A (en) * | 2020-09-30 | 2021-03-30 | 北京工业大学 | Flexible job shop scheduling method based on multilevel neighborhood structure and hybrid genetic algorithm |
| CN112859761A (en) * | 2020-12-06 | 2021-05-28 | 北京工业大学 | Distributed forging flow shop energy-saving scheduling method considering centralized heat treatment |
| US11262065B2 (en) * | 2018-11-30 | 2022-03-01 | DOOSAN Heavy Industries Construction Co., LTD | System and method for optimizing combustion of boiler |
| CN115826537A (en) * | 2023-01-29 | 2023-03-21 | 广东省科学院智能制造研究所 | Flexible scheduling method for multi-robot production line |
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Cited By (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107704985A (en) * | 2017-08-11 | 2018-02-16 | 浙江工业大学 | A kind of differential evolution Flexible Workshop Optimization Scheduling of dynamic strategy |
| CN110501978A (en) * | 2018-05-18 | 2019-11-26 | 中国科学院沈阳自动化研究所 | A kind of robot product workshop scheduled production dispatching method |
| CN109522104A (en) * | 2018-10-15 | 2019-03-26 | 华南理工大学 | Utilize the method for differential evolution algorithm optimization two goal task of Iaas scheduling |
| CN109522104B (en) * | 2018-10-15 | 2021-09-21 | 华南理工大学 | Method for optimizing scheduling of two target tasks of Iaas by using differential evolution algorithm |
| US11262065B2 (en) * | 2018-11-30 | 2022-03-01 | DOOSAN Heavy Industries Construction Co., LTD | System and method for optimizing combustion of boiler |
| CN110221583A (en) * | 2019-05-20 | 2019-09-10 | 清华大学 | A kind of Intelligent assembly shop-floor management method based on HoloLens |
| CN110221583B (en) * | 2019-05-20 | 2020-08-07 | 清华大学 | Intelligent assembly production line simulation method based on Holo L ens |
| CN112580922B (en) * | 2020-09-30 | 2024-03-22 | 北京工业大学 | Flexible job shop scheduling method based on multistage neighborhood structure and hybrid genetic algorithm |
| CN112580922A (en) * | 2020-09-30 | 2021-03-30 | 北京工业大学 | Flexible job shop scheduling method based on multilevel neighborhood structure and hybrid genetic algorithm |
| CN112859761A (en) * | 2020-12-06 | 2021-05-28 | 北京工业大学 | Distributed forging flow shop energy-saving scheduling method considering centralized heat treatment |
| CN112859761B (en) * | 2020-12-06 | 2022-04-22 | 北京工业大学 | Distributed forging flow shop energy-saving scheduling method considering centralized heat treatment |
| CN115826537A (en) * | 2023-01-29 | 2023-03-21 | 广东省科学院智能制造研究所 | Flexible scheduling method for multi-robot production line |
| CN115826537B (en) * | 2023-01-29 | 2023-05-02 | 广东省科学院智能制造研究所 | Flexible scheduling method for multi-robot production line |
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