CN107862411B - Large-scale flexible job shop scheduling optimization method - Google Patents

Large-scale flexible job shop scheduling optimization method Download PDF

Info

Publication number
CN107862411B
CN107862411B CN201711094745.9A CN201711094745A CN107862411B CN 107862411 B CN107862411 B CN 107862411B CN 201711094745 A CN201711094745 A CN 201711094745A CN 107862411 B CN107862411 B CN 107862411B
Authority
CN
China
Prior art keywords
workpiece
batch
workpieces
genes
gene
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.)
Active
Application number
CN201711094745.9A
Other languages
Chinese (zh)
Other versions
CN107862411A (en
Inventor
邹益胜
尹慢
王爽
石朝
王若鑫
张剑
付建林
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Southwest Jiaotong University
Original Assignee
Southwest Jiaotong University
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Southwest Jiaotong University filed Critical Southwest Jiaotong University
Priority to CN201711094745.9A priority Critical patent/CN107862411B/en
Publication of CN107862411A publication Critical patent/CN107862411A/en
Application granted granted Critical
Publication of CN107862411B publication Critical patent/CN107862411B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06QINFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00Administration; Management
    • G06Q10/04Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06NCOMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00Computing arrangements based on biological models
    • G06N3/12Computing arrangements based on biological models using genetic models
    • G06N3/126Evolutionary algorithms, e.g. genetic algorithms or genetic programming
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06QINFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00Administration; Management
    • G06Q10/06Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063Operations research, analysis or management
    • G06Q10/0631Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06316Sequencing of tasks or work

Landscapes

  • Engineering & Computer Science (AREA)
  • Business, Economics & Management (AREA)
  • Human Resources & Organizations (AREA)
  • Physics & Mathematics (AREA)
  • Economics (AREA)
  • Strategic Management (AREA)
  • Theoretical Computer Science (AREA)
  • Biophysics (AREA)
  • Entrepreneurship & Innovation (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • General Business, Economics & Management (AREA)
  • Tourism & Hospitality (AREA)
  • Quality & Reliability (AREA)
  • Operations Research (AREA)
  • Marketing (AREA)
  • Game Theory and Decision Science (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Development Economics (AREA)
  • Evolutionary Biology (AREA)
  • Biomedical Technology (AREA)
  • General Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Physiology (AREA)
  • Computational Linguistics (AREA)
  • Data Mining & Analysis (AREA)
  • Evolutionary Computation (AREA)
  • Genetics & Genomics (AREA)
  • Molecular Biology (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Educational Administration (AREA)
  • General Factory Administration (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The large-scale flexible job shop scheduling method recombines large-scale production tasks to reduce the scale, and then solves and optimizes by utilizing a self-adaptive improved genetic algorithm. The method comprises the following specific steps: (1) firstly, clustering and batching workpieces which have similar processing technology, same workpiece size in the same range and same blank material, thereby reducing the problem solving scale; (2) setting algorithm initial parameters, adopting a three-layer gene coding technology, an OBX crossing mode and a certain variation strategy, combining a simulation experiment to select a crossing length, and optimizing and solving by utilizing a self-adaptive improved genetic algorithm. The method can reduce the problem solving scale and improve the solving speed; and reduces workpiece completion time and drag delays.

Description

Large-scale flexible job shop scheduling optimization method
Technical Field
The invention relates to the technical field of intelligent optimization algorithm of discrete combination problem. In particular to a scheduling optimization method for a large-scale flexible job shop.
Background
The problem of workshop scheduling of no more than 20 x 50 (machine tool x workpiece) is a medium and small scale scheduling problem, and the problem of large scale workshop scheduling has the following situations [ LIANG Xu, WANG Jia, H UANG Ming.New coding method for creating a scheduling project [ J ]. Computer Integrated manufacturing systems, 2008,10(14): 1974. 1982 ] the number of workpieces J >50, the number of machines M >20, ② when J < 50, M >20, J.times.M >1000, ③ when J < 50, M < 20, J.times.M >1000, nearly 60 years, many researchers have proposed NP problems for the production scheduling and scheduling problems of job shops, but most of the solutions of medium and small scales are usually small scale solutions, most of the solutions of medium and small scales and quality algorithms cannot be directly used for solving NP problems based on intelligent scheduling and solving of intelligent scheduling problems based on the conventional decomposition method, and the solution of the problems of large scale scheduling and large scale scheduling algorithms cannot be solved for solving the problems based on the intelligent decomposition method.
Disclosure of Invention
The invention aims to provide a large-scale flexible job shop scheduling method based on workpiece batch, which has high solving speed, reduces the completion time of workpieces and the drag delay of the workpieces, and aims to solve the problems in the prior art.
The purpose of the invention is realized as follows: the invention adopts a clustered workpiece batching method for production tasks of a flexible job shop, recombines large-scale production tasks to reduce scale, and then solves an optimized scheduling method by utilizing a self-adaptive improved genetic algorithm. Firstly, clustering and batching workpieces which are similar in machining process, have the same workpiece size and are made of the same blank material to reduce problem solving scale, randomly forming different batches, enabling each workpiece to have respective delivery date, and scheduling according to the earliest delivery date in the batches after batching.
Secondly, establishing a mathematical model of the scheduling problem of the large-scale flexible job shop
The large-scale flexible job shop scheduling problem in question is detailed as being performed on M devices (M ═ Mk|M1,M2...MmN workpieces are machined (J) 1,2,. m)l|J1,J2, ...J n1, 2.. N)), each workpiece including N steps of a predetermined machining sequence, each step being capable of machining on a plurality of machines. After batching, R-type workpieces R ═ { R ═ are formedi|R1,R2,...RrI is 1,2, r, the processing time of the jth procedure of the ith workpiece on the device k is Tijk,TpiP-th representing i-th type of workCompletion time of the last process of a batch, DsIndicating lead time of the workpiece s, DpiIndicating the lead time of the p-th batch of the i-th workpiece. The scheduling objective is to minimize the maximum completion time and the total stall.
Target function minf α1f'12f'2(1)
Wherein: f. of1=min(maxTpi)p=1,2...Bi;i=1,2......r (2)
Figure GDA0002364212830000021
Formula (2) f1Representing a minimum maximum completion time; formula (3) f2Indicating that the total lingering period is minimal.
Constraint conditions are as follows:
Figure GDA0002364212830000022
Figure GDA0002364212830000023
the formula (5) shows that the processing time of the jth procedure of the pth batch of the ith workpiece is equal to the sum of the processing times of all the workpieces in the batch
Sip(j-1)k+Tip(j-1)k+Wip(j-1)k≤Sipjk'p=1,2...Bi;i=1,2...r;j=1,2...N;k,k'=1,2...m (6)
The expression (6) shows that the start time of the next process of the same workpiece in the same batch is more than or equal to the completion time of the previous process
Sipjk+Tipjk+Wipjk≤Si'p'j'kp,p'=1,2...Bi;i,i'=1,2...r;j,j'=1,2...N;k=1,2...m (7)
The formula (7) shows that the start time of the next batch of workpieces is more than or equal to the finish time of the previous batch of workpieces occupying the same machine
Figure GDA0002364212830000031
The expression (8) indicates that the total number of all the batches of workpieces in each type of workpiece is equal to the total number of all the workpieces
Dpi=minDsi=1,2...r;s=1,2......Cip,p=1,2...Bi(9)
Expression (9) indicates that the lead time of the p-th lot of the i-th workpiece is equal to the earliest lead time in the lot
The specific symbolic meanings are shown in Table 2.
TABLE 1 meanings of symbols
Figure GDA0002364212830000032
Third, the three-layer coding is adopted to code the gene in the genetic algorithm program
The patent adopts a three-layer coding mode for adapting to the problem of large-scale flexible job scheduling. Assuming that there are two types of workpieces, each having two processes, as shown in fig. 2, the first layer represents the number of batches formed after the workpiece is batched, and integer coding is used to represent that the type 1 workpiece is divided into 2 batches. The second layer represents the processing sequence of the workpiece steps, and adopts a coding scheme based on workpieces, wherein 101 represents the first batch of the type 1 workpieces, 102 represents the second batch of the type 1 workpieces, 101 appears in the process gene for the first time to represent the first step, and so on, and the processing sequence represented by the process gene is 101 → 201 → 102 → 101 → 201 → 102. The third level represents the machine selected for processing by the workpiece process, and the first process representing the workpiece 101 selects the first machine 2 from the set of selectable machines using integer coding.
Fourth, genetic algorithm parameter initialization
According to the principle and basis of initial parameter selection, the population size is set to be 40, the cross probability is 0.1, the mutation probability is 0.04, and the maximum genetic generation number is 300.
Fifthly, generating an initial population
According to the coding mode, the initial population is generated in a random mode, and in order to keep the legality of the initial population, the constraint is added when the initial population is generated, namely the number of times of the constraint workpiece numbers appearing in the process gene section is equal to the number of workpiece processes.
Sixthly, calculating the population fitness value
And (4) calculating the objective function value of each individual by using the formulas (1) to (3), distributing the fitness value, and selecting the cross variation operation with higher fitness to enter the next generation.
Seventh, selection
The selection operator uses a roulette method, which is widely used for selection operations because of its convenience. In this method, the probability that an individual is selected is related to its own fitness value, with the greater the probability that the fitness value is retained.
Eighth, selecting OBX crossover operator to perform genetic algorithm crossover
After the population is crossed and shuffled, two individuals are randomly selected, as shown in fig. 4, and the process gene crossing is intercepted, in the patent, an improved crossing operator Based on Order-Based cross selector (OBX) is adopted, the crossing step is shown in fig. 4, as shown in fig. 4a, genes to be crossed are randomly selected and selected in a parent P1, a crossed gene pool Pos (201,101,102) is formed, but as the first type of workpiece batch in the batch genes of Chrom2 is 1,102 workpieces do not exist in the process gene of Chrom2, 102 is deleted from the crossed gene pool, and finally, the genes for crossing have Pos (201, 101). If the gene 201 is found in the parent P2 and there are many processes, so there are many genes 201 in P2, one is randomly selected as shown in FIG. 4b, then the selected gene in P2 is deleted, the other genes in the gene pool are crossed, and finally the genes selected in P1 are sequentially used to fill in the vacant genes in P2 to form the offspring C2 as shown in FIG. 4C. While the alternative genes and genes that cannot be used for crossover are retained in P1, and then the gaps in P1 are sequentially filled with the remaining genes in P2 and individuals 202 not in P1 (second group of workpieces of the second group of workpieces) to form offspring C1 as shown in fig. 4C.
The chromosome crossing length can influence the performance of the algorithm, and the patent researches the relation between the chromosome crossing length and the algorithm solving precision and the operation speed. And selecting 10 to 100 percent of the chromosome length for crossing, respectively and repeatedly carrying out simulation operation to calculate the average value of the chromosome length, and calculating the sum of weighted values to find that the crossing length is optimal when the crossing length accounts for 10 percent of the chromosome length. In order to find out a better target value, the patent selects 10 to 20 percent of the chromosome length to carry out crossing, and repeatedly simulates and calculates the average value of the chromosome length, and then calculates a weighted value, and finds that selecting 12 percent of the chromosome length to carry out crossing can obtain a more accurate solution and improve the operation speed, so that 12 percent of the crossing length is selected.
Ninth, selecting mutation strategy to legalize the mutated gene
The variation is divided into batch variation and machine variation, wherein the batch variation is shown in fig. 5, and the process genes and machine genes need to be decoded again to form new chromosomes after each batch variation to ensure the validity of the chromosomes, if the batch of the first type of workpieces is decreased by 1, the process genes are correspondingly decreased by one workpiece 102, and if the batch of the second type of workpieces is increased by 1, the process genes are increased by one workpiece 202, and both machine genes select corresponding machines according to the process genes. Machine variation as in FIG. 6, for example, Parent (1,9) variation of 2, indicates selection of M11Machine No. 3 in (2, 3).
Tenth, adopting adaptive genetic algorithm to carry out optimization solution
The sine self-adaptation is a self-adaptation method that the crossing rate and the specific variation rate change according to the individual average fitness value and the maximum fitness value and according to a linear function curve. The method includes the steps that a high crossing rate and a high variation rate are selected in the initial stage of an optimization process, so that a high convergence speed can be obtained, diversity of a population is kept, after multiple iterations, in order to avoid damage to an optimal solution, a low crossing rate and a low variation rate are selected to conduct detailed search, formulas used by the method are detailed in formula (10) and formula (11) [ Yang bin, Susan, Niuhong, Wangmeng, adaptive genetic algorithm for solving a fuzzy job shop scheduling problem [ J ]. mechanical science and technology, 2013, (01):16-21 ]. Experiments prove that the convergence speed and the convergence precision of the algorithm can be improved by the sine self-adaptive genetic algorithm, and the globality and the precision of algorithm searching can be ensured by the method.
Cross probability:
Figure GDA0002364212830000061
the mutation probability:
Figure GDA0002364212830000062
in the formula fmaxThe maximum fitness value in the current population is obtained; f. ofavgThe average fitness value in the current population is obtained; f' is the larger fitness value of the two individuals to be crossed; f is the fitness value of the individual to be mutated; p is a radical ofc1、pm1Is a coefficient and takes values in the interval of (0, 1).
Eleventh, decoding
Decoding is the inverse operation of coding, the procedure processing sequence of each batch of various workpieces is obtained by the procedure gene section of the chromosome, the corresponding processing machine is obtained by the machine gene section, and the starting time and the ending time of each procedure are calculated according to the formulas (4) to (9).
The patent provides a large-scale job shop scheduling method based on workpiece batching, and the method is characterized in that parts which are similar in machining process and have the same pipe diameter size in the same range and same in blank material are clustered and batched to form different batches randomly, each workpiece has a respective delivery date, and scheduling is carried out according to the earliest delivery date in the batches after batching. And then optimizing the batch number and the batch processing sequence of the batch by using an OBX-based cross adaptive genetic algorithm. The method can reduce the problem solving scale and improve the solving speed; and reduces workpiece completion time and drag delays.
The invention has the beneficial effects that:
(1) reduce the problem solving scale and improve the solving speed
Workpieces with similar characteristics are subjected to batch processing according to a batch principle, and then batch times are optimized by using an adaptive genetic algorithm based on an OBX cross mode, so that the problem scale is reduced, and the solving speed is greatly improved.
(2) Reducing work-piece completion time and lag
After workpieces of the same type are batched, the processing preparation time of the workpieces can be shortened, the workpiece batching times are optimized, and the workpiece delay can be reduced.
The method sets algorithm initial parameters, adopts three-layer gene coding technology, OBX crossing mode and certain variation strategy, combines simulation experiment to select crossing length, and utilizes self-adaptive improved genetic algorithm to optimize and solve. The invention provides a scheduling method for batching according to the production characteristic similarity of workpieces and solving a large-scale flexible job shop by using an improved genetic algorithm, which can reduce the problem solving scale and improve the solving speed; and reduces workpiece completion time and drag delays. The method has important significance and obvious practical engineering application value for solving the large-scale workshop operation scheduling.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 chromosome coding map.
FIG. 3 parent chromosomal sequence.
FIG. 4 is a cross-flow diagram based on OBX.
FIG. 5 is a batch variation flow chart.
FIG. 6 is a machine variation flow chart.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
Examples 1
Example 1 the JSP problem of 230 x 18 scale was used, i.e. 230 workpieces were machined on 18 machines. Each workpiece comprises four processes, and the processing processes are in the sequence of Qi1, Qi2, Qi3 and Qi 4. Wherein Qi1, Qi2 and Qi3 are machining operations, and can only be selected to be operated on a machining machine; qi4 is the detection operation, only can choose to operate on the machine being detected. And the distribution of machines is such that machines 1-15 are processing machines and machines 16-18 are inspection machines.
EXAMPLES example 2
Example 2 the JSP problem on a 460 x 18 scale was adopted, i.e. 460 workpieces were machined at 18, the machining machines and inspection machines being distributed as in example 1.
Detailed description of the invention
First, similar lots based on workpiece characteristics
The method includes the steps of firstly, clustering and batching parts which are similar in machining process, have the same workpiece size and are made of the same blank material, randomly forming different batches, enabling each workpiece to have a respective delivery time, and scheduling according to the earliest delivery time in the batches after batching. For example, there are 10 pieces of pipe work, the main characteristics of which are shown in table 1. The pipe diameter has two size ranges of 6mm-12mm and 14mm-38mm, the main process of the workpiece is replaced by A, B, C, D, E, F, G, wherein E and F can be processed by the same machine, under the condition of the same process sequence, the process is similar in the case that the same machine can be used for the same process or different processes, such as B → C → F → G and B → C → E → G, the process flows are similar. The batch results obtained according to the above batch method were: a first group (1, 5, 9) with a lead time of 2017/07/1; a second group (2, 10) with a lead time of 2017/07/1; and a third group (3, 4, 6, 7, 8) with a lead time of 2017/07/2.
TABLE 1 workpiece Property Table
Figure GDA0002364212830000091
Second, construct mathematical model
The optimized mathematical model of example 1 was constructed according to equations (1) - (9):
target function min f α1f1'+α2f2'(1)
Wherein: f. of1=min(maxTpi)i=1,2,.....48;p=1,2......Bi(2)
Figure GDA0002364212830000101
Constraint equation:
Figure GDA0002364212830000102
Figure GDA0002364212830000103
Sip(j-1)k+Tip(j-1)k+Wip(j-1)k≤Sipjk'
(6)
i=1,2,.....48;p=1,2......Bi;j=1,2,3,4;k,k'=1,2......18
Sipjk+Tipjk+Wipjk≤Si'p'j'k
(7)
i,i'=1,2,.....r;p=1,2......Bi;j,j'=1,2,3,4;k=1,2......18
Figure GDA0002364212830000104
Dpi=minDsi=1,2,.....r;s=1,2......Cip(9)
third, optimization using improved genetic algorithm of OBX crossover operator
The operation modes of other examples are consistent, after a mathematical model is obtained, according to the principle and basis of initial parameter selection, the population scale is set to be 40, the cross probability is 0.1, the mutation probability is 0.04, and the maximum genetic algebra is 300 generations.
And (3) grouping the workpieces according to the rules by adopting MATLAB programming, randomly generating an initial population, selecting excellent individuals according to a certain probability after decoding, entering a next generation cross and variation updating population, and circularly iterating until a maximum iteration algebra is reached, and outputting the optimal completion time and a corresponding scheduling solution.
The two examples with different scales respectively use the non-batch adaptive genetic algorithm and the batch adaptive genetic algorithm of the patent to carry out operation ten times so as to carry out relevant data comparison, thereby illustrating the effectiveness of the optimization method in the invention. The optimal solution and related data of the JSP problem of each scale after calculation are shown in Table 4. According to different experimental data results, the performance is compared, and the performance indexes such as minimum completion time/delay and operation efficiency are greatly improved according to the following data.
Minimum completion time and search performance
Table 4 data table of experimental results
Figure GDA0002364212830000111
As can be seen from table 4, the lingering periods of two different large-scale JSP problems after batch scheduling are both 0, while the non-batch scheduling methods have lingering in different degrees; the maximum completion time is reduced by at least 21 percent and is reduced by at most 25 percent; the operation efficiency is improved by at least 61 percent and is improved by 66 percent to the maximum extent.

Claims (5)

1. A scheduling optimization method for a large-scale flexible job shop is characterized by comprising the following steps: establishing a mathematical model of the flexible job shop scheduling problem, degrading the problem scale based on a workpiece batch scheduling method, and performing optimization solution by using an adaptive genetic algorithm to form a set of scheduling optimization method for solving the large-scale flexible job shop, wherein the method comprises the following steps:
first, similar lots based on workpiece characteristics
The method comprises the steps of firstly, clustering and batching parts which are similar in machining process, have the same workpiece size and are made of the same blank material, randomly forming different batches, enabling each workpiece to have respective delivery date, and scheduling according to the earliest delivery date in the batches after batching;
secondly, establishing a mathematical model of the scheduling problem of the large-scale flexible job shop
The large-scale flexible job shop scheduling problem is detailed in that M devices (M ═ M)k|M1,M2...MmN workpieces are machined (J) 1,2,. m)l|J1,J2,...Jn1,2,. N }), each workpiece comprising N predetermined machining sequence steps, each step being able to be machined on a plurality of machines; after batching, R-type workpieces R ═ { R ═ are formedi|R1,R2,...Rr1,2, r, the jth process of the ith workpiece is carried out in the equipmentMachining time on k is Tijk,TpiIndicating the finishing time of the last process of the p-th batch of the i-th workpiece, DsIndicating lead time of the workpiece s, DpiIndicating the lead time of the p batch of the ith type of workpiece; the scheduling objective is to minimize the maximum completion time and the total delay;
target function min f α1f1'+α2f2' (1)
Wherein: f. of1=min(maxTpi)p=1,2...Bi;i=1,2......r (2)
Figure FDA0002364212820000011
Formula (2) f1Representing a minimum maximum completion time; formula (3) f2Indicating that the total lag period is minimal;
constraint conditions are as follows:
Figure FDA0002364212820000012
Figure FDA0002364212820000013
equation (5) shows that the processing time of the jth process of the pth batch of the ith workpiece on the equipment k is equal to the sum of the processing times of all the workpieces in the batch
Sip(j-1)k+Tip(j-1)k+Wip(j-1)k≤Sipjk'p=1,2...Bi;i=1,2...r;j=1,2...N;k,k'=1,2...m (6)
The formula (6) represents the start time S of the next process for the same workpiece in the same batchipjk′Completion time of preceding process or more
Sipjk+Tipjk+Wipjk≤Si'p'j'kp,p'=1,2...Bi;i,i'=1,2...r;j,j'=1,2...N;k=1,2...m (7)
Equation (7) represents the operation of the next batch of workpieces occupying the same machineTime Si′p′j′kThe finishing time of the workpieces of the previous batch is more than or equal to
Figure FDA0002364212820000021
The expression (8) indicates that the total number of all the batches of workpieces in each type of workpiece is equal to the total number of all the workpieces
Dpi=min Dsi=1,2...r;s=1,2......Cip;p=1,2...Bi(9)
The delivery date of the p-th batch of the ith workpiece is equal to the earliest delivery date in the batch, and the specific symbols are as follows:
α1representing function f1The weight of (c);
α2representing function f2The weight of (c);
f1' means f1Normalizing the processed function value;
f2' means f2Normalizing the processed function value;
Sipjkindicating the starting time of the jth process of the jth batch of the ith workpiece on the equipment k;
Wipjkthe adjustment time of the jth process of the ith batch of workpieces on the equipment k is shown;
Xipjkrepresenting a decision variable, and taking a value of 1 when the jth procedure of the pth batch of i-type workpieces is processed on the equipment k, or taking a value of 0;
tsjkshowing a workpiece JsThe j-th procedure in the device k;
Tipjkthe processing time of the jth process of the jth batch of the i-type workpieces on the equipment k is shown;
Biindicating the number of batches formed by the ith type of workpiece batches;
Ciprepresenting the batch number of the p-th batch of the ith type of workpieces;
third, the three-layer coding is adopted to code the gene in the genetic algorithm program
Adopting a three-layer coding mode, wherein the first layer represents the number of batches formed after the workpieces are batched, the second layer represents the processing sequence of the workpiece procedures, and the third layer represents a machine selected by the workpiece procedures;
fourth, genetic algorithm parameter initialization
According to the principle and basis of initial parameter selection, setting the population scale to be 40, the cross probability to be 0.1, the mutation probability to be 0.04 and the maximum genetic algebra to be 300 generations;
fifthly, generating an initial population
Generating an initial population in a random mode according to a coding mode, and adding constraint when generating the initial population in order to keep the legality of the initial population, wherein the number of times of restraining the workpiece number in a process gene segment is equal to the number of workpiece processes;
sixthly, calculating the population fitness value
Calculating the objective function value of each individual by using the formulas (1) to (3), distributing the fitness value, and selecting the cross variation operation of the next generation with higher fitness;
seventh, selection
The selection operator adopts a roulette method, in the method, the probability that an individual is selected is related to the fitness value of the individual, and the higher the fitness value is, the higher the probability of being reserved is;
eighth, selecting OBX crossover operator to perform genetic algorithm crossover
Randomly selecting two individuals after the population is subjected to cross shuffling, intercepting the process gene cross, and performing cross by adopting an improved cross operator Based on an Order-Based crossbar (OBX); and the relationship between the chromosome crossing length and the algorithm solving precision and the operation speed is explored through simulation, and a proper chromosome crossing length is selected;
ninth, selecting mutation strategy to legalize the mutated gene
The variation is divided into batch variation and machine variation, and the process genes and the machine genes need to be decoded again to form new chromosomes after each batch variation so as to ensure the legality of the chromosomes;
tenth, adopting adaptive genetic algorithm to carry out optimization solution
Optimizing according to the sine self-adaptive genetic algorithm of the formula (10) and the formula (11) to improve the convergence speed and the convergence precision of the algorithm and ensure the globality and the precision of algorithm searching;
cross probability:
Figure FDA0002364212820000031
the mutation probability:
Figure FDA0002364212820000041
in the formula fmaxThe maximum fitness value in the current population is obtained; f. ofavgThe average fitness value in the current population is obtained; f' is the larger fitness value of the two individuals to be crossed; f is the fitness value of the individual to be mutated; p is a radical ofc1、pm1Is a coefficient and takes value in the interval of (0, 1);
eleventh, decoding
Decoding is the inverse operation of coding, the procedure processing sequence of each batch of various workpieces is obtained by the procedure gene section of the chromosome, the corresponding processing machine is obtained by the machine gene section, and the starting time and the ending time of each procedure are calculated according to the formulas (4) to (9).
2. The large-scale flexible job shop scheduling optimization method according to claim 1, characterized in that: the third layer coding mode in the step three is specifically as follows: under the condition that two types of workpieces exist and each workpiece has two working procedures, the first layer represents the number of batches formed after the workpieces are batched, and integer coding Chrom (1,1) is adopted to represent that the type 1 workpiece is divided into 2 batches; the second layer represents the processing sequence of the workpiece procedures, and adopts a coding mode based on workpieces, wherein 101 represents the first batch of the type 1 workpieces, 102 represents the second batch of the type 1 workpieces, 101 appears in the procedure gene for the first time to represent the first procedure, and the like, and the processing sequence represented by the procedure gene is 101 → 201 → 102 → 101 → 201 → 102; the third level represents the machine selected for the workpiece process, and is encoded using integer codes, Chrom (1,9) showing the first pass of the workpiece 101 in the optional machine set MijThe first machine 2 is selected.
3. The large-scale flexible job shop scheduling optimization method according to claim 1, characterized in that: the step eight is based on the interleaving step of the improved interleaving operator of OBX as follows: randomly selecting genes to be crossed in a parent P1 to form a crossed gene pool Pos (201,101,102), wherein the first type of workpiece batch in the batch genes of Chrom2 is 1, so that 102 workpieces do not exist in the process genes of Chrom2, 102 are deleted from the crossed gene pool, and Pos exists in the genes finally used for crossing (201, 101); finding the genes 201 in the parent P2, wherein a plurality of genes 201 exist in P2 due to a plurality of processes, selecting one gene at random, deleting the selected gene in P2, crossing other genes in a gene pool, and finally filling the vacant genes in P2 with the selected gene in P1 to form a child C2; and the alternative genes and genes which cannot be used for crossing are reserved in the P1, and then the vacancy in the P1 is sequentially filled by using the genes remained in the P2 and removing the individual 202 which is not in the P1, namely the second batch of workpieces to form the offspring C1.
4. The large-scale flexible job shop scheduling optimization method according to claim 1, characterized in that: the selection mode of the appropriate chromosome length in the eighth step is specifically as follows: selecting 10 to 100 percent of the length of the chromosome to carry out crossing, respectively and repeatedly carrying out simulation operation to calculate the average value of the length of the chromosome, and then calculating the sum of weighted values to find that the crossing length is optimal when the crossing length accounts for 10 percent of the length of the chromosome; in order to find out a better target value, 10% to 20% of the chromosome length is selected to be crossed, simulation operation is repeated to obtain an average value, then a weighted value is obtained, and the fact that the chromosome length is selected to be crossed by 12% is found to obtain a more accurate solution and improve the operation speed, so that the cross length of 12% is selected.
5. The large-scale flexible job shop scheduling optimization method according to claim 1, characterized in that: in the tenth step, when the optimization is performed according to the sine adaptive genetic algorithm, a larger cross rate and a larger variation rate are selected at the initial stage of the optimization process to obtain a faster convergence rate and keep the diversity of the population, and after multiple iterations, a smaller cross rate and a smaller variation rate are selected for careful search to avoid the optimal solution from being damaged.
CN201711094745.9A 2017-11-09 2017-11-09 Large-scale flexible job shop scheduling optimization method Active CN107862411B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201711094745.9A CN107862411B (en) 2017-11-09 2017-11-09 Large-scale flexible job shop scheduling optimization method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201711094745.9A CN107862411B (en) 2017-11-09 2017-11-09 Large-scale flexible job shop scheduling optimization method

Publications (2)

Publication Number Publication Date
CN107862411A CN107862411A (en) 2018-03-30
CN107862411B true CN107862411B (en) 2020-04-28

Family

ID=61701459

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201711094745.9A Active CN107862411B (en) 2017-11-09 2017-11-09 Large-scale flexible job shop scheduling optimization method

Country Status (1)

Country Link
CN (1) CN107862411B (en)

Families Citing this family (21)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108717289B (en) * 2018-04-09 2020-11-17 湘潭大学 Assembly line layout optimization method
CN109034633B (en) * 2018-08-04 2021-11-12 郑州航空工业管理学院 Flexible job shop scheduling method for solving problem with moving time by improved genetic algorithm
CN109032150B (en) * 2018-10-16 2021-06-25 山东师范大学 Genetic algorithm segmentation optimization-based dynamic scheduling method for rail-mounted automatic guided vehicle
CN109270904A (en) * 2018-10-22 2019-01-25 中车青岛四方机车车辆股份有限公司 A kind of flexible job shop batch dynamic dispatching optimization method
CN109858515A (en) * 2018-12-24 2019-06-07 合肥工业大学智能制造技术研究院 The method and system of Order Batch configuration are carried out for the supply chain to intelligence manufacture
CN109902954B (en) * 2019-02-27 2020-11-13 浙江工业大学 Flexible job shop dynamic scheduling method based on industrial big data
CN110221585B (en) * 2019-06-14 2021-10-08 同济大学 Energy-saving scheduling control method for mixed flow shop considering equipment maintenance
CN110782085B (en) * 2019-10-23 2022-03-29 武汉晨曦芸峰科技有限公司 Casting production scheduling method and system
CN110632907B (en) * 2019-10-30 2020-11-20 山东师范大学 Scheduling optimization method and system for distributed assembly type replacement flow shop
CN112990515A (en) * 2019-12-02 2021-06-18 中船重工信息科技有限公司 Workshop resource scheduling method based on heuristic optimization algorithm
CN111160723A (en) * 2019-12-12 2020-05-15 上海大学 Dynamic flexible job shop scheduling method
CN111123864A (en) * 2019-12-12 2020-05-08 吴慧 Dynamic scheduling method for job shop
CN111105164B (en) * 2019-12-24 2022-04-15 北京理工大学 Workshop scheduling method, device and equipment
CN111507641B (en) * 2020-04-27 2024-04-16 上海华力集成电路制造有限公司 Batch processing equipment scheduling method and device
CN112540567A (en) * 2020-10-21 2021-03-23 吉林省齐智科技有限公司 Online flexible measurement self-adaptive machining method for automobile mold
CN112633662A (en) * 2020-12-17 2021-04-09 北京工业大学 Encoding and decoding method for flexible job shop scheduling under limited transportation condition
CN112668789B (en) * 2020-12-30 2023-11-24 重庆大学 Self-adaptive batch scheduling method for flexible job shop belt preparation procedure
CN112862207B (en) * 2021-03-04 2022-05-13 广东工业大学 Task scheduling solving method aiming at unknown machine adjustment time and related sequences
CN112949077B (en) * 2021-03-16 2022-09-06 北京理工大学 Flexible job shop intelligent scheduling decision method combining transportation equipment constraint
CN113377073B (en) * 2021-06-28 2022-09-09 西南交通大学 Flexible job shop scheduling optimization method based on double-layer multi-agent system
CN116755393A (en) * 2023-05-06 2023-09-15 成都飞机工业(集团)有限责任公司 Large-scale flexible job shop scheduling method, system, equipment and medium

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102929263A (en) * 2012-11-16 2013-02-13 北京理工大学 Hybrid flow shop scheduling method
CN103309316A (en) * 2013-05-28 2013-09-18 北京理工大学 Scheduling method of multi-stage variation hybrid flow shop with batch processor

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8412551B2 (en) * 2004-10-21 2013-04-02 Abb Research Ltd. Formal structure-based algorithms for large scale resource scheduling optimization

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102929263A (en) * 2012-11-16 2013-02-13 北京理工大学 Hybrid flow shop scheduling method
CN103309316A (en) * 2013-05-28 2013-09-18 北京理工大学 Scheduling method of multi-stage variation hybrid flow shop with batch processor

Also Published As

Publication number Publication date
CN107862411A (en) 2018-03-30

Similar Documents

Publication Publication Date Title
CN107862411B (en) Large-scale flexible job shop scheduling optimization method
CN107784380B (en) Optimization method and optimization system for routing inspection shortest path
CN108460463B (en) High-end equipment assembly line production scheduling method based on improved genetic algorithm
CN110543151A (en) Method for solving workshop energy-saving scheduling problem based on improved NSGA-II
WO2016169286A1 (en) Workshop layout method for discrete manufacturing system
CN106875094A (en) A kind of multiple target Job-Shop method based on polychromatic sets genetic algorithm
CN112882449B (en) Multi-variety small-batch multi-target flexible job shop energy consumption optimization scheduling method
CN109460859B (en) Workshop layout optimization method
CN110163409B (en) Convolutional neural network scheduling method applied to replacement flow shop
CN111079987A (en) Semiconductor workshop production scheduling method based on genetic algorithm
CN111667071B (en) Traditional job shop scheduling method based on improved genetic algorithm
CN111222642A (en) Multi-target flexible job shop scheduling method based on improved niche genetic algorithm
CN112084632B (en) Hardware digital production line layout optimization method combining man-machine engineering
CN107275801A (en) A kind of array element arrangement method based on the inheritance of acquired characters of L-type array antenna
CN111290283B (en) Additive manufacturing single machine scheduling method for selective laser melting process
CN105608295B (en) The multi-objective genetic algorithm of coking furnace pressure and RBF neural Optimization Modeling method
CN102073311A (en) Method for scheduling machine part processing line by adopting discrete quantum particle swarm optimization
CN115981262B (en) IMOEA-based hydraulic cylinder part workshop production scheduling method
CN112749776A (en) Job shop scheduling method based on improved hybrid genetic algorithm
CN101114312A (en) Method for designing ASSEL roll profile based on neurotransmission network technique
CN108446814B (en) Tree searching method and device for same-sequence assembly line workshop scheduling problem
CN109255484A (en) The discrete manufacturing recourses cooperative optimization method and system of data-driven
CN116360355A (en) Method for solving workshop scheduling problem based on NSGA-III algorithm
CN115907399A (en) Intelligent scheduling method for discrete manufacturing flexible production of electronic product
CN114021934A (en) Method for solving workshop energy-saving scheduling problem based on improved SPEA2

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant