A reentrant hybrid flow shop scheduling method based on the IMOEA / D algorithm

Abstract

This invention discloses a reentrant hybrid flow shop scheduling method based on the IMOEA / D algorithm. Specifically, it first establishes a BPM-RHFSP multi-objective optimization mathematical model with the optimization objectives of minimizing maximum completion time, total delay time, and total equipment energy cost. This transforms the actual production job scheduling problem into a combinatorial optimization mathematical model problem. Then, based on IMOEA / D, it solves the problem model by designing a variable threshold batching strategy for batch processing job decoding; multi-region global search and random variable neighborhood search; and reinforcement search for individuals within the elite solution set. This invention can effectively coordinate the processing of multiple equipment, improve the rationality of resource allocation, shorten the workshop manufacturing cycle and product delay time, and reduce energy costs.

Description

Technical Field

[0001] This invention belongs to the field of job shop scheduling, and particularly relates to a reentrant hybrid flow shop scheduling method based on the IMOEA / D algorithm. Background Technology

[0002] In complex product production lines, typically exemplified by product coating, semiconductor wafer manufacturing, and circuit board production, workpiece processing requires both batch processing machines and single-processor machines. Batch processing machines, such as annealing furnaces, can process multiple workpieces at once, while single-processor machines, such as milling machines, can only process one workpiece at a time. Furthermore, due to the limited manufacturing resources and complex processes of complex product production lines, workpieces need to be processed repeatedly at the same workstations in a structured manner. Taking blade coating as an example, blades are a crucial component of gas turbines, but their processing is complex and resource-intensive. Especially during coating operations, the same process flow is required for multiple processing steps at stations such as sandblasting, shot blasting, painting, low-temperature drying, and high-temperature curing. The low-temperature drying and high-temperature curing stations require different types of heat treatment furnaces for batch processing of blades. To ensure the quality of the coating, blades need to be repeatedly re-entered to specific workstations for processing, further exacerbating resource constraints and increasing the complexity of resource scheduling. The formulation of production plans for this type of production line can be abstracted as a reentrant hybrid flow-shop scheduling problem considering batch processing machines (BPM-RHFSP). In actual production, the maximum completion time of the product, the total delay time, and the total energy consumption cost of the equipment can directly reflect the production efficiency of the workshop, customer satisfaction, and product production costs. It can be seen that the multi-objective optimization of BPM-RHFSP is of great significance for on-time delivery of workpieces, reduction of production costs, and improvement of product quality.

[0003] BPM-RHFSP requires decision-making on scheduling schemes for jobs on single-processor and batch-processor machines. The scheduling schemes on the two types of machines are coupled with each other. At the same time, the problem of reentrant jobs preempting limited batch-processor resources significantly increases the difficulty of resource allocation and job batch scheduling. It has the characteristics of reentrant scheduling and batch-processor scheduling. Therefore, the problem is often decomposed into two aspects: Reentrant Hybrid Flow-shop Scheduling Problem (RHFSP) and Hybrid Flow-shop Scheduling Problem with Batch Processing Machine (BPM-HFSP).

[0004] In solving the BPM-HFSP batch scheduling subproblem, fixed-threshold batching policies (FTBPs) are commonly used, including fixed-capacity-threshold-batching-policy (FCTBP) and fixed-time-threshold-batching-policy (FTTBP). However, the presence of re-entrant workpieces in the production system leads to instability and increased resource allocation complexity, making batching more difficult. Decision-makers often need to adjust the batching thresholds based on the characteristics of each batch processing step, a requirement that fixed thresholds cannot meet. Variable-threshold batching is needed to obtain a more reasonable scheduling scheme. Regarding RHFSP, current research primarily focuses on single-processor systems. Further integrating batch processors as processing resources requires scheduling decision-makers to allocate limited batch processor resources to re-entrant workpieces, significantly increasing the problem's complexity.

[0005] Clearly, in the BPM-RHFSP problem, the two sub-problems mentioned above are highly coupled. The decision on the batching scheme directly affects the subsequent production of the reentrant production system, while reentrant workpieces will increase the complexity of workpiece batching. Further research is needed on BPM-RHFSP. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies in solving the reentrant hybrid pipeline workshop scheduling problem that considers batch processing machines, this invention provides a reentrant hybrid pipeline workshop scheduling method based on the IMOEA / D algorithm.

[0007] The present invention provides a reentrant hybrid flow shop scheduling method based on the IMOEA / D algorithm, comprising the following steps:

[0008] Step 1: Consider the description and related assumptions of reentrant hybrid pipeline scheduling for batch processing machines.

[0009] The reentrant hybrid pipeline scheduling of a batch processor is described as follows: n workpieces need to follow the same processing flow O = {O1, O2, ..., O...} j ,…,O oThe processing consists of m stages, each consisting of a single-processing stage and a batch-processing stage. Multiple batch-processing stages can exist simultaneously, and any stage can be a batch-processing stage. Each batch-processing stage contains batch processing machines that can process a finite number of workpieces simultaneously. Each single-processing stage contains a single-processing machine that processes a single workpiece. Each stage has at least one parallel machine, and at least one stage has more than one parallel machine. After a workpiece arrives at a certain stage, it selects a machine from the corresponding machine set for processing. Due to process requirements, the workpiece repeatedly accesses the production system L-1 times. Different access times allow for different process flows for the workpiece, i.e., there are skippable processes. However, the processing direction of the workpiece is unidirectional each time it is accessed. Multiple indicators are optimized by determining the machine allocation scheme for workpieces in each process, the processing sequence in single-processing processes, and the batching scheme for workpiece sets in batch-processing processes.

[0010] The following assumptions are also followed:

[0011] (1) At zero moment, all workpieces and machines can participate in processing activities;

[0012] (2) The buffer capacity between adjacent stages is unlimited;

[0013] (3) Batch size is only related to the number of workpieces;

[0014] (4) The workpiece processing process must not be interrupted or preempted;

[0015] (5) The preparation time and logistics transfer time required before the workpiece starts are included in the workpiece processing time.

[0016] (6) The occurrence of disturbance events is not considered in the workpiece machining process;

[0017] (7) The workpiece can be delivered immediately after completion, that is, the completion time is equal to the workpiece delivery time.

[0018] Step 2: Establish a mathematical model for optimizing the scheduling objectives of a reentrant hybrid flow shop that takes into account batch processing machines.

[0019] The optimization objective is to minimize the maximum completion time, total delay time, and total equipment energy cost.

[0020] The objective function is:

[0021] min(f1,f2,f3)(1)

[0022] in:

[0023]

[0024] Where: C i J represents i The completion time, e i,j,kIndicates process JO i,j At the completion time of machine k, JO i,j Indicates workpiece J i The j-th process, j = 1, 2, ..., 0, D i J represents i Delivery period, W represents the energy cost coefficient. k This represents the load of machine k, PC. k Q represents the average load energy consumption of machine k per unit time. k NC represents the maximum completion time of machine k. k Let J represent the average idle energy consumption of machine k per unit time, and J represent the set of workpieces, J = {J1, J2, ..., J...} i ,…,J n}, r h Let h be the number of parallel machines in stage h.

[0025] Wherein: Equation (2) is the calculation of the maximum completion time; Equation (3) is the calculation of the total delay time; Equation (4) is the calculation of the total energy consumption cost of the equipment.

[0026] Constraints:

[0027]

[0028] Wherein: T p,k,b t represents the processing time of the b-th batch processed on machine k in the batch processing stage p. i,j,k JO i,j During the processing time of machine k, C p,k,b E represents the set of operations processed on machine k in batch stage p, representing the b-th batch. p,k,b e represents the completion time of the b-th batch processed on machine k in the batch processing stage p. i,j,k Indicates process JO i,j At the completion time of machine k, S p,k,b s represents the start time of the b-th batch processed on machine k in the batch processing stage p. i,j,k Indicates process JO i,j During the start-up time of machine k, Y i,j,p,k,b As a decision variable, if process JO i,j In the b-th batch of machine k in stage p, then Y i,j,p,k,b =1, otherwise Y i,j,p,k,b =0, V p X represents the capacity of machine p in the batch processing stage. i,j,h,k As a decision variable, if process JO i,j If X is processed on machine k at stage h, then i,j,h,k =1, otherwise X i,j,h,k=0, L represents the number of times the workpiece accesses the production system; B p,k Let b represent the set of batches processed on machine k in batch processing stage p, where b = 1, 2, ..., |B|. p,k |,SO h This represents the set of processes that need to be processed on machine h in the process flow.

[0029] Wherein: Equation (5) indicates that the processing time of the batch processor is equal to the longest processing time required for all workpieces in the batch; Equation (6) indicates that the start processing time of the batch processor is no earlier than the latest value of the batch arrival time and the idle time of the batch processor; Equations (7) and (8) indicate that the same batch of workpieces starts and ends processing at the same time, respectively; Equation (9) indicates that for any batch, the number of workpieces processed by the batch processor at one time cannot exceed its maximum capacity; Equation (10) indicates that each workpiece must visit each stage at least once, and the number of times any stage is visited repeatedly does not exceed the number of re-entries; Equation (11) indicates that a workpiece can only be in one batch when performing batch processing, and must be in one of the batches.

[0030] Step 3: Solve the multi-objective optimization problem using the IMOEA / D algorithm based on decomposition.

[0031] Step 1: Initialize the weight vector set and partition the neighborhood B of each weight vector. i ={i1,i2,…,i T}; Initialize the population X = {X1, X2, ..., X} N}, that is, generating the initial population encoding; initializing the reference point Z. * Individual index i = 1; Initialize the external file EP using the non-dominated solution set in X.

[0032] Step 2: For X i A new solution y is obtained by performing a multi-region global search and a random variable neighborhood search. y is then decoded, and the reference point is updated using the objective function value of y.

[0033] Step 3: Update the neighborhood solution: for For X j Decode the solution; if the Chebyshev function value of the new solution y is less than X... j Let X j =y and update X j Objective function value.

[0034] Step 4: Update the external file EP: Decode all solutions in EP, remove all solutions in EP that are dominated by y, and add y to EP if there is no solution in EP that can dominate y.

[0035] Step 5: Let i = i + 1. If i ≤ N, return to Step 2; otherwise, go to Step 6.

[0036] Step 6: Obtain the elite solution set and perform an enhanced search based on the elite solution set.

[0037] Step 7: If the algorithm termination condition is met, output EP; otherwise, set i = 1 and return to Step 2.

[0038] Furthermore, in step 3, during population initialization, to determine batch size division and workpiece sorting, a dual-sequence encoding method is proposed to represent a feasible solution to the problem. Sequence one is the batch sequence π. b Sequence 2 is the workpiece sorting sequence π s Furthermore, a decoding method for the problem was proposed.

[0039] 1) Batch Sequence

[0040] Batch sequence π b =[π b1 ,...,π bk ,...,π bq ] T This is used to represent the number of batches and batch size constructed during each batch processing operation of the workpiece set, where π bk Indicates batch processing operation O bk The batch subsequence, Indicates the process O in the processing of the workpiece set. bk The batch size of the h-th batch constructed at time; assuming O bk The machine processing requires stage l, during initialization. The values ​​are shown in equations (12) and (13).

[0041]

[0042] Where 'a' represents the workpiece during machining O bk Number of batches constructed; V l For stage l, the machine capacity; δ bk The capacity threshold determines the O in the set of workpieces being processed. bk Search space size for batches; δ bk Based on the arrival of the workpiece at batch processing step O bk The relationship between the time interval of the equipment buffer, the equipment capacity, and the time required for a single processing run is determined; when O bk When the preceding process is a single-processing process, the threshold value is set as shown in equation (14); while when the preceding process is a batch processing process, since the workpieces are released in batches, the average interval time r is calculated. j It has little guiding significance for batch processing; experiments have shown that when the average time for all workpieces in the preceding process is less than 0... bk If 50% of the output is used, then a post-batch processing step δ is set.bk =1, otherwise δ bk =0.5, which can obtain a better batching scheme during the iterative search process.

[0043]

[0044] Where, r bk For workpieces to reach batch processing step O bk The average interval time of the device buffer, P bk For the workpiece to be assembled in O bk Maximum working hours.

[0045] 2) Workpiece sorting sequence

[0046] When stage 1 is not a batch processing stage, the workpiece at time zero is considered to be released from a virtual batch processing device; a series of consecutive single-processing operations following the batch processing operation are called a consecutive single-processing operation set, or simply an operation set, and the i-th operation set is denoted as OS. si Assuming there are h process sets, then π s =[π s1 ,...,π sk ,...,π sh ] T Sort sequence, where π sk Representing the workpiece in OS sk The processing sequence, This is the workpiece number.

[0047] During decoding, a dual-sequence encoding and variable threshold batching strategy are used to implement the decoding process. Decoding is performed in segments according to the work process, and an active decoding method is adopted to fully utilize the idle time intervals between processes. The decoding steps are as follows:

[0048] S1: Traverse all processes in O in ascending order of process number. If the current process O... j If it is a batch processing step, proceed to S2; otherwise, proceed to S3.

[0049] S2: Solve the batch scheduling problem using a variable threshold batching strategy, then proceed to S4;

[0050] S3: Assume O j Belongs to the process set OS k Then read the workpiece sorting sequence π from left to right. sk Active decoding is used to determine the workpiece. The machine that can be completed earliest is selected as the processing machine; if there are multiple such machines, the one with the lowest processing power is selected.

[0051] S4: If there are processes that have not been traversed, go to S1; otherwise, output the scheduling Gantt chart and end.

[0052] Furthermore, the variable threshold batching strategy is as follows:

[0053] A batching rule (Compromise Programming with Delivery and Processing Time, CPDPT) is proposed to determine the batching sequence of workpieces. When constructing the batching scheme, the batching quality index I of each workpiece is calculated by weighting the uniformity of workpiece delivery time and the uniformity of processing time within the buffer area. i As shown in equation (15); the decision-maker adjusts the weight coefficients as needed to select the preferred optimization objective;

[0054]

[0055] In the formula, S w The set of workpieces in the buffer during batch decision-making; λ is the weighting coefficient; batch quality index I. i The smaller the size, the higher the batching priority. Workpieces are grouped according to I... i Ascending order as batch order; D i T is the delivery period for workpiece i; i,j For process JO i,j Working hours.

[0056] The batching sequence and the heuristic batching rule CPDPT constitute VTBP, which is used to solve the workpiece batching scheduling subproblem. The triggering event is that the batch processor is idle, so that the k-th batch processing operation O in the process flow can be processed. bk Taking the decoding of bk∈{1,2,…,o} as an example, the process is as follows:

[0057] Step 1: Obtain the arrival time of each workpiece in the batch processing step O bk Available machine buffer time and batch subsequence

[0058]

[0059] Step 2: Traverse π bk ,if If this indicates that a workpiece has not completed the current batch processing step, proceed to Step 3; otherwise, proceed to Step 6.

[0060] Step 3: Select the processing machine: Select the earliest idle machine and determine the number of workpieces (BP) that will arrive in the buffer during the idle time;

[0061] Step 4: If BP is greater than Sort the workpieces in the buffer according to the CPDPT rule, and take min(BP,V) workpieces in order to form a batch, while adjusting the batch size of the remaining batches; otherwise, sort all workpieces to be processed in ascending order of arrival time, and take them in order. Batching individual workpieces;

[0062] Step 5: Batch processing, update machine completion time, return to Step 2;

[0063] Step 6: Output the workpiece in batch processing step O bk The batching scheme.

[0064] Furthermore, the multi-region global search in step 3 specifically involves:

[0065] Choose a parent individual from the neighborhood, and then choose another parent individual from the neighborhood or EP with the same probability for crossover operation; for the workpiece sorting sequence, use the POX crossover operator to generate offspring individuals. First, select two parent individuals X1 and X2 to generate a workpiece set JS. Move the genes belonging to JS in X1 to the new solution X according to their original positions. child In the middle, the genes in X2 that do not belong to JS are inserted into X in sequence. child The vacant position.

[0066] For batch sequences, a subsequence crossover operator is used to generate offspring individuals. First, two parent individuals X1 and X2 are selected. Several subsequences are randomly selected from X1 and used to replace the subsequences at the same positions in X2 to obtain X. child .

[0067] Furthermore, the randomized neighborhood search in step 3 specifically involves:

[0068] Design the following six neighborhood structures:

[0069] NS1: Select group batch subsequence π bk NS2: Add a batch and adjust the batch size of other batches; NS3: Select the batch subsequence π bk Reduce one batch size and adjust the batch sizes of other batches; NS3: Randomly select a critical process block and obtain the ratio of the process in the block to the process at the beginning of the block in terms of π. s NS4: Similar to NS3, swap the gene positions of the processes in the block and the processes at the end of the block; NS5: Randomly select several subsequences, randomly select two positions in each subsequence, and swap the positions of the two genes; NS6: Randomly select several subsequences, randomly select two positions in each subsequence, and reverse the order of the processes.

[0070] The randomized neighborhood search process is as follows:

[0071] Step 1: Obtain the individual X for variable neighborhood search child Set the number of neighborhood searches to N;

[0072] Step 2: Randomly select a neighborhood structure NS i , for X child Perform a neighborhood search to obtain a new solution X. new ;

[0073] Step 3: If the Chebyshev function value of the new solution decreases or the current neighborhood search count equals N, let X child =X new End the search; otherwise, return to Step 2.

[0074] Furthermore, the reinforcement search based on the elite solution set in step 3 specifically involves:

[0075] After each iteration, the optimal solution obtained from the search is used to further explore the solution space to fully develop the potential of the population. Population diversity is increased by replacing individuals to prevent premature convergence. The external file EP and the set of the top 20% of individuals with the best performance for a single objective in the population, SOES, are merged, deduplicated, and used as the elite solution set ES. To improve the algorithm's depth search capability under the same batch scheme, the search is strengthened to operate only on the workpiece sorting sequence. The strengthened search process is as follows:

[0076] Step 1: Obtain the elite solution set ES = {Y1, Y2, ..., Y} n Given the current population P, set the neighborhood search count N; initialize the new non-dominated solution set. Set the number of neighborhood searches, N;

[0077] Step 2: Traverse the elite solution set ES, assuming the current individual is Y. i Proceed to Step 3;

[0078] Step 3: Generate a random number r. If r < 0.5, proceed to Step 4 to perform a global search; otherwise, proceed to Step 5 to perform a neighborhood search.

[0079] Step 4: Randomly select individual Y from ES k With Y i A new solution Y is obtained by performing POX crossover. new Proceed to Step 7;

[0080] Step 5: Randomly select a neighborhood structure from NS3 to NS6, and apply it to Y. i Performing a neighborhood search yields a new solution Y. new ;

[0081] Step 6: If Ynew Unaffected by Y i If the number of dominant or current neighborhood searches equals N, proceed to Step 7; otherwise, return to Step 5.

[0082] Step 7: If Y new Dominate Y i Then replace Y in ES. i If Y new With Y i If they do not control each other, then Y will... new Add to the solution set NSP;

[0083] Step 8: If Y new Unaffected by Y i Domination involves randomly replacing an individual in P that does not belong to SOES, thereby increasing the diversity of the original population.

[0084] Step 9: If all individuals have been traversed, let ES = NSP∪ES, and use the non-dominated individuals that are not repeated in ES as the updated EP; otherwise, return to Step 2.

[0085] The beneficial technical effects of this invention are as follows:

[0086] (1) This invention further considers the diversity of deployable equipment types in reentrant hybrid flow workshops, typically represented by semiconductor production lines and blade coating production lines. That is, the workshop uses both single-processor and batch-processor machines as processing resources. A multi-objective optimization mathematical model of BPM-RHFSP is established, making the model more suitable for actual production scenarios. The BPM-RHFSP problem not only needs to solve the integrated scheduling problem of highly coupled single-processing and batch-processing processes, but also needs to allocate limited batch-processor resources to reentrant workpieces. This exacerbates the complexity of resource allocation and workpiece batching scheme construction, resulting in a significant increase in problem complexity. It is of great significance for coordinating the processing of multiple equipment in complex product production lines and improving the rationality of resource allocation. However, there is very little research on BPM-RHFSP at present.

[0087] (2) This invention employs an improved decomposition-based multi-objective optimization algorithm to solve the BPM-RHFSP problem. A variable threshold batching strategy is designed to solve the workpiece batching scheduling subproblem, enabling flexible batching of workpieces. Secondly, during the update process of the decomposed subproblems, to avoid the algorithm getting trapped in local optima, this invention designs six neighborhood structures and corresponding variable neighborhood search strategies to enhance the algorithm's search capability. Simultaneously, to address the problem of reduced population diversity in the later stages of algorithm iteration, a reinforcement search is performed on the elite solution set to further improve the algorithm's depth search capability and population diversity. Attached Figure Description

[0088] Figure 1This is a schematic diagram of the BPM-RHFSP problem.

[0089] Figure 2 This is a flowchart of the IMOEA / D algorithm of the present invention. Detailed Implementation

[0090] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0091] The present invention provides a reentrant hybrid flow shop scheduling method based on an improved multiobjective evolutionary algorithm (IMOEA / D), comprising the following steps:

[0092] Step 1: Consider the description and related assumptions of reentrant hybrid pipeline scheduling for batch processing machines.

[0093] The reentrant hybrid pipeline scheduling of a batch processor is described as follows: n workpieces need to follow the same processing flow O = {O1, O2, ..., O...} j ,…,O o The process involves m stages, each consisting of single-processing and batch-processing stages. Multiple batch-processing stages can coexist, and any stage can be a batch-processing stage. Each batch-processing stage contains batch machines capable of processing a finite number of workpieces simultaneously. Each single-processing stage contains single-workpiece processing machines. Each stage has at least one parallel machine, and at least one stage has more than one parallel machine. After a workpiece reaches a stage, it selects a machine from the corresponding machine set for processing. Due to process requirements, the workpiece repeatedly accesses the production system L-1 times. Different access numbers allow for different process flows for the workpiece, meaning there are skippable processes. However, the processing direction of each access is unidirectional. Multiple performance indicators are optimized by determining the machine allocation scheme for each process, the processing sequence in single-processing stages, and the batching scheme for workpiece sets in batch-processing stages. A schematic diagram of the problem is shown below. Figure 1 As shown.

[0094] The following assumptions are also followed in this problem:

[0095] (1) At zero moment, all workpieces and machines can participate in processing activities;

[0096] (2) The buffer capacity between adjacent stages is unlimited;

[0097] (3) Batch size is only related to the number of workpieces;

[0098] (4) The workpiece processing process must not be interrupted or preempted;

[0099] (5) The preparation time and logistics transfer time required before the workpiece starts are included in the workpiece processing time.

[0100] (6) The occurrence of disturbance events is not considered in the workpiece machining process;

[0101] (7) The workpiece can be delivered immediately after completion, that is, the completion time is equal to the workpiece delivery time.

[0102] Step 2: Establish a mathematical model for optimizing the scheduling objectives of a reentrant hybrid flow shop that takes into account batch processing machines.

[0103] To better describe the mathematical model, the symbols and parameters are defined as shown in Table 1.

[0104] Table 1 Symbol Definitions

[0105]

[0106] The optimization objective is to minimize the maximum completion time, total delay time, and total equipment energy cost.

[0107] The objective function is:

[0108] min(f,f2,)(1)

[0109] in:

[0110]

[0111] Wherein: Equation (2) is the calculation of the maximum completion time; Equation (3) is the calculation of the total delay time; Equation (4) is the calculation of the total energy consumption cost of the equipment.

[0112] Constraints:

[0113]

[0114] Wherein: Equation (5) indicates that the processing time of the batch processor is equal to the longest processing time required for all workpieces in the batch; Equation (6) indicates that the start processing time of the batch processor is not earlier than the maximum value of the batch arrival time and the idle time of the batch processor; Equations (7) and (8) indicate that the same batch of workpieces starts and ends processing at the same time, respectively; Equation (9) indicates that for any batch, the number of workpieces processed by the batch processor at one time cannot exceed its maximum capacity; Equation (10) indicates that each workpiece must visit each stage at least once, and the number of times any stage is visited repeatedly does not exceed the number of re-entries; Equation (11) indicates that a workpiece can only be in one batch when performing batch processing, and must be in one of the batches.

[0115] Step 3: Solve the multi-objective optimization problem using the IMOEA / D algorithm based on decomposition.

[0116] This invention addresses the shortcomings of fixed-threshold batching strategies for solving batch scheduling subproblems and the traditional MOEA / D algorithm by designing IMOEA / D: 1) A variable-threshold batching strategy for decoding batch processing operations is designed. This strategy determines the batch size through batching sequences and the batching priority of workpieces through heuristic batching rules CPDPT, and achieves adaptive adjustment of batch size through iterative search of batching sequences; 2) Different neighborhood structures typically correspond to different solution spaces. Variable neighborhood search can effectively improve the algorithm's search depth and breadth in the solution space. Therefore, six neighborhood structures and a multi-neighborhood collaborative search strategy are designed based on critical path, batch size, and random search; 3) Elite solutions record the global and local information obtained by the algorithm during the search process. After each iteration, a reinforcement search is performed on the individuals in the elite solution set, and the population individuals are updated to prevent the population diversity from decreasing in the later stages. The IMOEA / D process is as follows: Figure 2 As shown. The specific steps are as follows:

[0117] Step 1: Initialize the weight vector set and partition the neighborhood B of each weight vector. i ={i1,i2,…,i T}; Initialize the population X = {X1, X2, ..., X} N}, that is, generating the initial population encoding; initializing the reference point Z. * Individual index i = 1; Initialize the external file EP using the non-dominated solution set in X.

[0118] Step 2: For X i A new solution y is obtained by performing a multi-region global search and a random variable neighborhood search. y is then decoded, and the reference point is updated using the objective function value of y.

[0119] Step 3: Update the neighborhood solution: for right Decode the solution; if the Chebyshev function value of the new solution y is less than X... j Let X j =y and update X j Objective function value.

[0120] Step 4: Update the external file EP: Decode all solutions in EP, remove all solutions in EP that are dominated by y, and add y to EP if there is no solution in EP that can dominate y.

[0121] Step 5: Let i = i + 1. If i ≤ N, return to Step 2; otherwise, go to Step 6.

[0122] Step 6: Obtain the elite solution set and perform an enhanced search based on the elite solution set.

[0123] Step 7: If the algorithm termination condition is met, output EP; otherwise, set i = 1 and return to Step 2.

[0124] Furthermore, in step 3, during population initialization, to determine batch size division and workpiece sorting, a dual-sequence encoding method is proposed to represent a feasible solution to the problem. Sequence one is the batch sequence π. b Sequence 2 is the workpiece sorting sequence π s A method for decoding the problem was designed.

[0125] 1) Batch Sequence

[0126] Batch sequence π b =[π b1 ,...,π bk ,...,π bq ] T This is used to represent the number of batches and batch size constructed during each batch processing operation of the workpiece set, where π bk Indicates batch processing operation O bk The batch subsequence, Indicates the process O in the processing of the workpiece set. bk The batch size of the h-th batch constructed at time; assuming O bk The machine processing requires stage l, during initialization. The values ​​are shown in equations (12) and (13).

[0127]

[0128] Where 'a' represents the workpiece during machining O bk Number of batches constructed; V l For stage l, the machine capacity; δ bk The capacity threshold determines the O in the set of workpieces being processed. bk Search space size for batches; δ bk Based on the arrival of the workpiece at batch processing step O bk The relationship between the time interval of the equipment buffer, the equipment capacity, and the time required for a single processing run is determined; when O bk When the preceding process is a single-processing process, the threshold value is set as shown in equation (14); while when the preceding process is a batch processing process, since the workpieces are released in batches, the average interval time r is calculated. j It has little guiding significance for batch processing; experiments have shown that when the average time for all workpieces in the preceding process is less than 0... bk If 50% of the output is used, then a post-batch processing step δ is set. bk =1, otherwise δ bk =0.5, which can obtain a better batching scheme during the iterative search process.

[0129]

[0130] Where, r bk For workpieces to reach batch processing step O bk The average interval time of the device buffer, P bk For the workpiece to be assembled in O bk Maximum working hours.

[0131] 2) Workpiece sorting sequence

[0132] When stage 1 is not a batch processing stage, the workpiece at time zero is considered to be released from a virtual batch processing device; a series of consecutive single-processing operations following the batch processing operation are called a consecutive single-processing operation set, or simply an operation set, and the i-th operation set is denoted as OS. si Assuming there are h process sets, then π s =[π s1 ,...,π sk ,...,π sh ] T Sort sequence, where π sk Representing the workpiece in OS sk The processing sequence, This is the workpiece number.

[0133] During decoding, a dual-sequence encoding and variable threshold batching strategy are used to implement the decoding process. Decoding is performed in segments according to the work process, and an active decoding method is adopted to fully utilize the idle time intervals between processes. The decoding steps are as follows:

[0134] S1: Traverse all processes in O in ascending order of process number. If the current process O... j If it is a batch processing step, proceed to S2; otherwise, proceed to S3.

[0135] S2: Solve the batch scheduling problem using a variable threshold batching strategy, then proceed to S4;

[0136] S3: Assume O j Belongs to the process set OS k Then read the workpiece sorting sequence π from left to right. sk Active decoding is used to determine the workpiece. The machine that can be completed earliest is selected as the processing machine; if there are multiple such machines, the one with the lowest processing power is selected.

[0137] S4: If there are processes that have not been traversed, go to S1; otherwise, output the scheduling Gantt chart and end.

[0138] Furthermore, the variable threshold batching strategy is as follows:

[0139] A batching rule for coordinating delivery and processing time uniformity (Compromise Programming with Delivery and Processing Time, CPDPT) is proposed to determine the batching order of workpieces. The selection of workpieces directly impacts the optimization objective when constructing the batching scheme. The batching quality index I for each workpiece is calculated by weighting the uniformity of delivery time and processing time within the buffer area. i As shown in equation (15); the decision-maker adjusts the weight coefficients as needed to select the preferred optimization objective;

[0140]

[0141] In the formula, S w The set of workpieces in the buffer during batch decision-making; λ is the weighting coefficient; batch quality index I. i The smaller the size, the higher the batching priority. Workpieces are grouped according to I... i Ascending order as batch order; D i T is the delivery period for workpiece i; i,j For process JO i,j Working hours.

[0142] The batching sequence and the heuristic batching rule CPDPT constitute VTBP, which is used to solve the workpiece batching scheduling subproblem. The triggering event is that the batch processor is idle, so that the k-th batch processing operation O in the process flow can be processed. bk Taking the decoding of bk∈{1,2,…,o} as an example, the process is as follows:

[0143] Step 1: Obtain the arrival time of each workpiece in the batch processing step O bk Available machine buffer time and batch subsequence

[0144]

[0145] Step 2: Traverse π bk ,if If this indicates that a workpiece has not completed the current batch processing step, proceed to Step 3; otherwise, proceed to Step 6.

[0146] Step 3: Select the processing machine: Select the earliest idle machine and determine the number of workpieces (BP) that will arrive in the buffer during the idle time;

[0147] Step 4: If BP is greater than Sort the workpieces in the buffer according to the CPDPT rule, and take min(BP,V) workpieces in order to form a batch, while adjusting the batch size of the remaining batches; otherwise, sort all workpieces to be processed in ascending order of arrival time, and take them in order. Batching individual workpieces;

[0148] Step 5: Batch processing, update machine completion time, return to Step 2;

[0149] Step 6: Output the workpiece in batch processing step O bk The batching scheme.

[0150] Multi-region global search:

[0151] To better utilize the local and global information obtained during the algorithm iteration process, a multi-region global search is proposed. This involves selecting a parent individual from the neighborhood and then selecting another parent individual from the neighborhood or EP with the same probability for crossover. For the workpiece sorting sequence, the POX (Precedence Preserving Order-based Crossover) operator is used to generate offspring individuals. First, two parent individuals X1 and X2 are selected to generate a workpiece set JS. Genes belonging to JS in X1 are then moved from their original positions to the new solution X. child In the middle, the genes in X2 that do not belong to JS are inserted into X in sequence. child The vacant position.

[0152] For batch sequences, a subsequence crossover operator is used to generate offspring individuals. First, two parent individuals X1 and X2 are selected. Several subsequences are randomly selected from X1 and used to replace the subsequences at the same positions in X2 to obtain X. child .

[0153] Randomized neighborhood search:

[0154] Variable neighborhood search improves the algorithm's search capability by continuously switching neighborhood structures, thus preventing the population from getting trapped in local optima. This invention designs the following six neighborhood structures.

[0155] NS1: Select group batch subsequence π bk NS2: Add a batch and adjust the batch size of other batches; NS3: Select the batch subsequence π bk Reduce one batch size and adjust the batch sizes of other batches; NS3: Randomly select a critical process block and obtain the ratio of the process in the block to the process at the beginning of the block in terms of π. sNS4: Similar to NS3, swap the gene positions of the processes in the block and the processes at the end of the block; NS5: Randomly select several subsequences, randomly select two positions in each subsequence, and swap the positions of the two genes; NS6: Randomly select several subsequences, randomly select two positions in each subsequence, and reverse the order of the processes.

[0156] Different neighborhood structures correspond to specific solution spaces. It is difficult to find the global optimum using only a single neighborhood structure. Therefore, in order to improve the algorithm's ability to search the solution space collaboratively under six neighborhood structures, a randomized variable neighborhood search process is designed as follows:

[0157] Step 1: Obtain the individual X for variable neighborhood search child Set the number of neighborhood searches to N;

[0158] Step 2: Randomly select a neighborhood structure NS i , for X child Perform a neighborhood search to obtain a new solution X. new ;

[0159] Step 3: If the Chebyshev function value of the new solution decreases or the current neighborhood search count equals N, let X child =X new End the search; otherwise, return to Step 2.

[0160] Enhanced search based on elite solution sets:

[0161] After each iteration, the optimal solution obtained from the search is used to further explore the solution space to fully develop the potential of the population. Population diversity is increased by replacing individuals to prevent premature convergence. The external file EP and the set of the top 20% of individuals with the best performance for a single objective in the population, SOES, are merged, deduplicated, and used as the elite solution set ES. To improve the algorithm's depth search capability under the same batch scheme, the search is strengthened to operate only on the workpiece sorting sequence. The strengthened search process is as follows:

[0162] Step 1: Obtain the elite solution set ES = {Y1, Y2, ..., Y} n Given the current population P, set the neighborhood search count N; initialize the new non-dominated solution set. Set the number of neighborhood searches, N;

[0163] Step 2: Traverse the elite solution set ES, assuming the current individual is Y. i Proceed to Step 3;

[0164] Step 3: Generate a random number r. If r < 0.5, proceed to Step 4 to perform a global search; otherwise, proceed to Step 5 to perform a neighborhood search.

[0165] Step 4: Randomly select individual Y from ES k With Y i A new solution Y is obtained by performing POX crossover. new Proceed to Step 7;

[0166] Step 5: Randomly select a neighborhood structure from NS3 to NS6, and apply it to Y. i Performing a neighborhood search yields a new solution Y. new ;

[0167] Step 6: If Y new Unaffected by Y i If the number of dominant or current neighborhood searches equals N, proceed to Step 7; otherwise, return to Step 5.

[0168] Step 7: If Y new Dominate Y i Then replace Y in ES. i If Y new With Y i If they do not control each other, then Y will... new Add to the solution set NSP;

[0169] Step 8: If Y new Unaffected by Y i Domination involves randomly replacing an individual in P that does not belong to SOES, thereby increasing the diversity of the original population.

[0170] Step 9: If all individuals have been traversed, let ES = NSP∪ES, and use the non-dominated individuals that are not repeated in ES as the updated EP; otherwise, return to Step 2.

[0171] Example:

[0172] Case design and evaluation metrics:

[0173] In the blade coating process, the workpiece requires two batch processing steps—low-temperature drying and high-temperature curing—each time it visits the production system. The low-temperature drying process is significantly shorter than the high-temperature curing process. Based on the problem model proposed in this invention and considering the characteristics of the blade coating process, a set of test cases was designed for verification. Each test case follows J... n1 R n2 This indicates that there are n1 workpieces waiting to be processed, and each workpiece needs to be re-entered n2 times. Ten experimental cases were randomly generated, and the range of values ​​for the parameters involved is shown in Table 2. To increase the diversity of the cases, the processing stages of the high-temperature curing process and the low-temperature drying process are arbitrary.

[0174] Table 2 shows the range of values ​​for each parameter in the example.

[0175]

[0176] The calculation method for the workpiece delivery period is shown in Equation (16).

[0177]

[0178] Among them, D i Let σ be the delivery date of workpiece i, and let σ be a random number between [0,1].

[0179] Currently, the performance of multi-objective optimization algorithms is often evaluated using three metrics: diversity, convergence, and dominance. This invention uses the C-Metric and Inversed Generational Distance (IGD) to evaluate the performance of the proposed algorithm. Since the true optimal Pareto Front (NOPF) of the example is unknown, an approximate NOPF front is used instead. First, the solution sets obtained by each algorithm after running 10 times on each example are non-dominated and merged to obtain the approximate NOPF for that example. Simultaneously, the average C-Metric and IGD obtained by each algorithm after 10 runs on the same example are compared.

[0180] IGD measures the convergence and diversity of the algorithm by calculating the average distance between the Pareto solution set and the NOPF solution set, as shown in Equation (17).

[0181]

[0182] Among them, P * For NOPF, |P * | represents the number of solutions in NOPF, P is the Pareto solution set obtained by the algorithm, and dis(x,P) represents the value of P. * The minimum Euclidean distance (IGD) between solution x and all solutions in P. The smaller the IGD, the better the overall performance of the solution set.

[0183] The C-index measures the dominance relationship between two algorithms by calculating the proportion of solutions in one Pareto solution set that are dominated by another Pareto solution set, as shown in Equation (18).

[0184]

[0185] Where C(P1,P2) represents the proportion of solutions in solution set P2 that are dominated by at least one solution in solution set P1, v < u indicates that solution v Pareto dominates u; |P2| is the number of solutions in P2. If C(P1,P2) > C(P2,P1), then Algorithm 1 has better dominance than Algorithm 2.

[0186] Batch strategy comparison experiment:

[0187] To verify the effectiveness of the proposed Variable Threshold Batching (VTBP) strategy, it was compared with the Fixed Capacity Threshold Batching Policy (FCTBP) and the Fixed Time Threshold Batching Policy (FTTBP). The solution algorithm for all strategies was IMOEA / D, with the only difference between the different batching strategies being the decoding process. Two device capacity thresholds—70% and 100%, denoted as FCTBP1 and FCTBP2—were set; two time thresholds—3*PT and 1*PT—were set as FTTBP1 and FTTBP2 (PT being the average time for all workpieces in the same batch processing step). Tables 3 and 4 respectively statistically analyze the average IGD and C-Metric indices obtained by running each of the five strategies independently for 10 iterations in each example.

[0188] Table 3. Statistical results of IGD indicators for different batching strategies.

[0189]

[0190] Table 4. Statistical results of C-Metric indicators for different batching strategies.

[0191]

[0192] The data in the table is analyzed as follows:

[0193] (1) In terms of IGD index, VTBP can obtain the best value in 7 out of 10 cases, and also achieves the best overall average value, which is 46.11% and 47.19% better than FCTBP and FTTBP strategies respectively, indicating that VTBP strategy has more advantages in diversity and convergence than other strategies.

[0194] (2) In terms of C-Metric, VTBP outperformed all other batching strategies in 7 cases. Meanwhile, in terms of overall average, the average proportion of solutions obtained by VTBP strategy dominated by FCTBP strategy and FTTBP strategy was 6.81% and 10.50%, respectively, while the average proportions dominated by FCTBP strategy and FTTBP strategy were 53.59% and 55.92%, respectively. This indicates that VTBP strategy has a greater advantage in dominance than other strategies.

[0195] Algorithm comparison experiment:

[0196] The selected comparison algorithms are MOEA / D, NSGA-II, and CSFLA. MOEA / D and NSGA-II are classic multi-objective optimization algorithms, while CSFLA is used to solve the RHFSP problem. All of the above algorithms use VTBP to solve the job batching and scheduling subproblem. Tables 5 and 6 show the average IGD and C-Metric indices obtained by running the four algorithms independently 10 times in each example.

[0197] Table 5. Statistical results of IGD index for different algorithms

[0198]

[0199] Table 6. Statistical results of C-Metric indices for different algorithms.

[0200]

[0201]

[0202] The data in the table is analyzed as follows:

[0203] (1) In terms of IGD index, IMOEA / D can obtain the best value in 8 out of 10 cases, and achieve the best overall average value, which is 25.45% better than the second best NSGA-II algorithm and 38.19% better than other algorithms on average. This shows that IMOEA / D has more advantages than other algorithms in terms of diversity and convergence.

[0204] (2) In terms of C-Metric, IMOEA / D outperformed all other algorithms in 6 cases. At the same time, in terms of the overall average, the average proportion of solutions obtained by IMOEA / D that were dominated by other algorithms was 18.54%, and the average proportion that dominated other algorithms was 61.89%, indicating that IMOEA / D had a greater advantage in dominance than other strategies.

Claims

1. A reentrant hybrid flow shop scheduling method based on the IMOEA / D algorithm, characterized in that, Includes the following steps: Step 1: Consider the description and related assumptions of reentrant hybrid flow shop scheduling for batch processing machines; The reentrant hybrid pipeline scheduling of a batch processor is described as follows: n workpieces need to follow the same processing flow O={O1,O2,…,O2} j ,…,O o The processing consists of m stages, each consisting of a single-processing stage and a batch-processing stage. Multiple batch-processing stages can exist simultaneously, and any stage can be a batch-processing stage. Each batch-processing stage contains batch processing machines that can process a finite number of workpieces simultaneously. Each single-processing stage contains a single-processing machine that processes a single workpiece. Each stage has at least one parallel machine, and at least one stage has more than one parallel machine. After a workpiece arrives at a certain stage, it selects a machine from the corresponding machine set for processing. Due to process requirements, the workpiece repeatedly accesses the production system L-1 times. The process flow of the workpiece is allowed to be different with different access numbers, i.e., there are skippable processes. However, the processing direction of the workpiece is unidirectional each time it is accessed. Multiple indicators are optimized by determining the machine allocation scheme for workpieces in each process, the processing sequence in the single-processing process, and the batching scheme for workpiece sets in the batch-processing process. The following assumptions are also followed: (1) At moment zero, all workpieces and machines are able to participate in processing activities; (2) The buffer capacity between adjacent stages is unlimited; (3) Batch size is only related to the number of workpieces; (4) The workpiece processing process must not be interrupted or preempted; (5) The preparation time and logistics transfer time required before the workpiece starts are included in the workpiece processing time. (6) The occurrence of disturbance events is not considered during the workpiece machining process; (7) The workpiece shall be delivered immediately after completion, that is, the completion time is equal to the delivery time of the workpiece. Step 2: Establish a mathematical model for optimizing the scheduling objectives of a reentrant hybrid flow shop that considers batch processing machines; The optimization objective is to minimize the maximum completion time, total delay time, and total equipment energy cost; The objective function is: （1） in: （2） （3） （4） Where: C i J represents i The completion time, e i,j,k Indicates process JO i,j At the completion time of machine k, JO i,j Indicates workpiece J i The j-th process, j=1, 2, …, 0, D i J represents i Delivery period, W represents the energy cost coefficient. k This represents the load of machine k, PC. k Q represents the average load energy consumption of machine k per unit time. k NC represents the maximum completion time of machine k. k Let J represent the average idle energy consumption of machine k per unit time, and J represent the set of workpieces, J={J1,J2,…,J…} i ,…,J n }, r h The number of parallel machines in stage h; Wherein: Equation (2) is the calculation of the maximum completion time; Equation (3) is the calculation of the total delay time; Equation (4) is the calculation of the total energy consumption cost of the equipment; Constraints: （5） （6） （7） （8） （9） （10） （11） Wherein: T p,k,b t represents the processing time of the b-th batch processed on machine k in the batch processing stage p. i,j,k JO i,j During the processing time of machine k, C p,k,b E represents the set of operations processed on machine k in batch stage p, representing the b-th batch. p,k,b e represents the completion time of the b-th batch processed on machine k in the batch processing stage p. i,j,k Indicates process JO i,j At the completion time of machine k, S p,k,b s represents the start time of the b-th batch processed on machine k in the batch processing stage p. i,j,k Indicates process JO i,j During the start-up time of machine k, Y i,j,p,k,b As a decision variable, if process JO i,j In the b-th batch of machine k in stage p, then Y i,j,p,k,b =1, otherwise Y i,j,p,k,b =0, V p X represents the capacity of machine p in the batch processing stage. i,j,h,k As a decision variable, if process JO i,j If X is processed on machine k at stage h, then i,j,h,k =1, otherwise X i,j,h,k =0, L represents the number of times the workpiece accesses the production system; B p,k Let b = 1, 2, ..., |B| represent the set of batches processed on machine k in the batch processing stage p. p,k |,SO h This represents the set of processes that need to be processed on machine h in the technological process. Wherein: Equation (5) indicates that the processing time of the batch processor is equal to the longest processing time required for all workpieces in the batch; Equation (6) indicates that the start processing time of the batch processor is no earlier than the latest value of the batch arrival time and the idle time of the batch processor; Equations (7) and (8) indicate that the same batch of workpieces starts and ends processing at the same time, respectively; Equation (9) indicates that for any batch, the number of workpieces processed by the batch processor at one time cannot exceed its maximum capacity; Equation (10) indicates that each workpiece must visit each stage at least once, and the number of times any stage is visited repeatedly does not exceed the number of re-entries; Equation (11) indicates that a workpiece can only be in one batch when performing batch processing operations, and must be in one of the batches; Step 3: Solve the multi-objective optimization problem using the IMOEA / D algorithm based on decomposition; Step 1: Initialize the weight vector set and partition the neighborhood B of each weight vector. i ={i1, i2,…,i T }; Initialize the population X = {X1, X2, ..., X} N }, that is, generating the initial population encoding; initializing the reference point. Individual index i=1; Initialize external file EP using the non-dominated solution set in X; Step 2: For X i A new solution y is obtained by performing a multi-region global search and a random variable neighborhood search. y is then decoded, and the reference point is updated using the objective function value of y. Step 3: Update the neighborhood solution: for , for X j Decode the solution; if the Chebyshev function value of the new solution y is less than X... j Let X j =y and update X j Objective function value; Step 4: Update the external file EP: Decode all solutions in EP, remove all solutions in EP that are dominated by y, and add y to EP if there is no solution in EP that can dominate y. Step 5: Let i = i + 1. If i ≤ N, return to Step 2; otherwise, go to Step 6. Step 6: Obtain the elite solution set and perform reinforcement search based on the elite solution set: Step 7: If the algorithm termination condition is met, output EP; otherwise, set i=1 and return to Step 2. In step 3, during population initialization, a dual-sequence encoding method is proposed to represent a feasible solution to the problem in order to determine batch size division and workpiece sorting. Sequence 1 is the batch sequence π. b Sequence 2 is the workpiece sorting sequence π s Furthermore, a decoding method for the problem was proposed. 1) Batch Sequence Batch sequence This is used to represent the number of batches and batch size constructed during each batch processing operation of the workpiece set, where , π bk Indicates batch processing operation O bk The batch subsequence, Indicates the process O in the processing of the workpiece set. bk The batch size of the h-th batch constructed at time; assuming O bk The machine processing requires stage l, during initialization. The values ​​of time are shown in equations (12) and (13); （12） （13） Where 'a' represents the workpiece during machining O bk Number of batches constructed; V l For stage l, the machine capacity; δ bk The capacity threshold determines the O in the set of workpieces being processed. bk Search space size for batches; δ bk Based on the arrival of the workpiece at batch processing step O bk The relationship between the time interval of the equipment buffer, the equipment capacity, and the time required for a single processing run is determined; when O bk When the preceding process is a single processing process, the threshold value is set as shown in equation (14); after experimentation, when the average working time of all workpieces in the preceding process is less than 0. bk If 50% of the output is used, then a post-batch processing step δ is set. bk =1, otherwise δ bk =0.5; （14） Where, r bk For workpieces to reach batch processing step O bk The average interval time of the device buffer, P bk For the workpiece to be assembled in O bk Maximum working hours; 2) Workpiece sorting sequence When stage 1 is not a batch processing stage, the workpiece at time zero is considered to be released from a virtual batch processing device; a series of consecutive single-processing operations following the batch processing operation are called a consecutive single-processing operation set, or simply an operation set, and the i-th operation set is denoted as OS. si Assuming there are h process sets, then Sort sequence, where , π sk Representing the workpiece in OS sk The processing sequence, For workpiece number; During decoding, a dual-sequence encoding and variable threshold batching strategy are used to implement the decoding process. Decoding is performed in segments according to the work process, and an active decoding method is adopted to fully utilize the idle time intervals between processes. The decoding steps are as follows: S1: Traverse all processes in O in ascending order of process number. If the current process O... j If it is a batch processing step, proceed to S2; otherwise, proceed to S3. S2: Solve the batch scheduling problem using a variable threshold batching strategy, then proceed to S4; S3: Assume O j Belongs to the process set OS k Then read the workpiece sorting sequence from left to right. Active decoding is used to determine the workpiece. The machine that can be completed earliest is selected as the processing machine; if there are multiple such machines, the one with the lowest processing power is selected. S4: If there are processes that have not been traversed, go to S1; otherwise, output the scheduling Gantt chart and end.

2. The reentrant hybrid flow shop scheduling method based on the IMOEA / D algorithm according to claim 1, characterized in that, The variable threshold batching strategy is specifically as follows: A batching rule, CPDPT, is proposed to coordinate the uniformity of delivery time and processing time, and to determine the batching sequence of workpieces. When constructing the batching scheme, the batching quality index I of each workpiece is calculated by weighting the uniformity of delivery time and processing time within the buffer area. i As shown in equation (15); Decision-makers adjust the weighting coefficients as needed to select their preferred optimization objective; （15） In the formula, S w The set of workpieces in the buffer area when making batch decisions; λ is the weighting coefficient; batch quality index I i The smaller the size, the higher the batching priority. Workpieces are grouped according to I... i Ascending order as batch order; D i T is the delivery period for workpiece i; i,j For process JO i,j Working hours; The batching sequence and the heuristic batching rule CPDPT constitute VTBP, which is used to solve the workpiece batching scheduling subproblem. The triggering event is that the batch processor is idle, so that the k-th batch processing operation O in the process flow can be processed. bk Taking the decoding of bk∈{1,2,…,o} as an example, the process is as follows: Step 1: Obtain the arrival time of each workpiece in the batch processing step O bk Available machine buffer time and batch subsequence ; Step 2: Traverse π bk ,if If the current batch processing step is not completed, proceed to Step 3; otherwise, proceed to Step 6. Step 3: Select the processing machine: Select the earliest idle machine and determine the number of workpieces (BP) that will arrive in the buffer during the idle time; Step 4: If BP is greater than The workpieces in the buffer are sorted according to the CPDPT rule, and min(BP,V) workpieces are batched in order, while the batch size of the remaining batches is adjusted. Otherwise, arrange all workpieces to be processed in ascending order of arrival time, and take them in order. Batching individual workpieces; Step 5: Batch processing, update machine completion time, return to Step 2; Step 6: Output the workpiece in batch processing step O bk The batching scheme.

3. The reentrant hybrid flow shop scheduling method based on the IMOEA / D algorithm according to claim 1, characterized in that, The multi-region global search in step 3 specifically involves: Choose a parent individual from the neighborhood, and then choose another parent individual from the neighborhood or EP with the same probability for crossover operation; for the workpiece sorting sequence, use the POX crossover operator to generate offspring individuals. First, select two parent individuals X1 and X2 to generate a workpiece set JS. Move the genes belonging to JS in X1 to the new solution X according to their original positions. child In the middle, the genes in X2 that do not belong to JS are inserted into X in sequence. child The vacant position; For batch sequences, a subsequence crossover operator is used to generate offspring individuals. First, two parent individuals X1 and X2 are selected. Several subsequences are randomly selected from X1 and used to replace the subsequences at the same positions in X2 to obtain X. child .

4. The reentrant hybrid flow shop scheduling method based on the IMOEA / D algorithm according to claim 1, characterized in that, The random variable neighborhood search in step 3 specifically involves: Design the following six neighborhood structures: NS1: Select group batch subsequence π bk NS2: Add a batch and adjust the batch size of other batches; NS3: Select the batch subsequence π bk Reduce one batch size and adjust the batch sizes of other batches; NS3: Randomly select a critical process block and obtain the ratio of the process in the block to the process at the beginning of the block in terms of π. s NS4: Swap the gene positions of the corresponding genes in the block and the gene positions of the gene positions of the process at the end of the block; NS5: Randomly select several subsequences, randomly select two positions in each subsequence, and swap the gene positions of the two genes; NS6: Randomly select several subsequences, randomly select two positions in each subsequence, and reverse the order of the processes in them. The randomized neighborhood search process is as follows: Step 1: Obtain the individual X for variable neighborhood search child Set the number of neighborhood searches to N; Step 2: Randomly select a neighborhood structure NS i , for X child Perform a neighborhood search to obtain a new solution X. new ; Step 3: If the Chebyshev function value of the new solution decreases or the current neighborhood search count equals N, let X child =X new End the search; otherwise, return to Step 2.

5. A reentrant hybrid flow shop scheduling method based on the IMOEA / D algorithm according to claim 1, characterized in that, The reinforcement search based on the elite solution set in step 3 specifically involves: After each iteration, the optimal solution obtained from the search is used to further explore the solution space to fully develop the potential of the population. Population diversity is increased by replacing individuals to prevent premature convergence. The external file EP and the set of the top 20% of individuals with the best performance for a single objective in the population, SOES, are merged, deduplicated, and used as the elite solution set ES. To improve the algorithm's depth search capability under the same batch scheme, the search is strengthened to operate only on the workpiece sorting sequence. The strengthened search process is as follows: Step 1: Obtain the elite solution set ES={Y1, Y2,…, Y…} n Given the current population P, set the neighborhood search count N; initialize the new non-dominated solution set. Set the number of neighborhood searches to N; Step 2: Traverse the elite solution set ES, assuming the current individual is Y. i Proceed to Step 3; Step 3: Generate a random number r. If r < 0.5, proceed to Step 4 to perform a global search; otherwise, proceed to Step 5 to perform a neighborhood search. Step 4: Randomly select individual Y from ES k With Y i A new solution Y is obtained by performing POX crossover. new Proceed to Step 7; Step 5: Randomly select a neighborhood structure from NS3 to NS6, and apply it to Y. i Performing a neighborhood search yields a new solution Y. new ; Step 6: If Y new Unaffected by Y i If the number of dominant or current neighborhood searches equals N, proceed to Step 7; otherwise, return to Step 5. Step 7: If Y new Dominate Y i Then replace Y in ES. i If Y new With Y i If they do not control each other, then Y will... new Add to the solution set NSP; Step 8: If Y new Unaffected by Y i Domination involves randomly replacing an individual in P that does not belong to SOES, thereby increasing the diversity of the original population. Step 9: If all individuals have been traversed, let ES = NSP∪ES, and use the non-dominated individuals that are not repeated in ES as the updated EP; otherwise, return to Step 2.

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