Aviation composite material hot-press forming single-machine batch scheduling method considering two-dimensional space characteristics

Abstract

The invention relates to the technical field of aviation composite material hot press molding scheduling, solves the technical problem that an existing method does not fully consider spatial constraint and time window limitation, and particularly relates to an aviation composite material hot press molding single-machine batch scheduling method considering two-dimensional spatial characteristics. Two-dimensional space characteristics of an autoclave and to-be-processed operation, release time of the operation and time window constraints are comprehensively considered, and a single-machine batch scheduling model with the purpose of minimizing completion time is constructed. And on the basis, solving the scheduling optimization model by adopting an extended whale optimization algorithm to obtain an optimal scheduling scheme. According to the scheme, the processing sequence and the processing time of batches and the placing positions of operation in the batches can be effectively arranged, and the utilization rate of the autoclave is improved to the maximum extent on the premise of meeting space and time constraints, so that the production efficiency is remarkably improved.

Description

Technical Field

[0001] The invention relates to the technical field of aviation composite material hot pressing molding scheduling, and in particular to a single-machine batch scheduling method for aviation composite material hot pressing molding considering two-dimensional spatial characteristics. Background Art

[0002] Composite materials are widely used in aircraft body structures, engine components, thermal protection systems and other parts due to their high strength, high modulus, low density and good fatigue resistance, and play a key role in improving performance and reducing energy consumption. The production of composite materials usually includes multiple complex processes, such as cutting, prepreg tape laying, hot pressing, demolding and polishing. At present, the use of composite materials in advanced military aircraft (such as F-22, F-35, B-2) has exceeded 25%, and the use of composite materials in new civil aircraft A380 and B787 has reached 25% and 50% respectively. The CR929 long-range twin-aisle wide-body aircraft plans to use composite materials on a large area of ​​​​the wing and fuselage structure, and the proportion of use is expected to exceed 50%.

[0003] As the demand for composite materials grows, the hot press molding process has become a production bottleneck due to high equipment costs and limited production capacity, seriously affecting the company's delivery capabilities and causing an imbalance between production and demand. Traditional batch scheduling methods usually express machine capacity through one-dimensional knapsack constraints. However, the autoclave and its jobs to be processed have inherent two-dimensional spatial characteristics that are not fully captured by traditional scheduling models and may lead to infeasible scheduling schemes. In addition, due to the unique properties of the materials involved, each job must be loaded into the autoclave and begin curing within a specified time window, otherwise the material will fail, resulting in a serious waste of resources. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a single-machine batch scheduling method for hot pressing molding of aviation composite materials taking into account two-dimensional spatial characteristics, which solves the technical problem that the prior methods do not fully consider spatial constraints and time window limitations. The present invention can effectively solve the problem that the prior methods do not fully consider spatial constraints and time window limitations, thereby improving the feasibility of scheduling and production efficiency.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions: a single-machine batch scheduling method for hot pressing molding of aviation composite materials considering two-dimensional spatial characteristics, the method comprising the following processes: Obtain basic data on the hot press molding process of aviation composite materials, including the size of the autoclave, the size of each job, the processing time of the job, the release time of the job and the time window; Based on basic data and assumptions, a single-machine batch scheduling model for hot pressing of aviation composite materials is constructed to minimize the completion time. The single-machine batch scheduling model includes machine environment, constraints and optimization objectives. The single-machine batch scheduling model is solved to obtain the optimal scheduling solution, which is then applied to the hot pressing molding process of aviation composite materials to improve scheduling efficiency.

[0006] Furthermore, the size of the autoclave and each job is rectangular, consisting of a width and a height; the release time is the time when the job is completed and released in the previous stage; and the time window is the time period during which each job can be processed.

[0007] Furthermore, the assumptions are: The autoclave used is a single-layer device, which is assumed to be available initially and available for all jobs upon release; the autoclave can only process one batch at a time and once processing starts, it cannot be interrupted; each job can only be processed by one machine; transportation time and adjustment time are ignored.

[0008] Furthermore, the expression of the single machine batch scheduling model is: ; In the formula, 1 indicates that the machine environment is a single machine environment; It represents the maximum finishing time of all tasks, which is used to evaluate the optimization goal; represents a two-dimensional packing constraint; represents parallel batch processing; Indicates the job release time; Indicates the job time window restrictions.

[0009] Furthermore, the optimization objective of the single-machine batch scheduling model is: ; In the formula, is the objective function of the single-machine batch scheduling model; For batch The end processing time; B is a batch set, with Represents a single batch for an index.

[0010] Furthermore, the constraints of the single-machine batch scheduling model specifically include: Processing time per batch Cannot be less than the processing time of any job in the batch ,Right now: ; If the batch has been assigned activities, the batch must be formed, i.e.: ; batch The start processing time must be greater than or equal to the arrival time of all jobs in the batch, that is: ; batch The start time of processing shall not be earlier than the previous batch The completion time is: ; batch The start processing time of the batch shall not exceed the latest start processing time of all jobs in the batch, that is: ; Each job can only be processed within one batch, that is: ; The job cannot exceed the boundaries of the machine, including the rightmost coordinate of the job cannot exceed the width of the machine, and the highest coordinate cannot exceed the height of the machine, that is: ; Adjacent operations in the same batch Axis or There is no overlap on the axis, that is: ; The spatial relationship between any pair of adjacent operations in the same batch is Axis or Axis alignment, that is: ; The decision variables are within the feasible range, that is: ; In the above formula, the batch set B By Index Represents a single batch; a collection of jobs By Index or Represents a single job; Indicates batch processing time; is a 0-1 decision variable. If the job Assigned to batch ,So , otherwise 0; Indicates the job processing time; is a 0-1 decision variable. If the batch In batches, then , otherwise 0; For batch End processing time; operation Time window usage It indicates that, For homework The release time, For homework The latest start time of processing; and Respectively represent the work Coordinates of the lower left corner and coordinates ; and Respectively represent the work The height and width of and Respectively represent the height and width of the machine; is a 0-1 decision variable. If the width Parallel to ,So , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job On the left side, then , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job Below, then , otherwise 0; and Respectively represent the work Coordinates of the lower left corner and coordinates ; is a 0-1 decision variable. If the job Assigned to batch ,So , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job On the left side, then , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job Below, then , otherwise 0.

[0011] Furthermore, solving the single-machine batch scheduling model to obtain the optimal scheduling solution includes the following steps: S31, initializing parameters, generating an initial population based on the best adaptation heuristic method; S32, calculating the first fitness value of each individual, and recording the best individual; S33, update parameter a, determine coefficient vectors A and C, coefficient vectors A and C are: ; ; In the above formula, a decreases linearly from 2 to 0 during the iteration process; r1 and r2 are random vectors in the range [0,1]; S34. Generate a random number between 0 and 1 ; S35. Judgment Is it less than 0.5? If so, determine whether |A| is less than 1; otherwise, perform the spiral position update. The expression for the spiral position update is: ; In the above formula, is the updated individual position; is the optimal individual position; is the current individual position; absolute value Represents the distance between individuals; is a constant that determines the shape of the logarithmic spiral, is a random number in the range of [-1, 1]; Represents the natural logarithm base e An exponential function with base ; If |A| is less than 1, the shrinking and encircling mechanism based on Lévy flight is executed; otherwise, the prey search based on Lévy flight is executed; S36, calculating the second fitness value of each individual, and sorting the population; S37, performing an annealing search mechanism on the population; S38. Determine whether the iteration stop condition is met. If so, output the optimal scheduling solution; otherwise, return to step S32.

[0012] Furthermore, the shrinking and encircling mechanism based on Lévy flight is: ; In the above formula, The individual position after the shrinkage and encirclement mechanism is executed; is the optimal individual position; is the current individual position, The absolute value represents the distance between individuals; ⊙ represents element multiplication, is a random step size The probability density function of Prey search based on Lévy flight, that is: ; In the above formula, for the individual’s position after performing a prey search; is a randomly selected individual position.

[0013] Furthermore, in step S31, the specific process includes the following steps: S311, according to the following rules to collect the work Sort by: First, by the release time of the job Arrange in ascending order; if the release time is the same, the latest start time of the job will be used Sort in ascending order; S312, initializing a skyline array SA of the machine, which is used to store the current heights of the placed jobs along the width W of the machine; S313: Form a subset according to the sequence sorted in step S311 , where jobs with the same release time form a subset and are removed from the job set Remove a subset ; S314, calculating the height difference HD between the current minimum gap and the height of the machine, the current minimum gap being the minimum gap at which the machine can be placed determined by identifying the minimum value of the skyline array SA; S315, in the subset Among all the jobs, compare their height and width to find the minimum value ; S316, if the subset If the working width is smaller than the height, rotate it 90° and sort it in descending order of width to determine the minimum value. ; S317, if the subset If it is empty, return to step S313; otherwise, determine the minimum gap based on the best adaptation heuristic method, that is: From the subset Select the job that best fits the gap , place it in the gap, update the skyline array SA, and place the job From the subset If no job fits into the smallest gap, fill the gap; S318, Update the skyline array SA, height difference HD and minimum value , if the height difference HD is less than the minimum value , then the current batch is formed, and the subset The jobs in the job collection are inserted back into the job collection in the original order. The beginning of the process and returns to step S312; otherwise, continue to step S317; S319, repeat the above steps S311-S318 until all jobs are grouped into batches; S3110. Based on the batch information obtained in step S319, encoding is performed to obtain an initial feasible solution.

[0014] Further, in step S37, the specific process includes the following steps: S371. Input initial population , initialization parameters, including initial temperature , final temperature , cooling rate and the maximum number of iterations ; S372, from the initial population Select the top 10% of individuals in terms of fitness value to form the subset SP; S373, select an individual from the subset SP, and initialize its optimal solution and its corresponding fitness value; S374, if the current temperature , and the current number of iterations , then randomly perturb the selected individual to generate a new individual; otherwise, select the next individual in the subset SP; S375. If the fitness value of the new individual is better than that of the current individual, the new individual is accepted; otherwise, the fitness difference is calculated. , and The probability of accepting new individuals, the fitness difference The fitness value of the new individual minus the fitness value of the current individual; S376, update temperature and number of iterations: , , and return to step S374 to continue execution; S377. When all individuals in the subset SP have been selected and processed, the final updated initial population is returned. .

[0015] By means of the above technical solution, the present invention provides a single-machine batch scheduling method for hot pressing molding of aviation composite materials taking into account two-dimensional spatial characteristics, which has at least the following beneficial effects: For the bottleneck process of hot pressing, the method proposed in this invention comprehensively considers the two-dimensional spatial characteristics of the autoclave and the jobs to be processed, the release time of the jobs and the time window constraints, and constructs a single-machine batch scheduling model with the goal of minimizing the completion time. By solving the single-machine batch scheduling optimization model, the processing order, processing time and placement of the jobs within the batch can be effectively arranged to ensure that the utilization rate of the autoclave is maximized while meeting the space and time constraints, thereby improving production efficiency.

[0016] The method of the present invention adopts an extended whale optimization algorithm, which combines an initial population generation method based on the best fit heuristic to effectively generate an initial feasible solution. At the same time, a contraction and encirclement mechanism based on Lévy flight and a prey search mechanism, as well as an annealing search mechanism, are introduced to enhance the algorithm's global exploration and local development capabilities. The extended whale optimization algorithm effectively overcomes the local optimal solution problem that traditional optimization methods may face, can quickly converge to the global optimal solution, and apply the optimal scheduling solution to the hot pressing process, thereby improving scheduling efficiency, shortening the production cycle, and further improving the overall performance and flexibility of the production system.

[0017] The present invention combines the actual hot pressing forming scenario and the two-dimensional spatial characteristics of the autoclave to capture the spatial constraints in the hot pressing forming process, comprehensively considers the release time and time window of the job, and ensures that each job is processed within the specified time range to meet the strict time constraints, thereby effectively solving the problem that the existing method does not fully consider the spatial constraints and time window limitations, and improves the feasibility of scheduling and production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings: Figure 1 It is a flow chart of a single-machine batch scheduling method for hot pressing molding of aviation composite materials in the present invention; Figure 2 It is a schematic diagram of composite material autoclave equipment and operation arrangement rules in the present invention; Figure 3 is an example diagram of a single machine batch scheduling model in the present invention; Figure 4 A flowchart of the extended whale optimization algorithm implemented in the present invention; Figure 5 This is an example diagram of the encoding scheme in the present invention. DETAILED DESCRIPTION

[0019] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods, so that the implementation process of how the present application uses technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly.

[0020] In this example, by analyzing the hot press molding process as a bottleneck in the manufacturing process of aviation composite materials and identifying the core characteristics of the hot press molding scheduling problem, it can be seen that the traditional batch scheduling method usually expresses the machine capacity through a one-dimensional knapsack constraint. However, the autoclave and its jobs to be processed have inherent two-dimensional spatial characteristics, which are not fully captured by traditional scheduling models and may lead to unfeasible scheduling schemes. In addition, due to the unique properties of the materials involved, each job must be loaded into the autoclave and begin curing within a specified time window, otherwise the material will fail, resulting in a serious waste of resources.

[0021] Regarding the technical defects of the above traditional methods, please refer to Figure 1-Figure 5 , this embodiment proposes a single-machine batch scheduling method for hot pressing molding of aviation composite materials taking into account two-dimensional spatial characteristics. This method targets the bottleneck process of hot pressing molding, comprehensively considers the two-dimensional spatial characteristics of the autoclave and the job to be processed, the release time of the job and the time window constraints, and constructs a single-machine batch scheduling model with the goal of minimizing the completion time. On this basis, the extended whale optimization algorithm is used to solve the scheduling optimization model to obtain the optimal scheduling solution. This solution can effectively arrange the processing sequence, processing time and placement of jobs within the batch, ensuring that the utilization rate of the autoclave is maximized while meeting the space and time constraints, thereby significantly improving production efficiency. The method comprises the following steps: S1. Obtain basic data of aviation composite materials in the hot pressing molding process, including the size of the autoclave and the size of each job, the processing time of the job, the release time of the job and the time window; wherein the size of the autoclave and each job are rectangular, consisting of width and height, the release time is the time when the job is completed and released in the previous stage (layup process), and the time window is the time period during which each job can be processed.

[0022] S2. Based on basic data and assumptions, a single-machine batch scheduling model for aviation composite hot pressing molding with the goal of minimizing completion time is constructed. Specifically, the single-machine batch scheduling model includes machine environment, constraints and optimization objectives.

[0023] The establishment of a single-machine batch scheduling model needs to be based on the following assumptions: the autoclave used is a single-layer device, which is assumed to be available initially and available for all jobs when released; the machine can only process one batch at a time, and once processing begins, it cannot be interrupted; each job can only be processed by one machine; transportation time and adjustment time are ignored.

[0024] In this embodiment, as a preferred method, the single batch scheduling model constructed in step S2 is the SBPM-RDTW (Single Batch Processing Machine Scheduling with Release Dates and TimeWindows) model. In order to clearly explain the SBPM-RDTW model, Figure 2 The schematic diagram of composite autoclave equipment and operation layout rules is shown. Figure 2 As shown in (a) of the figure, the composite autoclave equipment contains an internal platform (highlighted in blue) that serves as a designated area for the workpieces. In the SBPM-RDTW model, both the autoclave and the workpieces are represented as rectangles. Specifically, the height of the machine is along the Axis definition, width along Axis definition, the lower left corner is set as the origin of the coordinate system. This model supports processing multiple different rectangular jobs at the same time. Figure 2 (b) shows the layout rules, which stipulate that jobs must not overlap, must be within the machine boundaries, and must be parallel to the machine boundaries. Each job can be rotated 90° to achieve a suitable placement.

[0025] The SBPM-RDTW model aims to determine which batch each job belongs to and determine its placement on the machine while satisfying certain constraints to minimize the completion time. To illustrate the model, an example is provided below. Suppose there is a job set Need to be hot pressed, each operation By its size, processing time, release time and time window To describe, such as Figure 3 According to the constraints of the two-dimensional packing problem, the jobs are divided into multiple batches, such as Figure 3 The processing time of each batch is determined by the longest processing time of the jobs in the batch. The earliest start time of each batch is determined by the maximum release time of the jobs in the batch. For example, Figure 3 In (c), the earliest start time of batch 1 is The latest start time of each batch is determined by the minimum upper limit of the time window of the jobs in the batch. Figure 3 In (c), the latest start time of batch 1 is .exist Figure 3 In (c), the completion time of batch 1 is recorded as , the completion time of batch 2 is recorded as , the completion time of batch 3 is recorded as The completion time of all jobs is the maximum completion time of all batches, that is, .

[0026] Specifically, the expression of the SBPM-RDTW model is: It can be expressed by a three-field representation (machine environment | constraint condition | optimization goal), that is: ; In the formula, 1 indicates that the machine environment is a single machine environment; It represents the maximum finishing time of all tasks, which is used to evaluate the optimization goal; , , , All are constraints; Among the above constraints, represents a two-dimensional packing constraint; represents parallel batch processing; Indicates the job release time; Indicates the job time window restrictions.

[0027] More specifically, the optimization goal of the single-machine batch scheduling model is: ; In the formula, is the objective function of the single-machine batch scheduling model; For batch The end processing time; B is a batch set, with The index represents a single batch; the optimization goal is to minimize the maximum end processing time of all batches.

[0028] More specifically, the constraints of the single-machine batch scheduling model include: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) In the above constraint formula, the batch set B By Index Represents a single batch; a collection of jobs By Index or Represents a single job; Constraints (1) Ensure the processing time of each batch Cannot be less than the processing time of any job in the batch ;in, Indicates batch The processing time, is a 0-1 decision variable. If the job Assigned to batch ,So , otherwise 0; Indicates the job processing time; Constraint (2) ensures that if a job is assigned to a batch, then the batch must be formed; where is a 0-1 decision variable. If the batch In batches, then , otherwise 0; Constraints (3) to (5) ensure that the processing time of each batch on the machine is reasonable; Time window usage It indicates that, For homework release time; For homework The latest start time of processing; constraint (3) specifies the batch The start processing time must be greater than or equal to the arrival time of all jobs in the batch; constraint (4) specifies the batch The start time of processing shall not be earlier than that of the previous batch Constraint (5) indicates the completion time of the batch The start processing time of the batch shall not exceed the latest start processing time of all jobs in the batch; Constraint (6) ensures that each job can only be processed within one batch; Constraints (7) to (8) require that the job cannot exceed the boundaries of the machine. Specifically, the rightmost coordinate of the job cannot exceed the width of the machine, and the highest coordinate cannot exceed the height of the machine. and Respectively represent the work Coordinates of the lower left corner and coordinates ; and Respectively represent the work The height and width of and Respectively represent the height and width of the machine; is a 0-1 decision variable. If the width Parallel to ,So , otherwise 0; Constraints (9) to (10) ensure that adjacent operations in the same batch Axis or No overlap on the axis; is a 0-1 decision variable. If the job The location is located in the job On the left side, then , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job Below, then , otherwise 0; and Respectively represent the work Coordinates of the lower left corner and coordinates ; is a 0-1 decision variable. If the job Assigned to batch ,So , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job On the left side, then , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job Below, then , otherwise 0; Constraint (11) ensures that the spatial relationship between any pair of adjacent jobs in the same batch is Axis or Axis alignment; Constraints (12) to (17) ensure that the decision variables are within the feasible range.

[0029] This embodiment aims at the bottleneck process of hot pressing molding. The proposed method comprehensively considers the two-dimensional spatial characteristics of the autoclave and the jobs to be processed, the release time of the jobs and the time window constraints, and constructs a single-machine batch scheduling model with the goal of minimizing the completion time. By solving the single-machine batch scheduling optimization model, the processing order, processing time and placement of the jobs in the batch can be effectively arranged to ensure that the utilization rate of the autoclave is maximized while meeting the space and time constraints, thereby improving production efficiency.

[0030] S3, using the extended whale optimization algorithm to solve the single-machine batch scheduling model to obtain the optimal scheduling solution, and applying the optimal scheduling solution to the aviation composite material hot pressing molding process to improve the scheduling efficiency. The SBPM-RDTW model proposed in the present invention is a typical NP-hard problem, so as a preferred implementation of step S3, the extended whale optimization algorithm is used to solve the NP-hard problem. Figure 4 As shown in the figure, the scheduling solution is solved by extending the whale optimization algorithm, including the following steps: S31, initialization parameters, using the best adaptation heuristic method to generate the initial population; this embodiment uses an effective encoding method, such as Figure 5 Each solution is given by values, where Represents the number of jobs. Each value is encoded as a real number in the range By sorting and decoding the values ​​in the solution, the order in which the jobs are processed on the machine can be determined, such as Figure 4 As shown. Based on this order, the decoded job sequence will be organized into batches according to specific constraints, and the completion time of the solution will be finally determined. More specifically, the method based on the best adaptation heuristic is as follows: S311, according to the following rules to collect the work Sort by: First, by the release time of the job Arrange in ascending order; if the release time is the same, the latest start time of the job will be used Sort in ascending order; S312, initializing a skyline array SA of the machine, which is used to store the current heights of the placed jobs along the width W of the machine; S313: Form a subset according to the sequence sorted in step S311 , where jobs with the same release time form a subset and are removed from the job set Remove a subset ; S314, calculating the height difference HD between the current minimum gap and the height of the machine, the current minimum gap being the minimum gap at which the machine can be placed determined by identifying the minimum value of the skyline array SA; S315, in the subset Among all the jobs, compare their height and width to find the minimum value ; S316, if the subset If the working width is smaller than the height, rotate it 90° and sort it in descending order of width to determine the minimum value. ; S317, if the subset If it is empty, return to step S313; otherwise, determine the minimum gap based on the best adaptation heuristic method, that is: From the subset Select the job that best fits the gap , place it in the gap, update the skyline array SA, and place the job From the subset If no job fits into the smallest gap, fill the gap; S318, Update the skyline array SA, height difference HD and minimum value , if the height difference HD is less than the minimum value , then the current batch is formed, and the subset The jobs in the job collection are inserted back into the job collection in the original order. The beginning of the process and returns to step S312; otherwise, continue to step S317; S319, repeat the above steps S311-S318 until all jobs are grouped into batches; S3110. Based on the batch information obtained in step S319, encoding is performed to obtain an initial feasible solution.

[0031] S32, calculate the first fitness value of each individual, and record the best individual. In this embodiment, the first fitness value here is the objective function value corresponding to the optimization target, and the calculation formula is: ; S33, update parameter a, determine coefficient vectors A and C, coefficient vectors A and C are: (18) (19) In the above formula, a decreases linearly from 2 to 0 during the iteration process; r1 and r2 are random vectors in the range [0,1]; S34. Generate a random number between 0 and 1 ; S35. Judgment Is it less than 0.5? If so, determine whether |A| is less than 1; otherwise, perform the spiral position update. The expression for the spiral position update is: (20) In the above formula, is the updated individual position; is the optimal individual position; is the current individual position; absolute value Represents the distance between individuals; is a constant that determines the shape of the logarithmic spiral, is a random number in the range of [-1, 1]; Represents the natural logarithm base e An exponential function with base ; If |A| is less than 1, the shrinking and encircling mechanism based on Lévy flight is executed; otherwise, the prey search based on Lévy flight is executed.

[0032] Furthermore, based on the contraction and encirclement mechanism of Lévy flight, that is: (twenty one) In the above formula, The individual position after the shrinkage and encirclement mechanism is executed; is the optimal individual position; is the current individual position, The absolute value represents the distance between individuals; ⊙ represents element multiplication, is a random step size The probability density function of .

[0033] Further, prey search based on Lévy flight, namely: (twenty two) In the above formula, for the individual’s position after performing a prey search; is the randomly selected individual position; is the current individual position, The absolute value represents the distance between individuals; ⊙ represents element multiplication, is a random step size The probability density function of S36. Calculate the second fitness value (i.e., the objective function value) of each individual and sort the population. The sorting method is to sort the second fitness value from small to large to ensure that the individual with the smallest fitness value in the minimization problem is ranked first.

[0034] S37, performing an annealing search mechanism on the population. As a preferred implementation of step S37, it specifically includes: S371. Input initial population , initialization parameters, including initial temperature , final temperature , cooling rate and the maximum number of iterations ; S372, from the initial population Select the top 10% of individuals in terms of fitness value to form the subset SP; S373, select an individual from the subset SP, and initialize its optimal solution and its corresponding fitness value; S374, if the current temperature , and the current number of iterations , then randomly perturb the selected individual to generate a new individual; otherwise, select the next individual in the subset SP; S375. If the fitness value of the new individual is better than that of the current individual, the new individual is accepted; otherwise, the fitness difference is calculated. , and The probability of accepting new individuals, the fitness difference The fitness value of the new individual minus the fitness value of the current individual; S376, update temperature and number of iterations: , , and return to step S374 to continue execution; S377. When all individuals in the subset SP have been selected and processed, the final updated initial population is returned. .

[0035] S38. Determine whether the iteration stop condition is met. If so, output the optimal scheduling solution; otherwise, return to step S32.

[0036] This embodiment uses an extended whale optimization algorithm, which combines an initial population generation method based on the best fit heuristic to effectively generate an initial feasible solution. At the same time, a contraction and encirclement mechanism based on Lévy flight and a prey search mechanism, as well as an annealing search mechanism, are introduced to enhance the algorithm's global exploration and local development capabilities. The extended whale optimization algorithm effectively overcomes the local optimal solution problem that traditional optimization methods may face, can quickly converge to the global optimal solution, and apply the optimal scheduling solution to the hot pressing process, thereby improving scheduling efficiency, shortening production cycles, and further improving the overall performance and flexibility of the production system.

[0037] In addition, this embodiment further illustrates the effectiveness and feasibility of a single-machine batch scheduling method for hot pressing molding of aviation composite materials taking into account two-dimensional spatial characteristics proposed by the present invention through the following experiments.

[0038] The experiment uses case data provided by an aviation composite material manufacturer, adopts the extended whale optimization algorithm for optimization and solution, and compares it with four baseline algorithms to comprehensively evaluate the algorithm performance. The baseline algorithms include genetic algorithm, particle swarm optimization algorithm, biogeographic optimization algorithm and basic whale optimization algorithm. All algorithms use the same initial population. The parameters of each algorithm are shown in Table 1. The population size is set to 30 and the number of iterations is 300. The experiment runs independently 30 times. All experiments are implemented using Python programming. The operating environment is a computer equipped with an Intel(R) Ultra 3800MHz processor, 1TB memory, and running the Microsoft Windows 11 operating system.

[0039] Table 1 Parameter settings algorithm parameter Genetic Algorithms Crossover rate = 0.8, mutation rate = 0.2 Particle Swarm Optimization Inertia weight = 0.5, cognitive learning factor = 1.5, social learning factor = 1.5 Biogeographic Optimization Algorithm Maximum migration rate = 1.0, maximum migration rate = 1.0, maximum mutation rate = 0.4 Basic whale optimization algorithm The parameter a decreases linearly from 2 to 0, b=0.5, and l is in the range [-1, 1] Extending the Whale Optimization Algorithm The parameter a decreases linearly from 2 to 0, b=0.5, and l is in the range [-1, 1] (1) Case data This case is a 12-meter-high and 20-meter-wide autoclave, which contains 115 operations. The relevant data for each operation is as follows: The operating heights (unit: meter) are in the following order: {3,5,4,9,6,9,2,9,1,5,2,3,2,2,5,6,4,9,6,7,2,2,9,2,1,2,2,6,4,2,9,5,9,2,3,3,4,8,6,1,3,7,9,7,7,3,1,7,4,9,9,7,5,1,5,7,4,2,6,5,1,2,4,1,7,2,4,2,9,7,7,9,3,4,3,3,9,2,1,8,4,3,8,9,4,5,4,8,6,8,5,5,9,8,4,3,7,2,9,7,8,1,1,8,6,5,3,2,6,2,5,4,7,8,6}; The operating widths (unit: meter) are in the following order: {7,3,8,7,7,8,8,5,1,7,5,3,3,9,7,8,8,3,4,1,6,9,7,9,6,9,1,6,5,1,3,5,1,7,4,1,7,4,8,2,5,2,1,2,8,5,4,5,8,2,7,3,7,4,7,7,5,2,6,2,1,8,9,3,4,7,3,6,7,4,9,3,6,5,8,6,3,6,7,7,9,3,5,1,1,7,4,4,2,4,7,9,9,7,3,4,9,2,6,3,3,3,8,5,2,3,6,1,8,8,3,1,9,7,3}; The processing time (unit: hour) is as follows: {3,6,1,1,2,9,7,4,6,2,8,2,5,4,6,2,1,7,8,8,7,2,5,4,8,7,9,5,9,2,2,9,1,4,1,7,6,4,9,5,3,4,1,4,6,2,2,9,8,7,8,4,2,8,2,1,6,3,4,1,9,2,9,5,9,4,9,1,2,3,4,3,7,9,3,4,4,9,1,7,8,2,7,5,1,2,8,8,8,9,2,5,4,4,5,8,5,6,5,2,5,6,3,7,5,8,1,1,4,9,7,4,9,7,4}; The release times (unit: hours) are in the following order: {3,80,32,44,15,1,74,40,84,88,13,76,28,41,31,59,94,98,89,92,55,41,4,6,15,45,23,10,94,48,68,0,11,0,52,32,30,84,40,6,65,58,89,89,70,85,6,33,57,84,11,27,54,18,44,45,23,6 9,58,62,83,26,4,64,61,63,27,56,63,25,30,45,3,40,56,95,21,8,26,2,59,70,64,29,87,32,8,19,50,67,90,10,77,48,30,64,10,86,0,9,46,22,45,26,4,80,67,82,80,46,71,94,92,78,77}; The latest start time for processing (unit: hours) is as follows: {83,174,115,98,96,60,131,134,167,136,70,140,87,102,98,134,171,151,137,155,118,98,70,87,96,114,74,58,171,123,163,93,62,77,112,92,116,143,99,83,133,147,138,138,120,155,61,102,107,137,81,85,139,106,92,131,82,132,1 08, 157, 150, 107, 74, 144, 132, 134, 120, 125, 148, 92, 90, 96, 73, 123, 111, 148, 97, 84, 75, 55, 135, 140, 125, 81, 163, 121, 56, 68, 108, 136, 158, 101, 127, 107, 89, 149, 89, 163, 64, 104, 110, 80, 119, 107, 88, 163, 115, 168, 157, 132, 153, 148, 154, 139, 161}; (2) Optimization solution The experimental results of the case are shown in Table 2, including six performance indicators: average value, optimal value, worst value, standard deviation, computing time and space utilization. The results show that compared with the benchmark algorithm, the extended whale optimization algorithm shows obvious advantages in key indicators. Specifically, the average fitness value of the extended whale optimization algorithm is 116.66, which is about 4.5% higher than the second best algorithm; the best fitness value is 112.00, which is 3.4% higher than the second best algorithm. Although the standard deviation of the extended whale optimization algorithm is slightly higher and the computing time is longer, its significant improvement in solution quality effectively compensates for these shortcomings. In addition, the extended whale optimization algorithm has the highest space utilization rate of 79.41%, further highlighting its superior performance. In summary, the extended whale optimization algorithm is significantly better than the benchmark algorithm in terms of performance and space utilization, demonstrating its practical application potential in composite material production.

[0040] Table 2 Case study results for each performance indicator

[0041] In summary, the present invention proposes a single-machine batch scheduling model for hot pressing molding of aviation composite materials that takes into account two-dimensional spatial characteristics for the bottleneck process of hot pressing molding, and uses the extended whale optimization algorithm based on the model for optimization and solution. The experimental results verify the effectiveness and feasibility of the scheduling method. Through the method proposed in the present invention, the processing sequence, processing time and placement of jobs within the batch can be effectively arranged to ensure that the utilization rate of the autoclave is maximized while meeting the spatial constraints and time window restrictions, thereby improving production efficiency.

[0042] Those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, so the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0043] Each embodiment in this specification is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the above embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.

[0044] The above implementation methods have been described in detail. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A single-machine batch scheduling method for hot pressing molding of aviation composite materials considering two-dimensional spatial characteristics, characterized in that: The Method The process includes: Obtain basic data on the hot press molding process of aviation composite materials, including the size of the autoclave, the size of each job, the processing time of the job, the release time of the job and the time window; Based on basic data and assumptions, a single-machine batch scheduling model for hot pressing of aviation composite materials is constructed to minimize the completion time. The single-machine batch scheduling model includes machine environment, constraints and optimization objectives. The single-machine batch scheduling model is solved to obtain the optimal scheduling solution, which is then applied to the hot pressing molding process of aviation composite materials to improve scheduling efficiency.

2. The single-machine batch scheduling method for hot pressing molding of aviation composite materials according to claim 1 is characterized in that: The size of the autoclave and each job is rectangular, consisting of width and height; the release time is the time when the job is completed and released in the previous stage; and the time window is the time period during which each job can be processed.

3. The single-machine batch scheduling method for hot pressing molding of aviation composite materials according to claim 1 is characterized in that: The assumptions are: The autoclave used is a single-layer device, which is assumed to be available initially and available for all jobs upon release; the autoclave can only process one batch at a time and once processing starts, it cannot be interrupted; each job can only be processed by one machine; transportation time and adjustment time are ignored.

4. The single-machine batch scheduling method for hot pressing molding of aviation composite materials according to claim 1 is characterized in that: The expression of the single machine batch scheduling model is: ； In the formula, 1 means that the machine environment is a single machine environment; It represents the maximum finishing time of all tasks, which is used to evaluate the optimization goal; represents a two-dimensional packing constraint; represents parallel batch processing; Indicates the job release time; Indicates the job time window restrictions.

5. The single-machine batch scheduling method for hot pressing molding of aviation composite materials according to claim 1 is characterized in that: The optimization goal of the single-machine batch scheduling model is: ； In the formula, is the objective function of the single-machine batch scheduling model; For batch The end processing time; B is a batch set, with Represents a single batch for an index.

6. The single-machine batch scheduling method for hot pressing molding of aviation composite materials according to claim 1 is characterized in that: The constraints of the single-machine batch scheduling model specifically include: Processing time per batch Cannot be less than the processing time of any job in the batch ,Right now: ； If the batch has been assigned activities, the batch must be formed, i.e.: ； batch The start processing time must be greater than or equal to the arrival time of all jobs in the batch, that is: ； batch The start time of processing shall not be earlier than that of the previous batch The completion time is: ； batch The start processing time of the batch shall not exceed the latest start processing time of all jobs in the batch, that is: ； Each job can only be processed within one batch, that is: ； The job cannot exceed the boundaries of the machine, including the rightmost coordinate of the job cannot exceed the width of the machine, and the highest coordinate cannot exceed the height of the machine, that is: ； Adjacent operations in the same batch Axis or There is no overlap on the axis, that is: ； The spatial relationship between any pair of adjacent operations in the same batch is Axis or Axis alignment, that is: ； The decision variables are within the feasible range, that is: ； In the above formula, the batch set B By Index Represents a single batch; a collection of jobs By Index or Represents a single job; Indicates batch processing time; is a 0-1 decision variable. If the job Assigned to batch ,So , otherwise 0; Indicates the job processing time; is a 0-1 decision variable. If the batch In batches, then , otherwise 0; For batch End processing time; operation Time window usage It indicates that, For homework The release time, For homework The latest start time of processing; and Respectively represent the work Coordinates of the lower left corner and coordinates ; and Respectively represent the work The height and width of and Respectively represent the height and width of the machine; is a 0-1 decision variable. If the width Parallel to ,So , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job On the left side, then , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job Below, then , otherwise 0; and Respectively represent the work Coordinates of the lower left corner and coordinates ; is a 0-1 decision variable. If the job Assigned to batch ,So , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job On the left side, then , otherwise 0; is a 0-1 decision variable. If the job The location is located in the job Below, then , otherwise 0.

7. The single-machine batch scheduling method for hot pressing molding of aviation composite materials according to claim 1 is characterized in that: Solving the single-machine batch scheduling model to obtain the optimal scheduling solution includes the following steps: S31, initializing parameters, generating an initial population based on the best adaptation heuristic method; S32, calculating the first fitness value of each individual, and recording the best individual; S33, update parameter a, determine coefficient vectors A and C, coefficient vectors A and C are: ； ； In the above formula, a decreases linearly from 2 to 0 during the iteration process; r1 and r2 are random vectors in the range [0,1]; S34. Generate a random number between 0 and 1 ; S35. Judgment Is it less than 0.5? If so, determine whether |A| is less than 1; otherwise, perform the spiral position update. The expression for the spiral position update is: ； In the above formula, is the updated individual position; is the optimal individual position; is the current individual position; absolute value Represents the distance between individuals; is a constant that determines the shape of the logarithmic spiral, is a random number in the range of [-1, 1]; Represents the natural logarithm base e An exponential function with base ; If |A| is less than 1, the shrinking and encircling mechanism based on Lévy flight is executed; otherwise, the prey search based on Lévy flight is executed; S36, calculating the second fitness value of each individual, and sorting the population; S37, performing an annealing search mechanism on the population; S38. Determine whether the iteration stop condition is met. If so, output the optimal scheduling solution; otherwise, return to step S32.

8. The single-machine batch scheduling method for hot pressing molding of aviation composite materials according to claim 7 is characterized in that: The shrinking and encircling mechanism based on Lévy flight is: ； In the above formula, The individual position after the shrinkage and encirclement mechanism is executed; is the optimal individual position; is the current individual position, The absolute value represents the distance between individuals; ⊙ represents element multiplication, is a random step size The probability density function of Prey search based on Lévy flight, that is: ； In the above formula, for the individual’s position after performing a prey search; is a randomly selected individual position.

9. The single-machine batch scheduling method for hot-pressing of aviation composite materials according to claim 7, characterized in that: In step S31, the specific process includes the following steps: S311, according to the following rules to collect the work Sort by: First, by the release time of the job Arrange in ascending order; if the release time is the same, the latest start time of the job will be used Sort in ascending order; S312, initializing a skyline array SA of the machine, which is used to store the current heights of the placed jobs along the width W of the machine; S313: Form a subset according to the sequence sorted in step S311 , where jobs with the same release time form a subset and are removed from the job set Remove a subset ; S314, calculating the height difference HD between the current minimum gap and the height of the machine, the current minimum gap being the minimum gap at which the machine can be placed determined by identifying the minimum value of the skyline array SA; S315, in the subset Among all the jobs, compare their height and width to find the minimum value ; S316, if the subset If the working width is smaller than the height, rotate it 90° and sort it in descending order of width to determine the minimum value. ; S317, if the subset If it is empty, return to step S313; otherwise, determine the minimum gap based on the best adaptation heuristic method, that is: From the subset Select the job that best fits the gap , place it in the gap, update the skyline array SA, and place the job From the subset If no job fits into the smallest gap, fill the gap; S318, Update the skyline array SA, height difference HD and minimum value , if the height difference HD is less than the minimum value , then the current batch is formed, and the subset The jobs in the job collection are inserted back into the job collection in the original order. The beginning of the process and returns to step S312; otherwise, continue to step S317; S319, repeat the above steps S311-S318 until all jobs are grouped into batches; S3110. Based on the batch information obtained in step S319, encoding is performed to obtain an initial feasible solution.

10. The single-machine batch scheduling method for hot pressing molding of aviation composite materials according to claim 7, characterized in that: In step S37, the specific process includes the following steps: S371. Input initial population , initialization parameters, including initial temperature , final temperature , cooling rate and the maximum number of iterations ; S372, from the initial population Select the top 10% of individuals in terms of fitness value to form the subset SP; S373, select an individual from the subset SP, and initialize its optimal solution and its corresponding fitness value; S374, if the current temperature , and the current number of iterations , then randomly perturb the selected individual to generate a new individual; otherwise, select the next individual in the subset SP; S375. If the fitness value of the new individual is better than that of the current individual, the new individual is accepted; otherwise, the fitness difference is calculated. , and The probability of accepting new individuals, the fitness difference The fitness value of the new individual minus the fitness value of the current individual; S376, update temperature and number of iterations: , , and return to step S374 to continue execution; S377. When all individuals in the subset SP have been selected and processed, the final updated initial population is returned. .

Images