CN107862411B - Large-scale flexible job shop scheduling optimization method - Google Patents
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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
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'1+α2f'2(1)
Wherein: f. of1=min(maxTpi)p=1,2...Bi;i=1,2......r (2)
Formula (2) f1Representing a minimum maximum completion time; formula (3) f2Indicating that the total lingering period is minimal.
Constraint conditions are as follows:
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
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
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:
the mutation probability:
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
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)
Constraint equation:
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
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
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.
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