CN103729694A - Method for solving flexible job-shop scheduling problem with improved GA based on polychromatic set hierarchical structure - Google Patents

Method for solving flexible job-shop scheduling problem with improved GA based on polychromatic set hierarchical structure Download PDF

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CN103729694A
CN103729694A CN201310737478.8A CN201310737478A CN103729694A CN 103729694 A CN103729694 A CN 103729694A CN 201310737478 A CN201310737478 A CN 201310737478A CN 103729694 A CN103729694 A CN 103729694A
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栾飞
曹巨江
傅卫平
宝昱彤
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Ruilin Mechanics Technology Co ltd
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Abstract

The invention discloses a method for solving the flexible job-shop scheduling problem with an improved GA based on a polychromatic set hierarchical structure. According to the method, an original process-machine tool contour matrix is split into matrixes of relation of process-benchmark, benchmark-equipment model, equipment model-asset number by establishing equipment benchmarks and setting process constraint, equipment constraint, machine tool constraint and unique constraint, and the data size of a constraint model is effectively reduced; furthermore, by optimizing chromosome lengths reasonably and setting blending operation of batch benchmarks, the time and space complexity of chromosomes is effectively reduced, and then the solving speed and practicality of the algorithm can be greatly improved.

Description

基于多色集合层次结构的改进GA求解柔性车间调度的方法An Improved GA Method for Solving Flexible Shop Scheduling Based on Multicolor Set Hierarchy

技术领域technical field

本发明属于柔性车间调度技术领域,涉及一种改进的遗传算法,具体涉及一种基于多色集合层次结构的改进GA求解柔性车间调度的方法。The invention belongs to the technical field of flexible workshop scheduling, and relates to an improved genetic algorithm, in particular to a method for solving flexible workshop scheduling based on an improved GA of a multi-color set hierarchical structure.

背景技术Background technique

柔性车间调度(Flexible Job-Shop Scheduling Problem,FJSP),其核心思想是:多批次多种类零部件可以在同类别多型号设备上加工生产。在正式加工前,每个零部件的工艺是唯一确定的,但工艺路线却是不定的,每道工序有多种加工设备的选择,即每个待加工零部件有多条工艺路线可以选择,且设备选择要基于设备能力平衡。相比传统的车间调度问题而言,FJSP问题是更加复杂的NP-hard问题,解决此类问题要求算法具有更高的复杂性,但由于其更接近生产的实际情况,使得其成为了目前内外调度领域的研究重点。The core idea of Flexible Job-Shop Scheduling Problem (FJSP) is that multiple batches of multiple types of parts can be processed and produced on the same type of equipment. Before formal processing, the process of each component is uniquely determined, but the process route is uncertain. Each process has a variety of processing equipment options, that is, each component to be processed has multiple process routes to choose from. And the selection of equipment should be based on the balance of equipment capabilities. Compared with the traditional workshop scheduling problem, the FJSP problem is a more complicated NP-hard problem. Solving this kind of problem requires a higher complexity of the algorithm, but because it is closer to the actual situation of production, it has become the current domestic and foreign Research focus in the field of scheduling.

近年来,学者们对柔性车间调度也展开了大量的研究;现有技术中,“周辉仁,郑丕谔,安小会等.基于遗传算法求解Job Shop调度优化的新方法[J].系统仿真学报,2009,21(11):3295-3306”和“Pezzella F.A genetic algorithmfor the flexible Job-Shop scheduling problem[J].Computers and OperationsResearch,2007,21(9):54-61”为了提高GA的搜索速度,提出了改善编码方式优化染色体的方法,使GA算法的时间与空间复杂度大大降低,但其调度状况过于理论化,未能考虑环境变化,不具柔性。In recent years, scholars have also carried out a lot of research on flexible workshop scheduling; in the existing technology, "Zhou Huiren, Zheng Pier, An Xiaohui, etc. A new method for solving Job Shop scheduling optimization based on genetic algorithm [J]. Journal of System Simulation, 2009, 21(11): 3295-3306" and "Pezzella F.A genetic algorithm for the flexible Job-Shop scheduling problem[J]. Computers and Operations Research, 2007, 21(9): 54-61" in order to improve the search speed of GA, A method of improving the coding method and optimizing the chromosome is proposed, which greatly reduces the time and space complexity of the GA algorithm, but its scheduling situation is too theoretical and does not consider environmental changes, so it is not flexible.

“张国辉,高亮,李培根等.改进遗传算法求解柔性作业车间调度问题[J].机械工程学报,2009,45(7):145-151”中,结合FJSP问题特点,采用适当的策略改进了染色体编码方式、交叉算子和变异算子,大大提高了算法求解精度,但其求解速度且没有提高。In "Zhang Guohui, Gao Liang, Li Peigen, etc. Improved Genetic Algorithms to Solve Flexible Job Shop Scheduling Problems [J]. Chinese Journal of Mechanical Engineering, 2009, 45(7): 145-151", combined with the characteristics of FJSP problems, using appropriate strategies to improve The chromosome coding method, crossover operator and mutation operator are improved, which greatly improves the accuracy of the algorithm, but the solution speed does not increase.

“纪树新,钱积新,孙优贤.车间作业调度遗传算法中的编码研究[J].信息与控制,1997,26(5):393-400”中,为了消除GA只能应用于成组技术JSS的局限性,提出了JSS连锁基因编码法,虽然提高了求解效率,但其染色体的空间复杂度仍较高。In "Ji Shuxin, Qian Jixin, Sun Youxian. Coding Research in Genetic Algorithms for Job Shop Scheduling [J]. Information and Control, 1997, 26(5): 393-400", in order to eliminate GA, it can only be applied to group technology JSS Due to the limitations of the method, the JSS linkage gene coding method is proposed. Although the solution efficiency is improved, the space complexity of the chromosome is still high.

“潘全科,朱剑英.基于Petri网和混合算法的作业车间优化[J].计算机集成制造系统,2007,13(3):580-584”、“陈维民,王波,卫玉柯.Petri网的遗传算法在Job-Shop问题中的应用研究[J].哈尔滨理工大学学报,2008,13(1):59-62”和“鞠全勇,朱剑英.基于混合遗传算法的动态车间调度系统的研究[J].中国机械工程,2007,18(1):40-43”中,首先建立了JSP的赋时变迁Petri网模型,然后应用遗传算法(Genetic algorithm,GA)、模拟退火(SimulatedAnnealing,SA)、粒子群优化(Particle Swarm Optimization PSO)算法其中一种或者混合二种算法解决该问题,其所用求解算法依然具有很高的时间和空间复杂度,没能有效地同时提高算法的求解速度和精度。"Pan Quanke, Zhu Jianying. Job Shop Optimization Based on Petri Net and Hybrid Algorithm [J]. Computer Integrated Manufacturing System, 2007, 13(3): 580-584", "Chen Weimin, Wang Bo, Wei Yuke. Genetic Algorithm of Petri Net Application research in Job-Shop problem [J]. Journal of Harbin University of Science and Technology, 2008, 13 (1): 59-62" and "Ju Quanyong, Zhu Jianying. Research on dynamic shop scheduling system based on hybrid genetic algorithm [J]. China Mechanical Engineering, 2007, 18(1): 40-43", first established the timed transition Petri net model of JSP, and then applied genetic algorithm (Genetic algorithm, GA), simulated annealing (Simulated Annealing, SA), particle swarm One of the Particle Swarm Optimization (PSO) algorithms or a combination of the two algorithms can solve this problem, but the solution algorithm used still has high time and space complexity, and cannot effectively improve the solution speed and accuracy of the algorithm at the same time.

“傅卫平,刘冬梅,来春为,王雯.基于多色集合的改进遗传算法求解多品种柔性调度问题[J].计算机集成制造系统,2011,17(5):1004-1011”和“刘冬梅,傅卫平等.改进遗传算法求解柔性车间调度问题[J].西北大学学报,2011,41(4):611-616”中,采用了更易描述数据逻辑关系的多色集合理论,排除了不可行解,极大地缩小了GA搜索解域,同时提出了用单层编码方式表示调度问题中的双重约束,降低了算法的时间和空间复杂度。但是该文献所述算法只能在简单情况下(工序对应设备二选一),生成染色体,与实际应用差距较大;且染色体采用的分段编码是以最大工序数为基准单位生成,这就导致了算法在实践中处理大规模多工序调度问题时出现染色体太长,无效数据过多等现象,需要进一步改进。"Fu Weiping, Liu Dongmei, Lai Chunwei, Wang Wen. An improved genetic algorithm based on multi-color sets to solve multi-variety flexible scheduling problems [J]. Computer Integrated Manufacturing Systems, 2011, 17(5): 1004-1011" and "Liu Dongmei, Fu Wei Ping. Improved Genetic Algorithm to Solve the Flexible Workshop Scheduling Problem[J]. In Northwest University Journal, 2011, 41(4): 611-616, the multi-color set theory, which is easier to describe the logical relationship of data, is used to exclude infeasible solutions , greatly reducing the GA search solution domain, and at the same time, a single-layer encoding method is proposed to represent the double constraints in the scheduling problem, which reduces the time and space complexity of the algorithm. However, the algorithm described in this document can only generate chromosomes in simple cases (choose one of the equipment corresponding to the process), which is far from the actual application; and the segmented coding used by the chromosome is generated based on the maximum number of processes as the benchmark unit, which is As a result, when the algorithm deals with large-scale multi-process scheduling problems in practice, the chromosomes are too long and there are too many invalid data, which needs further improvement.

发明内容Contents of the invention

本发明的目的在于克服上述现有技术的缺点,提供一种基于多色集合层次结构的改进GA求解柔性车间调度的方法,该方法引入了多层次的约束描述方法,将原来巨大的围道矩阵切分,降低了约束模型的冗余数据量,增加算法实际应用的可能性;此外还改进了染色体的编码方式,去除了大量的无效基因,从空间复杂度角度进一步优化算法,提高收敛速度。The purpose of the present invention is to overcome the shortcoming of above-mentioned prior art, provide a kind of method based on the improved GA of multi-color set hierarchical structure to solve the method of flexible shop scheduling, this method has introduced the constraint description method of multilevel, the original huge confinement matrix Segmentation reduces the amount of redundant data in the constraint model and increases the possibility of practical application of the algorithm; in addition, it improves the coding method of chromosomes, removes a large number of invalid genes, further optimizes the algorithm from the perspective of space complexity, and improves the convergence speed.

为达到上述目的,本发明采用的技术方案包括以下步骤:In order to achieve the above object, the technical solution adopted in the present invention comprises the following steps:

1)建立柔性车间调度问题的数学模型;1) Establish a mathematical model of the flexible workshop scheduling problem;

2)建立基于PST层次结构的车间调度约束模型;2) Establish a shop scheduling constraint model based on the PST hierarchy;

3)根据工序-基准,基准-设备编号,设备编号-资产编号围道布尔矩阵,生成工艺-设备实数围道矩阵,进而产生遗传隐性编码序列表,列标对应机床编码,行标对应隐性基因位;其中,表中内容为工序的加工时间,隐性基因码位对应工件的工序编号,通过搜索相应的工序-基准,基准-设备编号,设备编号-资产编号围道布尔矩阵,从而找到对应于特定工序的机床编码,再根据机床的可用性特征,选择相应的机床编码作为染色体的显性编码。3) According to the procedure-benchmark, benchmark-equipment number, equipment number-asset number contour Boolean matrix, generate a process-equipment real number contour matrix, and then generate a genetic recessive coding sequence table, the column label corresponds to the machine tool code, and the row label corresponds to the implicit Among them, the content in the table is the processing time of the process, and the recessive gene code bit corresponds to the process number of the workpiece, by searching the corresponding process-baseline, benchmark-equipment number, equipment number-asset number enclosing the Boolean matrix, thus Find the machine tool code corresponding to a specific process, and then select the corresponding machine tool code as the dominant code of the chromosome according to the availability characteristics of the machine tool.

所述的步骤1)中,建立柔性车间调度问题的数学模型的具体方法为:In the step 1), the specific method of establishing the mathematical model of the flexible shop scheduling problem is as follows:

FJSP能够被描述为,假设M为加工设备的数量,N为待加工工件数量,P为工序数,I为所有设备的集合;Ieg代表工件e的第g道工序的可用设备集合,

Figure BDA0000447597290000031
Je为工件e的工序数;X为所有工件的加工次序,Segk表示工件e的第g道工序在设备k上加工的开始时间;Eegk为工件e的第g道工序在设备k上的加工结束时间;Tegk为工件e的第g道工序在设备k上的持续加工时间,且k∈Ieg则有Eegk=Segk+Tegk;Ep表示最后工序的完工时间;MS表示所有工件的最后完工时间;FJSP can be described as, assuming that M is the number of processing equipment, N is the number of workpieces to be processed, P is the number of processes, and I is the set of all equipment; Ieg represents the set of available equipment for the gth process of the workpiece e,
Figure BDA0000447597290000031
J e is the process number of workpiece e; X is the processing sequence of all workpieces, S egk represents the start time of the g-th process of workpiece e being processed on equipment k; E egk is the g-th process of workpiece e on equipment k The processing end time; T egk is the continuous processing time of the gth process of the workpiece e on the equipment k, and k∈I eg has E egk =S egk + T egk ; E p represents the completion time of the last process; MS represents The final completion time of all workpieces;

当工件i的第j道工序和工件e的第g道工序在同一台设备上执行,若工序j先于工序g加工时,Qijeg=1,否则Qijeg=0;若工件e的第g道工序在机床k上加工,则Xegk=1,否则Xegk=0;When the j-th process of workpiece i and the g-th process of workpiece e are executed on the same equipment, if process j is processed before process g, Q ijeg = 1, otherwise Q ijeg = 0; if the g-th process of workpiece e If a procedure is processed on machine k, then X egk =1, otherwise X egk =0;

若某FJSP共有S种可能的加工顺序,要求总的作业时间最短的加工排序,先求取每个加工顺序x(x∈{1,...,S})对应的作业时间;显然,顺序x中最后加工工序的完工时间即所有工件的最后完工时间,则有If there are S possible processing sequences in a certain FJSP, and the processing sequence with the shortest total operation time is required, first obtain the operation time corresponding to each processing sequence x(x∈{1,...,S}); obviously, the sequence The completion time of the last processing procedure in x is the final completion time of all workpieces, then

MS=Ep            (1)MS=E p (1)

目标函数F(x)为The objective function F(x) is

F(x)=min(MSx)=min((Ep)x)       (2)F(x)=min(MS x )=min((E p ) x ) (2)

X=1,…,SX=1,...,S

S.T.Segk-Ee(g-1)n≥0STS egk -E e(g-1)n ≥0

e=1,…,N;g=1,…,Je;Xegk=1,Xe(g-1)n=1       (3)e=1,...,N;g=1,...,J e ;X egk =1,X e(g-1)n =1 (3)

Segk-Eigk≥0 SegkEigk≥0

e=1,…,N;g=1,…,Je;Xijk=1,Xegk=1,Qijeg=1       (4)。e=1, . . . , N; g=1, . . . , J e ; X ijk =1, X egk =1, Q ijeg =1 (4).

所述的步骤2)中,车间调度约束模型的约束关系为:In the step 2), the constraint relationship of the shop-shop scheduling constraint model is:

首先设置设备基准,每个设备基准包含相似工艺的几种设备型号,每个设备型号又包含几台该种型号的具体设备,每台具体设备又与对应的资产编号相对应,而工序最终要在具体设备上来完成加工,因此就可以通过工序与基准的约束关系,设备基准与设备型号的约束关系,设备型号与资产编号的约束关系,间接地建立工序与具体设备的约束关系,从而实现将庞大的工序机床围道矩阵分割为小的关系矩阵,以降低矩阵的规模和数据量,提高算法的求解速度。First, set the equipment benchmark. Each equipment benchmark contains several equipment models with similar processes. Each equipment model contains several specific equipment of this type. Each specific equipment corresponds to the corresponding asset number. The processing is completed on the specific equipment, so the constraint relationship between the process and the specific equipment can be established indirectly through the constraint relationship between the process and the benchmark, the constraint relationship between the equipment benchmark and the equipment model, and the constraint relationship between the equipment model and the asset number, so as to realize the The huge process machine tool contour matrix is divided into small relational matrices to reduce the scale and data volume of the matrix and improve the solution speed of the algorithm.

所述的步骤3)中,根据机床的可用性特征,选择相应的机床编码作为染色体的显性编码具体为:In step 3), according to the availability characteristics of the machine tool, select the corresponding machine tool code as the dominant code of the chromosome, specifically:

3.1)建立基于层次结构围道布尔矩阵的约束模型:3.1) Establish a constraint model based on the hierarchical structure of the Boolean matrix:

使用基准与设备型号、设备型号与资产编号、自相关、工艺设备、工艺设备实数的层次结构围道布尔矩阵作为约束模型,产生遗传隐性编码序列表,GA的操作都在约束模型的范围内进行;Use the hierarchical structure surrounding Boolean matrix of benchmark and equipment model, equipment model and asset number, autocorrelation, process equipment, and process equipment real numbers as a constraint model to generate a genetic recessive coding sequence table, and the operation of GA is within the scope of the constraint model conduct;

3.2)染色体的编码:3.2) Chromosome coding:

3.3)染色体的解码:3.3) Chromosome decoding:

根据染色体里面的相应信息,搜索工艺-设备实数围道矩阵,来确定每个机床上的所有工序的加工时间参数;According to the corresponding information in the chromosome, search the process-equipment real number contour matrix to determine the processing time parameters of all processes on each machine tool;

3.4)选择操作:3.4) Select operation:

将上一代种群中适应度值最好的个体所对应的染色体直接选择进入下一代种群;The chromosomes corresponding to the individuals with the best fitness value in the previous generation population are directly selected into the next generation population;

3.5)交叉操作:3.5) Cross operation:

随机选择两个父代染色体,两个随机数0<a<b<N,其中,N为染色体基因数,找出两个父代染色体上对应a,b之间的片段彼此进行交换;Randomly select two parent chromosomes, two random numbers 0<a<b<N, where N is the number of chromosome genes, and find out the segments corresponding to a and b on the two parent chromosomes to exchange with each other;

3.6)变异。3.6) Variation.

所述染色体编码的具体方法为:The specific method of the chromosome coding is:

首先确定染色体长度为各工件的有效工序数之和:First determine the chromosome length as the sum of the effective number of processes of each job:

(a)当为单件多品种的生产模式时:(a) When it is a single-piece multi-variety production mode:

有n类工件各一件,GA染色体长度为其中Lg为对应第g个零件的工序数;There are n types of workpieces each, and the length of the GA chromosome is Where L g is the number of processes corresponding to the gth part;

(b)当为多件多品种生产模式时:(b) When it is a multi-piece multi-variety production mode:

有n类工件共J件J=n1+n2+...+ni+...+nn,其中n1、n2、...、ni、...、nn分别表示第i类工件的数量i∈n,每类工件有pi道工序,则需要先对工件的加工次序进行编码,对工件加工次序进行随机排序,生成显性染色体;There are n types of workpieces, a total of J pieces J=n 1 +n 2 +...+n i +...+n n , where n 1 , n 2 ,..., n i ,..., n n are respectively Indicates the number i∈n of the i-th type of workpieces, and each type of workpiece has p i processes, it is necessary to encode the processing order of the workpieces first, and randomly sort the processing order of the workpieces to generate dominant chromosomes;

当同种零件的数量小于100件时,将其合并成一个任务;最后根据基准与设备型号、设备型号与资产编号围道矩阵,生成隐性染色体;When the number of parts of the same type is less than 100, merge them into one task; finally, generate recessive chromosomes according to the matrix of benchmarks and equipment models, equipment models and asset numbers;

当同种零件的数量超过100则采用分批策略,分批后的单个任务体间是随机排序的。When the number of parts of the same kind exceeds 100, the batch strategy is adopted, and the individual tasks after batching are randomly sorted.

所述变异的具体方法为:The specific method of the variation is:

3.6.1)设定变异率,确定需要变异的基因位;3.6.1) Set the mutation rate and determine the gene bits that need to be mutated;

3.6.2)搜索基准与设备型号、设备型号与资产编号围道矩阵,找到此基因位能够替换机床的编码,产生新的染色体;3.6.2) Search the benchmark and equipment model, equipment model and asset number matrix, find out that this gene bit can replace the code of the machine tool, and generate a new chromosome;

3.6.3)计算新染色体的目标函数,比较新旧染色体对应的目标函数值,进而选择较优的进入下一代。3.6.3) Calculate the objective function of the new chromosome, compare the objective function values corresponding to the old and new chromosomes, and then select the better one to enter the next generation.

与现有技术相比,本发明具有以下有益效果:Compared with the prior art, the present invention has the following beneficial effects:

本发明根据工序-基准,基准-设备编号,设备编号-资产编号围道布尔矩阵,生成工艺-设备实数围道矩阵,进而产生遗传隐性编码序列表,列标对应机床编码,行标对应隐性基因位;其中,表中内容为工序的加工时间,隐性基因码位对应工件的工序编号,通过搜索相应的工序-基准,基准-设备编号,设备编号-资产编号围道布尔矩阵,从而找到对应于特定工序的机床编码,再根据机床的可用性特征,选择相应的机床编码作为染色体的显性编码。本发明的改进GA算法在编码、解码和变异的随机执行过程均是在工序-基准,基准-设备编号,设备编号-资产编号围道矩阵约束内进行的,是一种可控范围内的随机,其作用在于降低了约束模型的数据量并除去了无效信息缩小了解空间的搜索范围,最终提高算法求解精度和速度。According to the process-reference, reference-equipment number, equipment number-asset number enclosing Boolean matrix, the present invention generates a process-equipment real number enclosing matrix, and then generates a genetic recessive coding sequence table, the column label corresponds to the machine tool code, and the row label corresponds to the implicit Among them, the content in the table is the processing time of the process, and the recessive gene code bit corresponds to the process number of the workpiece, by searching the corresponding process-baseline, benchmark-equipment number, equipment number-asset number enclosing the Boolean matrix, thus Find the machine tool code corresponding to a specific process, and then select the corresponding machine tool code as the dominant code of the chromosome according to the availability characteristics of the machine tool. The random execution process of the improved GA algorithm of the present invention in encoding, decoding and mutation is carried out within the constraints of the procedure-reference, reference-equipment number, equipment number-asset number confinement matrix, and is a kind of random execution within the controllable range. , its role is to reduce the amount of data in the constraint model and remove invalid information to narrow the search range of the understanding space, and ultimately improve the accuracy and speed of the algorithm.

进一步的,本发明所采用的染色体基因位编码方法,除去了无效基因位,降低了算法的空间与时间复杂度,从而提高GA的搜索效率。Further, the method for encoding chromosome gene bits adopted in the present invention removes invalid gene bits, reduces the space and time complexity of the algorithm, and thus improves the search efficiency of the GA.

附图说明Description of drawings

图1为本发明的层次约束关系图;Fig. 1 is a hierarchical constraint relationship diagram of the present invention;

图2为本发明任务分配PS层次结构模型图;Fig. 2 is a PS hierarchical structure model diagram of task assignment of the present invention;

图3为本发明实例1的遗传收敛曲线图;Fig. 3 is the hereditary convergence curve figure of example 1 of the present invention;

图4为本发明实例1的调度甘特图;Fig. 4 is the scheduling Gantt chart of the example 1 of the present invention;

图5为本发明实例2的遗传收敛曲线图;Fig. 5 is the genetic convergence curve figure of the example 2 of the present invention;

图6为本发明实例2的调度结果甘特图;Fig. 6 is the scheduling result Gantt chart of the example 2 of the present invention;

图7为本发明的流程图。Fig. 7 is a flowchart of the present invention.

具体实施方式Detailed ways

下面结合附图和实施例对本发明做进一步详细描述:Below in conjunction with accompanying drawing and embodiment the present invention is described in further detail:

实施例:Example:

1)柔性车间调度问题的数学模型1) Mathematical model of flexible shop scheduling problem

FJSP能够被描述为,假设M为加工设备的数量,N为待加工工件数量,P为工序数,I为所有设备的集合;Ieg代表工件e的第g道工序的可用设备集合,

Figure BDA0000447597290000071
Je为工件e的工序数;X为所有工件的加工次序,Segk表示工件e的第g道工序在设备k上加工的开始时间;Eegk为工件e的第g道工序在设备k上的加工结束时间;Tegk为工件e的第g道工序在设备k上的持续加工时间,且k∈Ieg则有Eegk=Segk+Tegk;Ep表示最后工序的完工时间;MS表示所有工件的最后完工时间;FJSP can be described as, assuming that M is the number of processing equipment, N is the number of workpieces to be processed, P is the number of processes, and I is the set of all equipment; Ieg represents the set of available equipment for the gth process of the workpiece e,
Figure BDA0000447597290000071
J e is the process number of workpiece e; X is the processing sequence of all workpieces, S egk represents the start time of the g-th process of workpiece e being processed on equipment k; E egk is the g-th process of workpiece e on equipment k The processing end time; T egk is the continuous processing time of the gth process of the workpiece e on the equipment k, and k∈I eg has E egk =S egk + T egk ; E p represents the completion time of the last process; MS represents The final completion time of all workpieces;

当工件i的第j道工序和工件e的第g道工序在同一台设备上执行,若工序j先于工序g加工时,Qijeg=1,否则Qijeg=0;若工件e的第g道工序在机床k上加工,则Xegk=1,否则Xegk=0;When the j-th process of workpiece i and the g-th process of workpiece e are executed on the same equipment, if process j is processed before process g, Q ijeg = 1, otherwise Q ijeg = 0; if the g-th process of workpiece e If a procedure is processed on machine k, then X egk =1, otherwise X egk =0;

若某FJSP共有S种可能的加工顺序,要求总的作业时间最短的加工排序,先求取每个加工顺序x(x∈{1,...,S})对应的作业时间;显然,顺序x中最后加工工序的完工时间即所有工件的最后完工时间,则有If there are S possible processing sequences in a certain FJSP, and the processing sequence with the shortest total operation time is required, first obtain the operation time corresponding to each processing sequence x(x∈{1,...,S}); obviously, the sequence The completion time of the last processing procedure in x is the final completion time of all workpieces, then

MS=Ep              (1)MS=E p (1)

目标函数F(x)为The objective function F(x) is

F(x)=min(MSx)=min((Ep)x)         (2)F(x)=min(MS x )=min((E p ) x ) (2)

X=1,…,SX=1,...,S

S.T.Segk-Ee(g-1)n≥0STS egk -E e(g-1)n ≥0

e=1,…,N;g=1,…,Je;Xegk=1,Xe(g-1)n=1        (3)e=1,...,N;g=1,...,J e ;X egk =1,X e(g-1)n =1 (3)

Segk-Eigk≥0 SegkEigk≥0

e=1,…,N;g=1,…,Je;Xijk=1,Xegk=1,Qijeg=1      (4)e=1,...,N; g=1,...,J e ;X ijk =1, X egk =1, Q ijeg =1 (4)

2)基于PST层次结构的FJSP约束模型2) FJSP constraint model based on PST hierarchy

2.1多色集合理论简介2.1 Introduction to polychromatic set theory

多色集合理论是一个新的系统建模理论及帮助信息处理的数学工具,该理论和方法自出现后在前苏联及现在俄罗斯企业界,特别是航空航天企业得到了广泛的推广与应用。该理论核心思想是将相同的数学模型应用在仿真不同的对象(产品、生产系统、设计和工艺过程等),描述元素之间的层次结构及复杂关系,并在集合层与逻辑层组织及处理信息,在数量层处理低层数据实际值问题。Multicolor set theory is a new system modeling theory and a mathematical tool to help information processing. Since its appearance, this theory and method have been widely promoted and applied in the former Soviet Union and the current Russian business circles, especially aerospace companies. The core idea of this theory is to apply the same mathematical model to simulate different objects (products, production systems, design and process, etc.), describe the hierarchical structure and complex relationship between elements, and organize and process them at the collection layer and logic layer Information, dealing with the actual value of low-level data at the quantitative level.

2.2车间实际生产约束条件分析2.2 Analysis of actual production constraints in the workshop

对于一般制造企业来说,实际的生产工作会受到大量人、机、料、法、环等因素的影响和制约,因此实际的车间调度工作需要考虑的因素众多,用普通的PST来描述这种约束关系,会导致个人颜色、统一颜色及体的围道矩阵都具有较大的数据量。如何才能够将多方面的影响及时地变更到描述元素关系的围道矩阵当中,是应用多色集合理论和智能算法解决调度问题的一个重要瓶颈。PST的层次结构模型为解决该瓶颈的提供了有效途径。For general manufacturing enterprises, the actual production work will be affected and restricted by a large number of factors such as people, machines, materials, methods, and the environment. Therefore, there are many factors that need to be considered in the actual workshop scheduling work. The ordinary PST is used to describe this Constraint relations will lead to a large amount of data in the individual color, uniform color, and body contour matrix. How to timely change multi-faceted influences into the contour matrix describing the relationship between elements is an important bottleneck in the application of multi-color set theory and intelligent algorithms to solve scheduling problems. The hierarchical structure model of PST provides an effective way to solve this bottleneck.

结合大量车间调度的实际经验分析发现,如果给车间内的设备设置相应设备基准和设备型号,可以将工序与设备基准序进行关联,设备基准与设备代码进行关联,设备代码再与车间的具体设备的资产编号进行关联,最后间接建立工序与设备对应关系,进而给企业的设备管理和车间调度工作带来很大便利。如果用一个单一的围道矩阵描述工序与设备的对应关系,势必会导致矩阵过大,而缺乏实用性。Combined with the actual experience analysis of a large number of workshop scheduling, it is found that if the corresponding equipment reference and equipment model are set for the equipment in the workshop, the process can be associated with the equipment reference sequence, the equipment reference can be associated with the equipment code, and the equipment code can be associated with the specific equipment in the workshop. The asset number is associated with each other, and finally the corresponding relationship between the process and the equipment is established indirectly, which brings great convenience to the equipment management and workshop scheduling work of the enterprise. If a single confinement matrix is used to describe the corresponding relationship between procedures and equipment, it will inevitably lead to too large a matrix and lack of practicability.

2.3基于PST层次结构的车间调度约束模型2.3 Shop Scheduling Constraint Model Based on PST Hierarchy

基于上述分析,考虑车间实际生产中各种影响因素,本发明在调度过程中设置了四种约束:工序约束是指按照实际的加工工艺,工序必须按照先后顺序进行排产;基准约束是指一道工序只能在指定的几种基准类型的设备上加工;机床约束是指每一个基准类型对应几种固定的机床型号;唯一约束是指每个工件的任意一工序在固定时刻只能在一台机器上加工。其约束关系为首先设置设备基准,每个设备基准包含相似工艺的几种设备型号,每个设备型号又包含几台该种型号的具体设备,每台具体设备又与对应的资产编号相对应,而工序最终要在具体设备上来完成加工,因此就可以通过工序与基准的约束关系,设备基准与设备型号的约束关系,设备型号与资产编号的约束关系,间接地建立工序与具体设备的约束关系,从而实现将庞大的工序机床围道矩阵分割为小的关系矩阵,以降低矩阵的规模和数据量,提高算法的求解速度,其具体层次结构如图1所示。Based on the above analysis and considering various influencing factors in the actual production of the workshop, the present invention sets four kinds of constraints in the scheduling process: the process constraint means that the processes must be scheduled according to the actual processing technology; the benchmark constraint means that a The process can only be processed on the equipment of several specified benchmark types; the machine tool constraint means that each benchmark type corresponds to several fixed machine tool models; the unique constraint means that any process of each workpiece can only be processed on one machine at a fixed time Processing on the machine. The constraint relationship is to first set the equipment benchmark, each equipment benchmark includes several equipment models of similar technology, each equipment model includes several specific equipment of this type, and each specific equipment corresponds to the corresponding asset number, And the process must be processed on specific equipment, so the constraint relationship between the process and the specific equipment can be indirectly established through the constraint relationship between the process and the benchmark, the constraint relationship between the equipment benchmark and the equipment model, and the constraint relationship between the equipment model and the asset number. , so as to realize the division of the huge process machine tool contour matrix into small relational matrices, so as to reduce the scale and data volume of the matrix, and improve the solution speed of the algorithm. The specific hierarchical structure is shown in Figure 1.

图1中左上角围道矩阵反映了零件的工序约束和基准设备类型约束,即每一道工序可以由哪个基准设备类型加工,可以通过该矩阵反映出来,无值的即不可以加工。右上角围道矩阵反映了基准设备类型与具体设备型号的机床约束。其中有1的,证明该基准设备类型包含该设备型号。下方围道矩阵反映了M车间设备型号与具体机床的对应关系,其中数值表示对应工序在该机床上的加工时间。在此基础上可以进一步得出其任务分配模型如图2所示。The contour matrix in the upper left corner of Figure 1 reflects the process constraints and reference equipment type constraints of the parts, that is, which reference equipment type can be processed by each process, which can be reflected by the matrix, and those without values cannot be processed. The upper right corner matrix reflects the machine tool constraints of the benchmark equipment type and the specific equipment model. If there is 1 among them, it proves that the reference device type includes the device model. The lower corridor matrix reflects the corresponding relationship between the equipment model of the M workshop and the specific machine tool, where the value indicates the processing time of the corresponding process on the machine tool. On this basis, its task allocation model can be further drawn as shown in Figure 2.

下面将通过3个工件的FJSP来介绍其PST层次结构约束模型的建立过程,其加工任务信息表如表1所示,其中列表示设备信息,行表示工件工序信息,表中的数据表示行对应工序在列对应机床上的加工时间,针对表1的相关信息和工艺相似性准则设置设备基准J1,J2,J3,设备型号为S1,S2,S3,资产编号M1,M2,M3,M4,M5,M6,即本次加工的6台设备,其相互之间的约束关系如式(5)、(6)所示。The following will introduce the establishment process of the PST hierarchy constraint model through the FJSP of the three workpieces. The processing task information table is shown in Table 1, where the columns represent the equipment information, the rows represent the workpiece process information, and the data in the table represent the row correspondence. The process is listed in the corresponding processing time on the machine tool, and the equipment benchmarks J1, J2, J3 are set according to the relevant information and process similarity criteria in Table 1, the equipment models are S1, S2, S3, and the asset numbers are M1, M2, M3, M4, M5 , M6, that is, the 6 equipments processed this time, and the constraint relationship between them is shown in formulas (5) and (6).

表1加工任务信息表Table 1 Processing task information table

Figure BDA0000447597290000101
Figure BDA0000447597290000101

Figure BDA0000447597290000111
Figure BDA0000447597290000111

Figure BDA0000447597290000112
Figure BDA0000447597290000112

其中Cij的点位表示该点横向代表的基准所包含的设备型号。从该矩阵中可以发现基准与设备型号间的关系。The point of C ij indicates the equipment model included in the benchmark represented by the point horizontally. From this matrix, the relationship between benchmarks and device models can be found.

其中Cij=1的点位表示横向代表的设备型号所对应的本车间内所有设备的资产编号。The point where C ij =1 represents the asset number of all equipment in this workshop corresponding to the equipment model represented by the horizontal direction.

综上可以得到节点集合的自相关矩阵[F(a)×F(a)]如下表2:In summary, the autocorrelation matrix [F(a)×F(a)] of the node set can be obtained as shown in Table 2:

表2[F(a)×F(a)]Table 2 [F(a)×F(a)]

Figure BDA0000447597290000121
Figure BDA0000447597290000121

根据表1相关数据和设定的工件对应的设备基准及表2[F(a)×F(a)]中记录的各节点间的关系,可以得到围道矩阵[A×F(A)]和体围道阵[A×A(F)]如表3和表4所示。其中F1—F6代表不同的工艺名称车、钳、镗、钻孔、铣、刨;J1、J2、J3分别代表三种不同的设备基准。且在本实例中与工序一一对应。a1—a15表示3个工件的工序列;M1—M6表示待加工机床。其中,Cij=1的点表示横坐标所代表元素与纵坐标所代表颜色有直接联系。According to the relevant data in Table 1 and the equipment reference corresponding to the set workpiece and the relationship between the nodes recorded in Table 2 [F(a)×F(a)], the contour matrix [A×F(A)] can be obtained and body circumference array [A×A(F)] are shown in Table 3 and Table 4. Among them, F1-F6 represent different process names of lathe, pliers, boring, drilling, milling, and planing; J1, J2, and J3 represent three different equipment benchmarks. And in this example, there is a one-to-one correspondence with the process. a1-a15 represent the sequence of three workpieces; M1-M6 represent the machine tool to be processed. Among them, the point of C ij =1 indicates that the element represented by the abscissa is directly related to the color represented by the ordinate.

表3工艺-设备布尔围道矩阵[A×F(A)]Table 3 Process-Equipment Boolean Confinement Matrix [A×F(A)]

Figure BDA0000447597290000131
Figure BDA0000447597290000131

表4[A×A(F)]中实数部分矩阵可以作为进一步隐性染色体编码的依据。由该矩阵可以得到可加工每一工序的设备及在该设备加工本序工作所需要的时间。The real part matrix in Table 4 [A×A(F)] can be used as the basis for further recessive chromosome coding. From this matrix, the equipment that can process each process and the time required to process the work in this equipment can be obtained.

表4工艺-设备实数围道矩阵[A×A(F)]Table 4 Process-Equipment Real Contour Matrix [A×A(F)]

Figure BDA0000447597290000141
Figure BDA0000447597290000141

以此为基础生成遗传隐性编码序列表如表5所示,列标对应机床编码,行标对应隐性基因位,表中内容为工序的加工时间,隐性基因码位对应工件的工序编号,来搜索相对的工序-基准,基准-设备编号,设备编号-资产编号围道矩阵,从而找到对应于特定工序的机床编码,再根据机床的可用性特征(占用或空闲),选择适当的机床编码作为染色体的显性编码。Based on this, the genetic recessive coding sequence table is generated as shown in Table 5. The column label corresponds to the machine tool code, and the row label corresponds to the recessive gene bit. The content in the table is the processing time of the process, and the recessive gene code bit corresponds to the process number of the workpiece. , to search the relative process-benchmark, benchmark-equipment number, equipment number-asset number confinement matrix, so as to find the machine tool code corresponding to a specific process, and then select the appropriate machine tool code according to the availability characteristics of the machine tool (occupied or idle). as a dominant code for a chromosome.

表5遗传隐性编码序列表Table 5 Genetic recessive coding sequence list

Figure BDA0000447597290000142
Figure BDA0000447597290000142

3)层次结构约束模型下的改进GA操作3) Improved GA operation under the hierarchy constraint model

如图7所示,图7为本发明改进遗传算法流程图;As shown in Figure 7, Figure 7 is a flowchart of the improved genetic algorithm of the present invention;

3.1基于层次结构围道布尔矩阵的约束模型3.1 Constraint Model Based on Hierarchical Confinement Boolean Matrix

本发明改进的GA使用基准与设备型号、设备型号与资产编号、自相关、工艺设备、工艺设备实数的层次结构围道布尔矩阵作为约束模型,GA的操作都在约束模型的范围内进行,具体操作如下。The improved GA of the present invention uses the hierarchical structure surrounding Boolean matrix of benchmark and equipment model, equipment model and asset number, autocorrelation, process equipment, and process equipment real numbers as a constraint model, and the operations of GA are all carried out within the scope of the constraint model, specifically The operation is as follows.

3.2染色体的编码3.2 Chromosome coding

首先确定染色体长度为各工件的有效工序数之和First determine the chromosome length as the sum of the effective number of processes of each workpiece

(a)当为单件多品种的生产模式时:有n类工件各一件,本发明改进GA染色体长度为其中Lg为对应第g个零件的工序数,n为该批次排产的工件数,以上面的3×6的单间调度为例生成染色体如下所示:(a) When it is a single-piece multi-variety production mode: there are n types of workpieces each, and the length of the GA chromosome improved by the present invention is Among them, L g is the number of processes corresponding to the g-th part, and n is the number of workpieces scheduled for this batch. Taking the above 3×6 single-room scheduling as an example, the chromosomes generated are as follows:

11 55 44 33 44 66 22 33 44 22 66 33 11 22 44 11

1-6代表工件1的加工机床信息;7-11表示工件2的加工机床信息;12-15表示工件3的加工机床信息。1-6 represent the processing machine information of workpiece 1; 7-11 represent the processing machine information of workpiece 2; 12-15 represent the processing machine information of workpiece 3.

(b)当为多件多品种生产模式时:(b) When it is a multi-piece multi-variety production mode:

当为多品种生产模式时:有n类工件共J件(J=n1+n2+...+ni+...+nn,其中n1、n2、...、ni、...、nn分别表示第i类工件的数量i∈n),每类工件有pi道工序,则需要先对工件的加工次序进行编码,如有A、B、C类工件各3件,则首先对工件加工次序进行随机排序,生成显性染色体。When it is a multi-variety production mode: there are n types of workpieces and a total of J pieces (J=n 1 +n 2 +...+n i +...+n n , where n 1 , n 2 ,..., n i , ..., n n respectively represent the number of workpieces of the i type (i∈n), each type of workpiece has p i processes, the processing order of the workpieces needs to be coded first, if there are A, B, and C types of workpieces For each of 3 pieces, the processing order of the workpieces is first randomly sorted to generate dominant chromosomes.

由学习曲线理论可知,重复操作可以增加员工操作的熟练度,缩短单个零件的加工时间,所以本发明的研究中采用同种类零件合批生产编码策略。当同种零件的数量小于100件时,将其合并成一个任务。上述例子可以编码如下(A*3代表其各工序加工时间都相应乘以该系数,即该零件个数)。According to the learning curve theory, repeated operations can increase the proficiency of employees and shorten the processing time of a single part. Therefore, the same type of parts batch production coding strategy is adopted in the research of the present invention. When the quantity of the same kind of parts is less than 100 pieces, combine them into one task. The above example can be coded as follows (A*3 means that the processing time of each process is multiplied by the coefficient, that is, the number of parts).

A11·3A 11 3 A1m·3A 1m 3 B11·3B 11 3 B1m·3B 1m 3 Ck1·3C k1 ·3 Ckm·3C km 3

最后根据基准与设备型号、设备型号与资产编号围道矩阵,生成隐性染色体。Finally, recessive chromosomes are generated according to the benchmark and equipment model, equipment model and asset number confinement matrix.

如果超过100则采用分批策略,因为如果一个工件的数量太多,合成一批次后会影响后续零件的加工。因为每个批次内部的零部件的交货期都是不一样的,所以为了满足其它零件也可以在规定的交货期到达指定库房,例如取100件作为分批临界点。设A工件150件,B工件211件,C工件50件,则:If it exceeds 100, the batching strategy is adopted, because if the number of a workpiece is too large, the processing of subsequent parts will be affected after a batch is synthesized. Because the delivery time of parts in each batch is different, in order to meet other parts can also arrive at the designated warehouse within the specified delivery time, for example, take 100 pieces as the critical point of batching. Suppose there are 150 pieces of workpiece A, 211 pieces of workpiece B, and 50 pieces of workpiece C, then:

A·100A·100 C·50C·50 B·100B·100 B·11B·11 A·50A·50 B·100B·100

分批后的单个任务体间是随机排序的。The individual tasks after batching are randomly sorted.

3.3染色体的解码3.3 Chromosome decoding

根据染色体里面的相应信息,搜索表5遗传隐性编码序列表,来确定每个机床上的所有工序的加工时间等参数。According to the corresponding information in the chromosome, search the genetic recessive coding sequence table in Table 5 to determine the processing time and other parameters of all processes on each machine tool.

3.4选择操作3.4 Select operation

将上一代种群中适应度值最好的个体所对应的染色体直接选择进入下一代种群。The chromosomes corresponding to the individuals with the best fitness value in the previous generation population are directly selected into the next generation population.

3.5交叉操作3.5 Cross-operation

随机选择两个父代染色体,两个随机数0<a<b<N(N为染色体基因数),找出两个父代染色体上对应a,b之间的片段彼此进行交换。Randomly select two parent chromosomes, two random numbers 0<a<b<N (N is the number of chromosome genes), and find out the segments corresponding to a and b on the two parent chromosomes to exchange with each other.

3.6变异3.6 Variation

3.6.1设定变异率,确定需要变异的基因位。3.6.1 Set the mutation rate and determine the gene bits that need to be mutated.

3.6.2搜索工序-基准、基准与设备型号、设备型号与资产编号围道矩阵,找到此基因位可替换机床的编码,产生新的染色体。3.6.2 Search the process-benchmark, benchmark and equipment model, equipment model and asset number encircling the matrix, find the code of the machine tool that can replace the gene bit, and generate a new chromosome.

3.6.3计算新染色体的目标函数,比较新旧染色体对应的目标函数值,进而选择较优的进入下一代。3.6.3 Calculate the objective function of the new chromosome, compare the objective function values corresponding to the old and new chromosomes, and then select the better one to enter the next generation.

根据工序-基准,基准-设备编号,设备编号-资产编号围道布尔矩阵,生成工艺-设备实数围道矩阵,进而产生遗传隐性编码序列表,列标对应机床编码,行标对应隐性基因位;其中,表中内容为工序的加工时间,隐性基因码位对应工件的工序编号,通过搜索相应的工序-基准,基准-设备编号,设备编号-资产编号围道布尔矩阵,从而找到对应于特定工序的机床编码,再根据机床的可用性特征,选择相应的机床编码作为染色体的显性编码。本发明的改进GA算法在编码、解码和变异的随机执行过程均是在工序-基准,基准-设备编号,设备编号-资产编号围道矩阵约束内进行的,是一种可控范围内的随机,其作用在于降低了约束模型的数据量并除去了无效信息缩小了解空间的搜索范围,最终提高算法求解精度和速度。本发明所采用的染色体基因位编码方法,除去了无效基因位,降低了算法的空间与时间复杂度,从而提高GA的搜索效率,具体数据可由表3得出。According to the procedure-benchmark, benchmark-equipment number, equipment number-asset number confinement Boolean matrix, a process-equipment real number confinement matrix is generated, and then a genetic recessive coding sequence table is generated, the column label corresponds to the machine tool code, and the row label corresponds to the recessive gene Wherein, the content in the table is the processing time of the procedure, and the recessive gene code bit corresponds to the procedure number of the workpiece, by searching the corresponding procedure-benchmark, benchmark-equipment number, equipment number-asset number surrounding the Boolean matrix, so as to find the corresponding According to the machine tool code for a specific process, and then according to the availability characteristics of the machine tool, the corresponding machine tool code is selected as the dominant code of the chromosome. The random execution process of the improved GA algorithm of the present invention in encoding, decoding and mutation is carried out within the constraints of the procedure-reference, reference-equipment number, equipment number-asset number confinement matrix, and is a kind of random execution within the controllable range. , its role is to reduce the amount of data in the constraint model and remove invalid information to narrow the search range of the understanding space, and ultimately improve the accuracy and speed of the algorithm. The method for encoding chromosome gene bits used in the present invention removes invalid gene bits, reduces the space and time complexity of the algorithm, and improves the search efficiency of GA. The specific data can be obtained from Table 3.

本发明的原理:Principle of the present invention:

遗传算法属于进化算法(Evolutionary Algorithms)的一种,通过模仿自然界的遗传与选择的过程来寻找最优解。适用于复杂问题的求解,现已被普遍应用于各个领域的研究当中。但是,从优化算法的角度和使用要求的角度来说,学术界从来都没有停止过对该算法的改进和优化,降低算法的时间及空间复杂度。Genetic algorithm is a kind of evolutionary algorithm (Evolutionary Algorithms), which finds the optimal solution by imitating the process of inheritance and selection in nature. It is suitable for solving complex problems and has been widely used in research in various fields. However, from the perspective of optimization algorithm and usage requirements, the academic community has never stopped improving and optimizing the algorithm to reduce the time and space complexity of the algorithm.

算法的优化方向Algorithm optimization direction

单层编码方式,即可以在一定程度上降低遗传编码的空间复杂度;同时在处理批量调度问题时,将产品类型作为一段染色体进行整体编码,而产品的各个工序则是以隐性染色体片段在围道矩阵中体现。The single-layer encoding method can reduce the space complexity of genetic encoding to a certain extent; at the same time, when dealing with batch scheduling problems, the product type is encoded as a segment of chromosome as a whole, and each process of the product is based on recessive chromosome segments. reflected in the perimeter matrix.

虽然单层编码方式有一定的优越性,有利于排产进行,但是染色体中存在大量的无效基因位。因为其将染色体长度定义为max(mi)×n(max(mi)为n类工件所包含的最大工序数)。这样就使整个染色体的长度很大程度上决定于每个批次任务中工序数最大的一个工件。染色体过长直接影响了遗传算法在迭代过程中的效率,增加了算法的空间复杂度。Although the single-layer coding method has certain advantages and is conducive to production scheduling, there are a large number of invalid gene bits in the chromosome. Because it defines the chromosome length as max(m i )×n (max(m i ) is the maximum number of processes contained in n types of workpieces). In this way, the length of the entire chromosome is largely determined by the workpiece with the largest number of procedures in each batch of tasks. Chromosome length directly affects the efficiency of the genetic algorithm in the iterative process and increases the space complexity of the algorithm.

单层编码的优化Optimization of single-layer encoding

1)染色体长度优化1) Chromosome length optimization

本发明染色体长度为其中Lg为对应零件的工序数,n为该批次排产的工件数。The chromosome length of the present invention is Among them, L g is the process number of the corresponding part, and n is the number of workpieces scheduled for this batch.

改善前(以3零件,最大工序数为6为例):Before improvement (take 3 parts, the maximum number of processes is 6 as an example):

11 44 66 77 00 00 22 33 44 00 00 00 11 33 55 11 77 33

改善后:Improved:

11 44 66 77 22 33 44 11 33 55 11 77 33

由上可以发现仅三个工件的染色体的长度就已经有显著缩短。从算法优化角度来说,在大量数据时可以明显地降低算法的空间复杂度。将本发明改进后算法与其对比如表6所示。From the above, it can be found that the length of the chromosomes of only three artifacts has been significantly shortened. From the perspective of algorithm optimization, the space complexity of the algorithm can be significantly reduced when there is a large amount of data. The improved algorithm of the present invention is compared with it as shown in Table 6.

表6算法优化对比Table 6 Algorithm optimization comparison

Figure BDA0000447597290000182
Figure BDA0000447597290000182

其中,G代表遗传算法的遗传代数;Z交配池中初始化的染色体个数;mi为第i类工件所包含的工序数;M为设备数量;J为基准设备数(远小于实际设备数)。Among them, G represents the genetic algebra of the genetic algorithm; Z is the number of chromosomes initialized in the mating pool; m i is the number of processes contained in the i-th type of workpiece; M is the number of equipment; J is the number of benchmark equipment (much smaller than the actual number of equipment) .

2)根据实际需求合批2) Batch according to actual needs

多件多品种调度时:假设n类工件共有j件(J=n1+n2+...+ni+...+nn,其中n1、n2、...、ni、...、nn分别表示第i类工件的数量,且i∈n),再设每类工件有pi道工序。When scheduling multiple pieces and varieties: Assume there are j pieces of n types of workpieces (J=n 1 +n 2 +...+n i +...+n n , where n 1 , n 2 ,...,n i ,..., n n respectively represent the number of workpieces of the i type, and i∈n), and each type of workpiece has p i processes.

现有技术中采用的方式如下,如有A、B、C类工件各3件,则对工件加工次序进行随机排序,生成显性染色体。The method adopted in the prior art is as follows, if there are 3 workpieces of each type A, B, and C, the processing sequence of the workpieces is randomly sorted to generate dominant chromosomes.

AA CC AA AA BB CC BB BB CC

再根据工序-机床围道矩阵,生成隐性染色体。其中A11为A类产品的第一道工序,以此类推。如下表所示。Then according to the process-machine tool contour matrix, recessive chromosomes are generated. Among them, A 11 is the first process of A-type products, and so on. As shown in the table below.

A11 A 11 A1m A 1m C11 C 11 C1m C 1m A21 A 21 A2m A 2m Ck1 K Ckm C km

由学习曲线理论可知,重复操作可以增加员工操作的熟练度,缩短单个零件的加工时间,所以本发明中采用同种类零件合批生产编码策略。当同种零件的数量小于100件时,将其合并成一个任务。上述例子可以编码如下A*3代表其各工序加工时间都相应乘以该系数,即该零件个数。According to the learning curve theory, repeated operations can increase the proficiency of employees and shorten the processing time of a single part. Therefore, the present invention adopts the batch production coding strategy for the same type of parts. When the quantity of the same kind of parts is less than 100 pieces, combine them into one task. The above example can be coded as follows: A*3 means that the processing time of each process is multiplied by the coefficient, that is, the number of parts.

A·50A·50 B·11B·11 C·50C·50

最后根据工序-机床围道矩阵,生成隐性染色体。Finally, recessive chromosomes are generated according to the process-machine tool contour matrix.

A11·3A 11 3 A1m·3A 1m 3 B11·3B 11 3 B1m·3B 1m 3 Ck1·3C k1 ·3 Ckm·3C km 3

如果超过100则采用分批策略,因为如果一个工件的数量太多,合成一批次后会影响后续零件的加工。因为每个批次内部的零部件的交货期都是不一样的,所以为了满足其它零件也可以在规定的交货期到达指定库房,根据实际经验取100件作为分批临界点。设A工件150件,B工件211件,C工件50件,则:If it exceeds 100, the batching strategy is adopted, because if the number of a workpiece is too large, the processing of subsequent parts will be affected after a batch is synthesized. Because the delivery date of each batch of internal parts is different, in order to meet other parts can also arrive at the designated warehouse within the specified delivery date, 100 pieces are taken as the critical point of batching according to actual experience. Suppose there are 150 pieces of workpiece A, 211 pieces of workpiece B, and 50 pieces of workpiece C, then:

A·100A·100 C·50C·50 B·100B·100 B·11B·11 A·50A·50 B·100B·100

分批后的单个任务体间是随机排序的。The individual tasks after batching are randomly sorted.

实例仿真Example simulation

实例1仿真:Example 1 simulation:

针对表1的算例,设置遗传算法的参数如下:种群大小为50,交叉率为0.6,变异率为0.8,最大进化带数100,在MATILAB7.0环境下进行仿真,得其GA进化曲线如图3所示,由图3可知此改进的GA算法能够在70代时,从147较快地收敛到134,其对应调度结果甘特图如图4所示。For the calculation example in Table 1, the parameters of the genetic algorithm are set as follows: the population size is 50, the crossover rate is 0.6, the mutation rate is 0.8, and the maximum number of evolutionary bands is 100. The GA evolution curve is obtained by simulation in the MATILAB7.0 environment: As shown in Figure 3, it can be seen from Figure 3 that the improved GA algorithm can quickly converge from 147 to 134 in the 70th generation, and the Gantt chart of the corresponding scheduling result is shown in Figure 4.

实例2仿真与比较:Example 2 simulation and comparison:

为了进一步验证算法正确性,选择实例2来进行仿真,设置2个工艺基准,4个设备编号,8台具体设备,得到最优解为121分钟。由图5的遗传进化曲线可知,此改进的遗传算法能在32代时,很快地从130收敛到121,且其求解的速度明显较快,其对应调度结果甘特图如图6所示。In order to further verify the correctness of the algorithm, choose Example 2 for simulation, set 2 process benchmarks, 4 equipment numbers, and 8 specific equipment, and the optimal solution is 121 minutes. It can be seen from the genetic evolution curve in Figure 5 that the improved genetic algorithm can quickly converge from 130 to 121 in the 32nd generation, and its solution speed is obviously faster, and the Gantt chart of the corresponding scheduling result is shown in Figure 6 .

实例3仿真与比较:Example 3 simulation and comparison:

为更加全面地比较和验证算法效果。在CPU主频2.5G,内存为512MB的计算机上,以VB6.0为开发平台,选取柔性作业调度的Kacem基准问题里面的8×8实例进行求解,设置2个工艺基准,4个设备编号,8台具体设备,计算10次。表7为本发明算法将所得结果与以局部最小化为分配模型的进化算法(Approach by Localization&Controlled Genetic Algorithhm,AL+CGA)、主-从遗传算法、多阶遗传算法、蚁群遗传算法的求解结果对比。In order to compare and verify the algorithm effect more comprehensively. On a computer with a CPU frequency of 2.5G and a memory of 512MB, using VB6.0 as the development platform, the 8×8 instance in the Kacem benchmark problem of flexible job scheduling is selected for solution, and 2 process benchmarks and 4 equipment numbers are set. 8 specific devices, calculated 10 times. Table 7 is the results obtained by the algorithm of the present invention and the evolutionary algorithm (Approach by Localization&Controlled Genetic Algorithhm, AL+CGA), master-slave genetic algorithm, multi-stage genetic algorithm, and ant colony genetic algorithm with local minimization as the distribution model. Compared.

表7Kacem8×8基准问题各方法求解结果对比Table 7 Comparison of the solution results of various methods for the Kacem8×8 benchmark problem

Figure BDA0000447597290000201
Figure BDA0000447597290000201

针对传统多色集合理论改进遗传算法的约束模型和染色体中冗余数据量较大的不足,本发明进一步提出运用多色集合层次结构模型对算法的约束模型进行改进,通过建立设备基准,设置工序约束,设备约束,机床约束,唯一约束的方式,将原来的工序-机床围道矩阵分割为基准与设备型号、设备型号与资产编号的关系矩阵,大大降低了约束模型的冗余数据量,另外通过对染色体长度的合理优化和设置批量基准的合批操作,有效地降低了染色体的时间和空间复杂度,同时也提高了算法模型的动态响应性,最后通过相同算例的仿真的结果比较,证明了PST层次结构的改进GA在求解精度和速度方面都较传统PST改进的GA有了提高,同时也通过选择Kacem8×8基准算例在相同配置计算机上的实验,证明了本发明算法的各种性能均较传统的各种算法有提高,进一步证明了算法在求解柔性作业车间调度问题方面的实用性和优越性。Aiming at the traditional multicolor set theory improving the constraint model of the genetic algorithm and the large amount of redundant data in the chromosome, the present invention further proposes to use the multicolor set hierarchical structure model to improve the constraint model of the algorithm, by establishing the equipment benchmark, setting the process Constraints, equipment constraints, machine tool constraints, and unique constraints, the original process-machine tool perimeter matrix is divided into a relationship matrix between benchmark and equipment model, equipment model and asset number, which greatly reduces the amount of redundant data in the constraint model. Through the reasonable optimization of the length of the chromosome and the batch operation of setting the batch benchmark, the time and space complexity of the chromosome is effectively reduced, and the dynamic responsiveness of the algorithm model is also improved. Finally, through the comparison of the simulation results of the same example, It is proved that the improved GA of PST hierarchical structure has improved compared with the traditional PST improved GA in terms of solution accuracy and speed. At the same time, the experiments of the Kacem8×8 benchmark example on the computer with the same configuration have proved that the algorithm of the present invention These performances are all improved compared with various traditional algorithms, which further proves the practicability and superiority of the algorithm in solving flexible job shop scheduling problems.

以上内容仅为说明本发明的技术思想,不能以此限定本发明的保护范围,凡是按照本发明提出的技术思想,在技术方案基础上所做的任何改动,均落入本发明权利要求书的保护范围之内。The above content is only to illustrate the technical ideas of the present invention, and cannot limit the protection scope of the present invention. Any changes made on the basis of the technical solutions according to the technical ideas proposed in the present invention shall fall within the scope of the claims of the present invention. within the scope of protection.

Claims (6)

1. the improvement GA based on polychromatic sets hierarchical structure solves a method for Flexible Workshop scheduling, it is characterized in that, comprises the following steps:
1) set up the mathematical model of Markov chain;
2) set up the Job-Shop restricted model based on PST hierarchical structure;
3) according to operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, generating process-equipment real number circuit matrix, and then produce hereditary recessive code sequence list, the corresponding lathe coding of row mark, the corresponding recessive gene of rower position; Wherein, the process time that in table, content is operation, the operation numbering of the corresponding workpiece of recessive gene code bit, by searching for corresponding operation-benchmark, benchmark-device numbering, device numbering-asset number circuit Boolean matrix, thus find the lathe coding corresponding to certain working procedure, according to the availability aspect of lathe, select corresponding lathe coding as chromosomal dominant coding again.
2. the improvement GA based on polychromatic sets hierarchical structure according to claim 1 solves the method for Flexible Workshop scheduling, it is characterized in that: in described step 1), the concrete grammar of setting up the mathematical model of Markov chain is:
FJSP can be described to, and supposes that M is the quantity of process equipment, and N is workpiece to be processed quantity, and P is process number, the set that I is all devices; I egrepresent the available devices set of the g procedure of workpiece e, j eprocess number for workpiece e; X is the process sequence of all workpiece, S egkthe start time that the g procedure of expression workpiece e is processed on equipment k; E egkfor the g procedure of the workpiece e process finishing time on equipment k; T egkfor the g procedure of workpiece e lasting process time on equipment k, and k ∈ I egthere is E egk=S egk+ T egk; E pthe completion date that represents finishing operation; MS represents the last completion date of all workpiece;
When the j procedure of workpiece i and the g procedure of workpiece e are carried out on same equipment, if operation j adds man-hour prior to operation g, Q ijeg=1, otherwise Q ijeg=0; If the g procedure of workpiece e is processed on lathe k, X egk=1, otherwise X egk=0;
If certain FJSP has the possible processing sequence of S kind, require total the shortest Machining Sequencing of activity duration, first ask for each processing sequence x (x ∈ 1 ..., S}) the corresponding activity duration; Obviously, in order x, the i.e. last completion date of all workpiece of the completion date of last manufacturing procedure, has
MS=E p (1)
Objective function F (x) is
F(x)=min(MS x)=min((E p) x) (2)
X=1,…,S
S.T.S egk-E e(g-1)n≥0
e=1,…,N;g=1,…,J e;X egk=1,X e(g-1)n=1 (3)
S egk-E igk≥0
e=1,…,N;g=1,…,J e;X ijk=1,X egk=1,Q ijeg=1 (4)。
3. the improvement GA based on polychromatic sets hierarchical structure according to claim 1 solves the method for Flexible Workshop scheduling, it is characterized in that: described step 2), the restriction relation of Job-Shop restricted model is:
First equipment benchmark is set, several unit types that each equipment benchmark comprises process similarity, each unit type comprises again the concrete equipment of several this kind of models, every concrete equipment is corresponding with corresponding asset number again, and operation finally will complete processing on concrete equipment, therefore just can be by the restriction relation of operation and benchmark, the restriction relation of equipment benchmark and unit type, the restriction relation of unit type and asset number, indirectly set up the restriction relation of operation and concrete equipment, thereby realize huge operation lathe circuit matrix is divided into little relational matrix, to reduce scale and the data volume of matrix, improve the speed that solves of algorithm.
4. the improvement GA based on polychromatic sets hierarchical structure according to claim 1 solves the method for Flexible Workshop scheduling, it is characterized in that: in described step 3), according to the availability aspect of lathe, select corresponding lathe coding to be specially as chromosomal dominant coding:
3.1) set up the restricted model based on hierarchical structure circuit Boolean matrix:
Use the hierarchical structure circuit Boolean matrix of benchmark and unit type, unit type and asset number, auto-correlation, process equipment, process equipment real number as restricted model, produce hereditary recessive code sequence list, the operation of GA is all carried out in the scope of restricted model;
3.2) chromosomal coding:
3.3) chromosomal decoding:
According to the corresponding information of chromosome the inside, search technique-equipment real number circuit matrix, determines parameter process time of all process steps on each lathe;
3.4) select operation:
The corresponding chromosome of individuality that fitness value in previous generation population is best is directly selected to enter population of future generation;
3.5) interlace operation:
Two parent chromosomes of random selection, two random number 0<a<b<N, wherein, N is chromogene number, finds out corresponding a on two parent chromosomes, the fragment between b exchanges each other;
3.6) variation.
5. the improvement GA based on polychromatic sets hierarchical structure according to claim 4 solves the method for Flexible Workshop scheduling, it is characterized in that, the concrete grammar of described chromosome coding is:
First determine effective process number sum that chromosome length is each workpiece:
(a) when being the production model of the many kinds of single-piece:
Have each of n class workpiece, GA chromosome length is
Figure FDA0000447597280000041
l wherein gprocess number for corresponding g part;
(b) when being the pattern of variety production more than many:
There is n class workpiece J part J=n altogether 1+ n 2+ ...+n i+ ...+n n, n wherein 1, n 2..., n i..., n nthe quantity i ∈ n that represents respectively i class workpiece, every class workpiece has p iprocedure, needs first the process sequence of workpiece to be encoded, and workpiece process sequence is carried out randomly ordered, generates dominant chromosome;
When the quantity of part of the same race is less than 100, be merged into a task; Finally, according to benchmark and unit type, unit type and asset number circuit matrix, generate recessive chromosome;
When quantity employing over 100 of part of the same race strategy in batches, between the individual task body after in batches, be randomly ordered.
6. the improvement GA based on polychromatic sets hierarchical structure according to claim 4 solves the method for Flexible Workshop scheduling, it is characterized in that, the concrete grammar of described variation is:
3.6.1) set aberration rate, determine the gene position that needs variation;
3.6.2) search benchmark and unit type, unit type and asset number circuit matrix, find this gene position can replace the coding of lathe, produces new chromosome;
3.6.3) calculate new chromosomal objective function, the target function value that new and old chromosome is corresponding, and then select preferably to enter the next generation.
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CN106933200A (en) * 2015-12-31 2017-07-07 中国科学院沈阳计算技术研究所有限公司 The control method of the solution Flexible Job-shop Scheduling Problems based on genetic algorithm
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CN105550825A (en) * 2016-01-15 2016-05-04 中南民族大学 Flexible factory work scheduling method based on MapReduce parallelization in cloud computing environment
CN106875094A (en) * 2017-01-11 2017-06-20 陕西科技大学 A kind of multiple target Job-Shop method based on polychromatic sets genetic algorithm
CN108053152A (en) * 2018-01-30 2018-05-18 陕西科技大学 The method that improved adaptive GA-IAGA based on polychromatic sets solves dynamic job shop scheduling
CN108364126A (en) * 2018-01-30 2018-08-03 陕西科技大学 The method that improved adaptive GA-IAGA based on polychromatic sets solves static Job-Shop
CN109034540A (en) * 2018-06-29 2018-12-18 长安大学 A kind of lathe serial arrangement dynamic prediction method based in article process stream
CN109034540B (en) * 2018-06-29 2021-09-07 长安大学 A Dynamic Prediction Method for Machine Tool Sequence Arrangement Based on WIP Process Flow
CN110796355A (en) * 2019-10-22 2020-02-14 江苏金陵智造研究院有限公司 Flexible job shop scheduling method based on dynamic decoding mechanism
CN111583055A (en) * 2020-05-09 2020-08-25 电子科技大学 A Product Grouping Method Based on Genetic Algorithm under Multiple Process Paths
CN112631214A (en) * 2020-11-27 2021-04-09 西南交通大学 Flexible job shop batch scheduling method based on improved invasive weed optimization algorithm
CN112631214B (en) * 2020-11-27 2022-03-18 西南交通大学 Batch scheduling method for flexible job shop based on improved invasive weed optimization algorithm
CN115034143A (en) * 2022-07-04 2022-09-09 广东工业大学 Multi-resource cooperative intelligent workshop equipment configuration optimization method
CN115034143B (en) * 2022-07-04 2025-05-06 广东工业大学 A multi-resource collaborative intelligent workshop equipment configuration optimization method

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