Distributed flexible fuzzy system transient performance prediction and its scheduling method

Abstract

The application discloses a distributed flexible fuzzy system transient performance prediction and scheduling method, and belongs to the field of production scheduling. The application carries out system modeling on a distributed flexible production system, and realizes high-precision batch completion time quantitative analysis prediction of the distributed flexible production system on the basis of the system modeling. The application has the advantages of high prediction precision and high efficiency for the distributed flexible fuzzy system transient performance. On the basis of the distributed flexible fuzzy system transient performance prediction method, according to the high-precision batch completion time quantitative analysis prediction result of the distributed flexible production system, different production scenes are classified into three scenes of optimal, medium and worst, an acceptance criterion is constructed, a genetic algorithm is improved based on the acceptance criterion, production scheduling of the distributed flexible fuzzy system is carried out according to the improved genetic algorithm, the precision and efficiency of the production scheduling are improved, and production energy is saved.

Description

Technical Field

[0001] This invention belongs to the field of production scheduling, and in particular relates to a method for predicting and scheduling the transient performance of a distributed flexible fuzzy system. Background Technology

[0002] Customization and small-batch production are key characteristics of distributed flexible manufacturing, which means that the system operates in a transient state most of the time, rendering traditional steady-state analysis inapplicable. On the other hand, various uncertainties arise in actual manufacturing processes. Due to differences in worker skill levels, random machine failures, order changes, and ambient temperature, machine processing efficiency is not constant. To achieve optimal production performance across various processing efficiencies, it is necessary to simultaneously optimize production indicators under different production scenarios or optimize weighted production indicators under different scenarios. However, current research on flexible manufacturing systems is mainly limited to steady-state performance studies, with limited research on transient performance analysis and a lack of consideration for production scheduling issues arising from uncertain processing efficiencies. Summary of the Invention

[0003] One of the main objectives of this invention is to provide a method for predicting the transient performance of distributed flexible fuzzy systems. This method involves system modeling of a distributed flexible production system and, based on this modeling, achieving high-precision quantitative analytical prediction of batch completion times. This invention offers the advantages of high accuracy and efficiency in predicting the transient performance of distributed flexible fuzzy systems.

[0004] The second main objective of this invention is to provide a production scheduling method for distributed flexible fuzzy systems, based on the aforementioned transient performance prediction method for distributed flexible fuzzy systems. According to the high-precision quantitative analytical prediction results of batch completion time of the distributed flexible production system, different production scenarios are classified into three types: optimal, moderate, and worst. An acceptability criterion is constructed, and a genetic algorithm is improved based on this criterion. The improved genetic algorithm is then used for production scheduling of the distributed flexible fuzzy system, improving the accuracy and efficiency of production scheduling and saving production energy. The production scheduling mainly consists of workpiece sequence scheduling and assembly line sequence scheduling.

[0005] The objective of this invention is achieved through the following technical solution.

[0006] This invention discloses a distributed flexible fuzzy system transient performance prediction and scheduling method. It models the flexible fuzzy system (hereinafter referred to as the system) and defines a transient performance index—batch completion time. Through data decoupling, four auxiliary production lines are constructed based on the original production line. Approximate batch completion times are calculated, and high-precision analytical prediction of the transient performance of the distributed flexible fuzzy system is performed, improving the accuracy and efficiency of transient performance index prediction. Furthermore, three different production scenarios are defined, including optimal, moderate, and worst-case scenarios. The performance indices of the three scenarios are weighted to obtain a fuzzy optimization index. A genetic algorithm with an acceptance criterion is used for scheduling optimization, ultimately obtaining the optimal scheduling strategy, improving the accuracy and efficiency of production scheduling, and saving production energy.

[0007] This invention discloses a method for predicting the transient performance of a distributed flexible fuzzy system, comprising the following steps:

[0008] Step 1: Classify different production scenarios into three types: optimal, medium, and worst. Construct an acceptance criterion, improve the genetic algorithm based on the acceptance criterion, initialize the hyperparameters of the improved genetic algorithm, and randomly initialize the workpiece code and pipeline code.

[0009] Step 1.1: Classify different production scenarios into three types: optimal, medium, and worst, and construct an acceptance criterion. Improve the genetic algorithm based on the acceptance criterion.

[0010] Step 1.2: Set the hyperparameters of the genetic algorithm, and assign values ​​to the population size, crossover probability, mutation probability, maximum number of iterations, temperature, and number of iterations for the workshop scheduling scheme.

[0011] The population size for the workshop scheduling scheme is set to `pop_size`, the crossover probability to `rate_crossover`, the mutation probability to `rate_mutation`, the maximum number of iterations to `max_generation`, the initial temperature of the acceptance criterion to `T`, and the lower limit of the temperature to `T`. f Let G be the number of population iterations, and let G = 1. Let V be the preset individual index, and let V = 1.

[0012] Step 1.3: Initialize the workpiece code and pipeline code for each individual in the workshop scheduling scheme population. Each individual has K serial flexible pipelines, producing a total of N types of workpieces. A matrix of size 2^N is generated, where the first row stores the workpiece codes for the N types of workpieces, and the second row stores the pipeline codes for the N types of workpieces. Scheduling is performed for cases where N > K; otherwise, scheduling is meaningless.

[0013] Step 1.4: Fill a 1·N matrix with elements from 1, 2, ..., N, ensuring no repetition. Use this matrix as the workpiece code for type N workpieces. The elements at corresponding positions represent the processing order of that workpiece type, with 1 indicating that the workpiece is processed first and N indicating that the workpiece is processed last.

[0014] Step 1.5: Fill the 1·N matrix with elements from 1, 2, ..., K, ensuring that the first K elements are 1 to K, and the remaining NK elements are randomly filled with elements from 1, 2, ..., K. The element at the corresponding position indicates which production line the workpiece of this type is processed on. Use this matrix as the production line code for N types of workpieces.

[0015] Step 2: Based on the individual index, perform flexible fuzzy system modeling on the individuals within the workshop scheduling scheme population to obtain the flexible fuzzy system model, which will be referred to as the system below. The distributed system consists of several identical serial flexible pipelines running in parallel; therefore, the following analysis focuses only on one serial flexible pipeline in production scenario S. This system consists of sequentially connected Bernoulli machines and buffers. System modeling includes system parameters, system states, and production sequence. System parameters include production line structure parameters, workpiece processing cycle, Bernoulli machine processing efficiency, and finite buffer parameters; system states include Bernoulli machine starvation state, Bernoulli machine blocking state, system running state, and system debugging state. Production sequence represents the order in which different types of workpieces are processed within the system.

[0016] Step 2.1: Determine the production line structure.

[0017] The system has Q types of workpieces to be produced, denoted as type j. The system consists of M Bernoulli machines and M-1 buffer zones, thus defining the production line structure. Each Bernoulli machine consists of m... i This indicates that the buffer is composed of b i express.

[0018] Step 2.2: Determine the system processing cycle.

[0019] All Bernoulli machines have the same and time-invariant processing cycle τ, and the time axis is segmented in units of processing cycle τ.

[0020] Step 2.3: Determine the reliability model of the Bernoulli machine.

[0021] All Bernoulli machines follow the Bernoulli machine reliability model: if the Bernoulli machine m i Let i = 1, 2, ..., M. In the production of product type j, j = 1, 2, ..., Q, if there is neither congestion nor starvation, then in a specific production scenario S, the probability of the Bernoulli machine achieving any workpiece within one processing cycle is: Correspondingly, the production failure probability is parameter Defined as a Bernoulli machine m i The efficiency of producing workpieces under production scenario S is higher in the optimal production scenario than in the medium production scenario, and higher in the medium production scenario than in the worst production scenario.

[0022] Step 2.4: Determine the starvation state of the Bernoulli machine.

[0023] At the beginning of a processing cycle, if the Bernoulli machine m i The machine is in operation, i = 2, 3, ..., M, but the Bernoulli machine m i The previous buffer b i-1 If the machine is empty at this time, then the Bernoulli machine is in a state of starvation during the processing cycle.

[0024] Step 2.5: Determine the blocking state of the Bernoulli machine.

[0025] If Bernoulli machine m i The machine is in operation, i = 1, 2, ..., M-1, but the Bernoulli machine m i Next buffer b i At this point, it is full, and the Bernoulli machine m i The next Bernoulli machine m i+1 If a workpiece cannot be retrieved from the buffer for processing at the start of the processing cycle, and the reason for this inability is a blockage or production failure, then the Bernoulli machine is in a blocked state during that processing cycle. Bernoulli machine m M It will not be in a blocked state.

[0026] Step 2.6: Determine the buffer parameters, including the buffer capacity.

[0027] Buffer capacity b i The capacity is determined by N i Let f = 1, 2, ..., M-1, N i ∈(0,∞).

[0028] Step 2.7: Determine the production sequence.

[0029] Type j, j = 1, 2, ..., Q, workpiece B j For each type of workpiece to be processed, all Bernoulli machines produce only that type of workpiece until the production of each type of product is completed. All Bernoulli machines determine the processing order of type j, i.e., the production order, based on the pre-given workpiece code.

[0030] Step 2.8: Determine whether the system is in running or debugging mode.

[0031] In the operational state of production type j, there are a total of B j Workpieces of type j, j = 1, 2, ..., Q, are produced. After the production of workpieces of type j, j = 1, 2, ..., Q-1, is completed, the process enters the adjustment state for the next type of workpiece. The production process ends when all workpieces of type Q are produced. The adjustment state of type j, j = 1, 2, 3, ..., Q, lasts for t seconds before the running state of type j. set，j One processing cycle. Where, t set，j It is a pre-designed random number that is sequence-dependent, meaning it is related to the previous workpiece.

[0032] Step 3: Define the transient performance index – batch completion time (CT) – based on the flexible fuzzy system model constructed in Step 2 and the actual operating conditions. i，j，S Defined as: Bernoulli machine m in production scenario S. i Let i = 1, 2, ..., M, and let M be the expected number of processing cycles the system has completed when producing workpiece of type j. The actual operating conditions include optimal, moderate, and worst operating conditions.

[0033] Step 4: Based on the characteristic of "no aftereffect" in the production process of the flexible fuzzy system established in Step 2, the original production line is decoupled and an auxiliary production line 1 consisting of Q M-machine production lines is constructed, so that each production line only produces products of a predetermined category.

[0034] Based on the flexible fuzzy system model established in step 2, this production process exhibits "no aftereffect," meaning the state of the system in the next processing cycle depends only on the state of the current processing cycle. Therefore, this stochastic process is a Markov chain. Let f i，j (n)∈{0,1,...,B} j Let i = 1, 2, ..., M, j = 1, 2, ..., Q, representing the number of workpieces of type j produced by the system at the beginning of processing cycle n. The original production line is decomposed into Q production lines, each producing only one type of product. These Q production lines are called auxiliary production lines 1. The only difference from the original production line is that the efficiency of the first machine in auxiliary production line 1 is time-varying; all other parameters are the same as those of the original production line, i.e., p′. i，j，S (n)=p i Let i = 2, 3, ..., M, j = 2, 3, ..., Q. The machine efficiency p′ is... 1，j，S (n) is calculated using the following formula:

[0035]

[0036] Step 5: Construct auxiliary production line 2, which consists of Q M-machine production lines. Auxiliary production line 2 consists of Q production lines. The Bernoulli machine and buffer parameters of auxiliary production line 2 are the same as those of auxiliary production line 1. The only difference is that auxiliary production line 2 has an unlimited supply of raw materials.

[0037] Step 6: Construct auxiliary production line 3 consisting of Q·M single-machine production lines and auxiliary production line 4 consisting of Q·M-1 dual-machine production lines, and combine the two sets of auxiliary production lines, treating all upstream and downstream machines and buffers as time-varying efficiency machines.

[0038] Further decomposition of auxiliary production line 2 results in Q·M single-machine production lines, referred to as auxiliary production line 3, and Q·M-1 dual-machine production lines, referred to as auxiliary production line 4. The Bernoulli machine efficiency in auxiliary production line 3 is... It produces a limited number of workpieces, while the efficiency of the Bernoulli machine in auxiliary production line 4 is... and

[0039] Step 7: Based on the auxiliary production line 3 and auxiliary production line 4 described in Step 6 and the flexible fuzzy system model described in Step 2, calculate the parameters of the two auxiliary production lines, including the efficiency of the Bernoulli machine in auxiliary production line 3. Efficiency of the Bernoulli machine in auxiliary production line 4 and

[0040] Step 7.1: Let This indicates that at the end of processing cycle n, buffer b in auxiliary production line 4... i，j What is the probability of having d workpieces? make This indicates that at the end of processing cycle n, the Bernoulli machine in auxiliary production line 3... Let the probability of producing d workpieces be given by... The initial conditions are:

[0041]

[0042]

[0043] Step 7.2: Let j = 1.

[0044] Step 7.3: Let n = 1.

[0045] Step 7.4: Let For all i = 2, 3, ..., M, calculate according to the following formula

[0046] Step 7.5: Let Then, calculate in descending order of i = 1, 2, ..., M-1. That is, calculate according to the following formula first. Final calculation

[0047]

[0048] Step 7.6: Let Then, for all i = 2, 3, ..., M, calculate according to the following formula.

[0049] Step 7.7: For all i = 1, 2, ..., M-1, calculate according to the following formula

[0050]

[0051] Among them, A j The transition probability matrix for the j-th production line in auxiliary production line 4 within processing cycle n is expressed as:

[0052]

[0053] Where c1 represents c2 indicates

[0054] Step 7.8: For all i = 1, 2, ..., M, calculate according to the following formula

[0055]

[0056] in, The transition probability matrix for auxiliary production line 3 is expressed as:

[0057]

[0058] Where c3 represents

[0059] Step 7.9: If j = 1, proceed to step 7.10. Otherwise, for all i = 1, 2, ..., M, calculate the time-varying probability of the first machine in step 5 according to the following formula:

[0060]

[0061] Step 7.10: Let n = n + 1, return to step 7.4, until the predicted number of processing cycles is reached.

[0062] Step 7.11: Let j = j + 1, return to step 7.4, until j = Q.

[0063] Step 8: Based on the flexible fuzzy system modeling results obtained in Step 2 and the four auxiliary production lines constructed in Steps 4 to 7, perform quantitative analysis and prediction of the transient performance of the system, calculate the batch completion time of the system under the predetermined production scenario, and improve the accuracy and efficiency of transient performance prediction for the distributed flexible fuzzy system.

[0064] Step 8.1: Based on the Bernoulli machine efficiency in auxiliary production line 3 obtained in step 7, calculate the efficiency using the following formula. Sum of probabilities Analytical prediction of batch completion time (CT) i，j，S :

[0065]

[0066] Step 8.2: Based on the batch completion time of each machine, obtain the batch completion time of the entire production line as CT. M，Q，S Extending this to the distributed scheduling problem of K pipelines, using CT... M,Q,S，K Let represent the completion time of the Kth production line. Then, we can obtain the batch completion time CT for individual V in that production scenario. S for

[0067] Step 8.3: Calculate the completion time for the three production scenarios based on machine efficiency according to the process from Step 2.1 to Step 8.1, using CT. S Let S = 1, 2, 3, and CT1 represent the batch completion time under the optimal production scenario.

[0068] Step 8.4: Calculate the expected batch completion time CT E .

[0069]

[0070] Step 8.5: Calculate the individual's optimization index CT v And adaptability.

[0071]

[0072] This invention relates to a transient performance prediction and scheduling method for a distributed flexible fuzzy system, including the aforementioned transient performance prediction method for a distributed flexible fuzzy system, as shown in steps 1 to 8, which performs high-precision quantitative analytical prediction of batch completion time for a distributed flexible production system based on the aforementioned transient performance prediction method for a distributed flexible fuzzy system.

[0073] This invention relates to a transient performance prediction and scheduling method for a distributed flexible fuzzy system, and further includes the following steps:

[0074] An acceptance criterion is constructed, and a genetic algorithm is improved based on the acceptance criterion. The improved genetic algorithm is then used for production scheduling in a distributed flexible fuzzy system, improving the accuracy and efficiency of production scheduling and saving production energy. The production scheduling mainly consists of workpiece sequence scheduling and pipeline sequence scheduling.

[0075] Step 9: Perform crossover operation in the genetic algorithm on the workpiece coding and pipeline coding of the system.

[0076] Step 9.1: Generate a random number R r If R r If the value is less than rate_crossover, proceed to step 9; otherwise, skip to step 11.

[0077] Step 9.2: Randomly select the workpiece code and production line code of another individual within the workshop scheduling scheme population, and perform cross-operation on both. This individual must not be a duplicate of itself.

[0078] Step 9.3: For the workpiece codes of two individuals, use the partial matching crossover algorithm. Randomly select two positions within the workpiece code as the start and end positions, and swap the elements between the two positions. After the swap, establish a mapping relationship. Perform conflict detection on the remaining conflicting codes until the conflict disappears.

[0079] Step 9.4: For the pipeline codes of the two individuals, use the multi-point crossover algorithm. Iterate through the elements at corresponding positions in the pipeline codes of the two individuals, generate a random number, and if the random number is less than rate_crossover, then swap the elements at the two positions.

[0080] Step 9.5: For steps 9.3 and 9.4, after completing all operations, it is necessary to determine whether to accept the generated new encoding. If the new encoding can achieve a shorter completion time CT_new, then the encoding is accepted; if the completion time of the new encoding is not optimized, then the encoding is accepted according to the preset acceptance criteria, and a random number R is generated. r The completion time before the crossover is CT v The current system temperature is T. Accept is 1, which means accepting the newly generated code, and Accept is 0, which means not accepting the newly generated code.

[0081]

[0082] Step 10: Perform mutation operations in the genetic algorithm on the workpiece code and pipeline code of the system. Use the exchange mutation method and the bit flip method on the workpiece code and pipeline code respectively to introduce new solutions and escape the local optimum region in the search space.

[0083] Step 10.1: Generate a random number R r If R r R r If the value is less than rate_mutation, proceed to step 10; otherwise, skip to step 11.

[0084] Step 10.2: For an individual workpiece code, use the exchange mutation method. Randomly select two elements within the workpiece code and exchange them to obtain a new workpiece code.

[0085] Step 10.3: For the pipelined encoding of an individual, use the bit-flipping method. Iterate through all elements in the pipelined encoding, generate a random number, and if the random number is less than rate_mutation, randomly select a value from the K-1 elements excluding the original element to replace the original value at that position.

[0086] Step 10.4: After steps 10.2 and 10.3, it is necessary to determine whether to accept the generated new code. The specific method is the same as in step 9.5.

[0087] Step 11: Perform the selection operation in the genetic algorithm, using the linear sorting selection algorithm to generate the plant scheduling scheme population for the next iteration.

[0088] Use a linear sorting selection algorithm. Set the maximum probability P. max The probability is 0.8, and the minimum probability P is... min The fitness of individuals in the workshop scheduling scheme population is 0.2. The individuals with the lowest fitness are ranked first, and the individuals with the highest fitness are ranked at position `pop_size`. Based on the ranking, each individual is linearly assigned a new fitness value, resulting in a new fitness value P(i).

[0089]

[0090] The greater the fitness, the greater the probability that the individual will be selected into the next generation of workshop scheduling scheme population, thus preserving excellent coding information.

[0091] Step 12: Iterate through the loop to obtain the population of workshop scheduling schemes in the genetic algorithm.

[0092] Step 12.1: Let V = V + 1, return to step 5.1, until V = pop_size.

[0093] Step 12.2: Let G = G + 1, T = T × 0.99, return to step 5.1, until G = max_generation.

[0094] It also includes step 13: Based on the final population obtained at the end of step 12, obtain the workpiece code and pipeline code of the optimal individual. Production scheduling is then arranged based on these codes to improve the accuracy and efficiency of production scheduling and save production energy.

[0095] Beneficial effects:

[0096] 1. The present invention discloses a method for predicting and scheduling transient performance of a distributed flexible fuzzy system. It performs system modeling on a distributed flexible production system and, based on the system modeling, achieves high-precision quantitative analytical prediction of batch completion time of the distributed flexible production system, which has the advantage of high accuracy.

[0097] 2. The present invention discloses a distributed flexible fuzzy system transient performance prediction and scheduling method, which defines three different production scenarios, including optimal, medium and worst scenarios, and obtains a fuzzy optimization index by weighting the performance indicators of the three production scenarios. It can cope with the optimization scheduling problem under different environments and has strong robustness.

[0098] 3. The present invention discloses a distributed flexible fuzzy system transient performance prediction and scheduling method, which uses a genetic algorithm with an acceptance criterion to optimize the scheduling of batch completion time indicators, and finally obtains the optimal scheduling strategy, thereby improving the accuracy and efficiency of production scheduling and saving production energy. Attached Figure Description

[0099] Figure 1 This is a flowchart of the distributed flexible fuzzy system transient performance prediction of the present invention.

[0100] Figure 2 This is a flowchart of the genetic algorithm with acceptance criteria of the present invention.

[0101] Figure 3 This is the coding design diagram of the scheduling strategy proposed in this invention.

[0102] Figure 4 This is a schematic diagram of the production system considered in this invention. In the diagram, circles represent Bernoulli machines, rectangles represent buffer zones, trapezoids represent different types of workpieces to be processed, and arrows indicate the direction of workpiece flow.

[0103] Figure 5 This is a schematic diagram of the auxiliary production line 1 proposed in this invention.

[0104] Figure 6 This is a schematic diagram of the auxiliary production line 2 proposed in this invention.

[0105] Figure 7 This is a schematic diagram of the auxiliary production line 3 proposed in this invention.

[0106] Figure 8 This is a schematic diagram of the auxiliary production line 4 proposed in this invention.

[0107] Figure 9 This is a schematic diagram of the partial matching cross algorithm in Embodiment 1 of the present invention.

[0108] Figure 10 This is a schematic diagram of the exchange mutation method in Embodiment 1 of the present invention.

[0109] Figure 11 This is a schematic diagram of the bit-flipping method in Embodiment 1 of the present invention.

[0110] Figure 12 This is a line graph of the optimization process of the genetic algorithm in Embodiment 1 of the present invention. The horizontal axis represents the number of iterations, and the vertical axis represents the average optimization index of the population. Detailed Implementation

[0111] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0112] Example 1:

[0113] like Figure 1 and Figure 2 As shown in the figure, the specific implementation steps of the distributed flexible fuzzy system transient performance prediction and scheduling method disclosed in this embodiment are as follows:

[0114] Step 1: Classify different production scenarios into three types: optimal, medium, and worst. Construct an acceptance criterion, improve the genetic algorithm based on the acceptance criterion, initialize the hyperparameters of the improved genetic algorithm, and randomly initialize the workpiece code and pipeline code.

[0115] Step 1.1: Classify different production scenarios into three types: optimal, medium, and worst, and construct an acceptance criterion. Improve the genetic algorithm based on the acceptance criterion.

[0116] Step 1.2: Set the hyperparameters of the genetic algorithm, and assign values ​​to the population size, crossover probability, mutation probability, maximum number of iterations, temperature, and number of iterations for the workshop scheduling scheme.

[0117] The genetic algorithm sets the population size to popsize = 60, the crossover probability to rate_crossover = 0.65, the mutation probability to rate_mutation = 0.5, the maximum number of iterations to max_generation = 20, the initial temperature for the acceptance criterion to T = 90, and the lower limit to the lower limit to T. f=80, the number of population iterations is G, let G=1. The preset individual index is V, let V=1.

[0118] Step 1.3: Initialize the job code and pipeline code for each individual in the population. Each individual has K = 3 serial flexible pipelines, producing a total of N = 10 types of jobs. Therefore, generate a matrix of size 2 * N = 2 * 10, where the first row stores the job codes for the N = 10 types of jobs, and the second row stores the pipeline codes for the N = 10 types of jobs. The coding design is as follows: Figure 3 As shown, for simplicity, the coding design of the first 5 workpieces is presented.

[0119] Step 1.4: Fill a 1·N matrix with elements from 1, 2, ..., 10, ensuring no repetition. Use this matrix as the workpiece code for N=10 workpiece categories. The elements at corresponding positions represent the processing order of that workpiece category, with 1 indicating that the workpiece is processed first and N indicating that the workpiece is processed last.

[0120] Step 1.5: Fill the 1·N matrix with elements from 1, 2, and 3, ensuring that the first K=3 elements are from 1 to K=3, and the remaining NK=7 elements are randomly filled with elements from 1, 2, and 3. The corresponding element indicates which production line the workpiece type is processed on. Use this matrix as the production line code for N=10 workpiece types.

[0121] Step 2: Based on the individual index, perform flexible fuzzy system modeling on each individual in the workshop scheduling scheme population to obtain the flexible fuzzy system model. Hereinafter, flexible fuzzy will be referred to simply as the system. The distributed system consists of several identical serial flexible pipelines running in parallel; therefore, the following analysis focuses only on one serial flexible pipeline in production scenario S. For example... Figure 4 As shown, the system consists of Bernoulli machines and buffers connected sequentially. System modeling includes system parameters, system states, and production sequence. System parameters include production line structure parameters, workpiece processing cycle, Bernoulli machine processing efficiency, and finite buffer parameters. System states include Bernoulli machine starvation state, Bernoulli machine blocking state, system running state, and system debugging state. Production sequence represents the order in which different types of workpieces are processed within the system.

[0122] Step 2.1: Determine the production line structure.

[0123] The system has Q = 10 types of workpieces to be produced, denoted as type j. The system consists of M = 5 Bernoulli machines and M-1 = 4 buffer zones. Each Bernoulli machine consists of m... i This indicates that the buffer is composed of b i express.

[0124] Step 2.2: Determine the system processing cycle.

[0125] All Bernoulli machines have the same and time-invariant processing cycle τ = 1s, and the time axis is segmented in units of processing cycle τ = 1s.

[0126] Step 2.3: Determine the reliability model of the Bernoulli machine.

[0127] All Bernoulli machines follow the Bernoulli machine reliability model: if the Bernoulli machine m i If i = 1, 2, ..., 5, and during the production of product type j, j = 1, 2, ..., 10, there is neither congestion nor starvation, then in a specific production scenario S, the probability of the Bernoulli machine completing any workpiece in one processing cycle is: Correspondingly, the production failure probability is Among them, parameters Defined as a Bernoulli machine m i The efficiency of producing workpieces under production scenario S is as follows: In the optimal production scenario, the machine efficiency is higher than that corresponding to the medium production scenario; in the medium production scenario, the machine efficiency is higher than that corresponding to the worst production scenario. When S=1, we consider the machine to be in the optimal production scenario. When S=2, we consider the machine to be in a moderate production scenario. When S=3, we consider the machine to be in the worst-case production scenario.

[0128] Step 2.4: Determine the starvation state of the Bernoulli machine.

[0129] At the beginning of a processing cycle, if the Bernoulli machine m i The machine is in operation, i = 2, 3, ..., 5, but the Bernoulli machine m i The previous buffer b i-1 If the machine is empty at this time, then the Bernoulli machine is in a state of starvation during the processing cycle.

[0130] Step 2.5: Determine the blocking state of the Bernoulli machine.

[0131] If Bernoulli machine m i The machine is in operation, i = 1, 2, ..., 4, but the Bernoulli machine m i Next buffer b i At this point, it is full, and the Bernoulli machine m i The next Bernoulli machine m i+1If a workpiece cannot be retrieved from the buffer for processing at the start of the processing cycle (due to blocking or production failure), the Bernoulli machine is in a blocked state during that processing cycle. Let's assume the Bernoulli machine is m... M It will not be in a blocked state.

[0132] Step 2.6: Determine the buffer parameters, including the buffer capacity.

[0133] Buffer capacity b i The capacity is determined by N i Let i = 1, 2, ..., 4, N i ∈(0, ∞). Where N1 = 2, N2 = 3, N3 = 2, N4 = 3.

[0134] Step 2.7: Determine the production sequence.

[0135] Type j, j = 1, 2, ..., 10, workpiece B j There are 10 workpieces to be processed, where B1 = 5, B2 = 10, B3 = 20, B4 = 20, B5 = 10, B6 = 5, B7 = 10, B8 = 20, B9 = 5, B... 10 =10. All Bernoulli machines produce only workpieces of that type until the production of each type of product is completed. All Bernoulli machines determine the processing sequence of type j according to the pre-given workpiece code.

[0136] Step 2.8: Determine whether the system is in running or debugging mode.

[0137] In the operational state of production type j, there are a total of B j Workpieces of type j, j = 1, 2, ..., 10, are produced. After all workpieces of type j, j = 1, 2, ..., 9, are produced, the process enters the adjustment state for the next type of workpiece. The production process ends when all workpieces of type Q = 10 are produced. The adjustment state of type j products, j = 1, 2, ..., 10, lasts for t seconds before the running state of type j. set，j One processing cycle, of which t set，j It is a pre-designed random number between 5 and 20, and it is sequence-dependent, meaning it is related to the previous workpiece.

[0138] Step 3: Define the transient performance index – batch completion time (CT) – based on the flexible fuzzy system model constructed in Step 2 and the actual operating conditions. i，j，s Defined as: Bernoulli machine m in production scenario S. i Let i = 1, 2, ..., 5, and represent the expected number of processing cycles the system has completed when producing workpiece of type j. The actual operating conditions include optimal, moderate, and worst-case operating conditions.

[0139] Step 4: Based on the characteristic of "no aftereffect" in the production process of the flexible fuzzy system established in Step 2, the original production line is decoupled, and an auxiliary production line 1 consisting of Q=10 M=5 machine production lines is constructed. Each production line is then instructed to produce only a predetermined category of products, such as... Figure 5 As shown.

[0140] Based on the system model established in step 2, this production process exhibits "no aftereffect," meaning that the state of the system in the next processing cycle depends only on the state of this current processing cycle. Therefore, this stochastic process is a Markov chain. Let f i，j (n)∈{0,1,…,B} j Let i = 1, 2, ..., 5, j = 1, 2, ..., 10, representing the number of workpieces of type j produced by the system at the beginning of processing cycle n. The original production line is decomposed into Q = 10 production lines, each producing only one type of product. These Q = 10 production lines are called auxiliary production lines 1. The only difference between auxiliary production lines and the original production line is that the efficiency of the first machine in auxiliary production line 1 is time-varying; all other parameters are the same as those of the original production line, i.e., p′. i，j，S (n)=p i , i = 2, 3, ..., 5, j = 2, 3, ..., 10. The machine efficiency p′ 1，j，S (n) is calculated using the following formula:

[0141]

[0142] Step 5: Construct auxiliary production line 2, consisting of Q=10 M=5 machine production lines. For simplicity, only one auxiliary production line 2 is shown. Auxiliary production line 2 is as follows: Figure 6 As shown. Auxiliary production line 2 consists of Q=10 production lines. The Bernoulli machine and buffer parameters of auxiliary production line 2 are the same as those of auxiliary production line 1. The only difference is that auxiliary production line 2 has an unlimited supply of raw materials.

[0143] Step 6: Construct auxiliary production line 3 consisting of Q·M = 50 single-machine production lines and auxiliary production line 4 consisting of Q·(M-1) = 40 dual-machine production lines. Combine the two sets of auxiliary production lines, treating all upstream and downstream machines and buffer zones as time-varying efficiency machines. Auxiliary production line 3 is as follows: Figure 7 As shown, auxiliary productivity 4, as Figure 8 As shown, for simplicity, only one auxiliary production line is displayed.

[0144] Further decomposition of auxiliary production line 2 results in Q·M = 50 single-machine production lines, referred to as auxiliary production line 3, and Q·(M-1) = 40 double-machine production lines, referred to as auxiliary production line 4. The Bernoulli machine efficiency in auxiliary production line 3 is... It produces a limited number of workpieces, while the efficiency of the Bernoulli machine in auxiliary production line 4 is... and

[0145] Step 7: Based on the auxiliary production line 3, auxiliary production line 4, and system model described in Step 6, calculate the parameters of the two auxiliary production lines, including the efficiency of the Bernoulli machine in auxiliary production line 3. Efficiency of the Bernoulli machine in auxiliary production line 4 and

[0146] Step 7.1: Let This indicates that at the end of processing cycle n, buffer b in auxiliary production line 4... i，j What is the probability of having d workpieces? make This indicates that at the end of processing cycle n, the Bernoulli machine in auxiliary production line 3... Let the probability of producing d workpieces be given by... The initial conditions are:

[0147]

[0148]

[0149] Step 7.2: Let j = 1.

[0150] Step 7.3: Let n = 1.

[0151] Step 7.4: Let For all i = 2, 3, ..., 5, calculate according to the following formula

[0152] Step 7.5: Let Then, calculate in descending order of i = 1, 2, ..., 4 That is, calculate according to the following formula first. Final calculation

[0153]

[0154] Step 7.6: Let Then, for all i = 2, 3, ..., 5M, calculate according to the following formula.

[0155] Step 7.7: For all i = 1, 2, ..., 4, calculate according to the following formula

[0156]

[0157] Among them, A j The transition probability matrix for the j-th production line in auxiliary production line 4 within processing cycle n is expressed as:

[0158]

[0159] Where c1 represents c2 indicates

[0160] Step 7.8: For all i = 1, 2, ..., M, calculate according to the following formula

[0161]

[0162] in, The transition probability matrix for auxiliary production line 3 is expressed as:

[0163]

[0164] Where c3 represents

[0165] Step 7.9: If j = 1, proceed to step 7.10. Otherwise, for all i = 1, 2, ..., 5, calculate the time-varying probability of the first machine in step 5 according to the following formula:

[0166]

[0167] Step 7.10: Let n = n + 1, return to step 7.4, until the predicted number of processing cycles n = 200 is reached.

[0168] Step 7.11: Let j = j + 1, return to step 7.4, until j = 10.

[0169] Step 8: Based on the flexible fuzzy system modeling results obtained in Step 2 and the four auxiliary production lines constructed in Steps 4 to 7, perform quantitative analysis and prediction of the transient performance of the system, calculate the batch completion time of the system under the predetermined production scenario, and improve the accuracy and efficiency of transient performance prediction for the distributed flexible fuzzy system.

[0170] Step 8.1: Based on the Bernoulli machine efficiency obtained in Step 7, calculate the efficiency of the auxiliary production line 2 according to the following formula. Sum of probabilities Analytical prediction of batch completion time (CT) i，j，S :

[0171]

[0172] Step 8.2: Based on the batch completion time of each machine, the batch completion time of this production line is CT. M,Q,S Extending this to the distributed scheduling problem of K pipelines, using CT... M，Q，S，K Let represent the completion time of the Kth production line. Then, we can determine the batch completion time CT of individual V in this production scenario. s for

[0173] Step 8.3: Calculate the completion time for the three production scenarios based on machine efficiency according to the process from Step 2.1 to Step 8.1, using CT. S Let S = 1, 2, 3, and CT1 represent the batch completion time under the optimal production scenario.

[0174] Step 8.4: Calculate the expected batch completion time CT E .

[0175]

[0176] Step 8.5: Calculate the individual's optimization index CT v And adaptability.

[0177]

[0178] This invention relates to a transient performance prediction and scheduling method for a distributed flexible fuzzy system, including the aforementioned transient performance prediction method for a distributed flexible fuzzy system, as shown in steps 1 to 8, which performs high-precision quantitative analytical prediction of batch completion time for a distributed flexible production system based on the aforementioned transient performance prediction method for a distributed flexible fuzzy system.

[0179] This invention relates to a transient performance prediction and scheduling method for a distributed flexible fuzzy system, and further includes the following steps:

[0180] An acceptance criterion is constructed, and a genetic algorithm is improved based on the acceptance criterion. The improved genetic algorithm is then used for production scheduling in a distributed flexible fuzzy system, improving the accuracy and efficiency of production scheduling and saving production energy. The production scheduling mainly consists of workpiece sequence scheduling and pipeline sequence scheduling.

[0181] Step 9: Perform crossover operation in the genetic algorithm on the workpiece coding and pipeline coding of the system.

[0182] Step 9.1: Generate a random number R r If R r If the value is less than rate_crossover = 0.65, proceed to step 9; otherwise, skip to step 10.

[0183] Step 9.2: Randomly select the workpiece code and pipeline code of another individual in the population (not the same as itself), and perform cross-operation on the two respectively.

[0184] Step 9.3: For the workpiece codes of two individuals, use the partial matching crossover algorithm. Randomly select two positions within the workpiece code as the start and end positions, and swap the elements between these two positions. After the swap, establish a mapping relationship. Perform conflict detection on the remaining conflicting codes until the conflicts disappear. The partial matching crossover algorithm is as follows: Figure 9 As shown, for simplicity, the cross-process of the first 5 workpieces is displayed.

[0185] Step 9.4: For the pipeline codes of two individuals, use the multi-point crossover algorithm. Iterate through the elements at corresponding positions in the pipeline codes of both individuals, generate a random number, and if the random number is less than rate_crossover = 0.65, then swap the elements at these two positions.

[0186] Step 9.5: For steps 9.3 and 9.4, after completing all operations, it is necessary to determine whether to accept the generated new encoding. If the new encoding can achieve a shorter completion time CT_new, then the encoding is accepted; if the completion time of the new encoding is not optimized, then the encoding is accepted according to a certain acceptance criterion, and a random number R is generated. r The completion time before the crossover is CT v The current system temperature is T. Accept is 1, which means accepting the newly generated code, and Accept is 0, which means not accepting the newly generated code.

[0187]

[0188] Step 10: Perform mutation operations in the genetic algorithm on the workpiece coding and pipeline coding of the system.

[0189] Step 10.1: Generate a random number R r If R r R r If the value is less than rate_mutation = 0.5, proceed to step 10; otherwise, skip to step 11.

[0190] Step 10.2: For an individual workpiece code, use the exchange mutation method. Randomly select two elements within the workpiece code and exchange them to obtain a new workpiece code. The exchange mutation method is as follows: Figure 10 As shown.

[0191] Step 10.3: For the individual pipelined encoding, use the bit-flipping method. Iterate through all elements within the pipelined encoding, generate a random number. If the random number is less than rate_mutation = 0.5, then randomly select one element from the K-1 = 2 elements excluding the current element to replace the original value at that position. The bit-flipping method is as follows... Figure 11 As shown.

[0192] Step 10.4: After steps 10.2 and 10.3, it is necessary to determine whether to accept the generated new code. The specific method is the same as in step 9.5.

[0193] Step 11: Perform the selection operation in the genetic algorithm to generate the population for the next iteration.

[0194] Use a linear sorting selection algorithm. Set the maximum probability P. max The probability is 0.8, and the minimum probability P is... min The fitness of individuals in the population is 0.2. The individuals with the lowest fitness are ranked first, and the individuals with the highest fitness are ranked at position `pop_size`. Based on this ranking, a new fitness value is linearly assigned to each individual, resulting in a new fitness value P(i).

[0195]

[0196] The greater the fitness, the greater the probability that the individual will be selected into the next generation of the population, thus preserving excellent encoded information.

[0197] Step 12: Iterative population management in the genetic algorithm. The optimization effect of the genetic algorithm is as follows: Figure 12 As shown.

[0198] Step 12.1: Let V = V + 1, return to step 4.1, until V = pop_size.

[0199] Step 12.2: Let G = G + 1, T = T × 0.99, return to step 4.1, until G = max_generation.

[0200] It also includes step 13: Based on the final population obtained at the end of step 12, obtain the workpiece code and pipeline code of the optimal individual. Production scheduling is then arranged based on these codes to improve the accuracy and efficiency of production scheduling and save production energy.

[0201] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for distributed flexible fuzzy system transient performance prediction, characterized by: Includes the following steps: Step 1: Classify different production scenarios into three types: optimal, medium, and worst, and construct an acceptance criterion. Improve the genetic algorithm based on the acceptance criterion, initialize the hyperparameters of the improved genetic algorithm, and randomly initialize the workpiece code and pipeline code. Step 1 is implemented as follows: Step 1.1: Classify different production scenarios into three types: optimal, medium, and worst, and construct an acceptance criterion. Improve the genetic algorithm based on the acceptance criterion. Step 1.2: Set the hyperparameters of the genetic algorithm, and assign values ​​to the population size, crossover probability, mutation probability, maximum number of iterations, temperature, and number of iterations for the workshop scheduling scheme; The population size of the workshop scheduling scheme is set to , the crossover probability is set to , the mutation probability is set to , the maximum iteration number of the population is , the initial temperature of the acceptance criterion is , the lower limit of the temperature is , the iteration number of the population is , let ; the preset individual index is , let ; Step 1.3: initialize the workpiece code and the pipeline code of each individual in the workshop scheduling scheme population; each individual has a serial flexible pipeline, and a total of workpieces need to be produced a matrix of size is generated, where the first row is used to store the workpiece code of the workpieces, and the second row is used to store the pipeline code of the workpieces; for the working condition, scheduling is performed, otherwise there is no scheduling significance; Step 1.4: Use Filling elements in A matrix with no duplicate elements; use this matrix as... The workpiece code for a workpiece class; the element at the corresponding position indicates the processing order of that workpiece class, with 1 indicating that the workpiece is processed first. This indicates that the workpiece was last to be processed. Step 1.5: Use Filling elements in The matrix ensures the front The elements are 1 to... The rest Each element is composed of The elements in the matrix are randomly filled, and the element at the corresponding position indicates which production line the workpiece of that type is processed on; this matrix is ​​used as... Streamline coding for similar workpieces; Step 2: According to the individual index, the individual in the workshop scheduling scheme population is sequentially modeled by the flexible fuzzy system to obtain the flexible fuzzy system model, which is referred to as the flexible fuzzy system below; the distributed system is composed of several identical serial flexible flow lines in parallel, so only one serial flexible flow line in the production scene below is analyzed; Step 2: According to the individual index, the individual in the workshop scheduling scheme population is sequentially modeled by the flexible fuzzy system to obtain the flexible fuzzy system model, which is referred to as the flexible fuzzy system below; the distributed system is composed of several identical serial flexible flow lines in parallel, so only one serial flexible flow line in the production scene below is analyzed; The system consists of Bernoulli machines and buffers connected in sequence. The system modeling includes system parameters, system states, and production sequence. The system parameters include production line structure parameters, workpiece processing cycle, Bernoulli machine processing efficiency, and finite buffer parameters. The system states include Bernoulli machine starvation state, Bernoulli machine blocking state, system running state, and system debugging state. The production sequence represents the order in which different types of workpieces are processed within the system. Step 3: Define the transient performance index – batch completion time – based on the flexible fuzzy system model constructed in Step 2 and the actual operating conditions. Defined as: in production scenarios Lower Bernoulli machine , Completed categories During workpiece production, the system has already calculated the expected number of processing cycles; the actual operating conditions include optimal, moderate, and worst operating conditions. Step 4: The flexible fuzzy system production process established according to Step 2 has the characteristic of "no aftereffect", so it is decoupled from the original production line, and an auxiliary production line 1 composed of machines is constructed, so that each production line only produces products of a predetermined category;​ Step 5: Constructing the auxiliary production line 2 composed of The auxiliary production line 2 is composed of The auxiliary production line 2 has the same Bernoulli machine and buffer parameters as the auxiliary production line 1, with the only difference being that the auxiliary production line 2 has an unlimited supply of raw materials. Step 6: Constructing auxiliary line 3 consisting of one single-machine production line and auxiliary line 4 consisting of one double-machine production line and combining the two auxiliary lines, all machines and buffers upstream and downstream are equivalent to time-varying machines in efficiency; Step 7: Calculate parameters of the auxiliary production line 3 and the auxiliary production line 4, including the efficiency of Bernoulli machines in the auxiliary production line 3 and the efficiency of Bernoulli machines in the auxiliary production line 4, based on the auxiliary production line 3, the auxiliary production line 4, and the flexible fuzzy system model of step 2 ;​​ Step 8: Based on the flexible fuzzy system modeling results obtained in Step 2 and the four auxiliary production lines constructed in Steps 4 to 7, perform quantitative analysis and prediction of the transient performance of the system, calculate the batch completion time of the system under the predetermined production scenario, and improve the accuracy and efficiency of transient performance prediction for the distributed flexible fuzzy system. Step 9: Perform the crossover operation in the genetic algorithm on the workpiece coding and pipeline coding of the system; Step 9.1: Generate a random number If Is less than Then proceed to the next operation of Step 9, otherwise jump to Step 11; Step 9.2: Randomly select the workpiece code and production line code of another individual in the workshop scheduling scheme population, and perform cross-operation on the two respectively; this individual is not duplicated from itself; Step 9.3: For the workpiece codes of two individuals, use the partial matching cross algorithm; randomly select two positions within the workpiece code as the start and end positions, swap the elements between the two positions, establish a mapping relationship after the swap, and perform conflict detection on the codes of the remaining positions until the conflict disappears. Step 9.4: For two individual pipeline encodings, use the multi-point crossover algorithm; traverse the elements in corresponding positions within both pipeline encodings, generate a random number, if the random number is less than then swap the elements in the two positions; Step 9.5: For steps 9.3 and 9.4, after completing all operations, it is necessary to determine whether to accept the generated new code; If the new encoding results in a smaller completion time then accept the encoding; If the newly encoded completion time is not optimized, then accept the encoding with a preset acceptance criterion, generate a random number , the completion time before crossover is , the current system temperature is , 1 indicates that the newly generated encoding is accepted, 0 indicates that the newly generated encoding is not accepted; Step 10: Mutation operation in the genetic algorithm for the workpiece encoding and the pipeline encoding, using the exchange mutation method and the bit flip method for the workpiece encoding and the pipeline encoding respectively, so as to introduce new solutions and jump out of the local optimal region in the search space; Step 11: Perform the selection operation in the genetic algorithm, using the linear sorting selection algorithm to generate the plant scheduling scheme population for the next iteration; Step 12: Iterate through the steps to obtain the plant scheduling scheme population in the genetic algorithm; Step 13: Based on the final population obtained at the end of Step 12, obtain the workpiece code and pipeline code of the optimal individual; arrange the production of workpieces according to the code to improve the accuracy and efficiency of production scheduling and save production energy.

2. The method of claim 1, wherein: Step 2 is implemented as follows: Step 2.1: Determine the production line structure; on said system a type of workpiece to be produced, denoted by a class ; said system consists of Bernoulli machines and buffer zones, i.e. the production line structure is determined; a Bernoulli machine is denoted by , a buffer zone is denoted by ; Step 2.2: Determine the system processing cycle; All Bernoulli machines have the same and time-invariant processing period The time axis is segmented in units of processing period ​ Step 2.3: Determine the reliability model of the Bernoulli machine; All Bernoulli machines obey Bernoulli machine reliability model: if Bernoulli machine , , in production category , , product process, neither block nor starvation, then the probability of the Bernoulli machine described in the specific production scene for any workpiece in a processing cycle is , ; the corresponding production failure probability is ; the parameter is defined as the efficiency of Bernoulli machine in the production scene , and the machine efficiency in the optimal production scene is higher than that in the medium production scene, and the machine efficiency in the medium production scene is higher than that in the worst production scene. Step 2.4: Determine the starvation state of the Bernoulli machine; At the beginning of a processing cycle, if the Bernoulli machine In working condition But Bernoulli's machine The previous buffer If the machine is empty at this time, then the Bernoulli machine is in a state of starvation during the processing cycle. Step 2.5: Determine the blocking state of the Bernoulli machine; If Bernoulli machine In working condition, But Bernoulli's machine Next buffer At this point, it is full, and the Bernoulli machine... The next Bernoulli machine If a workpiece cannot be retrieved from the buffer for processing at the start of the processing cycle, and the reason for this inability is a blockage or production failure, then the Bernoulli machine is in a blocked state during that processing cycle. It will not be in a blocked state; Step 2.6: Determine the buffer parameters, which include XX and XX; Buffer capacity The capacity is from express, , ; Step 2.7: Determine the production sequence; type , The workpiece has For each type of workpiece to be processed, all Bernoulli machines produce only that type of workpiece until the production of each type of product is completed; all Bernoulli machines determine the type based on a pre-given workpiece code. The processing sequence, i.e., determining the production sequence; Step 2.8: Determine whether the system is in running or debugging mode; In terms of production types The running process states, totaling , , types The workpieces are produced; when the type , After the production of a certain type of workpiece is completed, it enters the adjustment state for the production of the next type; when the type Once all workpieces have been produced, the production process ends; types product, The adjustment state in the type Before the running state, continue One processing cycle; among which, It is a pre-designed random number that is sequence-dependent, meaning it is related to the previous workpiece.

3. The method for predicting the transient performance of a distributed flexible fuzzy system as described in claim 2, characterized in that: Step 4 is implemented as follows: Based on the flexible fuzzy system model established in step 2, this production process exhibits "no aftereffect," meaning the state of the system in the next processing cycle depends only on the state of this current processing cycle; therefore, this stochastic process is a Markov chain; let , , This indicates the processing cycle. Initially, the system produced various types of products. The number of workpieces; breaking down the original production line into... There are 1 production line, each producing only one type of product. This production line is called auxiliary production line 1. The only difference between it and the original production line is that the efficiency of the first machine in auxiliary production line 1 is time-varying; all other parameters are the same as those of the original production line. , The machine efficiency Calculated using the following formula:

4. The method for predicting the transient performance of a distributed flexible fuzzy system as described in claim 3, characterized in that: Step 6 is implemented as follows: The auxiliary production line 2 is further decomposed into: A single-machine production line, referred to as auxiliary production line 3, and A dual-machine production line is called auxiliary production line 4; The Bernoulli machine efficiency in auxiliary production line 3 is... It produces a limited number of workpieces, while the Bernoulli machine in auxiliary production line 4 has an efficiency of... and .

5. The method for predicting the transient performance of a distributed flexible fuzzy system as described in claim 4, characterized in that: Step 7 is implemented as follows: Step 7.1: Let Indicates the processing cycle At the end, the buffer in auxiliary production line 4 have The probability of a workpiece, making ;make Indicates the processing cycle At the end, the Bernoulli machine in auxiliary production line 3 Complete production Let the probability of a workpiece be given. The initial conditions are: ， ； Step 7.2: Let ; Step 7.3: Let ; Step 7.4: Let For all Calculate according to the following formula : Step 7.5: Let Then, according to Descending order calculation That is, calculate according to the following formula first. Finally, calculate : ； Step 7.6: Let Then, for all Calculate according to the following formula : ； Step 7.7: For all Calculate according to the following formula : in, During the processing cycle The fourth auxiliary production line The transition probability matrix of the production line is expressed as: in, express , express ; Step 7.8: For all Calculate according to the following formula : in, The transition probability matrix for auxiliary production line 3 is expressed as: in, express ; Step 7.9: If If so, proceed to step 7.10; otherwise, for all Calculate the time-varying probability of the first machine in step 5 using the following formula: Step 7.10: Let Return to step 7.4 until the predicted number of processing cycles is reached; Step 7.11: Let Return to step 7.4 until... .

6. The method for predicting the transient performance of a distributed flexible fuzzy system as described in claim 5, characterized in that: Step 8 is implemented as follows: Step 8.1: Based on the Bernoulli machine efficiency in auxiliary production line 3 obtained in step 7, calculate the efficiency using the following formula. Sum of probabilities Analytically predict batch completion time : Step 8.2: Based on the batch completion time of each machine, the batch completion time of the entire production line is calculated as follows: ; Promoted to In the distributed scheduling problem of pipelines, Indicates the first The completion time of the assembly line is then the time required for that individual. Batch completion time in this production scenario for ; Step 8.3: Calculate the completion time for the three production scenarios based on machine efficiency according to the process from Step 2.1 to Step 8.

1. express, , This represents the batch completion time under the optimal production scenario; Step 8.4: Calculate the expected batch completion time ; Step 8.5: Calculate the individual's optimization index and fitness; 。 7. The method for predicting the transient performance of a distributed flexible fuzzy system as described in claim 6, characterized in that: Step 6 is implemented as follows: Step 10.1: Generate a random number ,if , Less than If the condition is met, proceed to step 10; otherwise, skip to step 11. Step 10.2: For an individual workpiece code, use the exchange mutation method; randomly select two elements within the workpiece code and exchange them to obtain a new workpiece code; Step 10.3: For the pipeline coding of an individual, use the bit-flipping method; Iterate through all elements in the pipelined code, generate a random number, and if the random number is less than... Then from the elements excluding that element One element is randomly selected from each element to replace the original value; Step 10.4: After steps 10.2 and 10.3, it is necessary to determine whether to accept the generated new code. The specific method is the same as in step 9.

5.

8. The method for predicting the transient performance of a distributed flexible fuzzy system as described in claim 7, characterized in that: Step 11 is implemented as follows: Use a linear sorting selection algorithm; set the maximum probability. The probability is 0.8, the minimum probability. The fitness of individuals within the population of the workshop scheduling scheme is 0.

2. The individuals with the lowest fitness are ranked first, and those with the highest fitness are ranked second. Based on the ranking, each individual is linearly assigned a new fitness value, resulting in a new fitness value. : The greater the fitness, the greater the probability that the individual will be selected into the next generation of workshop scheduling scheme population, thus preserving excellent coding information; Step 12 is implemented as follows: Step 12.1: Let Return to step 5.1 until... ; Step 12.2: Let , Return to step 5.1 until... .

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