A distributed flexible flow shop scheduling method, system, storage medium and terminal

Abstract

The present invention discloses a scheduling method for a distributed flexible assembly line workshop, belongs to the technical field of data processing, and solves the problem that other factors are not fully considered in workshop scheduling in the prior art. The scheduling method in the present invention adopts a model-based two-stage monarch butterfly optimization method to process the scheduling problem. First, the population is initialized for workpieces, factories and machines to obtain an initial scheduling solution. Then, the monarch butterfly optimization method is used as the main optimization operator to optimize the operation sequence of the scheduling solution. Secondly, a feature-based search strategy is used to optimize the machine sequence of the scheduling solution. Finally, the optimal solution is output to determine the scheduling solution. Through the above-mentioned scheduling method, workers and transportation factors are fully considered, and the scheduling efficiency of the workshop is guaranteed. In addition, the present invention also introduces a neural network model for matching optimization operators, and optimizes the scheduling problem in real time, further ensuring the scheduling effect.

Description

Technical Field

[0001] The present invention belongs to the technical field of data processing, and in particular, relates to a scheduling method, system, storage medium and terminal of a distributed flexible flow shop. Background Art

[0002] The scheduling problem of distributed flexible assembly lines is an important and challenging problem in the manufacturing industry. Against the backdrop of increasingly fierce global competition, manufacturing companies need to improve production efficiency, shorten delivery times, and reduce costs to meet the diverse needs of customers. The scheduling problem of distributed flexible assembly lines aims to reasonably assign tasks to machines in multiple factories distributed in different geographical locations and determine the order of task execution in order to optimize production performance, thereby improving the company's production efficiency and enhancing its market competitiveness. Therefore, the research on scheduling methods for distributed flexible assembly lines is a hot topic of concern in academia and industry.

[0003] At present, with the continuous advancement of technology, the application of traditional optimization algorithms in flow shop scheduling problems can no longer meet the personalized and customized needs of customers. With the progress of society, the scheduling problem of flow shops has become complicated, and traditional optimization algorithms can no longer solve this problem. In the prior art, when studying scheduling problems, a series of problems are defined as minf(x), x = [x1, x2, ..., x D ], where the goal is to find the maximum or minimum value f(x) and output the optimal solution x, so as to continuously optimize the flow shop scheduling problem to meet the needs of the manufacturing industry and customers. However, when the scale of the scheduling problem expands to a certain number, the original mathematical method is difficult to solve the problem of continuous optimization. Therefore, different mechanisms of metaheuristics have been proposed and used to solve complex continuous optimization problems. Metaheuristic algorithms have become the mainstream method for solving scheduling optimization problems due to their good versatility and powerful optimization ability. In addition, as a novel swarm intelligence algorithm, the monarch butterfly optimization algorithm imitates the migration and reproduction behavior of monarch butterflies, and has the advantages of rich population diversity and strong global search ability. These characteristics make it show great potential in solving many optimization problems, especially discrete combinatorial optimization problems.

[0004] In the actual production process, the factors affecting the workshop scheduling performance include but are not limited to the processing capacity of the machine and the process route of the workpiece, and the fatigue of the workers and the transportation within the factory have also become key factors affecting the workshop scheduling performance. The fatigue of the workers directly affects their work efficiency and product quality. The transportation time of the workpiece between different machines will also significantly affect the workshop scheduling effect. Therefore, when studying the scheduling problem of distributed flexible assembly lines, it is necessary to fully consider factors such as worker fatigue and workpiece transportation. However, the existing workshop scheduling methods do not fully consider the factors of worker fatigue and workpiece transportation, resulting in poor results of the existing workshop scheduling methods. Therefore, the present invention aims to explore the performance of the monarch butterfly optimization algorithm in solving the scheduling problem of distributed flexible assembly lines, and to provide a scheduling method for distributed flexible assembly lines on the basis of fully considering factors such as worker fatigue and workpiece transportation. Summary of the invention

[0005] The purpose of this section is to summarize some aspects of embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0006] To solve the problems raised in the background technology, the present invention adopts the following technical solutions.

[0007] A distributed flexible flow shop scheduling method adopts a model-based two-stage monarch butterfly optimization method to handle scheduling problems, including the following steps:

[0008] First, the population is initialized for workpieces, factories, and machines to obtain the initial scheduling solution;

[0009] Then, the operation sequence of the scheduling solution is optimized by using the monarch butterfly optimization method as the main optimization operator;

[0010] Secondly, a feature-based search strategy is used to optimize the machine sequence of the scheduling solution;

[0011] Finally, the Pareto solution set is output and the scheduling solution is determined.

[0012] Preferably, in the above-mentioned scheduling method, when the scheduling problem is processed by the model-based two-stage monarch butterfly optimization method, a suitable optimization operator is matched for the scheduling solution by a feature-driven neural network model, the feature-driven neural network model is a decision model based on a fully connected neural network, the input of the feature-driven neural network model is a set of statistical features based on a Gantt chart, and the output is the value of the optimization operator;

[0013] In the input of the feature-driven neural network model, the features of the scheduling solution are composed of 4 arrays, namely:

[0014] The first array: normalized data of machine downtime;

[0015] The second array: the ratio of the machine's idle time to the total boot time;

[0016] The third group: worker fatigue level;

[0017] The fourth array: the ratio of the number of machine-processed workpieces to the total number of workpieces.

[0018] Preferably, in the above scheduling method, when the feature-based search strategy is used to optimize the machine sequence of the scheduling solution, the Pareto front solution is optimized twice by the feature-based search strategy containing 6 optimization operators, wherein the 6 optimization operators in the feature-based search strategy are as follows:

[0019] S1 randomly selects a plant and changes the processing plant;

[0020] S2 exchanges the coding order of any two operations within the key factory;

[0021] S3 randomly selects an operation of a mutable machine and changes its operation machine to a machine with fewer tasks;

[0022] S4 randomly exchanges artifacts between factories;

[0023] S5 randomly changes the processing order of a workpiece;

[0024] S6 randomly swaps the order of any two operations in the encoding.

[0025] Preferably, in the above-mentioned scheduling method, optimization operators S1 and S5 ensure that any factory allocation plan is within the search space of the feature-based search strategy; optimization operator S2 directly adjusts the operation order within the key factory; optimization operator S3 exchanges a random task in the current machine to a relatively idle machine, optimization operator S4 is a strategy for exchanging workpieces between factories; optimization operator S6 arbitrarily changes the operation order.

[0026] Preferably, in the above-mentioned scheduling method, in the model-based two-stage monarch butterfly optimization method, the model includes the following objective function:

[0027] min(f1, f2, f3)

[0028] f1=C max

[0029] f2=TC=1.3·(PE+IE+AE)TC i，j，j′ TBi，j，j′ )

[0030] i∈{1,2,...,n};j,j′∈{1,2,...,m f，k}

[0031] f3=FI max

[0032]

[0033] Among them: min(f1, f2, f3) is the set of factor functions that affect the scheduling problem;

[0034] C max is the maximum time to complete the work;

[0035] TC is the total cost;

[0036] PE is the processing energy consumption of the workpiece;

[0037] IE is the standby energy consumption of the machine;

[0038] AE is auxiliary energy consumption;

[0039] TC i,j，j′ TB i,j，j′ For transportation costs;

[0040] i is the workpiece number;

[0041] j is the machine number;

[0042] i,j,j′ means the workpiece is transferred from machine j to machine j′;

[0043] FI max The maximum fatigue level of the worker;

[0044] FI j，t is the worker fatigue degree of machine j in the processing state at time t;

[0045] MS j，t The processing status of machine j at time t.

[0046] Preferably, in the above scheduling method, the model also includes the following constraints:

[0047]

[0048]

[0049] S i，k+1 -(S i，k +p i，k )≥0

[0050] Y i，j，k +Yi+1，j，k，f ≤1

[0051] S i+1，k -(S i，k +p i，k )-B(2-Y i，j，k，f -Y i，j，k +Y i+1，j，k，f )≥0

[0052] C i，k =S i，k +p i，k

[0053] C i，s ≤T

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] Where: F is the number of factories;

[0060] f is the factory number;

[0061] X i，f If job i is assigned to factory f, it is 1, otherwise it is 0;

[0062] Y ii，j，k，f is the processing status of job i on machine j in stage k of factory f, 1 if processed, 0 otherwise;

[0063] S i , k is the start time of workpiece i in stage k;

[0064] p i，k is the processing time of workpiece i at stage k;

[0065] B is an integer;

[0066] C i，k is the completion time of job i in stage k;

[0067] T is the total number of time periods;

[0068] b i，k，t It means that workpiece i is executed in stage k at period t;

[0069] Z i，j，k，f，tIt means that if the processing time of job i on machine j in stage k of factory f is t, it is 1, otherwise it is 0;

[0070] It means that if workpiece i is in working state in the kth stage of factory f during period t, it is 1, otherwise it is 0;

[0071] It means that if workpiece i is in the idle state in the kth stage of factory f during period t, it is 1, otherwise it is 0;

[0072] m f , k represents the number of parallel machines in the kth stage in factory f.

[0073] On the other hand, the present invention also provides a distributed flexible flow shop scheduling system, including an objective function and constraints for constraining the objective function, wherein the objective function is:

[0074] min(f1, f2, f3)

[0075] f1=C max

[0076] f2=TC=1.3·(PE+IE+AE)+(∑TC i，j，j′ TB i，i，j，j′ )

[0077] i∈{1,2,...,n};j,j′∈{1,2,...,m f，k}

[0078] f3=FI max

[0079]

[0080] Among them: min(f1, f2, f3) is the set of factor functions that affect the scheduling problem;

[0081] C max is the maximum time to complete the work;

[0082] TC is the total cost;

[0083] PE is the processing energy consumption of the workpiece;

[0084] IE is the standby energy consumption of the machine;

[0085] AE is auxiliary energy consumption;

[0086] TC i，j，j′ TB i，j，j′ For transportation costs;

[0087] i is the workpiece number;

[0088] j is the machine number;

[0089] i, j, j′ means the workpiece is transferred from machine j to machine j′;

[0090] FI max The maximum fatigue level of the worker;

[0091] FI j，t is the worker fatigue degree of machine j in the processing state at time t;

[0092] MS j，t The processing status of machine j at time t.

[0093] Preferably, in the above scheduling system, the constraint condition is:

[0094]

[0095]

[0096] S i，k+1 -(S i，k +p i，k )≥0

[0097] Y i，j，k，f +Y i+1，j，k，f ≤1

[0098] S i+1，k -(S i，k +p i，k )-B(2-Y i，j，k，f -Y i，j，k，f +Y i+1，j，k，f )≥0

[0099] C i，k =S i，k +p i，k

[0100] C i，s ≤T

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] Where: F is the number of factories;

[0107] f is the factory number;

[0108] X i,f If job i is assigned to factory f, it is 1, otherwise it is 0;

[0109] Y i,j,k,f is the processing status of job i on machine j in stage k of factory f, 1 if processed, 0 otherwise;

[0110] S i,k is the start time of workpiece i in stage k;

[0111] p i,k is the processing time of workpiece i at stage k;

[0112] B is an integer;

[0113] C i,k is the completion time of job i in stage k;

[0114] T is the total number of time periods;

[0115] b i,k,t It means that workpiece i is executed in stage k at period t;

[0116] Z i,j,k,f,t It means that if the processing time of job i on machine j in stage k of factory f is t, it is 1, otherwise it is 0;

[0117] It means that if workpiece i is in working state in the kth stage of factory f during period t, it is 1, otherwise it is 0;

[0118] It means that if workpiece i is in the idle state in the kth stage of factory f during period t, it is 1, otherwise it is 0;

[0119] m f,k represents the number of parallel machines in the kth stage of factory f.

[0120] Another aspect of the present invention provides a storage medium for receiving a program input by a user, wherein the computer program stored in the storage medium enables an electronic device to execute the above-mentioned distributed flexible assembly line scheduling method.

[0121] On the other hand, the present invention also provides an information data processing terminal, which includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor executes the above-mentioned distributed flexible assembly line scheduling method.

[0122] Compared with the prior art, the present invention has the following beneficial effects:

[0123] (1) The present invention is a model-based two-stage monarch butterfly optimization method for dealing with the scheduling problem of a distributed flexible assembly line workshop. In the first stage, the monarch butterfly optimization method is used as the main optimization operator to optimize the operation sequence of the scheduling solution. In the second stage, the Pareto front solution is secondary optimized through a feature-based search strategy including 6 optimization operators. In this way, the model-based two-stage monarch butterfly optimization method is used to deal with the workshop scheduling problem, fully considering the factors of workers and transportation, so that the scheduling problem can be effectively solved in the workshop, thereby ensuring the scheduling efficiency and scheduling effect of the workshop.

[0124] (2) In order to efficiently match appropriate optimization operators when optimizing scheduling problems, the scheduling method of the present invention also introduces a feature-based neural network model. The input of the model is the statistical characteristics of the Gantt chart of a single scheduling solution, and the output is the use value of each optimization operator. The model can search for the above-mentioned optimization operators and optimize the scheduling problem in real time, further ensuring the effectiveness of the scheduling method, making the scheduling method have better performance and ensuring the scheduling effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] Figure 1 It is a schematic diagram of the distributed flexible flow shop scheduling in the present invention;

[0126] Figure 2 This is an example of the scheduling solution in the present invention;

[0127] Figure 3 Assigning a schematic diagram to the factory of the workpiece in the present invention;

[0128] Figure 4 It is a structural schematic diagram of the neural network model in the present invention;

[0129] Figure 5 is a schematic diagram of a feature-based search strategy in the present invention;

[0130] Figure 6 It is the main effect diagram of the experimental results in the present invention;

[0131] Figure 7 is the interactive effect diagram of the experimental results in the present invention;

[0132] Figure 8 is the Pareto solution set of the experimental results in the present invention;

[0133] Fig. 9 It is a box plot of the experimental results in the present invention. DETAILED DESCRIPTION

[0134] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings.

[0135] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0136] In order to more clearly describe the problem to be solved by the present invention, the present invention describes the scheduling problem of a distributed flexible assembly line shop as follows.

[0137] The scheduling method of the distributed flexible assembly line in the present invention fully considers factors such as worker fatigue and workpiece transportation. Therefore, the scheduling problem of the distributed flexible assembly line can be described as follows: n workpieces are assigned to F factories with different geographical locations, each factory contains a flexible assembly line, and all assigned workpieces need to go through S stages. The kth stage consists of m f,k Since different constraints and assumptions will lead to different scheduling problems, in order to better describe the problem, consider the following assumptions:

[0138] Once a workpiece is assigned to a factory, its processing operations must be completed in this factory;

[0139] Each workpiece can be processed from time zero, and the processing cannot be interrupted;

[0140] At any time, a workpiece can only be processed on one machine, and a machine can only process one job at a time;

[0141] Regardless of the machine preparation time, all machines can start processing after the workpiece arrives;

[0142] The buffer between any two adjacent stages is infinite.

[0143] like Figure 1 As shown in FIG. 1 , it is a scheduling diagram of a distributed flexible flow shop in the present invention. The main processing process of the workpiece is mainly divided into the allocation of the workpiece, that is, allocation to a reasonable factory for processing. After the workpiece is allocated to the factory, the workpiece needs to be allocated to the processing machine of the factory for processing, that is, machine allocation. After the workpiece is allocated to the machine, a reasonable processing sequence needs to be provided for processing the workpiece, that is, the sorting problem. Therefore, in the present invention, the scheduling problem of a distributed flexible flow shop considering transport and worker factors (Flexible flow shop scheduling problem considering transport and worker factors, DFFSP-WS) can be decomposed into three sub-problems, namely:

[0144] (1) Assign the most reasonable processing workshop to each workpiece, that is, factory allocation.

[0145] (2) Determine the processing machines for each process in each workshop, that is, machine allocation.

[0146] (3) Arrange a reasonable processing sequence for the workpieces in each workshop, that is, the sorting problem.

[0147] In the present invention, the optimization objectives of the distributed flexible flow shop scheduling problem (DF FSP-WS) considering workers and transportation factors are as follows: the maximum completion time C max , total cost and maximum worker fatigue. Among them, the maximum completion time C max It conflicts with worker fatigue because worker fatigue is affected by worker rest time (machine standby time), and under the same operation sequence, longer standby time means greater C max The total cost involves machine energy consumption cost and transportation cost, among which the minimum transportation cost and the minimum solution are different, and the factory energy consumption includes standby energy consumption and daily energy consumption, so the worker fatigue target and the total cost target are also in conflict with each other.

[0148] The present invention utilizes a two-stage monarch butterfly optimization method (MTMBO) to find a set of feasible solutions to solve the scheduling problem of a distributed flexible flow shop, wherein the two-stage monarch butterfly optimization algorithm includes two stages, the first stage is to use the monarch butterfly optimization method (MBO) as the main optimization operator to optimize the operation sequence of the scheduling solution, and the second stage is to design a feature-based search strategy (FSS) containing 6 optimization operators to perform secondary optimization on the Pareto frontier solution, thereby optimizing the scheduling problem of the distributed flexible flow shop and ensuring the production and processing efficiency of the manufacturing industry.

[0149] In order to better illustrate the scheduling method of the distributed flexible assembly line in the present invention, the symbols and their definitions used in the present invention are shown in Table 1.

[0150] Table 1 Symbols and their definitions

[0151]

[0152]

[0153] The present invention provides a scheduling system for a distributed flexible assembly line, including a mixed integer programming model, which is used to solve the above-mentioned scheduling problem of the distributed flexible assembly line, especially taking into account the factors of workers and transportation, with the main purpose of optimizing the production process, ensuring the efficient use of resources, and improving the flexibility and response speed of production. By accurately scheduling workers and material transportation, it is possible to better adapt to changes in production demand, reduce waiting time and idle resources in production, thereby improving overall production efficiency and reducing costs. In addition, this scheduling strategy also helps to improve product quality and speed up delivery, enhancing the market competitiveness of enterprises.

[0154] The above mixed integer programming model includes an objective function and constraints, which are as follows.

[0155] Objective function:

[0156] min(f1, f2, f3) (1)

[0157] f1=C max (2)

[0158] f2=TC=1.3·(PE+IE+AE)+(∑TC i，j，j′ TB i，，j，j′ ) (3)

[0159] i∈{1,2,...,n}; j,j′∈{1,2,...,m f，k}

[0160] f3=FI max (4)

[0161]

[0162] Constraints:

[0163]

[0164]

[0165] S i，k+1 -(S i，k +p i，k )≥0 (8)

[0166] Y i，j，k，f +Y i+1，j，k，f ≤1 (9)

[0167] S i+1，k -(S i，k +p i，k )-B(2-Y i，j，k，f -Y i，jk，f +Y i，j，k，f)≥0 (10)

[0168] C i，k =S i，k +p i，k (11)

[0169] C i，s ≤T (12)

[0170]

[0171]

[0172]

[0173]

[0174]

[0175] in,

[0176] Formula (1) is the overall goal;

[0177] Formula (2) defines the maximum completion time;

[0178] Formula (3) defines the total cost TC, which includes energy consumption cost and transportation cost. Factory energy consumption is divided into processing energy (PE), standby energy (IE) and auxiliary energy (AE);

[0179] Formula (4) defines the maximum worker fatigue FI max ;

[0180] Formula (5) Maximum worker fatigue FI max , where the initial fatigue level of each worker is 0;

[0181] Formula (6) ensures that each workpiece must be accurately assigned to a factory;

[0182] Formula (7) ensures that each operation can be processed at each stage it must pass through and only one available machine can be selected;

[0183] Formula (8) ensures that the operation of a job can only start the next stage of operation after the operation of the previous stage is completed;

[0184] Formula (9)-Formula (10) ensures that for two jobs processed on the same machine, the next job can only start after the previous job is completed;

[0185] Formula (11) defines the completion time of each workpiece in each stage;

[0186] Formula (12) ensures that the completion time of each job cannot be greater than the total number of time periods;

[0187] Formula (13) ensures that the processing time of each workpiece i in each stage is equal to p i , k;

[0188] Formula (14) defines the working state of the machine;

[0189] Formula (15) ensures that each machine can only be in one of the two states: working and standby;

[0190] Formula (16) defines the power consumed by the machine in working state PE;

[0191] Formula (17) defines the standby energy consumption IE of the machine.

[0192] In the present invention, a two-stage monarch butterfly optimization method is used to optimize the scheduling problem of a distributed flexible flow shop taking into account labor and transportation factors, thereby solving the scheduling problem of workpieces in the workshop. The scheduling method of a distributed flexible flow shop in the present invention includes the following steps:

[0193] First, the population of factories, machines and workpieces is initialized to obtain a fixed number of initial scheduling solutions;

[0194] Then, the operation sequence of the scheduling solution is optimized by using the monarch butterfly optimization method (MBO) as the main optimization operator. The operation sequence not only directly determines the quality of the scheduling solution, but also determines the local optimization potential of the current scheduling solution. In addition, the change of the operation sequence also affects the maximum completion time of the scheduling solution, the worker fatigue index and the total scheduling cost. Subsequently, the feature-based search strategy (FSS) is used to optimize the machine sequence of the scheduling solution to solve the allocation problem of machines and factories; compared with the MBO optimization operator, FSS is a random search strategy and is suitable for the optimization of a single scheduling solution; all Pareto front individuals are the optimization targets of FSS, while the elite strategy in MBO will make full use of the useful information carried by the Pareto front individuals and improve the fitness value of the entire population; and in the present invention, the Pareto front solution is secondary optimized by a feature-based search strategy (FSS) containing 6 optimization operators, wherein the 6 optimization operators in the feature-based search strategy (FSS) and their optimization principles are shown in Table 2.

[0195] Table 2 Optimization operators and optimization principles in feature-based search strategies

[0196]

[0197] In the implementation scheme of the present invention, a reasonable factory allocation plan is the key to improving the scheduling solution optimization potential. S1 and S5 ensure that any factory allocation plan is within the search space; the maximum completion time and the maximum worker fatigue are affected by the factory allocation; the key factory refers to the factory where the machine that stops last is located. Optimizing the completion time of the key factory is to optimize the completion time of the entire scheduling plan.

[0198] S2 is an optimization operator that directly adjusts the operation sequence in the key factory. This is the optimization scheme that most directly affects the maximum completion time. Compared with the proposed completely random operation sequence adjustment scheme, it has higher search efficiency. However, the search space of S2 is smaller, which makes it not suitable for the optimization of all scheduling solutions. The machine sequence not only determines the machine where each operation is located, but also determines the factory where the workpiece is located.

[0199] S3 exchanges a random task in the current machine to a relatively idle machine. This is a direct strategy to reduce the maximum worker fatigue. However, the existence of multiple factories makes the machine switching strategy within the factory limited.

[0200] S4 is a strategy for exchanging workpieces between factories, which fills the limitation;

[0201] S6 is to arbitrarily exchange the order of two operations, which also fills the limitation.

[0202] In addition, since the solution generated by the monarch butterfly optimization method is a continuous solution, while the scheduling solution is a discrete solution, in order to ensure the efficiency of the feature-based search strategy, the present invention provides a coding method, which solves the problem of different lengths of factory codes and machine codes in traditional distributed scheduling problems. At the same time, the workpiece allocation task is integrated into the machine allocation, making the factory allocation a method that can be continuously optimized, such as Figure 2 as well as Figure 3 As shown in Figure 1, the encoding solution of the model-based two-stage monarch butterfly optimization method is a matrix consisting of two arrays, the first array is the operation sequence, and the second array is the machine sequence. In the machine sequence part, the distributed factory is regarded as a single factory with machine flexibility. The selection of machines follows the rules of the distributed factory. At the same time, the machine where the first process of each workpiece is located determines the processing factory where it is located. Figure 2 as well as Figure 3 It can be seen that the machine where a workpiece is located depends on the machine assigned to its first process. When the first process is assigned to Factory 1, its subsequent processes are all assigned to Factory 1 for processing.

[0203] Moreover, in the present invention, the above-mentioned six optimization operators have different optimization methods for different feature information. In order to select a suitable optimization operator for a specific scheduling solution, the present invention adopts a feature-driven neural network model to match a suitable optimization operator for a specific scheduling solution.

[0204] In the present invention, the feature-driven neural network model (FNN) is a decision model based on a fully connected neural network. The input of the feature-driven neural network model (FNN) is a set of statistical features based on a Gantt chart, and the output of the feature-driven neural network model (FNN) is the value of six optimization operators. The prediction process of the feature-driven neural network model (FNN) is as follows: Figure 4 As shown, each Pareto front individual in each iteration executes a feature-based search strategy (FSS). The principle of the feature-based search strategy (FSS) in the present invention is as follows: Figure 5 shown.

[0205] In the input of the feature-driven neural network model (FNN), the features of the scheduling solution are composed of four arrays. The first array F1 is the normalized data of the downtime of each machine. The downtime of each machine can directly obtain the key factory and the key machine that affects the maximum completion time. This information plays a decisive role in optimizing the maximum completion time. The second array F2 directly describes the ratio of the idle time of each machine to the total start-up time. The idle time of the machine is an important indicator to determine the fatigue of the workers and also an indicator to reflect the utilization of the machine. When the idle ratios between machines differ greatly, the machine exchange strategy and the factory exchange strategy are both reasonable strategies for optimizing the fatigue of the workers and the maximum completion time. Compared with F2, F3 directly shows the fatigue of the workers on each machine, which is the most direct reference indicator of the fatigue of the workers. A reasonable workpiece allocation scheme can improve the utilization of the machine and reduce the maximum completion time. F4 provides the ratio of the number of workpieces processed by each machine to the total number of workpieces. F4 provides reference data for the optimization operators S1, S3, S4 and S5. The output of the feature-driven neural network model (FNN) is the selection value of each optimization operator in the feature-based search strategy (FSS). The selection value describes the value of selecting a certain optimization operator for the current scheduling solution. The higher the selection value, the more suitable the optimization operator is for the current scheduling solution.

[0206] The neural network model used by the feature-driven neural network model (FNN) is a fully connected neural network with a 5-layer structure. The design of the neural network structure directly determines the prediction complexity and prediction accuracy of the final feature-based search strategy (FSS) model. Too few neural nodes limit the final accuracy of the feature-based search strategy (FSS), and too many neural nodes will lead to excessive model complexity. After preliminary trial and error experiments, the input layer has 4 neural nodes, the output layer has 6 neural nodes, and the middle layer has 3 layers, using 600, 128 and 16 neural nodes respectively.

[0207] In the training phase of the feature-driven neural network model (FNN), the monarch butterfly optimization method based on random selection strategy (MTMBO-R) is used to optimize different test sets with the same production standard. The 20,000 historical experiences generated during the optimization process are used as the training set of the feature-driven neural network model (FNN). The historical experience consists of three parts, namely, the feature information of the current scheduling solution, the optimization operator executed by the current scheduling solution, and the reward obtained after executing the optimization operator. Formula (18) shows the calculation method of the reward value. When the scheduling solution generated by the optimization operator is dominated by the original scheduling solution, the reward value is 0, when the new solution and the old solution do not dominate each other, the reward value is 20, and when the new solution dominates the old solution, the reward value is 100. The setting of the reward value directly affects the decision criteria of the feature-driven neural network model (FNN). It is necessary to retain a mutually non-dominated solution generated by the Pareto frontier individuals, because it not only improves the overall quality of the population, but also improves the diversity of the Pareto frontier. In this reward function, the absolute quality of the solution is more valuable than the diversity of the solution, which also causes the feature-driven neural network model (FNN) to be more inclined to produce higher quality solutions rather than ensuring the diversity of the Pareto frontier.

[0208] The selection of optimization operators depends entirely on historical experience. Each scheduling solution has a set of feature information. The feature-driven neural network model (FNN) will give the selection value of each optimization operator based on the feature information. The adjustment of the selection value is completed by formula (19), where Q' a is the optimized choice value, Q a is the original selected value, R a It is the reward value obtained after selecting optimization operator a in a certain experience. From the formula, we can see that the selection value of an optimization operator depends on the reward obtained by selecting the optimization operator under the current feature information. Sufficient historical experience provides conditions for updating the selection value. The higher the reward value obtained by an optimization operator under a certain feature information, the higher the probability of obtaining a reward, and the higher the selection value of the feature.

[0209]

[0210] Q′ a =Q a +0.01·(R a -Q a ) (19)

[0211] In the present invention, the model-based two-stage monarch butterfly optimization method is a learning metaheuristic algorithm based on the monarch butterfly optimization method. There are two core differences between the model-based two-stage monarch butterfly optimization method and the monarch butterfly optimization method. First, a feature-based search strategy (FSS) is used in conjunction with 6 different optimization operators to enhance the local search capability of the model-based two-stage monarch butterfly optimization method. Second, a feature-driven neural network model (FNN) is introduced to select appropriate search strategies for different scheduling solutions.

[0212] In the present invention, the model-based two-stage monarch butterfly optimization method (MTMBO) is divided into an optimization process with the monarch butterfly optimization method (MBO) as the main optimization operator and an optimization process based on a feature search strategy (FSS). The monarch butterfly optimization method (MBO) is a group intelligence optimization method that imitates the migration behavior of monarch butterflies, which is used for efficient global search capabilities and strong convergence speed. The monarch butterfly optimization method (MBO) operator is used to optimize the operation sequence of the scheduling solution. The operation sequence not only directly determines the quality of the scheduling solution, but also determines the local optimization potential of the current scheduling solution. The feature-based search strategy (FSS) is mainly used to optimize the machine sequence of the scheduling solution, that is, to solve the allocation problem of machines and factories. Compared with the monarch butterfly optimization method (MBO), the feature-based search strategy (FSS) has a smaller search space and higher search efficiency, but the FSS that is not suitable for the current scheduling solution will limit the search efficiency of the FSS. The pre-trained neural network model learns the characteristics of the problem and is used to select appropriate search strategies for different scheduling solutions to ensure search efficiency.

[0213] In order to further illustrate the optimization process of the model-based two-stage monarch butterfly optimization method (MTMBO) in the present invention, the present invention provides the process of the model-based two-stage monarch butterfly optimization method, as shown in Table 3.

[0214] Table 3 Process of the two-stage model-based monarch butterfly optimization method

[0215]

[0216] As shown in Table 3, the main process of the model-based two-stage monarch butterfly optimization method in this embodiment is as follows.

[0217] First, the population is initialized using a random method to obtain a fixed number of initial scheduling solutions. Then, the pre-trained neural network model (FNN) is loaded. The training data of the model comes from the historical data generated by the model-based two-stage monarch butterfly optimization method (MTMBO) on the same but different test sets. The optimization process of the model-based two-stage monarch butterfly optimization method is divided into two parts, namely the monarch butterfly optimization method (MBO) optimization operator and the feature-based search strategy. In the monarch butterfly optimization operator part, the mutation and selection strategies in the monarch butterfly optimization method (MBO) are executed on each individual in the population to optimize the operation sequence of the scheduling solution, and finally an optimized complete population is obtained. The feature-based search strategy contains 6 different optimization operators, each of which is used to optimize a scheduling solution in the Pareto frontier, and which optimization operator is selected for a specific scheduling solution depends on the prediction results of the neural network model. The neural network model (FNN) assigns a suitable optimization operator to each scheduling solution based on the statistical characteristics of the scheduling solution to improve the efficiency of the search strategy. Finally, the monarch butterfly optimization and feature-based search strategies are repeated until the termination condition is reached, and the optimal Pareto solution set found is finally output to determine the scheduling solution to solve the scheduling problem of distributed flexible flow shops considering workers and transportation factors.

[0218] Specifically, in order to further illustrate the above-mentioned scheduling method, the present invention provides the following embodiment 1. Embodiment 1 uses multiple test examples to illustrate the scheduling method of the distributed flexible assembly line workshop in the present invention. The "one embodiment" or "embodiment" referred to herein refers to a specific feature, structure or characteristic that can be included in at least one implementation of the present invention. The "in one embodiment" that appears in different places in this specification does not refer to the same embodiment, nor is it a separate or selective embodiment that is mutually exclusive with other embodiments. The present invention provides the following embodiments.

[0219] Example 1

[0220] The test instance used in this embodiment is based on the standard test set of flexible flow shop scheduling problems, and 22 test instances are randomly generated through 11 generation criteria. Three multi-objective optimization algorithms: H ADE, NSGA-II and MOEA / D are used to evaluate the performance of the algorithm. All algorithms are written in Python and run on a personal computer configured with Windows 10 system, AMD Ryzen 95900X CPU and 32GB memory. Each algorithm is run independently 20 times on each test instance, and the relevant performance indicators are recorded to ensure the repeatability and accuracy of the experimental results.

[0221] Experimental setup

[0222] In this embodiment, a series of experiments based on the flexible flow shop scheduling problem are designed, involving 22 test instances, named TW1 to TW22. These instances are generated by the same generation criteria and are divided into two subsets: TW1 to TW11 and TW12 to TW22. In order to further optimize the model, 22 training instances are generated, which are generated by the same generation criteria but different from the test set, and are used to collect historical performance data of the model-based two-stage monarch butterfly optimization method (MTMBO) during the training process.

[0223] The machine parameter settings in the experiment include the machine's working energy consumption and standby energy consumption, which are randomly drawn from 30 to 60 and 1 to 5, respectively. The transfer distance between different stages of the workpiece is set as a random number from 10 to 30, and the transfer cost per unit distance is a random number from 1 to 5. In addition, the factory's per unit energy consumption cost is fixed at 1.3, which helps to simulate the energy consumption in the actual production environment.

[0224] In order to ensure the accuracy and reproducibility of the experimental results, this experiment paid attention to the selection of the stopping criterion. Considering that the prediction time of the neural network in the model-based two-stage monarch butterfly optimization method (MTMBO) is significantly affected by the operating environment, and the recurrence problem that may be caused by the stopping criterion based on the CPU running time, this embodiment uses the number of fitness evaluations of the scheduling solution as the main stopping criterion. Such a setting helps to bypass the result fluctuations that may be caused by the time-based criterion, thereby improving the stability and fairness of the experiment.

[0225] In terms of performance evaluation, this embodiment uses three indicators, namely response value (RV), inverse generation distance (IGD) and normalized hypervolume (HV), to evaluate the performance of the algorithm. The response value (RV) reflects the dominant relationship between the solutions of each algorithm in the comparison process, and the inverse generation distance (IGD) evaluates the diversity and quality of the algorithm solutions. Its reference point is set to (1.01, 1.01, 1.01) to test the global search capability of the algorithm. The normalized hypervolume (HV) indicator measures the coverage ability of the Pareto frontier generated by the algorithm in the target space, and is an important tool for evaluating the performance of multi-objective optimization algorithms.

[0226] Parameter settings

[0227] This example uses a parameter experiment to evaluate the impact of two key parameters in the model-based two-stage monarch butterfly optimization method (MTMBO) - population size (NP) and optimization operator execution times (NL) on the algorithm performance. The parameter NP is set to four levels: 10, 30, 80, 150, and the parameter NL is also set to four levels: 1, 5, 10, 20. All possible combinations of the two parameters are tested on the test instance sets TW1 to TW11, and each combination is repeated 10 times to ensure the reliability of the results.

[0228] The purpose of the experiment is to evaluate the specific impact of different parameter combinations on algorithm performance by recording and analyzing the response value RV of each run. As a key indicator for measuring algorithm processing speed and efficiency, the response value RV can effectively reflect the algorithm performance under different parameter settings. By calculating the average value of RV under each parameter combination, we can intuitively understand the contribution of each parameter to the algorithm performance.

[0229] The experimental results will be presented through main effect plots and interaction effect plots. Figure 6 as well as Figure 7 As shown in the figure, the main effect diagram reveals the change of the response value RV when a single parameter changes, while the interaction effect diagram shows the joint impact of the two parameters on the performance of the model-based two-stage monarch butterfly optimization method (MTMBO) when they interact with each other. In the main effect diagram, the RV is the largest when the NP value is 80, and the RV value is the largest when the NL value is 5. This is because the optimization degree of the operation sequence is insufficient when the NP is too small, which not only directly affects the quality of the scheduling solution, but also indirectly limits the optimization potential of the scheduling solution in the feature-based search strategy (FSS) stage. The number of NL directly controls the optimization performance of the search strategy. Too few NL values ​​will limit the performance of the search strategy, and too large NL values ​​will rob algorithm resources, thereby indirectly limiting the optimization quality of the operation sequence. In the interaction effect diagram, when NP is 80 and NL is 5, the algorithm has the maximum RV value, and when NP is 30 and NL is 1, the algorithm obtains the maximum RV. Combined with the analysis of the main effect diagram, any excessive NP and NL values ​​will lead to a decrease in the overall performance of the algorithm. Only when NP and NL are set in a suitable ratio can the model-based two-stage monarch butterfly optimization method (MTMBO) obtain the best overall performance. Therefore, in this embodiment, the NP value in the model-based two-stage monarch butterfly optimization method (MTMBO) is set to 30 and the NL value is set to 1.

[0230] Effectiveness of feature-based search strategies

[0231] This experiment aims to verify the effectiveness of feature-based search strategy (FSS) in the multi-objective optimization algorithm MTMBO. By comparing the version of MTMBO with FSS and its version without FSS strategy (MTMBO-L), the role of FSS in improving the algorithm performance is evaluated.

[0232] The test case sets used in the experiment are TW1 to TW11, which are used to comprehensively evaluate the algorithm's ability to handle complex multi-objective problems. The comparison algorithm is MTMBO-L, a variant of MTMBO that does not integrate the FSS strategy but uses a random method to complete the optimization of machine sequences. MTMBO-L provides a direct control group to more accurately evaluate the actual impact of FSS.

[0233] To comprehensively evaluate the performance of the algorithm, this experiment continues to use three key performance indicators: HV (Hypervolume), IGD (Inverted Generational Distance), and RV (Response Value). HV is used to measure the diversity of the solution set, IGD evaluates the overall performance of the algorithm, and RV describes the superiority of the final solution obtained by the algorithm.

[0234] Under the same conditions, MTMBO and MTMBO-L are run on the test instance sets TW1 to TW11, and the performance of the two versions on various performance indicators is recorded. The results are shown in Table 4.

[0235] Table 4 Comparison results between MTMBO and MTMBO-L

[0236]

[0237]

[0238] The results in Table 4 show that the MTMBO version using FSS is significantly better than MTMBO-L in terms of IGD and RV values, proving the effectiveness of FSS in improving the quality and superiority of solutions. Although the two perform similarly in terms of HV value, this shows that FSS contributes less to the diversity of the solution set. The main reason is that FSS is an optimization operator for the Pareto frontier, and the higher quality scheduling solutions dominate the original solutions, which in turn reduces the diversity of the Pareto frontier.

[0239] Effectiveness of feature-driven neural network models

[0240] This experiment aims to verify the effectiveness of the feature-based neural network model (FNN) integrated in the MTMBO algorithm. The MTMBO version with FNN is compared with the MTMBO version without FNN (MTMBO-R), where the optimization operator selection strategy of MTMBO-R is random selection. This experiment focuses on the role of FNN in improving the performance of the algorithm. The test instance sets used are TW1 to TW11, which are designed for complex multi-objective optimization problems and aim to comprehensively evaluate the processing capabilities of the algorithm. In the comparative experiment, MTMBO-R is used as the control group without FNN integration in order to accurately evaluate the specific contribution of FNN.

[0241] This experiment continues to use three key performance indicators: HV, IGD, and RV. HV is used to measure the diversity of the solution set, IGD evaluates the overall performance of the algorithm, and RV describes the superiority of the final solution obtained by the algorithm to intuitively demonstrate the effectiveness of FNN. The results are shown in Table 5.

[0242] Table 5 Comparison results between MTMBO and MTMBO-R

[0243]

[0244] The results in Table 5 show that after integrating FNN, the MTMBO algorithm is significantly better than MTMBO-R in IGD and RV values, while the HV value is not much different from the comparison algorithm. Such results prove the effectiveness of FNN in improving the quality and superiority of algorithm solutions, but its contribution to improving the diversity of solution sets is relatively limited. The design purpose of FNN is to select appropriate optimization operators for scheduling solutions and ultimately improve the search efficiency of FSS and reduce the resource consumption of FSS. The introduction of FNN improves the quality of solutions generated by MTMBO, but its improvement in the diversity of solutions is not obvious.

[0245] Comparison Algorithms

[0246] This experiment is used to verify the performance of four algorithms: MTMBO, HADE, MOEA / D and NSGAII on the TW test set. The main body of the comparison algorithm is used to optimize the operation sequence of the scheduling solution, and the optimization of the machine sequence relies on a random method. The test data is evaluated by two performance indicators, IGD value and HV value. Each test case (TW1 to TW22) is run independently 20 times and the original data is recorded. The results are shown in Table 6 and Figure 8 and Fig. 9 shown.

[0247] Table 6 Comparison results of MTMOB, HADE, MOEA / D and NSGAII

[0248]

[0249] Table 6 shows the evaluation data of the test results of each algorithm, among which the IGD index of MTMBO is better than HADE and MOEA / D in the TW test set. In the comparison with NSGAII, MTMBO is better than NSGAII on 19 test instances. In general, MTMBO performs better than the comparison algorithms in the IGD index, which is mainly attributed to the combination of FSS and MBO. FSS is used to optimize the Pareto front individuals to obtain the dominant solution and improve the quality of the Pareto front solution, while the elite strategy and random search method in MBO enable the dominated solutions in the population to achieve the purpose of rapid evolution with the help of the optimized Pareto front. The combination of FSS and MBO is the key to ensure that MTMBO obtains a high-quality solution set.

[0250] Depend on Figure 8 as well as Fig. 9 It can be seen that the average HV index of MTMBO is 0.35, which is the same as NSGA-II. The experiment uses the normalized HV value to test the diversity of the solution set generated by the algorithm. In general, the HV value of MTMBO is not significantly different from that of the comparison algorithm. This is because FSS is an optimization scheme that focuses on the Pareto frontier. When other solutions in the population remain unchanged, optimizing the Pareto frontier solution does not directly increase the number of frontier solutions. The generation of high-quality scheduling solutions will dominate at least one scheduling solution, thereby reducing the number of Pareto frontier solutions. The MBO operator and optimization selection strategy in MTMBO ensure that the diversity of the solution set will not decrease significantly. The genetic strategy in MBO improves the search efficiency of the dominated solution, and replaces the non-dominated solutions generated by FSS with dominated solutions, further maintaining the number of Pareto frontier solutions.

[0251] MTMBO shows good comprehensive performance in multi-objective optimization problems, especially in its ability to approach the true Pareto frontier and maintain the diversity of solution sets. Compared with other algorithms, MTMBO provides a balanced solution that effectively balances the quality and diversity of solutions. Figure 8 The box plot of IGD values ​​for comparative experimental results shows that the overall performance of MTMBO is better than that of the comparative algorithms.

[0252] The MTMBO algorithm shows good comprehensive performance in multi-objective optimization problems, especially in terms of its ability to approach the true Pareto frontier and maintain the diversity of the solution set. Compared with other algorithms, MTMBO provides a balanced solution that effectively balances the quality and diversity of the solution.

[0253] In summary, the scheduling method in the present invention comprehensively considers the factors of transportation and workers, solves the scheduling problem of distributed flexible assembly line workshops through a two-stage monarch butterfly optimization method based on a model, and conducts parameter experiments for MTMBO to verify the effectiveness of FSS and examine the influence of two parameters on algorithm performance. The experimental results show that the appropriate parameter combination is the key to improving algorithm performance. When NP is 30 and NL is 1, MTMBO has the best performance compared with other parameter combinations. The effectiveness experiment of the feature-based search strategy was introduced to verify the effectiveness of FSS. The experimental results show that compared with the random method, the search efficiency of FSS is significantly better than that of the random method. The comprehensive performance of MTMBO integrated with FSS on TW is better than that of MTMBO-L. The effectiveness experiment of the feature-driven neural network model was introduced to verify the effectiveness of FNN. The experimental results show that the introduction of FNN improves the quality of the solution set generated by MTMBO, and FNN improves the search efficiency of FSS. Finally, a comparative experiment was introduced to verify the performance of MTMBO when compared with different types of algorithms. The experimental results showed that the quality of the solution set generated by MTMBO was better than that of the comparative algorithm, while in terms of the diversity of solutions, MTMBO had no obvious advantage. Therefore, the application of MTMBO in solving the distributed flexible flow shop scheduling problem has a better effect.

[0254] In addition, on the other hand, this embodiment further provides a storage medium for receiving the above-mentioned computer program input by a user, and the stored computer program enables the electronic device to execute the above-mentioned distributed flexible assembly line scheduling method based on the two-stage monarch butterfly optimization method of the model, and the above-mentioned storage medium is assembled in an information data processing terminal, which includes a memory and a processor, and the memory stores the above-mentioned computer program. When the computer program is executed by the processor, the processor executes the above-mentioned distributed flexible assembly line scheduling method based on the two-stage monarch butterfly optimization method of the model to solve the scheduling problem of the workshop.

[0255] The above content is a further detailed description of the present invention in combination with specific implementation methods. It cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the scope of protection determined by the claims submitted for the present invention.

Claims

1. A distributed flexible flow shop scheduling method, characterized in that: The model-based two-stage monarch butterfly optimization method is used to deal with the scheduling problem, which includes the following steps: First, the population is initialized for workpieces, factories, and machines to obtain the initial scheduling solution; Then, the operation sequence of the scheduling solution is optimized by using the monarch butterfly optimization method as the main optimization operator; Secondly, a feature-based search strategy is used to optimize the machine sequence of the scheduling solution; Finally, the Pareto solution set is output and the scheduling solution is determined.

2. The method for scheduling a distributed flexible assembly line according to claim 1, characterized in that: When the scheduling problem is handled by the model-based two-stage monarch butterfly optimization method, a feature-driven neural network model is used to match the appropriate optimization operator for the scheduling solution. The feature-driven neural network model is a decision model based on a fully connected neural network. The input of the feature-driven neural network model is a set of statistical features based on the Gantt chart, and the output is the value of the optimization operator. In the input of the feature-driven neural network model, the features of the scheduling solution are composed of 4 arrays, namely: The first array: normalized data of machine downtime; The second array: the ratio of the machine's idle time to the total boot time; The third group: worker fatigue level; The fourth array: the ratio of the number of machine-processed workpieces to the total number of workpieces.

3. The method for scheduling a distributed flexible assembly line according to claim 2, characterized in that: When the feature-based search strategy is used to optimize the machine sequence of the scheduling solution, the Pareto front solution is optimized twice by the feature-based search strategy containing 6 optimization operators. The 6 optimization operators in the feature-based search strategy are as follows: S1 randomly selects a plant and changes the processing plant; S2 exchanges the coding order of any two operations within the key factory; S3 randomly selects an operation of a mutable machine and changes its operation machine to a machine with fewer tasks; S4 randomly exchanges artifacts between factories; S5 randomly changes the processing order of a workpiece; S6 randomly swaps the order of any two operations in the encoding.

4. The method for scheduling a distributed flexible assembly line according to claim 3, characterized in that: Optimizers S1 and S5 ensure that any factory allocation plan is within the search space of the feature-based search strategy; Optimizer S2 directly adjusts the operation order within the key factory; Optimizer S3 exchanges a random task in the current machine to a relatively idle machine, and Optimizer S4 is a strategy for exchanging workpieces between factories; Optimizer S6 arbitrarily changes the operation order.

5. The method for scheduling a distributed flexible assembly line according to claim 1, characterized in that: In the model-based two-stage monarch butterfly optimization method, the model includes the following objective function: min(f1,f2,f3) f1=C max f2=TC=1.3·(For+IE+AE)+ΣTC i,j,j' ·TB i,j,j' i∈{1,2,...,n};j,j'∈{1,2,...,m f,k } <h2 style=";text-align:left;direction:ltr">f3=FI<h2 style=";text-align:left;direction:ltr"> max Among them: min(f1,f2,f3) is the set of factor functions that affect the scheduling problem; C max is the maximum time to complete the work; TC is the total cost; PE is the processing energy consumption of the workpiece; IE is the standby energy consumption of the machine; AE is auxiliary energy consumption; TC i,j,j' TB i,j,j' For transportation costs; i is the workpiece number; j is the machine number; i, j, j' is the transfer of workpieces from machine j to machine j'; FI max The maximum fatigue level of the worker; FI j,t is the worker fatigue degree when machine j is in processing state at time t; MS j,t The processing state of machine j at time t; TB i,j,j' is 0 or 1, if workpiece i is transferred from machine j to machine j', it is 1, otherwise it is 0; TC i,j,j' is the total cost of transferring job i from machine j to machine j'; m f,k is the number of parallel machines in the kth stage of factory f.

6. The method for scheduling a distributed flexible assembly line according to claim 4, characterized in that: The model also includes the following constraints: S i,k+1 -(S i,k +p i,k )≥0 AND i,j,k,f +Y i+1,j,k,f ≤1 S i+1,k -(S i,k +p i,k )-B(2-Y i,j,k,f -Y i,j,k,f +Y i+1,j,k,f )≥0 C i,k =S i,k +p i,k C i,s ≤T Where: F is the number of factories; f is the factory number; n is the number of workpieces; k is the stage number; S represents the number of processing stages; C i,S represents the completion time of workpiece i in stage S; X i,f If job i is assigned to factory f, it is 1, otherwise it is 0; Y i,j,k,f is the processing status of job i on machine j in stage k of factory f, 1 if processed, 0 otherwise; S i,k is the start time of workpiece i in stage k; p i,k is the processing time of workpiece i at stage k; B is an integer; C i,k is the completion time of job i in stage k; T is the total number of time periods; b i,k,t It means that workpiece i is executed in stage k at period t; Z i,j,k,f,t It means that if the processing time of job i on machine j in stage k of factory f is t, it is 1, otherwise it is 0; It means that if workpiece i is in working state in the kth stage of factory f during period t, it is 1, otherwise it is 0; It means that if workpiece i is in the idle state in the kth stage of factory f during period t, it is 1, otherwise it is 0; m f,k represents the number of parallel machines in the kth stage of factory f.

7. A distributed flexible flow shop scheduling system, characterized in that: It includes the objective function and the constraints used to constrain the objective function, where the objective function is: min(f1,f2,f3) f1=C max f2=TC=1.3·(For+IE+AE)+ΣTC i,j,j' ·TB i,j,j' i∈{1,2,...,n};j,j'∈{1,2,...,m f,k } <h2 style=";text-align:left;direction:ltr">f3=FI<h2 style=";text-align:left;direction:ltr"> max Among them: min(f1,f2,f3) is the set of factor functions that affect the scheduling problem; C max is the maximum time to complete the work; TC is the total cost; PE is the processing energy consumption of the workpiece; IE is the standby energy consumption of the machine; AE is auxiliary energy consumption; TC i,j,j' TB i,j,j' For transportation costs; i is the workpiece number; j is the machine number; i, j, j' is the transfer of workpieces from machine j to machine j'; FI max The maximum fatigue level of the worker; FI j,t is the worker fatigue degree when machine j is in processing state at time t; MS j,t The processing state of machine j at time t; TB i,j,j' is 0 or 1, if workpiece i is transferred from machine j to machine j', it is 1, otherwise it is 0; TC i,j,j' represents the total cost of transferring workpiece i from machine j to machine j'; m f,k represents the number of parallel machines in the kth stage of factory f.

8. The distributed flexible assembly line scheduling system according to claim 7 is characterized in that: The constraints are: S i,k+1 -(S i,k +p i,k )≥0 AND i,j,k,f +Y i+1,j,k,f ≤1 S i+1,k -(S i,k +p i,k )-B(2-Y i,j,k,f -Y i,j,k,f +Y i+1,j,k,f )≥0 C i,k =S i,k +p i,k C i,s ≤T Where: F is the number of factories; f is the factory number; n is the number of workpieces; k is the stage number; S represents the number of processing stages; C i,S represents the completion time of workpiece i in stage S; X i,f If job i is assigned to factory f, it is 1, otherwise it is 0; Y i,j,k,f is the processing status of job i on machine j in stage k of factory f, 1 if processed, 0 otherwise; S i,k is the start time of workpiece i in stage k; p i,k is the processing time of workpiece i at stage k; B is an integer; C i,k is the completion time of job i in stage k; T is the total number of time periods; b i,k,t It means that workpiece i is executed in stage k at period t; Z i,j,k,f,t It means that if the processing time of job i on machine j in stage k of factory f is t, it is 1, otherwise it is 0; It means that if workpiece i is in working state in the kth stage of factory f during period t, it is 1, otherwise it is 0; It means that if workpiece i is in the idle state in the kth stage of factory f during period t, it is 1, otherwise it is 0; m f,k represents the number of parallel machines in the kth stage of factory f.

9. A storage medium for receiving a user input program, characterized in that: The stored computer program enables the electronic device to execute the distributed flexible assembly line scheduling method as described in any one of claims 1-6.

10. An information data processing terminal, characterized in that: The terminal includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the distributed flexible assembly line scheduling method as described in any one of claims 1-6.

Images