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

Large-scale flexible job shop scheduling optimization method Download PDF

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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
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邹益胜
尹慢
王爽
石朝
王若鑫
张剑
付建林
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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)

1.一种大规模柔性作业车间调度优化方法,其特征在于:建立柔性作业车间调度问题的数学模型,基于工件组批调度方法降解问题规模,利用自适应遗传算法优化求解,形成一套求解大规模柔性作业车间调度优化方法,步骤如下:1. a large-scale flexible job shop scheduling optimization method, it is characterized in that: set up the mathematical model of flexible job shop scheduling problem, degrade the problem scale based on workpiece group batch scheduling method, utilize adaptive genetic algorithm to optimize and solve, form a set of solution large scale. Scale flexible job shop scheduling optimization method, the steps are as follows: 第一、基于工件特性相似组批First, group batches based on similar workpiece characteristics 该方法首先将加工工艺类似、工件尺寸在同一范围内且毛坯材质相同的零件进行聚类组批,随机组成不同的批次,每个工件都有各自的交付期,组批之后按照本批当中最早交付期进行调度;In this method, the parts with similar processing technology, the same workpiece size and the same blank material are clustered into batches, and randomly formed into different batches. Each workpiece has its own delivery date. Scheduling at the earliest delivery date; 第二、构建大规模柔性作业车间调度问题的数学模型Second, build a mathematical model of large-scale flexible job shop scheduling problem 大规模柔性作业车间调度问题详细描述为,在m台设备(M={Mk|M1,M2...Mm,k=1,2,...m})上加工n件工件(J={Jl|J1,J2,...Jn,l=1,2,...n}),每个工件包含N个事先确定加工顺序的工序,每个工序可以在多台设备上加工;组批之后形成r类工件R={Ri|R1,R2,...Rr,i=1,2,...r},第i类工件的第j道工序在设备k上加工时间为Tijk,Tpi表示第i类工件的第p批次最后一道工序的完工时间,Ds表示工件s的交付期,Dpi表示第i类工件的第p批次的交付期;调度目标是使最大完工时间最小及总拖延期最小;The large-scale flexible job shop scheduling problem is described in detail as: processing n workpieces on m devices (M={M k |M 1 , M 2 ... M m , k=1, 2, ... m}). (J={J l |J 1 , J 2 ,...J n ,l=1,2,...n}), each workpiece contains N processes whose processing order is determined in advance, and each process can be Processing on multiple equipments; after batching, the r-type workpiece is formed R={R i |R 1 , R 2 ,...R r ,i=1,2,...r}, the jth of the i-th workpiece The processing time of a process on equipment k is T ijk , T pi represents the completion time of the last process of the p-th batch of the ith type of workpiece, D s represents the delivery date of the workpiece s, and D pi represents the p-th of the i-th type of workpiece. The delivery time of the batch; the scheduling objective is to minimize the maximum completion time and the total delay; 目标函数:min f=α1f1'+α2f2' (1)Objective function: min f=α 1 f 1 '+α 2 f 2 ' (1) 其中:f1=min(maxTpi)p=1,2...Bi;i=1,2......r (2)where: f 1 =min(maxT pi )p=1,2...B i ; i=1,2...r (2)
Figure FDA0002364212820000011
Figure FDA0002364212820000011
式(2)f1表示最小最大完工时间;式(3)f2表示总拖延期最小;Formula (2) f 1 represents the minimum and maximum completion time; Formula (3) f 2 represents the minimum total delay time; 约束条件:Restrictions:
Figure FDA0002364212820000012
Figure FDA0002364212820000012
Figure FDA0002364212820000013
Figure FDA0002364212820000013
式(5)表示第i类工件第p批次的第j道工序在设备k上加工时间等于本批次所有工件加工时间之和Equation (5) indicates that the processing time of the jth process of the pth batch of the i-th workpiece on the equipment k is equal to the sum of the processing time of all the workpieces in this 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)S ip(j-1)k +T ip(j-1)k +W ip(j-1)k ≤S ipjk' p=1,2...B i ; i=1,2...r ;j=1,2...N;k,k'=1,2...m (6) 式(6)表示同一批次同一个工件的后一道工序的开工时间Sipjk′大于等于前道工序的完工时间Equation (6) indicates that the start-up time S ipjk' of the subsequent process of the same batch of the same workpiece is greater than or equal to the completion time of the previous process Sipjk+Tipjk+Wipjk≤Si'p'j'k p,p'=1,2...Bi;i,i'=1,2...r;j,j'=1,2...N;k=1,2...m (7)S ipjk +T ipjk +W ipjk ≤S i'p'j'k p,p'=1,2...B i ;i,i'=1,2...r;j,j'=1 ,2...N; k=1,2...m (7) 式(7)表示占用同一台机器,后一个批次工件的开工时间Si′p′j′k大于等于前一个批次工件的完工时间Equation (7) indicates that the same machine is occupied, and the start time Si'p'j'k of the next batch of workpieces is greater than or equal to the completion time of the previous batch of workpieces
Figure FDA0002364212820000021
Figure FDA0002364212820000021
式(8)表示每类工件所有批次工件数量总和等于所有工件数总和Equation (8) indicates that the total number of all batches of each type of workpiece is equal to the total number of all workpieces Dpi=min Ds i=1,2...r;s=1,2......Cip;p=1,2...Bi (9)D pi =min D s i =1,2...r;s=1,2...C ip ;p=1,2...B i (9) 式(9)表示第i类工件的第p批次的交付期等于本批中最早交付期,具体符号含义如下:Equation (9) indicates that the delivery date of the p-th batch of the i-th workpiece is equal to the earliest delivery date in this batch, and the meanings of the specific symbols are as follows: α1表示函数f1的权重;α 1 represents the weight of the function f 1 ; α2表示函数f2的权重;α 2 represents the weight of the function f 2 ; f1'表示f1归一化处理后的函数值;f 1 ' represents the function value after the normalization of f 1 ; f2'表示f2归一化处理后的函数值;f 2 ' represents the function value after the normalization of f 2 ; Sipjk表示第i类工件的第p批次第j道工序在设备k上开始加工时间;S ipjk represents the processing time of the p-th batch of the j-th workpiece of the i-th workpiece starting processing time on the equipment k; Wipjk表示第i类工件第p批次第j道工序在设备k上的调整时间;W ipjk represents the adjustment time of the jth operation of the pth batch of the i-th workpiece on the equipment k; Xipjk表示决策变量,当i类工件的第p批次第j道工序在设备k上加工时,取值为1,否则为0;X ipjk represents the decision variable, when the p-th batch of the j-th process of the i-type workpiece is processed on the equipment k, the value is 1, otherwise it is 0; tsjk表示工件Js的第j道工序在设备k上加工时间;t sjk represents the processing time of the jth operation of the workpiece J s on the equipment k; Tipjk表示i类工件的第p批次第j道工序在设备k上加工时间;T ipjk represents the processing time of the p-th batch of the j-th operation on the equipment k of the i-type workpiece; Bi表示第i类工件组批形成的批次数;B i represents the number of batches formed by the i-th type of workpiece group; Cip表示第i类工件第p批次的批量数;C ip represents the batch number of the p-th batch of the i-th workpiece; 第三、采用三层编码进行遗传算法程序中的基因编码Third, use three-layer coding for gene coding in genetic algorithm program 采用三层编码方式,第一层表示工件组批后形成的批次数量,第二层表示工件工序的加工顺序,第三层表示工件工序加工所选择的机器;The three-layer coding method is adopted, the first layer represents the batch quantity formed after the workpiece is grouped, the second layer represents the processing sequence of the workpiece process, and the third layer represents the machine selected for the workpiece process processing; 第四、遗传算法参数初始化Fourth, genetic algorithm parameter initialization 按照初始参数选用的原则和依据,设立种群规模为40,交叉概率0.1,变异概率0.04,最大遗传代数为300代;According to the principle and basis for the selection of initial parameters, the population size is set to 40, the crossover probability is 0.1, the mutation probability is 0.04, and the maximum genetic generation is 300 generations; 第五、生成初始种群Fifth, generate the initial population 按照编码方式,采用随机的方式产生初始种群,并且为了保持初始种群的合法性,在产生初始种群时添加约束,即在工序基因段约束工件号出现的次数应等于工件工序数;According to the coding method, the initial population is generated in a random way, and in order to maintain the legitimacy of the initial population, constraints are added when the initial population is generated, that is, the number of occurrences of the workpiece number constrained in the process gene segment should be equal to the number of workpiece processes; 第六、计算种群适应度值Sixth, calculate the population fitness value 利用公式(1)-(3)计算每个个体的目标函数值,分配适应度值,选择适应度较高进入下一代的交叉变异操作;Use formulas (1)-(3) to calculate the objective function value of each individual, assign the fitness value, and select the crossover mutation operation with higher fitness to enter the next generation; 第七、选择Seventh, choose 选择算子采用轮盘赌注的方法,在此方法中个体被选择的概率和其自身的适应度值相关,适应度值越大被保留下来的概率就越大;The selection operator adopts the roulette method. In this method, the probability of an individual being selected is related to its own fitness value. The larger the fitness value, the higher the probability of being retained; 第八、选择OBX交叉算子进行遗传算法交叉Eighth, select OBX crossover operator for genetic algorithm crossover 种群经交叉洗牌后,随机选择两个个体,并截取其工序基因交叉,采用基于Order-Based Crossover(OBX)的改进交叉算子进行交叉;并通过仿真探索染色体交叉长度与算法求解精度及运算速度之间的关系,选择合适的染色体交叉长度;After the population is crossed and shuffled, two individuals are randomly selected, and their process gene crossover is intercepted, and the improved crossover operator based on Order-Based Crossover (OBX) is used for crossover; The relationship between the speed, choose the appropriate chromosome crossover length; 第九、选择变异策略,以使变异后的基因合法化Ninth, choose a mutation strategy to legitimize the mutated gene 变异分为批次变异和机器变异,每次批次变异后工序基因和机器基因都需要重新解码形成新的染色体,以保证染色体的合法性;Variation is divided into batch variation and machine variation. After each batch variation, process genes and machine genes need to be re-decoded to form new chromosomes to ensure the legitimacy of chromosomes; 第十、采用自适应遗传算法进行优化求解Tenth, the use of adaptive genetic algorithm to optimize the solution 按照公式(10)及式(11)的正弦自适应遗传算法进行优化,以提高算法的收敛速度及收敛精度,以保证算法搜索的全局性和精确性;According to formula (10) and formula (11), the sine adaptive genetic algorithm is optimized to improve the convergence speed and convergence accuracy of the algorithm, so as to ensure the globality and accuracy of the algorithm search; 交叉概率:Crossover probability:
Figure FDA0002364212820000031
Figure FDA0002364212820000031
变异概率:Mutation probability:
Figure FDA0002364212820000041
Figure FDA0002364212820000041
式中fmax为当前种群中最大适应度值;favg为当前种群中平均适应度值;f′为两个待交叉个体中较大的适应度值;f为待变异个体的适应度值;pc1、pm1为系数,在(0,1)区间内取值;where f max is the maximum fitness value in the current population; f avg is the average fitness value in the current population; 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 c1 and p m1 are coefficients, which take values in the (0,1) interval; 第十一、解码Eleventh, decoding 解码为编码的逆操作,由染色体的工序基因段得出各类工件每个批次的工序加工顺序,机器基因段得出其相应的加工机器,并且根据式(4)-(9)计算出每道工序的开始及结束时间。The decoding is the inverse operation of the encoding, the process sequence of each batch of various workpieces is obtained from the process gene segment of the chromosome, and the corresponding processing machine is obtained from the machine gene segment, and calculated according to formulas (4)-(9) The start and end time of each operation.
2.根据权利要求1所述的一种大规模柔性作业车间调度优化方法,其特征在于:所述步骤第三中的三层编码方式具体为:在有两类工件,每个工件有两道工序情况下,第一层表示工件组批后形成的批次数量,采用整数编码Chrom(1,1)表示第1类工件分为2批;第二层表示工件工序的加工顺序,采用基于工件的编码方式,其中101表示第1类工件的第一个批次,102表示第1类工件的第二个批次,101第一次出现在工序基因内表示其第一道工序,依次类推,工序基因表示的加工顺序为101→201→102→101→201→102;第三层表示工件工序加工所选择的机器,采用整数编码,Chrom(1,9)表示工件101的第一道工序在可选机器集Mij内选择第一台机器2。2. a kind of large-scale flexible job shop scheduling optimization method according to claim 1 is characterized in that: the three-layer coding mode in the third step is specifically: when there are two types of workpieces, each workpiece has two In the case of the process, the first layer represents the number of batches formed after the workpiece is batched, and the integer code Chrom(1,1) is used to indicate that the first type of workpiece is divided into 2 batches; the second layer represents the processing sequence of the workpiece process, using the workpiece-based , where 101 represents the first batch of the first type of workpiece, 102 represents the second batch of the first type of workpiece, the first occurrence of 101 in the process gene represents its first process, and so on, The processing sequence represented by the process gene is 101→201→102→101→201→102; the third layer represents the machine selected for the workpiece process processing, using integer coding, Chrom(1,9) indicates that the first process of the workpiece 101 is in Select the first machine 2 in the set of optional machines Mij . 3.根据权利要求1所述的一种大规模柔性作业车间调度优化方法,其特征在于:所述步骤第八中基于OBX的改进交叉算子的交叉步骤如下:在父代P1中随机选择待交叉基因,形成交叉基因池Pos(201,101,102),由于在Chrom2的批次基因中第一类工件批次为1,因此在Chrom2的工序基因中没有102工件,故从交叉基因池中删除102,最终用于交叉的基因有Pos(201,101);在父代P2中找到基因201,由于有多道工序所以在P2中会有多个201,则随机选择一个,然后删除P2中被选中的基因,交叉基因池中其他的基因同理,最后用P1中被选中的基因顺次填补P2中空缺的基因形成子代C2;而P1中则保留备选中的基因以及不能用于交叉的基因,然后用P2中剩余的基因并去除P1中没有的个体202即第二类工件的第二批工件依次填补P1中的空缺形成子代C1。3. A kind of large-scale flexible job shop scheduling optimization method according to claim 1, it is characterized in that: in described step 8, the intersection step of the improved intersection operator based on OBX is as follows: Cross genes to form a cross gene pool Pos (201, 101, 102). Since the first type of workpiece batch is 1 in the batch gene of Chrom2, there is no 102 workpiece in the process gene of Chrom2, so delete 102 from the cross gene pool, and finally The gene used for crossover is Pos(201,101); gene 201 is found in parent P2, because there are multiple processes, there will be multiple 201 in P2, then one is randomly selected, then the selected gene in P2 is deleted, and the crossover is performed. The same is true for other genes in the gene pool. Finally, the selected genes in P1 are used to fill in the vacant genes in P2 to form the offspring C2; while in P1, the genes in the candidates and the genes that cannot be used for crossover are reserved, and then use The remaining genes in P2 and the individuals 202 not in P1 are removed, that is, the second batch of workpieces of the second type of workpieces fill the vacancies in P1 in turn to form offspring C1. 4.根据权利要求1所述的一种大规模柔性作业车间调度优化方法,其特征在于:所述步骤第八中合适的染色体长度的选择方式具体为:选择染色体长度的10%到100%进行交叉,并各自反复进行仿真运算求其平均值,然后求加权值汇总后,发现交叉长度在占染色体长度为10%时最优;为了找出更优的目标值,又选择染色体长度的10%到20%进行交叉,并反复仿真运算求其平均值,然后求加权值,发现选择染色体长度12%进行交叉可以获得更精确的解和提高运算速度,所以选择12%的交叉长度。4. A large-scale flexible job shop scheduling optimization method according to claim 1, characterized in that: the method for selecting a suitable chromosome length in the eighth step is specifically: selecting 10% to 100% of the chromosome length for Crossover, and repeatedly perform simulation operations to obtain the average value, and then sum up the weighted values. It is found that the crossover length is optimal when it accounts for 10% of the chromosome length; in order to find a better target value, 10% of the chromosome length is selected. Crossover to 20%, and repeat the simulation operation to calculate the average value, and then calculate the weighted value. It is found that choosing 12% of the chromosome length for crossover can obtain a more accurate solution and improve the operation speed, so choose 12% of the crossover length. 5.根据权利要求1所述的一种大规模柔性作业车间调度优化方法,其特征在于:所述步骤第十中按照正弦自适应遗传算法进行优化时,在优化过程的初始阶段选取较大的交叉率和变异率以获得较快的收敛速度且保持种群的多样性,经多次迭代后,为避免最优解被破坏,此时选取较小的交叉率和变异率进行细致搜索。5. a kind of large-scale flexible job shop scheduling optimization method according to claim 1, is characterized in that: when carrying out optimization according to sinusoidal adaptive genetic algorithm in described step tenth, in the initial stage of optimization process, select the larger one. The crossover rate and mutation rate are used to obtain a faster convergence rate and maintain the diversity of the population. After several iterations, in order to avoid the destruction of the optimal solution, a smaller crossover rate and mutation rate are selected for detailed search.
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