Flexible job shop scheduling method considering grouping characteristics

Abstract

The invention relates to a flexible job shop scheduling method considering grouping characteristics, belongs to the technical field of flexible job shop production scheduling, solves the problem of poor comparison effect between a scheduling scheme and an actual processing situation in the prior art, and comprises the following steps: S1, determining a job switching type and executing grouping classification to obtain a grouping classification result; s2, determining decision variables and basic parameters considering grouping characteristics according to the obtained job switching types and grouping classification results; s3, constructing an objective function considering grouping characteristics; s4, establishing a flexible job-shop scheduling problem constraint condition considering the grouping characteristics, and obtaining a flexible job-shop scheduling mathematical model considering the grouping characteristics; s5, solving the flexible job shop scheduling mathematical model considering the grouping characteristics by using an improved genetic algorithm to obtain a scheduling scheme with the optimal fitness; and S6, outputting the obtained scheduling scheme with the optimal fitness as an optimal scheme.

Description

Technical Field

[0001] The present invention relates to the technical field of flexible job shop production scheduling, and in particular to a flexible job shop scheduling method considering grouping characteristics. Background Art

[0002] The high-variety, small-batch production characteristics lead to frequent job switching during the production process, significantly reducing machine utilization and production efficiency. Job switching refers to all preparatory activities from the end of one job on a machine to the start of processing the next job, mainly including material preparation, tool replacement, fixture installation and debugging, etc. The time for job switching activities is called setup time. Survey data shows that in the production process of high-variety, small-batch manufacturing companies, mechanical processing time accounts for approximately 54% of the production cycle, while setup time such as changing workpieces and fixtures accounts for 40% of the production cycle. Because workpieces have similar structural, material, and process characteristics, workpiece groups are formed. Taking full advantage of these objectively existing similar characteristics, classifying them into groups and formulating machine processing sequences by group can achieve better completion time and product quality. This group sequence effect is called group characteristic.

[0003] Traditional scheduling methods that consider grouping typically only consider the impact of job switching on setup time, assuming that job switching between different groups involves setup time, but not within the same group. This imposes extremely high requirements on the similarity of workpiece groups, resulting in poor comparison between group scheduling schemes and actual processing conditions. In actual manufacturing, workpieces are processed in groups, and different processing sequences do not produce identical outputs in terms of time and quality.

[0004] In the actual manufacturing process, different job sequence relationships on the same machine will result in different setup times and product quality. Job switching activities include activities such as changing tools, fixtures, installation and debugging. The time generated by job switching activities is called setup time. Among them, installation activities include installing the workpiece and installing the cutting tool, etc., and debugging activities include adjusting the size of the tool, positioning the tool and the workpiece, adjusting the cutting speed and feed rate, and aligning the machining diameter. Complex parts often need to be processed through multiple steps and are therefore affected by manufacturing errors in different steps. In each step, because the sources of errors are different (such as machine tools, fixtures, and tools), and the errors are accumulated, transmitted, and evolved between different steps with machining characteristics as the carrier, various deviations are ultimately reflected in the quality problems of the finished parts. Due to differences in the machining characteristics of the workpiece, such as differences in workpiece size, machining accuracy, machining technology, etc., the job switching time and quality are different.

[0005] Therefore, there is a need in the art for an improved flexible job shop scheduling method that can take into account the grouping characteristics of workpieces during processing and production, and provide a scheduling solution that is highly consistent with actual processing conditions. Summary of the Invention

[0006] In view of the above problems, the present invention provides a flexible job shop scheduling method taking group characteristics into consideration, which solves the problem in the prior art that the scheduling scheme has a poor comparison effect with the actual processing situation.

[0007] The present invention provides a flexible job shop scheduling method considering group characteristics, comprising the following steps:

[0008] Step S1: For a flexible job shop production scenario with group characteristics, determine the job switching type of the job shop scheduling problem considering the group characteristics, perform group classification, and obtain the group classification result;

[0009] Step S2: Determine the decision variables and basic parameters considering the group characteristics according to the obtained job switching type and group classification results;

[0010] Step S3: constructing an objective function that takes group characteristics into consideration, including establishing a product output value term and an efficiency loss term in the objective function that takes group characteristics into consideration;

[0011] Step S4: Based on the objective function considering the grouping characteristics, establishing the constraint conditions of the flexible job shop scheduling problem considering the grouping characteristics, and obtaining a mathematical model of the flexible job shop scheduling problem considering the grouping characteristics;

[0012] Step S5: using an improved genetic algorithm to solve the flexible job shop scheduling mathematical model that takes grouping characteristics into consideration, and obtaining a scheduling solution with optimal fitness;

[0013] In step S6, the obtained scheduling plan with the best fitness is output as the optimal plan, and the job shop performs scheduling according to the optimal plan.

[0014] Optionally, step S1 specifically includes the following steps:

[0015] Step S1.1, in a flexible job shop production scenario with group characteristics, determining the job switching types of the job shop scheduling problem considering the group characteristics, the job switching types including workpiece switching, intra-group switching, and inter-group switching;

[0016] Step S1.2, using fuzzy cluster analysis method to perform group classification of job shop scheduling problem considering group characteristics, including constructing processing feature matrix, constructing workpiece similarity matrix, calculating fuzzy equivalence matrix, and clustering grouping to obtain group classification results.

[0017] Optionally, step S1.2 specifically includes the following steps:

[0018] Step S1.2.1, construct the workpiece processing feature matrix, provide n workpieces to be grouped, and the workpiece set is O = {o1, o2, ... i ,…,o n}, set m indicators to represent the processing features of the workpiece, and the processing feature set is r = {r1, r2, ... r k ,…,r m}, where k represents the index of the processing feature and k = 1, 2, ..., m, where any processing feature r k Contains d k There are h processing sub-features:

[0019] h=d1+d2+…+d m ,

[0020] The machining feature attributes of the i-th workpiece are expressed as:

[0021]

[0022] Among them, R iz The machining feature attribute indicating whether the i-th workpiece contains the z-th machining sub-feature is a 0 / 1 variable. If the workpiece i contains the z-th machining sub-feature, the value is 1; otherwise, the value is 0. z represents the index of the machining sub-feature and z = 1, 2, …, h.

[0023] Get the total processing feature matrix R of all n workpieces = [R1R2…R n ];

[0024] Step S1.2.2, constructing the workpiece similarity matrix includes calculating the similarity coefficient between workpieces using the maximum-minimum method, and the calculation formula is as follows:

[0025]

[0026] Among them, x ii′ Represents the similarity coefficient between workpiece i and workpiece i′, R iz Indicates whether workpiece i contains the machining feature attribute of the machining sub-feature z, R i′z The machining feature attribute indicating whether workpiece i′ contains the zth machining sub-feature;

[0027] The similarity matrix between the i-th workpiece and all workpieces is: X i =[X i1 ,X i2 ,…X ii′ ,…X in ];

[0028] Based on the similarity coefficients between all workpieces, the similarity matrix of all workpieces is obtained as X = [X1X2…X i …X n ];

[0029] Step S1.2.3, based on the similarity matrix of all workpieces obtained, the fuzzy equivalence matrix is constructed using the transitive closure method;

[0030] Step S1.2.4, performing clustering grouping on the obtained fuzzy equivalence matrix to obtain a clustering grouping result, which is the group classification result.

[0031] Optionally, step S1.2.3 specifically includes: starting from the similarity matrix X of all workpieces, sequentially using the square method to obtain X 2 ,X 4 ,…X R , until the index R satisfies X R =X 2R , we get the fuzzy equivalent matrix T = X R .

[0032] Optionally, step S1.2.4 specifically includes:

[0033] The obtained fuzzy equivalent matrix T is intercepted using the set threshold λ:

[0034]

[0035] Among them, λ is a given threshold, T λ is the intercept matrix of λ under the threshold λ, t ii′ represents the corresponding element in the fuzzy equivalence matrix T, t(λ) ii′ T represents the fuzzy equivalent matrix T obtained by truncation of λ λ The corresponding elements of the intercept matrix;

[0036] Based on the truncation matrix T obtained by truncation of the fuzzy equivalent matrix λ , obtain the grouping situation under the threshold as the clustering grouping result.

[0037] Optionally, in step S2: the basic parameters considering the grouping characteristics include: the number of machines, the number of workpieces, the workpiece grouping situation, the number of processes for each workpiece, the optional processing machines for each process of each workpiece, the operation time of each process of each workpiece on different machines and the setting time coefficient, the job switching coefficient of different job switching of each workpiece, the processing qualification rate of different job switching of each workpiece, the value and efficiency loss penalty coefficient of each workpiece, wherein the workpiece grouping situation is the group classification result obtained in step S1; the decision variables considering the grouping characteristics include: the processing machine selected for each process of each workpiece, and the sequence relationship of each process on each machine.

[0038] Optionally, step S3 specifically includes the following steps:

[0039] Step S3.1: Establish the product output value term in the objective function that takes into account the grouping characteristics. The product output value term is calculated by the circulation qualification rate. In this case, each workpiece is a product after the production is completed. Each product corresponds to a corresponding workpiece in the production process, and the total number of products is the same as the total number of workpieces n.

[0040] Calculate the circulation qualification rate of products:

[0041]

[0042] Among them, RTY i Indicates the circulation qualification rate of product i, FYT ij It represents the first pass rate of product i process j, N pi represents the total number of processes for product i, j represents the process number and j∈[1,2,…,N pi ];

[0043] Calculate product output value based on product circulation qualification rate:

[0044]

[0045] Among them, PV represents the product output value, V i Represents the value of product i, RTY i represents the circulation qualification rate of product i;

[0046] Step S3.2, establish the efficiency loss term in the objective function considering group characteristics:

[0047] Ts ij =st iji′j′k ×se×T ij

[0048] Tc ij =Ts ij +Tp ij

[0049] Among them, Ts ij represents the setup time of process j for workpiece i, se is the setup time coefficient and represents the ratio of setup time to operation time, T ij Tc is the expected operation time of process j for workpiece i. ij represents the actual operation time of process j of workpiece i, Tp ij represents the processing time of process j of workpiece i, st iji′j′kIt is the job change coefficient, representing the degree of time savings in setup times generated by different job change types. That is, when operating on process j of workpiece i and then process j' of workpiece i' on machine k, the actual setup time of process j of workpiece i should be the proportionality coefficient of the expected setup time;

[0050] Obtain the efficiency loss term in the objective function considering group characteristics:

[0051] RL = (T max - T0) × R(T max )

[0052] Where, RL represents the efficiency loss, T max represents the makespan, T0 represents the specified delivery time, and R(t) represents the delivery delay penalty term. If the manufacturing task is completed within the specified delivery time, when T max < T0, the delivery delay penalty term is 0;

[0053] Step S3.3, construct the objective function considering group characteristics. The objective function considering group characteristics includes the product output value term and the efficiency loss term:

[0054] Max.Obj = PV - RL

[0055] Where, Obj represents the overall benefit of the manufacturing process.

[0056] Optionally, the constraint conditions for the flexible job shop scheduling problem considering group characteristics in step S4 include: all machines, workpieces, and raw materials are available simultaneously at time zero; each machine can only process one workpiece at a time; there is no priority difference between workpieces, and once a workpiece starts processing, it will not be interrupted; each workpiece has a specified process sequence; the setup times of processes are separate; the production environment is stable, and machine failures and workpiece insertion orders are not considered.

[0057] Optionally, step S5 specifically includes the following steps:

[0058] Step S5.1, set the parameters of the improved genetic algorithm, including: setting the population size, selection rate, crossover rate, mutation rate, and the maximum number of iterations;

[0059] Step S5.2, based on the gene encoding of the improved genetic algorithm with multi-type working hour perturbations, establish the encoding rule using the complete encoding method. For the operation code OS for process arrangement, the machine code MS for machine allocation, and the group class code GS for workpiece grouping, each chromosome consists of three parts: OS, MS, and GS, and the encoding length is the number of processes;

[0060] Step S5.3: Initialize the population using random generation according to the established coding rules. The population consists of multiple chromosomes, each of which contains multiple genes. Each gene includes the workpiece processing step, processing machine, and group number. Each chromosome represents a scheduling solution for the flexible job shop.

[0061] Step S5.4: Based on the genetic decoding method of the improved genetic algorithm for multi-type work-hour disturbances, an insert-type greedy decoding method that takes grouping characteristics into consideration is used to decode the initial population to obtain a preliminary scheduling solution.

[0062] Step S5.5, improving the fitness calculation of the genetic algorithm, specifically including substituting the decoded preliminary scheduling plan into and calculating the objective function established in step S3 to obtain the objective function value, which is the fitness of the individual;

[0063] Step S5.6, determine whether the termination condition is met, that is, determine whether the current number of iterations reaches the maximum number of iterations. If so, the current scheduling scheme is the scheduling scheme with the best fitness, and execute step S6; otherwise, execute step S5.7;

[0064] Step S5.7, for the population in the current scheduling plan, the improved genetic algorithm is selected by using a roulette wheel selection method to obtain a selected population;

[0065] Step S5.8, performing crossover of the improved genetic algorithm on the selected population, including process crossover and machine crossover, to obtain a crossover population;

[0066] Step S5.9, perform mutation of the improved genetic algorithm on the population after crossover, including process mutation and machine mutation, to obtain the population after crossover, obtain new individual codes, and obtain an improved scheduling plan based on the new individual codes, and return to step S5.5.

[0067] Compared with existing technologies, the flexible job shop scheduling method proposed in this invention, which considers grouping characteristics, has at least the following beneficial effects: It considers and utilizes the grouping characteristics of workpieces in a manufacturing system. By varying different sequence relationships in flexible job shop scheduling, a larger optimization space is obtained, effectively expanding the optimization space of the scheduling problem. The granularity of grouping is subdivided, and job switching types are divided into three categories: workpiece switching, intra-group switching, and inter-group switching. A specific method for clustering groups based on similar characteristics is proposed, which helps to set grouping-related parameters in line with the actual needs of the manufacturing process and can more effectively simulate actual processing conditions. An optimization objective for the flexible job shop scheduling problem that considers grouping characteristics is established. This optimization objective represents the total revenue of the manufacturing enterprise and can guide the solution algorithm to search for the optimal scheduling solution that simultaneously considers quality and time. Furthermore, the optimization objective has a simple structure, and its coefficients do not need to be determined subjectively, making it less susceptible to subjective factors. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. By referring to the drawings, the features and advantages of the present invention can be more clearly understood. The drawings are schematic and should not be understood as limiting the present invention in any way. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0069] Figure 1 A flowchart of a flexible job shop scheduling method considering group characteristics is shown according to an embodiment of the present invention.

[0070] Figure 2 A flowchart of solving a flexible job shop scheduling method considering group characteristics using an improved genetic algorithm according to an embodiment of the present invention is shown.

[0071] Figure 3 A schematic diagram of different job switching types in an embodiment of a flexible job shop scheduling method considering group characteristics provided according to an embodiment of the present invention is shown.

[0072] Figure 4a A schematic diagram of setting time in an embodiment of applying a flexible job shop scheduling method considering group characteristics provided according to an embodiment of the present invention is shown.

[0073] Figure 4b A schematic diagram of setting time in an embodiment of applying a flexible job shop scheduling method considering group characteristics provided according to an embodiment of the present invention is shown.

[0074] Figure 4cA schematic diagram of setting time in an embodiment of applying a flexible job shop scheduling method considering group characteristics provided according to an embodiment of the present invention is shown.

[0075] Figure 5 A schematic diagram illustrating coding in an embodiment of applying a flexible job shop scheduling method considering group characteristics provided according to an embodiment of the present invention is shown.

[0076] Figure 6 A schematic diagram illustrating decoding in an embodiment of applying a flexible job shop scheduling method considering group characteristics provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0077] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features therein can be combined with each other without conflict.

[0078] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0079] A flexible job shop scheduling method considering group characteristics according to an embodiment of the present invention is described in detail below with reference to the accompanying drawings.

[0080] like Figure 1 As shown, according to an embodiment of the present invention, a flexible job shop scheduling method considering group characteristics is provided, which includes the following steps.

[0081] Step S1: For a flexible job shop production scenario with group characteristics, determine the job switching type of the job shop scheduling problem considering the group characteristics, and perform group classification to obtain the group classification result. Step S1 specifically includes the following steps.

[0082] Step S1.1, in a flexible job shop production scenario with grouping characteristics, determine the job switching type of the job shop scheduling problem considering the grouping characteristics. Among them, the job switching types of the flexible job shop scheduling problem considering the grouping characteristics may include: workpiece switching, intra-group switching and inter-group switching. In a flexible job shop production scenario with grouping characteristics, changing the processing sequence of the machines in the flexible job shop can obtain different completion times and product qualities, so different processing sequences on the machines are classified from the perspective of job switching. For example, Figure 3As shown in the schematic example, the workpiece switching is that the two previous and next operation tasks processed on the same machine belong to two processes of the same workpiece, the intra-group switching is that the two previous and next operation tasks processed on the same machine belong to two processes of different workpieces in the same group, and the inter-group switching is that the two previous and next operation tasks processed on the same machine belong to two processes of different workpieces in different groups.

[0083] Step S1.2 performs group classification for the flexible job shop scheduling problem considering group characteristics, obtaining group classification results. The group classification for the flexible job shop scheduling problem considering group characteristics utilizes a fuzzy cluster analysis method, including constructing a processing feature matrix, constructing a workpiece similarity matrix, calculating a fuzzy equivalence matrix, and performing clustering. Step S1.2 specifically includes the following steps.

[0084] Step S1.2.1, construct the workpiece processing feature matrix. Specifically, assume that there are n workpieces to be grouped, and the workpiece set is O = {o1, o2, ... i ,…,o n}, there are m indicators representing the processing features of the workpiece, and the processing feature set is r={r1,r2,…r k ,…,r m}, where k represents the index of the processing feature and k = 1, 2, ..., m, and any processing feature r k Contains d k There are h processing sub-features:

[0085] h=d1+d2+…+d m ,

[0086] Among them, the processing feature r1 has d1 processing sub-features, the processing feature r2 has d2 processing sub-features, and so on.

[0087] The machining feature attributes of the i-th workpiece are expressed as:

[0088]

[0089] Among them, R iz The machining feature attribute indicating whether the i-th workpiece contains the z-th machining sub-feature is a 0 / 1 variable. If the workpiece i contains the z-th machining sub-feature, the value is 1, otherwise it is 0. z represents the index of the machining sub-feature and is selected from the set of h machining sub-features of the workpiece, where z = 1, 2, …, h.

[0090] The machining feature set r represents all machining features of workpieces that require attention, and may include part geometry, material, machine, tooling, fixture method, machining accuracy, employee knowledge level, etc. The machining sub-feature represents a more specific feature type included in a machining feature type.

[0091] The schematic description is as follows. For example, let the processing feature r k is the geometric feature of the workpiece, and the geometric features of the workpiece include three types, r k Including 3 kinds of processing sub-features {part geometric feature 1, part geometric feature 2, part geometric feature 3}, if the i-th workpiece includes part geometric feature 1, but does not include part geometric feature 2 and part geometric feature 3, then

[0092] Determine the sub-features of the machining feature and obtain the total machining feature matrix R = [R1R2…R n ].

[0093] Step S1.2.2, constructing the workpiece similarity matrix includes calculating the similarity coefficient between workpieces using the maximum-minimum method, and the calculation formula is as follows:

[0094]

[0095] Among them, x ii′ Represents the similarity coefficient between workpiece i and workpiece i′, R iz Indicates whether workpiece i contains the machining feature attribute of the machining sub-feature z, R i′z A machining feature attribute indicating whether workpiece i′ contains the zth machining sub-feature.

[0096] Based on the similarity coefficients between all workpieces, the similarity matrix of all workpieces is obtained as X = [X1, X2, ... X i ,…X n ]. The similarity matrix between the i-th workpiece and all workpieces is X i =[X i1 ,X i2 ,…X ii′ ,…X in ]. The similarity matrix of a workpiece includes the similarity coefficient between the workpiece and itself, and the coefficient is 1.

[0097] Step S1.2.3, based on the similarity matrix of all workpieces, construct a fuzzy equivalence matrix. The fuzzy equivalence matrix is obtained by calculating the similarity matrix X of all workpieces using the transitive closure method. Specifically, starting from the similarity matrix X, the square method is used to obtain X 2 ,X 4 ,…X R , until the index R satisfies X R =X 2R When , we get the fuzzy equivalent matrix T = X R .

[0098] Step S1.2.4, clustering is performed on the obtained fuzzy equivalence matrix to obtain a clustering result, which is the group classification result. The clustering includes intercepting the obtained fuzzy equivalence matrix T using a set threshold λ:

[0099]

[0100]

[0101] Among them, λ is a given threshold, T λ is the intercept matrix of λ under the threshold λ, t ii′ represents the corresponding element in the fuzzy equivalence matrix T, t(λ) ii′ T represents the fuzzy equivalent matrix T obtained by truncation of λ λ The corresponding elements of the intercept matrix.

[0102] Based on the intercept matrix obtained by intercepting the fuzzy equivalence matrix, the grouping situation under the threshold is obtained as the clustering grouping result. Among them, the workpieces with the same arrangement of the intercept matrix are grouped into one group.

[0103] Step S2: Determine the decision variables and basic parameters that take group characteristics into consideration based on the obtained job switching type and group classification results.

[0104] The basic parameters considered in step S2 for grouping characteristics may include: the number of machines, the number of workpieces, the workpiece grouping, the number of processes for each workpiece, the available processing machines for each process of each workpiece, the operating time and setup time coefficient for each process of each workpiece on different machines, the job switching coefficient for switching between different processes of each workpiece, the processing pass rate for switching between different processes of each workpiece, the value of each workpiece, and the efficiency loss penalty coefficient. The workpiece grouping is the grouping classification result obtained in step S1. The remaining parameters are basic scheduling parameters and can be determined based on the actual manufacturing process.

[0105] The decision variables considered in the group characteristics in step S2 may include: the processing machine selected for each process of each workpiece, and the sequence relationship of each process on each machine.

[0106] Step S3: constructing an objective function that takes group characteristics into consideration, including establishing a product output value item and an efficiency loss item in the objective function that takes group characteristics into consideration.

[0107] Step S3.1 establishes a product output value term within the objective function that considers grouping characteristics. This product output value term is calculated based on the circulation qualification rate. Each workpiece is produced as a product, and each product corresponds to a workpiece in the production process. In other words, there is a one-to-one correspondence between each product and each workpiece. The i-th product corresponds to the i-th workpiece, and the total number of products, n, is the same as the total number of workpieces, n.

[0108] First, calculate the product's circulation pass rate. The circulation pass rate (RYT) is an important indicator of product quality in a multi-step manufacturing process. It is calculated by multiplying the first pass rate (FYT) of each process of the completed workpiece (i.e., product) by the product. The calculation formula is as follows:

[0109]

[0110] Among them, RTY i Indicates the circulation qualification rate of product i, FYT ij It represents the first pass rate of product i process j, N pi represents the total number of processes of product i, j represents the number of the process of product i and j∈[1,2,…,N pi ].

[0111] Next, the product output value item is calculated based on the product circulation qualification rate. The product output value in the objective function considering the group characteristics refers to the total value of the products produced in a certain period of time. The expected product output value can be calculated by the following formula:

[0112]

[0113] Among them, PV represents the product output value, i represents the product serial number, n represents the total number of products, V i Represents the value of product i, RTY i It represents the circulation qualification rate of product i.

[0114] Step S3.2, establish the efficiency loss term in the objective function considering the group characteristics, and the efficiency loss term is calculated by the maximum completion time.

[0115] First, calculate the maximum completion time. The maximum completion time refers to the time required to complete all workpieces on a given machine. Specifically, for any process of any workpiece, its operation time includes two parts: setup time and processing time, such as Figure 4a As shown, the calculation formula is as follows:

[0116] Ts ij =st iji′j′k ×se×T ij

[0117] Tc ij =Ts ij +Tp ij

[0118] Among them, Tc ij represents the actual operation time of process j of workpiece i, T ij Ts represents the expected operation time of process j for workpiece i. ijDenote the setup time of operation j of workpiece i as \(T_p\). ij Denote the processing time of operation j of workpiece i as \(T_{se}\), where \(se\) is the setup time coefficient, representing the proportion of setup time in the operation time, and \(st\). iji′j′k Denote the job switching coefficient as \(k\), which represents the degree of savings in setup time generated by different job switching types. That is, when performing operations of operation \(j'\) of workpiece \(i'\) and operation j of workpiece i successively on machine k, the actual setup time of operation j of workpiece i should be the proportionality coefficient of the expected setup time. And the setup time of the operation is separable, that is, when the previous operation has not been completed, the job switching activity of the next operation of the workpiece can be performed in advance on another idle machine. For example Figure 4b , Figure 4c as shown in the schematic example of

[0119] Next, calculate the efficiency loss term in the objective function considering the group characteristics. This efficiency loss term represents the default loss of delivery delay caused by the concentration of products processed on one or several machines, resulting in long-term idle of some machines. Its calculation formula is as follows:

[0120] \(RL=(T max -T_0)\times R(T max )

[0121] where \(RL\) represents the efficiency loss, \(T max represents the makespan, \(T_0\) represents the specified delivery time, and \(R(t)\) represents the delivery delay penalty term, which can be fitted according to the requirements of the actual production order. If the manufacturing task is completed within the specified delivery time, that is, when \(T max <T_0\), the delivery delay penalty term is 0.

[0122] Specifically, the concave function \(R(t)=a\times t b represents the delivery delay penalty function. Where \(a\) and \(b\) are coefficients, which can be fitted according to the requirements of the actual production order, and \(R(T max ) = a\times T max b , representing the delay penalty coefficient brought by the makespan, and it is set that if the manufacturing task is completed within the specified delivery time, that is, when \(T max <T_0\), the delivery delay penalty term \(R(\cdot)\) is 0.

[0123] Step S3.3, construct the objective function considering the group characteristics. The objective function considering the group characteristics includes two items: product output value and efficiency loss, which respectively reflect the considerations of quality and time, and the difference between the two is used to represent the overall benefit of the manufacturing process. The expression of the objective function considering the group characteristics is as follows:

[0124] Max.Obj = PV - RL.

[0125] Where Obj represents the overall benefit of the manufacturing process.

[0126] Step S4: Based on the objective function considering grouping characteristics, constraints of the flexible job shop scheduling problem considering grouping characteristics are established to obtain a mathematical model of the flexible job shop scheduling problem considering grouping characteristics.

[0127] The constraints of the flexible job shop scheduling problem considering group characteristics described in step S4 may include: all machines, workpieces and raw materials are available at the same time at time zero; each machine can only process one workpiece at a time; there is no priority difference between workpieces, and once a workpiece starts processing, it will not be interrupted; each workpiece has a specified process sequence, and when one process of the workpiece is completed, it moves to the next processing machine; the setup time of the process is separable, that is, when the previous process has not been completed, the job switching activity of the next process of the workpiece can be executed in advance on another idle machine; the production environment is stable, and machine failures, workpiece insertion orders, etc. are not considered.

[0128] Step S5: Use the improved genetic algorithm to solve the flexible job shop scheduling mathematical model that takes into account the group characteristics, and obtain the scheduling solution with the best fitness. The improved genetic algorithm solution includes parameter setting, gene encoding, initialization, selection, crossover, mutation, decoding and fitness calculation. Figure 2 As shown, step S5 specifically includes the following steps.

[0129] Step S5.1, setting the parameters of the improved genetic algorithm, including: setting the population size, selection rate, crossover rate, mutation rate and maximum number of iterations.

[0130] Step S5.2, based on the genetic coding of the improved genetic algorithm with multi-type working time disturbance, the coding rules are established using the complete coding method, with the process code OS for process arrangement, the machine code MS for machine allocation, and the group code GS for workpiece grouping. Each chromosome consists of three parts: OS, MS, and GS. The coding length is the number of processes, as shown in the following example. Figure 5 The schematic example shown is shown in Figure 1. The specific number i in the operation code OS represents the i-th workpiece, and the number j of times this number appears represents the j-th operation of the i-th workpiece. The machine code MS represents the processing machine in the machine set selected for the corresponding operation, and the group code GS represents the group number of the current workpiece.

[0131] In step S5.3, according to the established coding rules, ... is initialized in a random generation manner to create an initial population. The initial population includes multiple chromosomes, each chromosome includes multiple genes, each gene includes a workpiece processing step, a processing machine, and a group classification number, and each chromosome represents a scheduling plan for the flexible job shop.

[0132] Step S5.4, based on the genetic decoding method of the improved genetic algorithm with multi-type working time disturbance, on the basis of traditional greedy decoding, uses the inserted greedy decoding method considering the grouping characteristics to decode the initial population and obtain a preliminary scheduling plan.

[0133] Specifically, such as Figure 6 As shown in the schematic example, during decoding, the process code and machine code are read from left to right in sequence. When the process sequence constraints are met, the process is inserted into the optimal feasible processing time corresponding to the machine, and the setup time is calculated based on the group code and the previous process of the machine. The setup time is inserted into the appropriate processing time of the machine to obtain the scheduling result.

[0134] Step S5.5, improving the fitness calculation of the genetic algorithm, includes substituting the decoded preliminary scheduling plan into and calculating the objective function established in step S3 to obtain the objective function value, which is the individual fitness.

[0135] Step S5.6, determine whether the termination condition is met, that is, determine whether the current number of iterations reaches the maximum number of iterations. If so, the current scheduling plan is the scheduling plan with the best fitness, and execute step S6; otherwise, execute step S5.7.

[0136] In step S5.7, the improved genetic algorithm is used to select the population in the current scheduling plan using a roulette wheel selection method to obtain a selected population. This roulette wheel selection method selects individuals based on their fitness ratio, with individuals with higher fitness being more likely to be selected. During the first round of the improved genetic algorithm selection, the current scheduling plan is the preliminary scheduling plan obtained in step S5.4.

[0137] Step S5.8, performing crossover of the improved genetic algorithm on the selected population, including process crossover and machine crossover, to obtain a population after crossover.

[0138] Specifically, the specific implementation of process crossover is as follows: select two mother individuals, denoted as Mother 1 and Mother 2. Two crossover positions are randomly generated. Mother 1 transfers the genes outside the two crossover positions to Offspring 1 (the positions of these genes in Offspring 1 are the same as in Mother 1, both outside the two crossover positions in Offspring 1). Then, Mother 2 searches for the missing processes in Offspring 1 and transfers them to Offspring 1 in the same order as in Mother 2, placing them within the two crossover positions in Offspring 1. Offspring 2 is generated in a similar manner to Offspring 1.

[0139] The specific implementation of machine crossover is: randomly generate a sequence with the same length as the chromosome of parent 1 and a value of 0 or 1. When the element in the sequence is 1, the machine corresponding to the position of parent 1 is exchanged with the machine corresponding to the same workpiece and process of parent 2.

[0140] In step S5.9, the improved genetic algorithm mutation method is applied to the crossover population, including both process mutation and machine mutation. This results in a crossover population and new individual codes. The improved scheduling solution is derived from these new individual codes, and the process returns to step S5.5. For the process chromosomes, a swap mutation is used, randomly selecting two or more positions to swap genes. For the machine chromosome codes, a single-point mutation is used, randomly selecting one or more genes to reallocate the machines capable of processing the process.

[0141] By executing the above improved genetic algorithm on the initial scheduling scheme, new individual codes can be obtained, the fitness is changed, and a higher fitness is obtained, that is, a better scheduling scheme.

[0142] In step S6, the obtained scheduling plan with the best fitness is output as the optimal plan, and the job shop can perform scheduling according to the optimal plan.

[0143] The following references Figures 3 to 6 , an embodiment of a flexible job shop scheduling method considering group characteristics provided according to an embodiment of the present invention is described.

[0144] The following uses the extended group characteristic cases GC.MK1 to GC.MK10 based on the flexible job shop scheduling problem benchmark cases MK1 to MK10 to verify the effectiveness of the present invention. Different from the MK case, the workpieces in the GC.MK case are not independent of each other, and different processing sequences of the same machine will result in different setup times and pass rates. In addition, the other data in the GC.MK case are the same as the MK benchmark case (such as the number of workpieces, the number of machines, and the optional processing machines for each process of each workpiece, etc.). The setup time coefficient se = 0.3, the job switching coefficient matrix corresponding to different job switching is A = [0, 2 / 3, 1], and the processing pass rate matrix corresponding to different job switching is B = [0.95, 0.99, 0.93], which represents the job switching coefficients and processing pass rates of the two processes before and after processing on the same machine, which belong to workpiece switching, intra-group switching, and inter-group switching, respectively.

[0145] Step S1: For a flexible job shop production scenario with group characteristics, determine the job switching type of the job shop scheduling problem considering the group characteristics, perform group classification, and obtain the group classification result.

[0146] Step S1.1, determine the job switching types of the job shop scheduling problem considering group characteristics as workpiece switching, intra-group switching, and inter-group switching. Figure 3 As shown, ij represents the jth process of the i-th workpiece, and workpiece 1 and workpiece 4 are grouped as a group, and workpiece 2 and workpiece 3 are grouped as a group.

[0147] In step S1.2, fuzzy cluster analysis is used to perform group classification of the job shop scheduling problem considering group characteristics.

[0148] Step S1.2.1, specifically, taking GC.MK02 as an example, there are 10 workpieces to be grouped, and the workpiece set is O = {o1, o2, ..., o 10}, each part has 7 indicators to represent its processing characteristics, the processing feature set is r = {r1, r2, ..., r7}, any processing feature r k Contains d k There are h kinds of processing sub-feature attributes, h = d1 + d2 + ... + d7. The processing feature attributes of the i-th workpiece can be expressed as:

[0149]

[0150] Among them, R iz It is a 0 / 1 variable, indicating whether workpiece i contains the zth processing sub-feature attribute. If it does, it is 1, and if it does not, it is 0.

[0151] The processing characteristics include part geometry, material, machine, tooling, clamping method, processing accuracy, and employee knowledge level. Determine the sub-features of the processing characteristics and obtain the processing feature matrix R = [R1R2…R 10 ],as follows:

[0152]

[0153] Step S1.2.2: Construct a workpiece similarity matrix and calculate the similarity coefficients between workpieces using the maximum-minimum method, as follows:

[0154]

[0155] Among them, x ii′ Represents the similarity coefficient between workpiece i and workpiece i′, R iz Indicates whether workpiece i contains processing sub-feature z, R i′z Indicates whether workpiece i′ contains the processing sub-feature z. The similarity matrix X of all workpieces can be calculated as follows.

[0156]

[0157] Step S1.2.3, construct the fuzzy equivalent matrix, which is calculated by the similarity matrix X using the transitive closure method. In this embodiment, X is obtained. 8 For the transitive closure, the fuzzy equivalence matrix T = X 8 .

[0158]

[0159] Step S1.2.4, take the threshold λ = 0.4667 to intercept the obtained fuzzy equivalent matrix T and obtain the intercept matrix:

[0160]

[0161] According to the obtained T λ The truncated array divides the workpieces into three groups: {o1,o2,o4,o6,o7,o8}, {o3,o9}, and {o5}. Workpieces with the same truncated array arrangement are grouped together.

[0162] Step S2: Based on the obtained job switching type and group classification results, determine the basic parameters for the job shop scheduling problem considering group characteristics. See Table 1 and the description above. The remaining parameters are the same as for benchmark cases Mk1-Mk10. The decision variables for considering group characteristics are the processing machine selected for each process for each workpiece and the sequence relationship between processes on each machine.

[0163] Table 1 Case parameters

[0164] n*m a b V <![CDATA[T0]]> GC.MK01 10X6 0.48 1.1 100 45 GC.MK02 10X6 0.5 1.1 100 30 GC.MK03 15X8 0.056 1.1 100 210 GC.MK04 15X8 0.55 1.1 100 65 GC.MK05 15X4 0.04 1.1 100 185 GC.MK06 10X10 0.1 1.1 100 130 GC.MK07 20X5 0.12 1.1 100 150 GC.MK08 20X10 0.012 1.1 100 530 GC.MK09 20X10 0.009 1.1 100 330 GC.MK10 20X15 0.008 1.1 100 260

[0165] Step S3, see Figures 4a to 4c , construct the objective function considering group characteristics as follows:

[0166] Max.Obj=PV-RL

[0167] Considering that the economic loss per unit time will usually increase with the increase of delivery delay time, the concave function R(t) = a×t b Describes the penalty for delivery delay. Where a and b are coefficients, which can be fitted based on actual production order requirements. The coefficient values obtained from this case are shown in Table 1. The relevant calculation parameters are given, and in the subsequent steps, the objective function calculation method provided in the above embodiment can be used to solve the problem.

[0168] Step S4, based on the objective function considering the grouping characteristics, establish the constraints of the flexible job shop scheduling problem considering the grouping characteristics: all machines, workpieces and raw materials are available at the same time at time zero; each machine can only process one workpiece at a time; there is no priority difference between workpieces, and once a workpiece starts processing, it will not be interrupted; each workpiece has a specified process sequence, and when a process of the workpiece is completed, it moves to the next processing machine; the setup time of the process is separable, that is, when the previous process has not been completed, the job switching activity of the next process of the workpiece can be executed in advance on another idle machine; the production environment is stable, and machine failures, workpiece insertion orders, etc. are not considered.

[0169] Step S5, see Figure 2 、 Figure 5 and Figure 6 The improved genetic algorithm was used to solve the constructed mathematical model for flexible job shop scheduling considering group characteristics, and a scheduling solution with optimal fitness was obtained. The solution results are shown in Table 2. As can be seen from Table 2, in 10 cases of different scales considering group characteristics, the average solution value and the optimal value found by the traditional genetic algorithm were higher than those of the traditional genetic algorithm. This indicates that the embodiment of the flexible job shop scheduling method considering group characteristics according to the embodiment of the present invention has a higher overall benefit for the manufacturing process than the traditional method.

[0170] Table 2 Solution results

[0171]

[0172] In step S6, in each of the above cases, the obtained scheduling plan with the best fitness is output as the optimal plan, and the job shop can perform scheduling according to the optimal plan.

[0173] All of the above optional technical solutions can be combined in any way to form optional embodiments of the present application, and will not be described in detail here.

[0174] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0175] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A flexible job shop scheduling method considering group characteristics, characterized in that: The following steps are involved: Step S1: For a flexible job shop production scenario with group characteristics, determine the job switching type of the job shop scheduling problem considering the group characteristics, perform group classification, and obtain the group classification result; Step S2: Determine the decision variables and basic parameters considering the group characteristics according to the obtained job switching type and group classification results; Step S3: constructing an objective function that takes group characteristics into consideration, including establishing a product output value term and an efficiency loss term in the objective function that takes group characteristics into consideration; Step S4: Based on the objective function considering the grouping characteristics, establishing the constraint conditions of the flexible job shop scheduling problem considering the grouping characteristics, and obtaining a mathematical model of the flexible job shop scheduling problem considering the grouping characteristics; Step S5: using an improved genetic algorithm to solve the flexible job shop scheduling mathematical model that takes grouping characteristics into consideration, and obtaining a scheduling solution with optimal fitness; In step S6, the obtained scheduling plan with the best fitness is output as the optimal plan, and the job shop performs scheduling according to the optimal plan.

2. The flexible job shop scheduling method considering group characteristics according to claim 1 is characterized in that: Step S1 specifically includes the following steps: Step S1.1, in a flexible job shop production scenario with group characteristics, determining the job switching types of the job shop scheduling problem considering the group characteristics, the job switching types including workpiece switching, intra-group switching, and inter-group switching; Step S1.2, using fuzzy cluster analysis method to perform group classification of job shop scheduling problem considering group characteristics, including constructing processing feature matrix, constructing workpiece similarity matrix, calculating fuzzy equivalence matrix, and clustering grouping to obtain group classification results.

3. The flexible job shop scheduling method considering group characteristics according to claim 2 is characterized in that: Step S1.2 specifically includes the following steps: Step S1.2.1, construct the workpiece processing feature matrix, provide n workpieces to be grouped, and the workpiece set is O = {o1, o2, ... i ,…,o n }, set m indicators to represent the processing features of the workpiece, and the processing feature set is r = {r1, r2, ... r k ,…,r m }, where k represents the index of the processing feature and k = 1, 2, ..., m, where any processing feature r k Contains d k There are h processing sub-features: h=d1+d2+…+d m , The machining feature attributes of the i-th workpiece are expressed as: Among them, R iz The machining feature attribute indicating whether the i-th workpiece contains the z-th machining sub-feature is a 0 / 1 variable. If the workpiece i contains the z-th machining sub-feature, the value is 1; otherwise, the value is 0. z represents the index of the machining sub-feature and z = 1, 2, …, h. Get the total processing feature matrix R of all n workpieces = [R1R2…R n ]; Step S1.2.2, constructing the workpiece similarity matrix includes calculating the similarity coefficient between workpieces using the maximum-minimum method, and the calculation formula is as follows: Among them, x ii′ Represents the similarity coefficient between workpiece i and workpiece i′, R iz Indicates whether workpiece i contains the machining feature attribute of the machining sub-feature z, R i′z The machining feature attribute indicating whether workpiece i′ contains the zth machining sub-feature; The similarity matrix between the i-th workpiece and all workpieces is: X i =[X i1 ,X i2 ,…X ii′ ,…X in ]; Based on the similarity coefficients between all workpieces, the similarity matrix of all workpieces is obtained as X = [X1X2…X i …X n ]; Step S1.2.3, based on the similarity matrix of all workpieces obtained, the fuzzy equivalence matrix is constructed using the transitive closure method; Step S1.2.4, performing clustering grouping on the obtained fuzzy equivalence matrix to obtain a clustering grouping result, which is the group classification result.

4. The flexible job shop scheduling method considering group characteristics according to claim 3 is characterized in that: Step S1.2.3 specifically includes: starting from the similarity matrix X of all workpieces, using the square method to obtain X 2 ,X 4 ,…X R , until the index R satisfies X R =X 2R , we get the fuzzy equivalent matrix T = X R .

5. The flexible job shop scheduling method considering group characteristics according to claim 4 is characterized in that: Step S1.2.4 specifically includes: The obtained fuzzy equivalent matrix T is intercepted using the set threshold λ: Among them, λ is a given threshold, T λ is the intercept matrix of λ under the threshold λ, t ii′ represents the corresponding element in the fuzzy equivalence matrix T, t(λ) ii′ T represents the fuzzy equivalent matrix T obtained by truncation of λ λ The corresponding elements of the intercept matrix; Based on the truncation matrix T obtained by truncation of the fuzzy equivalent matrix λ , obtain the grouping situation under the threshold as the clustering grouping result.

6. The flexible job shop scheduling method considering group characteristics according to claim 1, characterized in that: In step S2: The basic parameters considered for grouping characteristics include: the number of machines, the number of workpieces, the workpiece grouping, the number of processes for each workpiece, the optional processing machines for each process of each workpiece, the operation time and setup time coefficient of each process of each workpiece on different machines, the job switching coefficient for different job switching of each workpiece, the processing qualification rate for different job switching of each workpiece, the value of each workpiece, and the efficiency loss penalty coefficient. The workpiece grouping is the grouping classification result obtained in step S1. The decision variables that consider group characteristics include: the processing machine selected for each process of each workpiece, and the sequence relationship of each process on each machine.

7. The flexible job shop scheduling method considering group characteristics according to claim 1 is characterized in that: Step S3 specifically includes the following steps: Step S3.1: Establish the product output value term in the objective function that takes into account the grouping characteristics. The product output value term is calculated by the circulation qualification rate. In this case, each workpiece is a product after the production is completed. Each product corresponds to a corresponding workpiece in the production process, and the total number of products is the same as the total number of workpieces n. Calculate the circulation qualification rate of products: Among them, RTY i Indicates the circulation qualification rate of product i, FYT ij It represents the first pass rate of product i process j, N pi represents the total number of processes for product i, j represents the process number and j∈[1,2,…,N pi ]; Calculate product output value based on product circulation qualification rate: Among them, PV represents the product output value, V i Represents the value of product i, RTY i represents the circulation qualification rate of product i; Step S3.2, establish the efficiency loss term in the objective function considering group characteristics: Ts ij =st iji′j′k ×se×T ij Tc ij =Ts ij +Tp ij Among them, Ts ij represents the setup time of process j for workpiece i, se is the setup time coefficient and represents the ratio of setup time to operation time, T ij Tc is the expected operation time of process j for workpiece i. ij represents the actual operation time of process j of workpiece i, Tp ij represents the processing time of process j of workpiece i, st iji′j′k is the job switching coefficient, which indicates the degree of setup time saving caused by different job switching types. That is, when the operations of process j′ of workpiece i′ and process j of workpiece i are performed on machine k successively, the actual setup time of process j of workpiece i should be proportional to the expected setup time. Obtain the efficiency loss term in the objective function considering group characteristics: RL=(T max -T0)×R(T max ) Among them, RL represents the efficiency loss, and T max represents the makespan, T0 represents the specified delivery time, and R(t) represents the delivery delay penalty term. If the manufacturing task is completed within the specified delivery time, when T max < T0, the delivery delay penalty term is 0; Step S3.3: Construct an objective function that takes group characteristics into consideration. The objective function that takes group characteristics into consideration includes a product output value term and an efficiency loss term: Max.Obj=PV-RL Where Obj represents the overall benefit of the manufacturing process.

8. The flexible job shop scheduling method considering group characteristics according to claim 1 is characterized in that: The constraints of the flexible job shop scheduling problem considering grouping characteristics in step S4 include: all machines, workpieces, and raw materials are available at the same time at time zero; each machine can only process one workpiece at a time; there is no priority difference between workpieces, and once a workpiece is processed, it will not be interrupted; each workpiece has a specified process sequence; the setup time of the process is separate; the production environment is stable, and machine failures and workpiece insertions are not considered.

9. The flexible job shop scheduling method considering group characteristics according to claim 1, characterized in that: Step S5 specifically includes the following steps: Step S5.1, setting the parameters of the improved genetic algorithm, including: setting the population size, selection rate, crossover rate, mutation rate, and maximum number of iterations; Step S5.2: Gene encoding based on the improved genetic algorithm for multi-type work-hour disturbances. A complete encoding method is used to establish encoding rules, including the process code OS for process arrangement, the machine code MS for machine allocation, and the group code GS for workpiece grouping. Each chromosome consists of three parts: OS, MS, and GS, and the encoding length is the number of processes. Step S5.3: Initialize the population using random generation according to the established coding rules. The population consists of multiple chromosomes, each of which contains multiple genes. Each gene includes the workpiece processing step, processing machine, and group number. Each chromosome represents a scheduling solution for the flexible job shop. Step S5.4: Based on the genetic decoding method of the improved genetic algorithm for multi-type work-hour disturbances, an insert-type greedy decoding method that takes grouping characteristics into consideration is used to decode the initial population to obtain a preliminary scheduling solution. Step S5.5, improving the fitness calculation of the genetic algorithm, specifically including substituting the decoded preliminary scheduling plan into and calculating the objective function established in step S3 to obtain the objective function value, which is the fitness of the individual; Step S5.6, determine whether the termination condition is met, that is, determine whether the current number of iterations reaches the maximum number of iterations. If so, the current scheduling scheme is the scheduling scheme with the best fitness, and execute step S6; otherwise, execute step S5.7; Step S5.7, for the population in the current scheduling plan, the improved genetic algorithm is selected using a roulette wheel selection method to obtain a selected population; Step S5.8, performing crossover of the improved genetic algorithm on the selected population, including process crossover and machine crossover, to obtain a crossover population; Step S5.9, perform mutation of the improved genetic algorithm on the population after crossover, including process mutation and machine mutation, to obtain the population after crossover, obtain new individual codes, and obtain an improved scheduling plan based on the new individual codes, and return to step S5.5.

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