Aviation composite hot-pressing batch scheduling method considering resource constraint and dual preparation time

Abstract

The invention discloses an aviation composite material hot-pressing batch scheduling method considering resource constraint and dual preparation time, particularly relates to the technical field of aviation composite material intelligent manufacturing, and aims to obtain related data of a hot-pressing forming process, including workpiece data and autoclave data, and to minimize the maximum completion time as a target; designing a batch scheduling objective function of the aviation composite hot-press forming process; establishing a two-dimensional multi-layer loading hot press molding process batch scheduling model considering resource constraint and dual preparation time; and taking the objective function as an optimization objective, taking the two-dimensional multi-layer loading hot-press forming process batch scheduling model as an optimization model, and adopting an improved genetic taboo algorithm based on batch processing time for solving to obtain a hot-press forming process batch scheduling scheme.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent manufacturing of aviation composite materials, and in particular to a method for scheduling hot pressing batches of aviation composite materials taking resource constraints and dual preparation time into consideration. Background Art

[0002] With the continuous improvement of aviation manufacturing technology, the proportion of composite materials used in structural parts continues to increase, and demand continues to grow, placing higher demands on the scheduling of their manufacturing process. The hot press forming process, due to its long process flow, fast production cycle, and high resource consumption, has become a key link in restricting the expansion of composite manufacturing capacity. In current actual production, the diverse batches of workpieces, tight delivery cycles, and frequent production schedule adjustments have caused increasing pressure on manufacturing organizations, and the hot press forming process faces significant challenges in scheduling and resource coordination.

[0003] The prepreg loading method in this process can be deconstructed into a two-dimensional boxing process, with the spatial arrangement of the workpieces limited by the size of the workpieces and equipment. Furthermore, multiple preparation stages are involved before the process starts, including time required for loading and unloading materials into and out of the tank, as well as technical preparation times for heating and vacuuming the process system. These two types of preparation times vary significantly under different batching strategies, forming a typical dual preparation time structure. Furthermore, the limited resources of thermocouples and vacuum nozzles are shared between workpieces, which can easily lead to problems such as low resource utilization and lengthy waiting times. Summary of the Invention

[0004] To this end, the present invention provides an aviation composite hot pressing batch scheduling method considering resource constraints and dual preparation time to solve the problems raised in the background technology.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for scheduling hot pressing batches of aviation composite materials considering resource constraints and dual preparation time, comprising the following steps: Step 1: Obtain relevant data of the hot press forming process, including workpiece data and autoclave data, and design the batch scheduling objective function for the hot press forming process of aviation composite materials with the goal of minimizing the maximum completion time; Step 2: Establish a two-dimensional multi-layer loading hot pressing process batch scheduling model considering resource constraints and double preparation time; Step 3: Taking the objective function as the optimization target and the two-dimensional multi-layer loading hot pressing process batch scheduling model as the optimization model, an improved genetic taboo algorithm based on batch processing time is used to solve the problem and obtain the hot pressing process batch scheduling solution.

[0006] Preferably, the step 1 establishes a hot pressing batch scheduling objective function: (1); (2); in, express The maximum completion time of a batch of workpieces, : batch collection; : batch index; :batch processing time, ; : The minimum batch size obtained based on the workpiece area and resource quantity; Formula (1) and Formula (2) define the objective function as minimizing the maximum completion time, and the maximum completion time is equal to the sum of the processing time of each batch.

[0007] Preferably, the step 2 constructs a two-dimensional multi-layer loading hot pressing process batch scheduling model that takes into account resource constraints and dual preparation time, including: uniqueness constraints of workpiece processing, workpiece resource carrying restrictions and dual preparation time, workpiece batch logic and process constraints, and spatial layout constraints.

[0008] Preferably, the uniqueness constraint of workpiece processing ensures that all workpieces to be processed can be processed only once, and the formula is as follows: (3); : Autoclave level collection; : Autoclave level index; : , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer; ; : artifact collection; : Artifact index.

[0009] Preferably, the workpiece resource load limit and the dual preparation time include: (1) Resource carrying capacity limit: The amount of resources required for each workpiece must not exceed the total amount of resources in the equipment carrying layer where it is located to avoid equipment overload and ensure processing feasibility. The formula is as follows: (4); :Workpiece the amount of resources required; : , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer; :The first in the autoclave The number of resources the layer contains; (2) Double preparation time. The double preparation time of a batch is divided into the preparation time for entering and exiting the tank and the technical preparation time. The preparation time for entering and exiting the tank is related to the number of batches. The technical preparation time is linearly related to the total area of ​​all workpieces in the batch. The calculation logic of the preparation time is clarified. The formula is as follows: (5); (6); :batch Preparation time for in and out of the tank, ; : Time of entering and exiting the tank; : ,batch Processed, otherwise 0, indicating batch Not processed, ; :batch Technical preparation time, ; : The influence of workpiece area on technical preparation time; :Workpiece length and width, ; : , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer, ; (3) Curing time. The batch curing time is determined by the maximum processing time of a single workpiece in the batch, as shown below: (7); ;batch The curing time, ; :Workpiece processing time, ; (4) Processing time: total batch processing time = curing time + technical preparation time. The composition of a single batch processing cycle is clarified. The formula is as follows: (8); :batch Technical preparation time, ; :batch Preparation time for in and out of the tank, .

[0010] Preferably, the workpiece batch logic and process constraints include: (1) Batch processing sequence: Batches are processed in order. The next batch can only start after the previous batch is completed to ensure the continuity of the production process and avoid parallel conflicts. The formula is as follows: (9); (2) Batch activation condition: a batch will be activated only when there are workpieces assigned to it, eliminating the existence of empty batches and optimizing resource and time costs. The formula is as follows: (10); (3) The relaxed solution enhances the constraint. The quality of the relaxed solution of the model is enhanced by effective inequalities. Formula (9)-Formula (10) provide high-quality lower bounds to help improve the solution efficiency and optimization accuracy (mostly used for algorithm optimization in mathematical modeling). The workpieces need to be arranged in descending order of processing time. The formula is as follows: (11); (12); (13); :The first in the autoclave The width of the layer; :The first in the autoclave the length of the layer; :The first in the autoclave The number of resources in the layer; :Workpiece length and width, ; : , workpiece Arranged into batches of The layer is processed, otherwise it is 0, indicating the workpiece Not assigned to a batch of Layer processing; Preferably, the spatial layout constraints include bearing range constraints, non-overlap constraints, and relative position constraints.

[0011] Preferably, the load range constraint means that the workpiece placement must not exceed the physical boundaries of the equipment load platform to ensure spatial adaptability. The formula is as follows: (14); (15); :Workpiece In the lower left corner of the batch coordinate, ; :Workpiece In the lower left corner of the batch coordinate, ; : , indicating the workpiece The length is parallel to the length of the machine; otherwise it is 0, indicating that the workpiece The length of the bracket is not parallel to the length of the machine.

[0012] Preferably, there is no overlap constraint, and any two workpieces must not overlap in the horizontal or vertical direction to avoid spatial conflicts and ensure the independence of the workpieces during processing. The formula is as follows: (16); (17); :Workpiece In the lower left corner of the batch coordinate, ; :Workpiece In the lower left corner of the batch coordinate, ; , indicating the workpiece Workpieces in the same batch On the left side; otherwise it is 0, indicating a workpiece Workpieces not in the same batch On the left, ; : , indicating the workpiece Workpieces in the same batch Otherwise it is 0, indicating a workpiece Workpieces not in the same batch Below, .

[0013] Preferably, relative position constraints clarify the relative position relationship between any two workpieces in the same batch and the same layer, and provide specific coordinates or orientation rules (such as left-right, front-back order) for spatial layout. The formula is as follows: (18); , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer.

[0014] Preferably, the solution process of the improved genetic taboo algorithm based on batch processing time is as follows: (1) Determine the encoding and decoding strategies: Encoding is performed based on the artifact sequence. The length of each chromosome is the artifact sequence. Each gene position on the chromosome represents an artifact. Different artifact arrangements represent different scheduling schemes. A greedy strategy is used for decoding to form an initial solution. (2) Determine the termination condition and fitness function: The termination condition is to determine whether the current number of iterations has reached the maximum number of iterations; the fitness function is the total completion time function of the workpiece, and its calculation formula is: ; (3) Initialize the population and perform fitness evaluation; (4) Perform roulette wheel selection, sequential crossover, and reverse mutation operations on the parent chromosome to calculate the fitness of the offspring chromosome; (5) Using the genetic algorithm solution as the initial solution of the tabu search algorithm; (6) Construct the taboo table, taboo length and neighborhood structure of the taboo search algorithm; (7) Perform tabu search operation and output the optimal solution.

[0015] Preferably, the neighborhood structure of the tabu search algorithm is: The purpose of neighborhood structure 1 is to reduce the curing time of the batch, and the steps are as follows: Step 1: Identify all workpieces in the batch, select the two batches with the longest curing time, and perform the following operations: Step 2: Arrange all workpieces in the two batches in descending order of processing time and insert them to the front, and then re-divide them into batches.

[0016] Step 3: Calculate the fitness value and determine whether to accept the new solution.

[0017] The purpose of neighborhood structure 2 is to reduce preparation time. The steps are as follows: Step 1: Identify all workpieces in a batch and the space utilization of the batch (total workpiece area / total autoclave area*100%). If the number of batches exceeds 3, select the three batches with the lowest space utilization and perform the following operations on them: Step 2: Arrange all workpieces in the two batches in descending order by area and insert them to the front, and then re-divide them into batches.

[0018] Step 3: Calculate the fitness value and determine whether to accept the new solution.

[0019] The present invention has the following advantages: This paper addresses the current scheduling status of the hot press forming process for aviation composite materials, models the problem as a two-dimensional batch scheduling problem that simultaneously considers resource constraints, dual preparation time, and the multi-layer tank-entry characteristics of workpieces. A mixed integer programming model is constructed with minimizing the maximum completion time as the objective function. In response to the complexity of the model, an improved genetic-tabu hybrid optimization algorithm based on batch processing time is designed to solve it, effectively reducing the overall production time of the process and effectively improving production rate and resource utilization. The method proposed in this invention has good scalability and is applicable to composite material manufacturing processes with similar scheduling characteristics. It can provide effective theoretical support and implementation path for the scheduling optimization of related processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic diagram of a method flow chart provided in an embodiment of the present invention; Figure 2 An algorithm flow chart of a specific example provided in an embodiment of the present invention; Figure 3 A flowchart of a neighborhood construction strategy provided by an embodiment of the present invention; Figure 4 This is a flowchart of the second neighborhood construction strategy provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0021] The following describes the implementation of the present invention using specific embodiments. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. Obviously, the embodiments described are only a portion of the present invention, not all of it. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0022] like Figure 1 As shown, this embodiment provides a method for scheduling hot pressing batches of aviation composite materials considering resource constraints and dual preparation time, including the following steps: Step 1: Obtain relevant data of the hot press forming process, including workpiece data and autoclave data, and design the batch scheduling objective function for the hot press forming process of aviation composite materials with the goal of minimizing the maximum completion time; Establish the hot pressing batch scheduling objective function: (1); (2); in, express The maximum completion time of a batch of workpieces, : batch collection; : batch index; :batch processing time, ; : The minimum batch size obtained based on the workpiece area and resource quantity; Formula (1) and Formula (2) define the objective function as minimizing the maximum completion time, and the maximum completion time is equal to the sum of the processing time of each batch.

[0023] Step 2: Establish a two-dimensional multi-layer loading hot pressing process batch scheduling model that considers resource constraints and dual preparation time, including: workpiece processing uniqueness constraints, workpiece resource carrying capacity limitations and dual preparation time, workpiece batch logic and process constraints, and spatial layout constraints.

[0024] The uniqueness constraint of workpiece processing ensures that all workpieces to be processed can be processed only once. The formula is as follows: (3); : Autoclave level collection; : Autoclave level index; : , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer; ; : artifact collection; : Artifact index.

[0025] Artifact resource capacity limits and dual preparation times, including: (1) Resource carrying capacity limit: The amount of resources required for each workpiece must not exceed the total amount of resources in the equipment carrying layer where it is located to avoid equipment overload and ensure processing feasibility. The formula is as follows: (4); :Workpiece the amount of resources required; : , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer; :The first in the autoclave The number of resources the layer contains; (2) Double preparation time. The double preparation time of a batch is divided into the preparation time for entering and exiting the tank and the technical preparation time. The preparation time for entering and exiting the tank is related to the number of batches. The technical preparation time is linearly related to the total area of ​​all workpieces in the batch. The calculation logic of the preparation time is clarified. The formula is as follows: (5); (6); :batch Preparation time for in and out of the tank, ; : Time of entering and exiting the tank; : ,batch Processed, otherwise 0, indicating batch Not processed, ; :batch Technical preparation time, ; : The influence of workpiece area on technical preparation time; :Workpiece length and width, ; : , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer, , ; (3) Curing time. The batch curing time is determined by the maximum processing time of a single workpiece in the batch, as shown below: (7); ;batch The curing time, ; :Workpiece processing time, ; (4) Processing time: total batch processing time = curing time + technical preparation time. The composition of a single batch processing cycle is clarified. The formula is as follows: (8); :batch Technical preparation time, ; :batch Preparation time for in and out of the tank, .

[0026] Workpiece batch logic and process constraints, including: (1) Batch processing sequence: Batches are processed in order. The next batch can only start after the previous batch is completed to ensure the continuity of the production process and avoid parallel conflicts. The formula is as follows: (9); (2) Batch activation condition: a batch will be activated only when there are workpieces assigned to it, eliminating the existence of empty batches and optimizing resource and time costs. The formula is as follows: (10); (3) The relaxed solution enhances the constraint. The quality of the relaxed solution of the model is enhanced by effective inequalities. Formula (9)-Formula (10) provide high-quality lower bounds to help improve the solution efficiency and optimization accuracy (mostly used for algorithm optimization in mathematical modeling). The workpieces need to be arranged in descending order of processing time. The formula is as follows: (11); (12); (13); :The first in the autoclave The width of the layer; :The first in the autoclave the length of the layer; :The first in the autoclave The number of resources in the layer; :Workpiece length and width, ; : , workpiece Arranged into batches of The layer is processed, otherwise it is 0, indicating the workpiece Not assigned to a batch of Layer processing; Spatial layout constraints, including carrying range constraints, non-overlap constraints, and relative position constraints.

[0027] The load range constraint means that the workpiece cannot be placed beyond the physical boundaries of the equipment's load platform to ensure spatial adaptability. The formula is as follows: (14); (15); :Workpiece In the lower left corner of the batch coordinate, ; :Workpiece In the lower left corner of the batch coordinate, ; : , indicating the workpiece The length is parallel to the length of the machine; otherwise it is 0, indicating that the workpiece The length of the bracket is not parallel to the length of the machine.

[0028] There is no overlap constraint. Any two workpieces must not overlap in the horizontal or vertical direction to avoid spatial conflicts and ensure the independence of the workpieces during processing. The formula is as follows: (16); (17); :Workpiece In the lower left corner of the batch coordinate, ; :Workpiece In the lower left corner of the batch coordinate, ; , indicating the workpiece Workpieces in the same batch On the left side; otherwise it is 0, indicating a workpiece Workpieces not in the same batch On the left, ; : , indicating the workpiece Workpieces in the same batch Otherwise it is 0, indicating a workpiece Workpieces not in the same batch Below, .

[0029] Relative position constraints clarify the relative position relationship between any two workpieces in the same batch and layer, and provide specific coordinates or orientation rules (such as left-right, front-back order) for spatial layout. The formula is as follows: (18); , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer.

[0030] Step 3: Taking the objective function as the optimization target and the two-dimensional multi-layer loading hot pressing process batch scheduling model as the optimization model, an improved genetic taboo algorithm based on batch processing time is used to solve the problem and obtain the hot pressing process batch scheduling solution.

[0031] like Figure 2 As shown in Figure 2, the solution process of the improved genetic taboo algorithm based on batch processing time is as follows: (1) Determine the encoding and decoding strategies: Encoding is performed based on the artifact sequence. The length of each chromosome is the artifact sequence. Each gene position on the chromosome represents an artifact. Different artifact arrangements represent different scheduling schemes. A greedy strategy is used for decoding to form an initial solution. (2) Determine the termination condition and fitness function: The termination condition is to determine whether the current number of iterations has reached the maximum number of iterations; the fitness function is the total completion time function of the workpiece, and its calculation formula is: ; (3) Initialize the population and perform fitness evaluation; (4) Perform roulette wheel selection, sequential crossover, and reverse mutation operations on the parent chromosome to calculate the fitness of the offspring chromosome; (5) Using the genetic algorithm solution as the initial solution of the tabu search algorithm; (6) Construct the taboo table, taboo length and neighborhood structure of the taboo search algorithm; (7) Perform tabu search operation and output the optimal solution.

[0032] Preferably, the neighborhood structure of the tabu search algorithm is: The purpose of neighborhood structure one is to reduce the curing time of the batch, e.g. Figure 3 As shown, the steps are as follows: Step 1: Identify all workpieces in the batch, select the two batches with the longest curing time, and perform the following operations: Step 2: Arrange all workpieces in the two batches in descending order of processing time and insert them to the front, and then re-divide them into batches.

[0033] Step 3: Calculate the fitness value and determine whether to accept the new solution.

[0034] The purpose of the neighborhood structure II is to reduce the preparation time, e.g. Figure 4 As shown, the steps are as follows: Step 1: Identify all workpieces in a batch and the space utilization of the batch (total workpiece area / total autoclave area*100%). If the number of batches exceeds 3, select the three batches with the lowest space utilization and perform the following operations on them: Step 2: Arrange all workpieces in the two batches in descending order by area and insert them to the front, and then re-divide them into batches.

[0035] Step 3: Calculate the fitness value and determine whether to accept the new solution.

[0036] This example constructs a scheduling example for a hot press forming process, solving it using the improved genetic tabu algorithm based on batch processing time. The naming convention for this scheduling example is M[number of workpieces][workpiece type]. Workpieces are divided into two categories, with the required resource quantities falling between [1, 15] and [1, 20], respectively. The dimensions of each layer of the autoclave are shown in Table 1.

[0037] Table 1 Dimensions of each layer of autoclave

[0038] The above processing information is input into the algorithm of the present invention, and the crossover probability is set. =0.9 and mutation probability =0.1, taboo length =10, population size =100, maximum number of iterations =100. To prove the effectiveness of the proposed algorithm, it is compared with the traditional genetic algorithm ( ) and the tabu search algorithm ( ) for comparison, with the same parameter settings as above.

[0039] First, we use Gurobi to solve a small-scale example of the proposed model. The results are as follows: As shown. Secondly, use the above three algorithms to repeat the solution 10 times and take the average. The algorithm solution results are compared. As shown. Among them, the calculation formula of the reduction ratio is As you can see, except for the 10-scale calculation, Comparison and The solution quality is improved, and the experimental results prove the effectiveness and practicability of the proposed algorithm, which can effectively reduce the processing time of the hot pressing forming process of aviation composites and improve its production efficiency.

[0040] Table 2 Gurobi solution results

[0041] Table 3 Comparison of algorithm solution results

[0042] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made thereto. Therefore, such modifications and improvements, without departing from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A hot pressing batch scheduling method for aviation composites considering resource constraints and dual preparation time, characterized by: The following steps are involved: Step 1: Obtain relevant data of the hot press forming process, including workpiece data and autoclave data, and design the batch scheduling objective function for the hot press forming process of aviation composite materials with the goal of minimizing the maximum completion time; Step 2: Considering resource constraints and double preparation time, a batch scheduling model for the two-dimensional multi-layer loading hot pressing process is established; Step 3: Taking the objective function as the optimization target and the two-dimensional multi-layer loading hot pressing process batch scheduling model as the optimization model, an improved genetic taboo algorithm based on batch processing time is used to solve the problem and obtain the hot pressing process batch scheduling solution.

2. The aviation composite hot pressing batch scheduling method considering resource constraints and dual preparation time according to claim 1 is characterized by: The step 1 establishes the hot pressing batch scheduling objective function: （1）； （2）； in, express The maximum completion time of a batch of workpieces, : batch collection; : batch index; :batch processing time, ; : The minimum batch size obtained based on the workpiece area and resource quantity; Formula (1) and Formula (2) define the objective function as minimizing the maximum completion time, and the maximum completion time is equal to the sum of the processing time of each batch.

3. The aviation composite hot pressing batch scheduling method considering resource constraints and dual preparation time according to claim 2 is characterized by: The second step constructs a two-dimensional multi-layer loading hot pressing process batch scheduling model that considers resource constraints and dual preparation time, including: uniqueness constraints of workpiece processing, workpiece resource carrying restrictions and dual preparation time, workpiece batch logic and process constraints, and spatial layout constraints.

4. The method for scheduling hot pressing batches of aviation composite materials considering resource constraints and dual preparation time according to claim 3 is characterized by: The uniqueness constraint of workpiece processing ensures that all workpieces to be processed can be processed only once. The formula is as follows: (3)； : Autoclave level collection; : Autoclave level index; : , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer, , : batch collection; : batch index; : a collection of artifacts, : Artifact index.

5. The method for scheduling hot pressing batches of aviation composite materials considering resource constraints and dual preparation time according to claim 3 is characterized in that: Artifact resource capacity limits and dual preparation times, including: (1) Resource carrying capacity limit: The amount of resources required for each workpiece must not exceed the total amount of resources in the equipment carrying layer where it is located to avoid equipment overload and ensure processing feasibility. The formula is as follows: (4)； :Workpiece The amount of resources required, ; : , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer; :The first in the autoclave The number of resources the layer contains; : The minimum batch size obtained based on the workpiece area and resource quantity; (2) Double preparation time. The double preparation time of a batch is divided into the preparation time for entering and exiting the tank and the technical preparation time. The preparation time for entering and exiting the tank is related to the number of batches. The technical preparation time is linearly related to the total area of ​​all workpieces in the batch. The calculation logic of the preparation time is clarified. The formula is as follows: (5)； (6)； :batch Preparation time for in and out of the tank, ; : Time of entering and exiting the tank; : ,batch Processed, otherwise 0, indicating batch Not processed, ; :batch Technical preparation time, ; : The influence of workpiece area on technical preparation time; :Workpiece length and width, ; : , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer, , ; (3) Curing time. The batch curing time is determined by the maximum processing time of a single workpiece in the batch, as shown below: (7)； ;batch The curing time, ; :Workpiece processing time, ; (4) Processing time: total batch processing time = curing time + technical preparation time. The composition of a single batch processing cycle is clarified. The formula is as follows: (8)； :batch Technical preparation time, ; :batch Preparation time for in and out of the tank, .

6. The aviation composite hot pressing batch scheduling method considering resource constraints and dual preparation time according to claim 5 is characterized by: Workpiece batch logic and process constraints, including: (1) Batch processing sequence: Batches are processed in order. The next batch can only start after the previous batch is completed to ensure the continuity of the production process and avoid parallel conflicts. The formula is as follows: （9）； (2) Batch activation condition: a batch will be activated only when there are workpieces assigned to it, eliminating the existence of empty batches and optimizing resource and time costs. The formula is as follows: （10）； (3) The relaxed solution enhances the constraint. The quality of the relaxed solution of the model is enhanced by effective inequalities. Formula (9)-Formula (10) provide high-quality lower bounds to help improve the solution efficiency and optimization accuracy. The workpieces need to be arranged in descending order of processing time. The formula is as follows: （11）； （12）； （13）； : Maximum completion time; :The first in the autoclave The width of the layer; :The first in the autoclave the length of the layer; :The first in the autoclave The number of resources in the layer; :Workpiece length and width, ; : , workpiece Arranged into batches of The layer is processed, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer for processing.

7. The method for scheduling hot pressing batches of aviation composite materials considering resource constraints and dual preparation time according to claim 3 is characterized by: Spatial layout constraints, including carrying range constraints, non-overlap constraints, and relative position constraints.

8. The method for scheduling hot pressing batches of aviation composite materials considering resource constraints and dual preparation time according to claim 7 is characterized in that: The load range constraint means that the workpiece cannot be placed beyond the physical boundaries of the equipment's load platform to ensure spatial adaptability. The formula is as follows: （14）； （15）； :Workpiece In the lower left corner of the batch coordinate, ; :Workpiece In the lower left corner of the batch coordinate, ; : , indicating the workpiece The length is parallel to the length of the machine; otherwise it is 0, indicating that the workpiece The length of the bracket is not parallel to the length of the machine.

9. The method for scheduling hot pressing batches of aviation composite materials considering resource constraints and dual preparation time according to claim 7, characterized in that: There is no overlap constraint. Any two workpieces must not overlap in the horizontal or vertical direction to avoid spatial conflicts and ensure the independence of the workpieces during processing. The formula is as follows: （16）； （17）； :Workpiece In the lower left corner of the batch coordinate, ; :Workpiece In the lower left corner of the batch coordinate, ; , indicating the workpiece Workpieces in the same batch On the left side; otherwise it is 0, indicating a workpiece Workpieces not in the same batch On the left, ; : , indicating the workpiece Workpieces in the same batch Otherwise it is 0, indicating a workpiece Workpieces not in the same batch Below, .

10. The aviation composite hot pressing batch scheduling method considering resource constraints and dual preparation time according to claim 7, characterized in that: Relative position constraints clarify the relative position relationship between any two workpieces in the same batch and the same layer, and provide specific coordinates or orientation rules for spatial layout. The formula is as follows: , indicating the workpiece Assigned to batch of Layer, otherwise it is 0, indicating the workpiece Not assigned to a batch of layer.

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