Distributed fuzzy flexible job shop scheduling method based on MSDBO algorithm

Abstract

The invention provides a distributed fuzzy flexible job shop scheduling method and system based on an MSDBO algorithm, a storage medium and electronic equipment, and relates to the field of flexible job shop scheduling. According to the method, firstly, production resources and workpiece machining tasks are obtained; secondly, representing the machining time of each process of any workpiece on the machine and the transfer time of any workpiece on different machines by adopting a triangular fuzzy number so as to obtain the fuzzy completion time of any workpiece; thirdly, on the basis of the production resources and the workpiece machining tasks, a mathematical model is constructed with the minimum maximum fuzzy completion time as an optimization target; and finally, solving the mathematical model by adopting a multi-strategy dung beetle optimization algorithm to obtain an optimal machine distribution sequence and an optimal workpiece processing sequence. The fuzzy machining time is introduced, the actual production condition is met, meanwhile, production resources of multiple factories are utilized, reasonable distribution of workpieces is achieved, and beneficial help is provided for improving the production efficiency of enterprises.

Description

Technical Field

[0001] The present invention relates to the field of flexible job shop scheduling, and in particular to a distributed fuzzy flexible job shop scheduling method, system, storage medium and electronic equipment based on MSDBO algorithm. Background Art

[0002] In the context of new energy battery manufacturing, the urgent global demand for sustainable development and clean energy continues to drive the production and research and development of new energy batteries, which are the core driving force for the development of emerging industries such as new energy vehicles and smart grids. However, the rapid development of this field has put forward higher requirements on the efficiency and quality of battery production. In the past few decades, the Flexible Job Shop Scheduling Problem (FJSP) has been widely studied due to its complexity and practicality.

[0003] In related technologies, traditional FJSP assumes that all work is completed in a single workshop, but with the rapid development of intelligent manufacturing, the production model of enterprises is undergoing fundamental changes. The transition from traditional centralized production to multi-point distributed production mode not only meets the market demand for efficient and flexible production, but is also an inevitable choice for optimizing resource allocation. The distributed factory model effectively shortens the supply chain, reduces transportation costs, and improves the response speed of the local market through a geographically dispersed layout. The core advantage of this model is that it can achieve resource sharing and capability complementarity among multiple production nodes, significantly improving the flexibility and efficiency of the entire production system.

[0004] In addition, most existing studies assume that the processing time of a job on a machine is a fixed value. However, in actual production, factors such as machine failures, dynamic job insertion, and equipment performance fluctuations make the production environment more complex, resulting in uncertain processing time. This complexity may cause the failure of scheduling tasks, so the uncertainty of processing time has to be considered. Summary of the invention

[0005] 1. Technical issues to be solved

[0006] In view of the deficiencies in the prior art, the present invention provides a distributed fuzzy flexible job shop scheduling method, system, storage medium and electronic device based on the MSDBO algorithm, which solves the technical problems of distributed fuzzy flexible job shop scheduling.

[0007] (II) Technical solution

[0008] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0009] A distributed fuzzy flexible job shop scheduling method based on MSDBO algorithm, comprising:

[0010] Acquire production resources and workpiece processing tasks; wherein the production resources include a distributed set of factories, each factory includes a number of machines, and each workpiece includes a number of processes to be processed;

[0011] The processing time of each process of any workpiece on the machine and the transfer time of any workpiece on different machines are expressed by triangular fuzzy numbers to obtain the fuzzy completion time of any workpiece;

[0012] Based on the production resources and workpiece processing tasks, a mathematical model is constructed with minimizing the maximum fuzzy completion time as the optimization goal;

[0013] The multi-strategy dung beetle optimization algorithm is used to solve the mathematical model to obtain the optimal machine allocation sequence and workpiece processing sequence.

[0014] Preferably, the processing time of each process of any of the workpieces on the machine and the transfer time of any of the workpieces on different machines are represented by triangular fuzzy numbers to obtain the fuzzy completion time of any of the workpieces; including:

[0015] Define J to represent the workpiece set, i is the workpiece number, i = 1, 2, ..., n, n is the total number of workpieces;

[0016] O i Indicates the processing step of workpiece i, j is the process number, j = 1, 2, ..., u i ,u i is the number of processes of workpiece i;

[0017] F represents the set of factories, q is the factory number, q = 1, 2, ..., f, f is the total number of factories;

[0018] M q represents the set of available machines in factory q, k is the machine number, k = 1, 2, ..., m q , m q is the total number of available machines in factory q;

[0019] Q q,k Indicates the machine The number of processing steps on the workpiece; N represents the number of processing steps used for the workpiece;

[0020] The processing time of each process of any workpiece on the machine is represented by triangular fuzzy numbers:

[0021]

[0022] in, Indicates process O ij exist The fuzzy processing time on is the kth machine in factory q; p 1 is the lower bound, p 3 is the upper bound, p 2 is the maximum possible value;

[0023] The transfer time of any workpiece on different machines is represented by triangular fuzzy numbers:

[0024] T=(t 1 ,t 2 ,t 3 ) (2)

[0025] Where T represents the fuzzy transfer time of the workpiece on different machines; t 1 is the lower bound, t 3 is the upper bound, t 2 is the maximum possible value;

[0026] The processes of the same workpiece must be processed in sequence, and when the previous process of the process is not processed on the same machine, the fuzzy start time needs to add the fuzzy transfer time of the workpiece, and limit the start processing time of each process on each machine in each factory:

[0027]

[0028]

[0029] in, Indicates process O i,j-1 The fuzzy completion time of is the decision variable, process O i,j-1 If it is processed on the kth machine in factory q, it is 1, otherwise it is 0; is the decision variable, process O i,j If it is processed on the kth machine in factory q, it is 1, otherwise it is 0;

[0030] represents the fuzzy completion time of the r-1th process processed on the kth machine in factory q; is the decision variable, process O ij If it is the rth process processed on the kth machine in factory q, it is 1, otherwise it is 0;

[0031] Set that once each process of any of the workpieces begins, the processing cannot be interrupted, and obtain the fuzzy completion time of any of the workpieces:

[0032]

[0033] in, Indicates process O i,j The fuzzy completion time of Indicates process O ij The fuzzy start time, O ij represents the j-th process of workpiece i; is a decision variable, which is 1 if job i is assigned to factory q and 0 otherwise.

[0034] Preferably, the mathematical model includes:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Where J represents the workpiece set; i is the workpiece number, i = 1, 2, ..., n; n is the total number of workpieces; O i Indicates the processing step of workpiece i; j is the process number, j = 1, 2, ..., u i ;u i is the number of processes of workpiece i; F represents the set of factories; q is the factory number, q = 1, 2, ..., f; f is the total number of factories; M q represents the set of available machines in factory q; k is the machine number, k = 1, 2, ..., m q ;m q is the total number of available machines in factory q; Q q,k Indicates the machine The number of processing steps on the workpiece; N represents the number of processing steps used for the workpiece;

[0041] Formula (6) is the objective function; min represents the minimization function; represents the maximum fuzzy completion time; represents the fuzzy completion time of job i;

[0042] Formula (7) indicates that the fuzzy completion time of each workpiece is the fuzzy completion time of its last process; represents the uth i The fuzzy completion time of a process;

[0043] Formula (8) indicates that the process of the same workpiece can only be processed in one factory;

[0044] Formula (9) indicates that a process can only be processed on one machine;

[0045] Formula (10) represents the decision variables.

[0046] Preferably, the method of solving the mathematical model by using a multi-strategy dung beetle optimization algorithm to obtain an optimal machine allocation sequence and workpiece processing sequence comprises:

[0047] S31, initialization algorithm parameters, dung beetle population N, problem latitude D, maximum number of iterations T max , maximum number of neighborhood searches q′;

[0048] The factory-process double-layer list structure is used to encode the location of the dung beetle individual, which is expressed as x = [π 1 ,π 2 ],π 1 Assign a code to the factory, π 2 Encode the workpiece processing sequence; and decode the dung beetle individuals into the workpiece processing sequence sequence and machine allocation sequence based on the current maximum fuzzy completion time minimization rule;

[0049] S32, initialize the population and calculate the fitness of the individuals in the population according to formula (6);

[0050] S33, generating a random number δ, if δ<0.9, updating the position of the rolling dung beetle in barrier-free mode according to a preset update strategy, otherwise updating the position of the rolling dung beetle according to an adaptive golden sine strategy;

[0051] S34, according to the update strategy, respectively updating the positions of the breeding dung beetles, the foraging dung beetles and the stealing dung beetles;

[0052] S35, determining whether the dung beetle individual is within the boundary, and executing an improved boundary correction strategy if it is beyond the boundary;

[0053] S36, using the local search algorithm VND to perform local search for the global optimal solution, and judging whether to perform position update based on the greedy rule;

[0054] S37, using an adaptive Cauchy-Gaussian mutation perturbation strategy to perturb the global optimal solution;

[0055] S38, number of iterations t=t+1;

[0056] S39, repeat S33 to S38 until the number of iterations t meets the termination criterion, output the global optimal solution and its fitness value, and decode the global optimal solution to obtain the optimal machine allocation sequence and workpiece processing order sequence.

[0057] Preferably, according to a preset update strategy, the positions of the rolling dung beetle, the breeding dung beetle, the foraging dung beetle and the stealing dung beetle are updated respectively; specifically including:

[0058] (1) For the ball-rolling dung beetle:

[0059] Generate a random number δ between 0 and 1. If δ<0.9, perform the location update in barrier-free mode, otherwise perform the location update in barrier-free mode.

[0060] (a) Accessible mode, the position update formula is defined as follows:

[0061] x e (t+1)=x e (g)+α×h×x e (t-1)+b×Δx,Δx=|x e (t)-X w | (11)

[0062] Among them, x e (t) represents the position of the e-th dung beetle in the population at the t-th iteration; the coefficient h∈(0,0.2] is the deflection coefficient constant, b∈(0,1) is a fixed constant, and α is a natural coefficient with a value of -1 or 1; X w represents the worst position in the current population, and Δx represents the change in light intensity, which is used to guide the position update of the dung beetle;

[0063] (b) In the obstacle mode, the tangent function is used to simulate the dancing behavior to determine the new rolling direction. The position update formula of the dung beetle's dancing behavior is defined as follows:

[0064] x e (t+1)=x e (t)+tan(θ)×|x e (t)-x e (t-1)| (12)

[0065] Among them, the deflection angle θ∈[0,π], when or π, the position of the dung beetle will not be updated;

[0066] (2) For breeding dung beetles

[0067] Introduce a boundary selection strategy to simulate the oviposition area selection of female dung beetles:

[0068]

[0069] Among them, X * Represents the local optimal position in the current population, Lb * and Ub * The lower and upper bounds of the spawning area are defined respectively. Lb and Ub are the lower and upper bounds of the optimization problem respectively;

[0070] After the egg-laying area is determined, the female dung beetle will lay eggs in this area, and the position update formula is defined as follows:

[0071] B e (t+1)=X * +b 1 ×(B e (t)-Lb * )+b 2 ×(B e (t)-Ub * ) (14)

[0072] Among them, B e (t) represents the position of the e-th dung beetle egg at the t-th iteration, b 1 and b 2 represents two independent random vectors whose dimensions are the same as the dimension D of the optimization problem;

[0073] (3) For foraging dung beetles

[0074] The update formula is as follows:

[0075]

[0076] Among them, X b is the global optimal position of the dung beetle population during the iteration process, Lb b and Ub b The lower and upper bounds of the foraging area are defined respectively;

[0077] The position update formula of the dung beetle is defined as follows:

[0078] x i (t+1)=X b +C 1 ×(x i (t)-Lb b )+C 2 ×(x i (t)-Ub b ) (16)

[0079] Among them, C 1 represents a random variable that follows a normal distribution, C 2 represents a random vector of size 1×D belonging to (0,1);

[0080] (4) For the stealing dung beetle

[0081] The position update formula is defined as follows:

[0082] x e (t+1)=X b +S×g×(|x e (t)-X * |+|x e (t)-X b|) (17)

[0083] Where S represents a fixed constant and g represents a random vector of size 1×D that follows a normal distribution.

[0084] Preferably, the adaptive golden sine strategy refers to:

[0085]

[0086]

[0087] Among them, ω 2 =(1-ω 1 ),ω max and ω min They are the inertia weight coefficient ω 1 The maximum and minimum values ​​of r 1 ∈[0,2π] and r 2 ∈[0,π] is a random number that follows a normal distribution, r 1 Determines the moving distance of the rolling dung beetle during the iteration process, r 2 Determine the position update direction of the dung beetle individual in the next iteration; γ 1 =p * τ+q * (1-τ) and γ 2 =q * τ+p * (1-τ) is obtained by introducing the golden section number The obtained coefficient, weight p * and q * The initial values ​​of are set to -π and π respectively, and then the coefficient γ 1 and γ 2 changes with the changes of.

[0088] Preferably, the improved boundary correction strategy refers to:

[0089]

[0090] Among them, lb f andub f are the upper and lower limits of each dimension of the dung beetle individual; x ef is the value of the e-th dung beetle individual at latitude f.

[0091] Preferably, the adaptive Cauchy-Gaussian variation perturbation strategy refers to:

[0092] x i (t+1)=x i (t)*(1+μ 1 *cauchy(σ)+μ 2*Gaussion(σ)) (21)

[0093] Among them, t represents the number of iterations, x i (t) represents the position of the i-th dung beetle in the population at the t-th iteration, and the mutation operator weight coefficient represents a random variable that follows a Cauchy distribution, expressed as δ is a random variable that obeys the standard normal distribution, and Gaussion (σ) represents a random variable that obeys the Gaussian distribution.

[0094] Preferably, the following four neighborhood structures are set:

[0095] Neighborhood structure 1: Select the factory with the longest maximum fuzzy completion time as the key factory, and randomly select a job in this factory and assign it to the factory with the shortest fuzzy completion time;

[0096] Neighborhood structure 2: Randomly exchange two different processes in a critical factory, which contains at least one critical process;

[0097] Neighborhood structure 3: Randomly select two different processes in the critical factory, which contains at least one critical process, and then insert the second process before the first process;

[0098] Neighborhood structure 4: Randomly select two different processes in the key factory, which contains at least one key process, and then sort all the processes between these two processes in reverse order;

[0099] The local search algorithm VND is used to perform local search for the global optimal solution, and whether to perform position update is determined based on the greedy rule; including:

[0100] S361, determine the initial solution as the optimal dung beetle position X b , let the neighborhood solution be equal to the initial solution, combined with the maximum neighborhood search times q′;

[0101] S362, execute neighborhood structure 1 q′ times, and if the generated new neighborhood solution is better than the original neighborhood solution, update the original neighborhood solution.

[0102] S363. If the final neighborhood solution is better than the initial solution, update the initial solution and proceed to S362; otherwise, proceed to S364.

[0103] S364, executing neighborhood structure 2 q′ times, if the generated new neighborhood solution is better than the original neighborhood solution, then updating the original neighborhood solution.

[0104] S365. If the final neighborhood solution is better than the initial solution, update the initial solution and proceed to S362; otherwise, proceed to S366.

[0105] S366, execute neighborhood structure 3 q′ times, and if the generated new neighborhood solution is better than the original neighborhood solution, update the original neighborhood solution.

[0106] S367. If the final neighborhood solution is better than the initial solution, update the initial solution and proceed to S362; otherwise, proceed to S368.

[0107] S368, executing neighborhood structure 4 q′ times, if the generated new neighborhood solution is better than the original neighborhood solution, then updating the original neighborhood solution.

[0108] S369. If the final neighborhood solution is better than the initial solution, the initial solution is updated and the process proceeds to S362; otherwise, the algorithm ends and determines whether to perform a position update based on the greedy rule and the process proceeds to S37.

[0109] A distributed fuzzy flexible job shop scheduling system based on MSDBO algorithm, comprising:

[0110] An acquisition module is used to acquire production resources and workpiece processing tasks; wherein the production resources include a distributed set of factories, each factory includes a number of machines, and each workpiece includes a number of processes to be processed;

[0111] A representation module is used to represent the processing time of each process of any of the workpieces on the machine and the transfer time of any of the workpieces on different machines by using triangular fuzzy numbers to obtain the fuzzy completion time of any of the workpieces;

[0112] A construction module is used to construct a mathematical model based on the production resources and the workpiece processing tasks with minimizing the maximum fuzzy completion time as the optimization goal;

[0113] The solution module is used to solve the mathematical model by adopting a multi-strategy dung beetle optimization algorithm to obtain an optimal machine allocation sequence and workpiece processing sequence.

[0114] A storage medium stores a computer program for distributed fuzzy flexible job shop scheduling based on the MSDBO algorithm, wherein the computer program enables a computer to execute the distributed fuzzy flexible job shop scheduling method as described above.

[0115] An electronic device, comprising:

[0116] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, the programs including a method for executing the distributed fuzzy flexible job shop scheduling method as described above.

[0117] (III) Beneficial effects

[0118] The present invention provides a distributed fuzzy flexible job shop scheduling method, system, storage medium and electronic device based on the MSDBO algorithm. Compared with the prior art, it has the following beneficial effects:

[0119] In the present invention, firstly, production resources and workpiece processing tasks are obtained; secondly, the processing time of each process of any workpiece on the machine and the transfer time of any workpiece on different machines are expressed by triangular fuzzy numbers to obtain the fuzzy completion time of any workpiece; again, based on the production resources and workpiece processing tasks, a mathematical model is constructed with minimizing the maximum fuzzy completion time as the optimization goal; finally, a multi-strategy dung beetle optimization algorithm is used to solve the mathematical model to obtain the optimal machine allocation sequence and workpiece processing sequence sequence. The present invention introduces fuzzy processing time, which is in line with actual production conditions, and at the same time utilizes the production resources of multiple factories to achieve reasonable allocation of workpieces, which provides useful help in improving enterprise production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0121] Figure 1 A block diagram of a distributed fuzzy flexible job shop scheduling method based on the MSDBO algorithm provided by an embodiment of the present invention;

[0122] Figure 2 A schematic diagram of a distributed flexible job shop manufacturing system is provided for an embodiment of the present invention;

[0123] Figure 3 A flowchart of a multi-strategy dung beetle optimization (MSDBO) algorithm is provided for an embodiment of the present invention;

[0124] Figure 4 A schematic diagram of a current maximum fuzzy completion time minimization (MCN) decoding rule is provided for an embodiment of the present invention;

[0125] Figure 5 A schematic diagram of encoding and decoding is provided for an embodiment of the present invention;

[0126] Figures 6 to 8 An example Gantt chart of an optimal machine allocation sequence and workpiece processing sequence is provided for an embodiment of the present invention. DETAILED DESCRIPTION

[0127] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0128] The embodiments of the present application solve the technical problem of distributed fuzzy flexible job shop scheduling by providing a distributed fuzzy flexible job shop scheduling method, system, storage medium and electronic device based on the MSDBO algorithm.

[0129] The technical solution in the embodiment of the present application is to solve the above technical problems, and the overall idea is as follows:

[0130] The embodiment of the present invention studies the distributed fuzzy flexible job shop scheduling problem with transfers (DFFJSPT) considering the workpiece transfer time.

[0131] Specifically, the embodiment of the present invention uses triangular fuzzy numbers to perform fuzzy processing on the processing time, and takes the minimization of the maximum fuzzy completion time as the goal, and proposes a Multi-Strategy DungBeetle Optimizer (MSDBO). The algorithm is inspired by the rolling, dancing, reproduction, foraging and stealing behaviors of dung beetles in nature. It was proposed by Professor Shen Bo's team of Donghua University in 2023. The optimization variable is regarded as the position of the dung beetle in the solution space, and its position is changed by simulating its behavior. It continuously iterates and optimizes in the multidimensional space, so as to find the global optimal solution that meets the requirements.

[0132] Furthermore, based on the distributed characteristics of DFFJSPT, a two-layer encoding strategy combining factory and process information was adopted. The machine allocation was determined by the greedy strategy during the decoding process, and the boundary correction algorithm was redesigned. In addition, the algorithm introduced the Adaptive Golden Sine Algorithm (Golden-SA) and the Adaptive Cauchy-Gaussian Mixture (ACGM), and the Variable Neighborhood Descent (VND) algorithm with four neighborhood structures, which significantly improved the search efficiency. It provides useful help for effectively utilizing the production resources of multiple factories, realizing the reasonable allocation of workpieces, and improving the production efficiency of enterprises.

[0133] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0134] Embodiment 1:

[0135] like Figure 1 As shown, an embodiment of the present invention provides a distributed fuzzy flexible job shop scheduling method based on the MSDBO algorithm, including:

[0136] S1. Acquire production resources and workpiece processing tasks; wherein the production resources include a distributed set of factories, each factory includes a number of machines, and each workpiece includes a number of processes to be processed;

[0137] S2, the processing time of each process of any of the workpieces on the machine and the transfer time of any of the workpieces on different machines are expressed by triangular fuzzy numbers to obtain the fuzzy completion time of any of the workpieces;

[0138] S3, based on the production resources and workpiece processing tasks, a mathematical model is constructed with minimizing the maximum fuzzy completion time as the optimization goal;

[0139] S4. Use a multi-strategy dung beetle optimization algorithm to solve the mathematical model and obtain the optimal machine allocation sequence and workpiece processing sequence.

[0140] The embodiment of the present invention introduces fuzzy processing time to meet actual production conditions, while utilizing production resources of multiple factories to achieve reasonable allocation of workpieces, thereby providing beneficial help in improving enterprise production efficiency.

[0141] First of all, it should be noted that the embodiment of the present invention is aimed at the distributed fuzzy flexible job shop scheduling problem (DFFJSPT) considering the workpiece transfer time. Figure 2 As shown, Figure 2 A schematic diagram of a distributed flexible job shop manufacturing system is given, and the related problems are described as follows:

[0142] Assume that there are n workpieces J = {J 1 ,J 2 ,…,J n}(i=1,2,…,n) are assigned to f factories located in different locations F={F 1 ,F 2 ,…,F f Each factory can be regarded as an FJSP and is assigned to factory F q The workpiece needs to be in the factory m q On the machine Processing, each workpiece Ji Contains u i The order of the processes is predetermined. represents the jth processing step of workpiece i. Each process requires the optional machine set in the assigned factory. Select a machine for processing.

[0143] Next, we will introduce the steps of the above scheme in detail:

[0144] In step S1, production resources and workpiece processing tasks are obtained; wherein the production resources include a distributed set of factories, each factory includes a number of machines, and each workpiece includes a number of processes to be processed.

[0145] This step obtains the production resources and workpiece processing task data used for mathematical modeling in the subsequent steps, and defines the symbols and descriptions shown in Table 1:

[0146] Table 1

[0147]

[0148]

[0149] In step S2, the processing time of each process of any of the workpieces on the machine and the transfer time of any of the workpieces on different machines are represented by triangular fuzzy numbers to obtain the fuzzy completion time of any of the workpieces.

[0150] In this step, the processing time of each process of any workpiece on the machine and the transfer time of any workpiece on different machines are discussed based on fuzzy set theory. Among them, the processing time of the process on the machine is expressed as a triangular fuzzy number, and the transfer time of the workpiece on different machines. It can be understood that the introduction of fuzzy set theory facilitates the subsequent setting of the scheduling goal of DFFJSPT, that is, assigning factories to workpieces and assigning each process to the appropriate processing machine in the corresponding factory according to constraints to minimize the maximum fuzzy completion time.

[0151] Specifically, the process of obtaining the fuzzy completion time of any of the workpieces is as follows:

[0152] The processing time of each process of any workpiece on the machine is represented by triangular fuzzy numbers:

[0153]

[0154] in, Indicates process O ij exist The fuzzy processing time on is the kth machine in factory q; p 1is the lower bound, p 3 is the upper bound, p 2 is the maximum possible value.

[0155] The transfer time of any workpiece on different machines is represented by triangular fuzzy numbers:

[0156] T=(t 1 ,t 2 ,t 3 ) (2)

[0157] Where T represents the fuzzy transfer time of the workpiece on different machines; t 1 is the lower bound, t 3 is the upper bound, t 2 is the maximum possible value.

[0158] The processes of the same workpiece must be processed in sequence, and when the previous process of the process is not processed on the same machine, the fuzzy start time needs to add the fuzzy transfer time of the workpiece, and limit the start processing time of each process on each machine in each factory:

[0159]

[0160]

[0161] in, Indicates process O i,j-1 The fuzzy completion time of is the decision variable, process O i,j-1 If it is processed on the kth machine in factory q, it is 1, otherwise it is 0; is the decision variable, process O i,j If it is processed on the kth machine in factory q, it is 1, otherwise it is 0;

[0162] represents the fuzzy completion time of the r-1th process processed on the kth machine in factory q; is the decision variable, process O ij It is 1 if the rth process is processed on the kth machine in factory q, otherwise it is 0.

[0163] Set that once each process of any of the workpieces begins, the processing cannot be interrupted, and obtain the fuzzy completion time of any of the workpieces:

[0164]

[0165] in, Indicates process O i,j The fuzzy completion time of Indicates process O ijThe fuzzy start time, O ij represents the j-th process of workpiece i; is a decision variable, which is 1 if job i is assigned to factory q and 0 otherwise.

[0166] In step S3, based on the production resources and workpiece processing tasks, a mathematical model is constructed with minimizing the maximum fuzzy completion time as the optimization goal.

[0167] It is necessary to clarify the following assumptions related to model construction in advance:

[0168] (1) Each manufacturing plant can complete the processing of any workpiece;

[0169] (2) Each workpiece can only be assigned to one factory for processing;

[0170] (3) The same machine can only process one workpiece at a time;

[0171] (4) The same process of the same workpiece can only be processed by one machine at the same time;

[0172] (5) Once a process for each workpiece begins, the processing cannot be interrupted;

[0173] (6) Different artifacts have the same priority;

[0174] (7) There are no order constraints between the processes of different workpieces, but there are order constraints between the processes of the same workpiece;

[0175] (8) All workpieces can be processed at time zero;

[0176] (9) The fuzzy processing time of the process on the machine includes the setup time, etc., but does not include the fuzzy transfer time of the workpiece between different machines;

[0177] (10) Have sufficient tools to complete the transfer of workpieces without considering loading and unloading time.

[0178] On this basis, and combined with the fuzzy completion time of the process obtained in step 2, this step constructs the following mathematical model:

[0179]

[0180]

[0181]

[0182]

[0183]

[0184] Wherein, formula (6) is the objective function; min represents the minimization function;

[0185] Formula (7) indicates that the fuzzy completion time of each workpiece is the fuzzy completion time of its last process;

[0186] Formula (8) indicates that the process of the same workpiece can only be processed in one factory;

[0187] Formula (9) indicates that a process can only be processed on one machine;

[0188] Formula (10) represents the decision variables.

[0189] In step S4, a multi-strategy dung beetle optimization algorithm is used to solve the mathematical model to obtain the optimal machine allocation sequence and workpiece processing sequence.

[0190] The embodiment of the present invention designs an MSDBO algorithm. According to the distributed characteristics of DFFJSPT, a two-layer encoding strategy combining factory and process information is adopted. The machine allocation is determined by the greedy strategy during the decoding process, and the boundary correction algorithm is redesigned. In addition, the algorithm introduces the adaptive golden sine strategy (Golden-SA) and the adaptive Cauchy-Gaussian mixture mutation strategy (ACGM), and cooperates with the variable neighborhood descent algorithm (VND) of four neighborhood structures to significantly improve the search efficiency.

[0191] Specifically, if Figure 3 As shown, this step includes:

[0192] S31, initialization algorithm parameters, dung beetle population N, problem latitude D, maximum number of iterations T max , the maximum number of neighborhood searches q′.

[0193] The encoding and decoding rules are as follows:

[0194] Considering the convergence of the solution space and the algorithm, the embodiment of the present invention adopts a double-layer list structure based on the factory sequence and the process sequence for encoding, and the machine allocation is decoded as follows: Figure 4 The current maximum fuzzy completion time minimization rule (MCN) is shown. 1 Indicates the factory assigned code, π 2 represents the workpiece processing sequence code. Each element in the list is a random number from 0 to 1. The factory code length is the number of workpieces, and the process code length is the total number of processes. The position of each dung beetle individual can be expressed as x = [π 1 ,π 2 ].

[0195] The individual positions of dung beetles are decoded into workpiece processing sequence and machine allocation sequence according to certain rules. For example, the factory encoding π1 =[1,2,1], the first "1" in the code means that the first workpiece is assigned to factory 1 for processing; process code π 2 =[1,2,2,1,3,2,3,3,1,2], the first "1" in the code means the first process O of workpiece 1 11 .

[0196] For example, Figure 5 As shown, Figure 5 A coding and decoding diagram is given.

[0197] S32, initialize the population and calculate the fitness of the individuals in the population according to formula (6).

[0198] S33. Generate a random number δ. If δ<0.9, update the position of the rolling dung beetle in barrier-free mode according to a preset update strategy. Otherwise, update the position of the rolling dung beetle according to an adaptive golden sine strategy.

[0199] Among them, according to the preset update strategy, the rolling ball dung beetle is updated; specifically including:

[0200] (1) For the ball-rolling dung beetle:

[0201] Generate a random number δ between 0 and 1. If δ<0.9, update the location based on formula (11) in barrier-free mode. Otherwise, update the location based on formula (13) in barrier-free mode.

[0202] (a) Accessible mode, the position update formula is defined as follows:

[0203] x e (t+1)=x e (g)+α×h×x e (t-1)+b×Δx,Δx=|x e (t)-X w | (11)

[0204] Among them, x e (t) represents the position of the e-th dung beetle in the population at the t-th iteration; the coefficient h∈(0,0.2] is the deflection coefficient constant, b∈(0,1) is a fixed constant, and α is a natural coefficient with a value of -1 or 1; X w represents the worst position in the current population, and Δx represents the change in light intensity, which is used to guide the position update of the dung beetle;

[0205] (b) In the obstacle mode, the tangent function is used to simulate the dancing behavior to determine the new rolling direction. The position update formula of the dung beetle's dancing behavior is defined as follows:

[0206] x e (t+1)=xe (t)+tan(θ)×|x e (t)-x e (t-1)| (12)

[0207] Among them, the deflection angle θ∈[0,π], when or π, the position of the dung beetle will not be updated.

[0208] Different from the traditional Dung Beetle Optimization Algorithm (DBO), the embodiment of the present invention introduces an adaptive golden sine strategy to improve dancing behavior in the obstacle mode. Specifically, inspired by the inertia weight idea in the improved particle swarm algorithm, the embodiment of the present invention proposes an adaptive golden sine (AGSA) strategy to further optimize the global exploration and local development capabilities of the algorithm, and introduces an adaptive variable inertia weight coefficient ω 1 , the improved formula is as follows:

[0209]

[0210]

[0211] Among them, ω 2 =(1-ω 1 ),ω max and ω min They are the inertia weight coefficient ω 1 The maximum and minimum values ​​of r 1 ∈[0,2π] and r 2 ∈[0,π] is a random number that follows a normal distribution, r 1 Determines the moving distance of the rolling dung beetle during the iteration process, r 2 Determine the position update direction of the dung beetle individual in the next iteration; γ 1 =p * τ+p * (1-τ) and γ 2 =q * τ+p * (1-τ) is obtained by introducing the golden section number The obtained coefficient, weight p * and q * The initial values ​​of are set to -π and π respectively, and then the coefficient γ 1 and γ 2 changes with the changes of.

[0212] S34. According to the update strategy, the positions of the breeding dung beetles, the foraging dung beetles and the stealing dung beetles are updated respectively.

[0213] Among them, according to the preset update strategy, the positions of the breeding dung beetles, the foraging dung beetles and the stealing dung beetles are updated respectively; specifically including:

[0214] (2) For breeding dung beetles

[0215] Introduce a boundary selection strategy to simulate the oviposition area selection of female dung beetles:

[0216]

[0217] Among them, X * Represents the local optimal position in the current population, Lb * and Ub * The lower and upper bounds of the spawning area are defined respectively. Lb and Ub are the lower and upper bounds of the optimization problem respectively;

[0218] After the egg-laying area is determined, the female dung beetle will lay eggs in this area, and the position update formula is defined as follows:

[0219] B e (t+1)=X * +b 1 ×(B e (t)-Lb * )+b 2 ×(B e (t)-Ub * ) (16)

[0220] Among them, B e (t) represents the position of the e-th dung beetle egg at the t-th iteration, b 1 and b 2 represents two independent random vectors whose dimensions are the same as the dimension D of the optimization problem;

[0221] (3) For foraging dung beetles

[0222] The update formula is as follows:

[0223]

[0224] Among them, X b is the global optimal position of the dung beetle population during the iteration process, Lb b and Ub b The lower and upper bounds of the foraging area are defined respectively;

[0225] The position update formula of the dung beetle is defined as follows:

[0226] x i (t+1)=X b +C 1 ×(x i (t)-Lb b )+C 2 ×(xi (t)-Ub b ) (18)

[0227] Among them, C 1 represents a random variable that follows a normal distribution, C 2 represents a random vector of size 1×D belonging to (0,1);

[0228] (4) For the stealing dung beetle

[0229] The position update formula is defined as follows:

[0230] x e (t+1)=X b +S×g×(|x e (t)-X * |+|x e (t)-X b |) (19)

[0231] Where S represents a fixed constant and g represents a random vector of size 1×D that follows a normal distribution.

[0232] S35, determining whether the dung beetle individual is within the boundary, and executing an improved boundary correction strategy if it is beyond the boundary.

[0233] The embodiment of the present invention proposes a new boundary correction strategy. This strategy does not simply pull the out-of-bounds position back to the boundary, but remaps the out-of-bounds part into the search interval through a modulo operation. The specific method is defined as follows:

[0234]

[0235] Among them, lb f andub f are the upper and lower limits of each dimension of the dung beetle individual; x ef is the value of the e-th dung beetle individual at latitude f.

[0236] S36. Use the local search algorithm VND to perform local search for the global optimal solution, and determine whether to update the position based on the greedy rule.

[0237] In order to enhance the local search performance of the algorithm, this embodiment designs a local search strategy including the following four neighborhood structures. These four neighborhood structures are used simultaneously in the search process to prevent the algorithm from falling into the local optimal solution too early, thereby enhancing the global search effect. Given that the maximum fuzzy completion time in DFFJSPT is determined by the key factory with the longest completion time among all factories, each neighborhood structure is designed around the key factory.

[0238] Neighborhood structure 1: Select the factory with the longest maximum fuzzy completion time as the key factory, and randomly select a job in this factory and assign it to the factory with the shortest fuzzy completion time;

[0239] Neighborhood structure 2: Randomly exchange two different processes in a critical factory, which contains at least one critical process;

[0240] Neighborhood structure 3: Randomly select two different processes in the critical factory, which contains at least one critical process, and then insert the second process before the first process;

[0241] Neighborhood structure 4: Randomly select two different processes in the key factory, which contains at least one key process, and then sort all the processes between these two processes in reverse order;

[0242] Accordingly, step S36 specifically includes:

[0243] S361, determine the initial solution as the optimal dung beetle position X b , let the neighborhood solution be equal to the initial solution, combined with the maximum neighborhood search times q′;

[0244] S362, execute neighborhood structure 1 q′ times, and if the generated new neighborhood solution is better than the original neighborhood solution, update the original neighborhood solution.

[0245] S363. If the final neighborhood solution is better than the initial solution, update the initial solution and proceed to S362; otherwise, proceed to S364.

[0246] S364, executing neighborhood structure 2 q′ times, if the generated new neighborhood solution is better than the original neighborhood solution, then updating the original neighborhood solution.

[0247] S365. If the final neighborhood solution is better than the initial solution, update the initial solution and proceed to S362; otherwise, proceed to S366.

[0248] S366, execute neighborhood structure 3 q′ times, and if the generated new neighborhood solution is better than the original neighborhood solution, update the original neighborhood solution.

[0249] S367. If the final neighborhood solution is better than the initial solution, update the initial solution and proceed to S362; otherwise, proceed to S368.

[0250] S368, executing neighborhood structure 4 q′ times, if the generated new neighborhood solution is better than the original neighborhood solution, then updating the original neighborhood solution.

[0251] S369. If the final neighborhood solution is better than the initial solution, the initial solution is updated and the process proceeds to S362; otherwise, the algorithm ends and determines whether to perform a position update based on the greedy rule of formula (21), and the process proceeds to S37.

[0252] Among them, considering that the positions of the four dung beetles will be continuously updated during the optimization process of DBO, the algorithm uses the greedy rule to compare the updated position with the original position to select individuals with better fitness to enter the next iteration. The greedy rule can be expressed as:

[0253]

[0254] Among them, x i (t) represents the dung beetle individuals in the current iteration population, x e(new) (t+1) represents the dung beetle individual after the position is updated, and f(x) represents the fitness function of the dung beetle individual x.

[0255] S37. Use the adaptive Cauchy-Gaussian mutation perturbation strategy to perturb the global optimal solution.

[0256] It should be noted that Gaussian mutation is widely used due to its good local search ability and fast algorithm convergence. However, it is weak in guiding individuals to jump out of the local optimal solution, which is not conducive to achieving global optimal convergence. In contrast, Cauchy mutation can produce a larger variation step length, which is conducive to improving the diversity of the population, thereby enhancing the global search ability of the algorithm.

[0257] Based on this, an embodiment of the present invention proposes an adaptive Cauchy-Gaussian mixture variation perturbation method (ACGM), the formula of which is as follows:

[0258] x i (t+1)=x i (t)*(1+μ 1 *cauchy(σ)+μ 2 *Gaussion(σ)) (22)

[0259] Among them, t represents the number of iterations, x i (t) represents the position of the i-th dung beetle in the population at the t-th iteration, and the mutation operator weight coefficient cauchy(σ) represents a random variable that follows the Cauchy distribution, expressed as δ is a random variable that obeys the standard normal distribution, and Gaussion (σ) represents a random variable that obeys the Gaussian distribution.

[0260] S38. Number of iterations t=t+1.

[0261] S39, repeat S33 to S38 until the number of iterations t meets the termination criterion, output the global optimal solution and its fitness value, and decode the global optimal solution to obtain the optimal machine allocation sequence and workpiece processing order sequence.

[0262] Further, after obtaining the optimal machine allocation sequence and workpiece processing sequence, the embodiment of the present invention can obtain a corresponding scheduling Gantt chart. Figures 6 to 8 As shown, an example Gantt chart of the optimal machine allocation sequence and workpiece processing sequence is given.

[0263] So far, the embodiment of the present invention has completed the entire process of the distributed fuzzy flexible job shop scheduling method based on the MSDBO algorithm.

[0264] Embodiment 2:

[0265] The embodiment of the present invention provides a distributed fuzzy flexible job shop scheduling system based on the MSDBO algorithm, including:

[0266] An acquisition module is used to acquire production resources and workpiece processing tasks; wherein the production resources include a distributed set of factories, each factory includes a number of machines, and each workpiece includes a number of processes to be processed;

[0267] A representation module is used to represent the processing time of each process of any of the workpieces on the machine and the transfer time of any of the workpieces on different machines by using triangular fuzzy numbers to obtain the fuzzy completion time of any of the workpieces;

[0268] A construction module is used to construct a mathematical model based on the production resources and the workpiece processing tasks with minimizing the maximum fuzzy completion time as the optimization goal;

[0269] The solution module is used to solve the mathematical model by adopting a multi-strategy dung beetle optimization algorithm to obtain an optimal machine allocation sequence and workpiece processing sequence.

[0270] Embodiment 3:

[0271] An embodiment of the present invention provides a storage medium storing a computer program for distributed fuzzy flexible job shop scheduling based on the MSDBO algorithm, wherein the computer program enables a computer to execute the distributed fuzzy flexible job shop scheduling method as described in Example 1.

[0272] Example 4

[0273] An embodiment of the present invention provides an electronic device, including:

[0274] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and the programs include a method for executing the distributed fuzzy flexible job shop scheduling method as described in Example 1.

[0275] It can be understood that the distributed fuzzy flexible job shop scheduling system based on the MSDBO algorithm, storage medium and electronic device provided in the embodiments of the present invention correspond to the distributed fuzzy flexible job shop scheduling method based on the MSDBO algorithm provided in the embodiments of the present invention. The explanations, examples and beneficial effects of the relevant contents can refer to the corresponding parts in the distributed fuzzy flexible job shop scheduling method, which will not be repeated here.

[0276] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0277] 1. The embodiment of the present invention introduces fuzzy processing time, which is in line with actual production conditions. At the same time, it utilizes the production resources of multiple factories to achieve reasonable allocation of workpieces, thus providing beneficial help in improving the production efficiency of enterprises.

[0278] 2. The embodiment of the present invention discusses the FJSP considering workpiece transfer in a distributed fuzzy environment. The characteristic of this problem is that the workpiece transfer is limited to machines within the factory. This is the first attempt to deal with the workpiece transfer problem in a distributed fuzzy environment. In view of the complexity of DFFJSPT, an MSDBO that mixes multiple improvement strategies on the basis of DBO is proposed to minimize the maximum fuzzy completion time. In MSDBO, a double-layer encoding strategy is designed according to the characteristics of DFFJSPT to ensure that the algorithm has good convergence and stability; a new boundary correction strategy is introduced to enhance the diversity of the population; the AGSA strategy is used to improve the dancing behavior of dung beetles, thereby enhancing the global search capability; and a VND local search method with four neighborhood structures is designed, which not only improves the local search efficiency, but also expands the solution space; in addition, the ACGM strategy is introduced to effectively improve the ability of the algorithm to jump out of the local optimal solution in the later stage of the search.

[0279] 3. The embodiments of the present invention are mainly derived from in-depth field research on a new energy battery manufacturing enterprise and its factories. The problem background is in line with reality, and the factors considered are the aspects that the enterprise can currently optimize and improve. The proposed solution can effectively utilize the production resources of multiple factories and achieve close alignment of the maximum fuzzy completion time between factories, significantly improving production efficiency and effectively reducing enterprise costs. It provides ideas for enterprises to achieve further lean production and provides decision-making theoretical support for enterprise managers, which has certain display reference significance.

[0280] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0281] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A distributed fuzzy flexible job shop scheduling method based on MSDBO algorithm, characterized in that: include: Obtain production resources and workpiece processing tasks; The production resources include a distributed set of factories, each factory includes a number of machines, and each workpiece includes a number of processes to be processed; The processing time of each process of any workpiece on the machine and the transfer time of any workpiece on different machines are expressed by triangular fuzzy numbers to obtain the fuzzy completion time of any workpiece; Based on the production resources and workpiece processing tasks, a mathematical model is constructed with minimizing the maximum fuzzy completion time as the optimization goal; The multi-strategy dung beetle optimization algorithm is used to solve the mathematical model to obtain the optimal machine allocation sequence and workpiece processing sequence.

2. The distributed fuzzy flexible job shop scheduling method according to claim 1, characterized in that: The processing time of each process of any of the workpieces on the machine and the transfer time of any of the workpieces on different machines are represented by triangular fuzzy numbers to obtain the fuzzy completion time of any of the workpieces; including: Define J to represent the workpiece set, i is the workpiece number, i = 1, 2, ..., n, n is the total number of workpieces; O i Indicates the processing step of workpiece i, j is the process number, j = 1, 2, ..., u i ,u i is the number of processes of workpiece i; F represents the set of factories, q is the factory number, q = 1, 2, ..., f, f is the total number of factories; M q represents the set of available machines in factory q, k is the machine number, k = 1, 2, ..., m q , m q is the total number of available machines in factory q; Q q,k Indicates the machine The number of processing steps on the workpiece; N represents the number of processing steps used for the workpiece; The processing time of each process of any workpiece on the machine is represented by triangular fuzzy numbers: in, Indicates process O ij exist The fuzzy processing time on is the kth machine in factory q; p1 is the lower bound, p3 is the upper bound, and p2 is the maximum possible value; The transfer time of any workpiece on different machines is represented by triangular fuzzy numbers: T=(t1,t2,t3) (2) Where T represents the fuzzy transfer time of workpieces on different machines; t1 is the lower bound, t3 is the upper bound, and t2 is the maximum possible value; The processes of the same workpiece must be processed in sequence, and when the previous process of the process is not processed on the same machine, the fuzzy start time needs to add the fuzzy transfer time of the workpiece, and limit the start processing time of each process on each machine in each factory: in, Indicates process O i,j-1 The fuzzy completion time of is the decision variable, process O i,j-1 If it is processed on the kth machine in factory q, it is 1, otherwise it is 0; is the decision variable, process O i,j If it is processed on the kth machine in factory q, it is 1, otherwise it is 0; represents the fuzzy completion time of the r-1th process processed on the kth machine in factory q; is the decision variable, process O ij If it is the rth process processed on the kth machine in factory q, it is 1, otherwise it is 0; Set that once each process of any of the workpieces is started, the processing cannot be interrupted, and obtain the fuzzy completion time of any of the workpieces: in, Indicates process O i,j The fuzzy completion time of Indicates process O ij The fuzzy start time, O ij represents the j-th process of workpiece i; is a decision variable, which is 1 if job i is assigned to factory q and 0 otherwise.

3. The distributed fuzzy flexible job shop scheduling method according to claim 2, characterized in that: The mathematical model includes: Where J represents the workpiece set; i is the workpiece number, i = 1, 2, ..., n; n is the total number of workpieces; O i Indicates the processing step of workpiece i; j is the process number, j = 1, 2, ..., u i ;u i is the number of processes of workpiece i; F represents the set of factories; q is the factory number, q = 1, 2, ..., f; f is the total number of factories; M q represents the set of available machines in factory q; k is the machine number, k = 1, 2, ..., m q ;m q is the total number of available machines in factory q; Q q,k Indicates the machine The number of processing steps on the workpiece; N represents the number of processing steps used for the workpiece; Formula (6) is the objective function; min represents the minimization function; represents the maximum fuzzy completion time; represents the fuzzy completion time of job i; Formula (7) indicates that the fuzzy completion time of each workpiece is the fuzzy completion time of its last process; represents the uth i The fuzzy completion time of a process; Formula (8) indicates that the process of the same workpiece can only be processed in one factory; Formula (9) indicates that a process can only be processed on one machine; Formula (10) represents the decision variables.

4. The distributed fuzzy flexible job shop scheduling method according to claim 3, characterized in that: The method adopts a multi-strategy dung beetle optimization algorithm to solve the mathematical model and obtain an optimal machine allocation sequence and workpiece processing sequence; including: S31, initialization algorithm parameters, dung beetle population N, problem latitude D, maximum number of iterations T max , maximum number of neighborhood searches q′; The position of dung beetle individuals is encoded using a factory-process double-layer list structure, expressed as x=[π1,π2], where π1 is the factory allocation code and π2 is the workpiece processing sequence code; and based on the current maximum fuzzy completion time minimization rule, the dung beetle individuals are decoded into workpiece processing sequence sequences and machine allocation sequences; S32, initialize the population and calculate the fitness of the individuals in the population according to formula (6); S33, generating a random number δ, if δ<0.9, updating the position of the rolling dung beetle in barrier-free mode according to a preset update strategy, otherwise updating the position of the rolling dung beetle according to an adaptive golden sine strategy; S34, updating the positions of the breeding dung beetles, the foraging dung beetles, and the stealing dung beetles respectively according to the updating strategy; S35, determining whether the dung beetle individual is within the boundary, and executing an improved boundary correction strategy if it is beyond the boundary; S36, using the local search algorithm VND to perform local search for the global optimal solution, and judging whether to perform position update based on the greedy rule; S37, using an adaptive Cauchy-Gaussian mutation perturbation strategy to perturb the global optimal solution; S38, number of iterations t=t+1; S39, repeat S33 to S38 until the number of iterations t meets the termination criterion, output the global optimal solution and its fitness value, and decode the global optimal solution to obtain the optimal machine allocation sequence and workpiece processing order sequence.

5. The distributed fuzzy flexible job shop scheduling method according to claim 4, characterized in that: According to the preset update strategy, the positions of the rolling dung beetle, the breeding dung beetle, the foraging dung beetle and the stealing dung beetle are updated respectively; specifically, the following are included: (1) For the ball-rolling dung beetle: Generate a random number δ between 0 and 1. If δ<0.9, perform the location update in barrier-free mode, otherwise perform the location update in barrier-free mode. (a) Accessible mode, the position update formula is defined as follows: x e (t+1)=x e (g)+α×h×x e (t-1)+b×Δx,Δx=|x e (t)-X w | (11) Among them, x e (t) represents the position of the e-th dung beetle in the population at the t-th iteration; the coefficient h∈(0,0.2] is the deflection coefficient constant, b∈(0,1) is a fixed constant, and α is a natural coefficient with a value of -1 or 1; X w represents the worst position in the current population, and Δx represents the change in light intensity, which is used to guide the position update of the dung beetle; (b) In the obstacle mode, the tangent function is used to simulate the dancing behavior to determine the new rolling direction. The position update formula of the dung beetle's dancing behavior is defined as follows: x e (t+1)=x e (t)+tan(θ)×|x e (t)-x e (t-1)| (12) Among them, the deflection angle θ∈[0,π], when or π, the position of the dung beetle will not be updated; (2) For breeding dung beetles Introduce a boundary selection strategy to simulate the oviposition area selection of female dung beetles: Among them, X * Represents the local optimal position in the current population, Lb * and Ub * The lower and upper bounds of the spawning area are defined respectively. Lb and Ub are the lower and upper bounds of the optimization problem respectively; After the egg-laying area is determined, the female dung beetle will lay eggs in this area, and the position update formula is defined as follows: B e (t+1)=X * +b1×(B e (t)-Lb * )+b2×(B e (t)-Ub * ) (14) Among them, B e (t) represents the position of the e-th dung beetle egg at the t-th iteration, b1 and b2 represent two independent random vectors, whose dimensions are the same as the dimension D of the optimization problem; (3) For foraging dung beetles The update formula is as follows: Among them, X b is the global optimal position of the dung beetle population during the iteration process, Lb b and Ub b The lower and upper bounds of the foraging area are defined respectively; The position update formula of the dung beetle is defined as follows: x i (t+1)=X b +C1×(x i (t)-Lb b )+C2×(x i (t)-Ub b ) (16) Where C1 represents a random variable that obeys a normal distribution, and C2 represents a random vector of size 1×D belonging to (0,1); (4) For the stealing dung beetle The position update formula is defined as follows: x e (t+1)=X b +S×g×(|x e (t)-X * |+|x e (t)-X b |) (17) Where S represents a fixed constant and g represents a random vector of size 1×D that follows a normal distribution.

6. The distributed fuzzy flexible job shop scheduling method according to claim 4, characterized in that: The adaptive golden sine strategy refers to: Among them, ω2=(1-ω1), ω max and ω min are the maximum and minimum values ​​of the inertia weight coefficient ω1, respectively; r1∈[0,2π] and r2∈[0,π] are random numbers that obey the normal distribution, r1 determines the moving distance of the rolling dung beetle during the iteration process, and r2 determines the position update direction of the dung beetle individual in the next iteration; γ1=p * τ+p * (1-τ) and γ2=q * τ+p * (1-τ) is obtained by introducing the golden section number The obtained coefficient, weight p * and q * The initial values ​​of are set to -π and π, respectively, and then change with the changes of coefficients γ1 and γ2; and / or The improved boundary correction strategy refers to: Among them, lb f andub f are the upper and lower limits of each dimension of the dung beetle individual; x ef is the value of the e-th dung beetle individual at latitude f; and / or The greedy rule is: Among them, x i (t) represents the dung beetle individuals in the current iteration population, x e(new) (t+1) represents the dung beetle individual after the position is updated, and f(x) represents the fitness function of the dung beetle individual x; and / or The adaptive Cauchy-Gaussian variation perturbation strategy refers to: x i (t+1)=x i (t)*(1+μ1*cauchy(σ)+μ2*Gaussion(σ)) (22) Among them, t represents the number of iterations, x i (t) represents the position of the i-th dung beetle in the population at the t-th iteration, and the mutation operator weight coefficient cauchy(σ) represents a random variable that follows the Cauchy distribution, expressed as δ is a random variable that obeys the standard normal distribution, and Gaussion (σ) represents a random variable that obeys the Gaussian distribution.

7. The distributed fuzzy flexible job shop scheduling method according to claim 4, characterized in that: The following four neighborhood structures are set: Neighborhood structure 1: Select the factory with the longest maximum fuzzy completion time as the key factory, and randomly select a job in this factory and assign it to the factory with the shortest fuzzy completion time; Neighborhood structure 2: Randomly exchange two different processes in a critical factory, which contains at least one critical process; Neighborhood structure 3: Randomly select two different processes in the critical factory, which contains at least one critical process, and then insert the second process before the first process; Neighborhood structure 4: Randomly select two different processes in the key factory, which contains at least one key process, and then sort all the processes between these two processes in reverse order; The local search algorithm VND is used to perform local search for the global optimal solution, and whether to perform position update is determined based on the greedy rule; including: S361, determine the initial solution as the optimal dung beetle position X b , let the neighborhood solution be equal to the initial solution, combined with the maximum neighborhood search times q′; S362, executing neighborhood structure 1 q′ times, if the generated new neighborhood solution is better than the original neighborhood solution, then updating the original neighborhood solution; S363, if the final neighborhood solution is better than the initial solution, update the initial solution and proceed to S362; otherwise, proceed to S364; S364, executing neighborhood structure 2 q′ times, if the generated new neighborhood solution is better than the original neighborhood solution, then updating the original neighborhood solution; S365, if the final neighborhood solution is better than the initial solution, update the initial solution and proceed to S362; otherwise, proceed to S366; S366, executing neighborhood structure 3 q′ times, if the generated new neighborhood solution is better than the original neighborhood solution, then updating the original neighborhood solution; S367, if the final neighborhood solution is better than the initial solution, update the initial solution and proceed to S362; otherwise, proceed to S368; S368, execute q ′ Secondary neighborhood structure 4, if the generated new neighborhood solution is better than the original neighborhood solution, the original neighborhood solution is updated; S369. If the final neighborhood solution is better than the initial solution, the initial solution is updated and the process proceeds to S362; otherwise, the algorithm ends and determines whether to perform a position update based on the greedy rule, and the process proceeds to S37.

8. A distributed fuzzy flexible job shop scheduling system based on MSDBO algorithm, characterized in that: include: Acquisition module, used to acquire production resources and workpiece processing tasks; The production resources include a distributed set of factories, each factory includes a number of machines, and each workpiece includes a number of processes to be processed; A representation module is used to represent the processing time of each process of any of the workpieces on the machine and the transfer time of any of the workpieces on different machines by using triangular fuzzy numbers to obtain the fuzzy completion time of any of the workpieces; A construction module is used to construct a mathematical model based on the production resources and the workpiece processing tasks with minimizing the maximum fuzzy completion time as the optimization goal; The solution module is used to solve the mathematical model by adopting a multi-strategy dung beetle optimization algorithm to obtain an optimal machine allocation sequence and a workpiece processing sequence.

9. A storage medium, characterized in that: It stores a computer program for distributed fuzzy flexible job shop scheduling based on the MSDBO algorithm, wherein the computer program enables the computer to execute the distributed fuzzy flexible job shop scheduling method as described in any one of claims 1 to 7.

10. An electronic device, characterized in that: include: one or more processors; Memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, the programs including a program for executing the distributed fuzzy flexible job shop scheduling method as described in any one of claims 1 to 7.

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