Composite material hot press molding production scheduling method based on man-hour uncertainty dynamic transmission mechanism

Abstract

The invention discloses a composite material hot press molding production scheduling method based on a man-hour uncertainty dynamic transmission mechanism. In order to solve the problems that in the hot press molding process of the composite material, the working hours have uncertainty and are easily transmitted and amplified among multiple batches and multiple devices, a working hour uncertainty dynamic transmission mechanism is constructed, and the propagation rule of the workpiece machining time uncertainty between a batch layer and a machine layer is described; on this basis, constraints including an equipment capacity constraint and a workpiece and equipment matching constraint are comprehensively considered, a scheduling optimization model with minimization of the maximum completion time as an optimization target is established, and an optimization adjustment strategy is deduced; and finally, designing a mixed meta-heuristic algorithm to solve the scheduling optimization model in combination with an optimization adjustment strategy, thereby realizing efficient search of an optimal scheduling scheme. According to the method provided by the invention, the influence of uncertainty on the design of the production scheduling scheme can be effectively reduced, and the scheduling efficiency and stability of the composite material hot press molding process are improved.

Description

Technical Field

[0001] This invention belongs to the field of production scheduling for hot pressing molding of aerospace composite materials under non-parallel machine environments, and specifically relates to a production scheduling method for hot pressing molding of composite materials based on a dynamic transmission mechanism of time uncertainty. Background Technology

[0002] With the large-scale delivery of advanced civil aircraft and the continuous research and development of next-generation military aircraft, the market demand for aerospace composite materials is experiencing explosive growth. In the aerospace composite manufacturing process, the hot pressing process is considered a bottleneck restricting overall production efficiency due to factors such as the limited number of autoclaves. To minimize the maximum completion time of this process, scheduling focuses on the design of workpiece batching schemes and the rational scheduling of batches on machines. In actual production environments, workpiece processing time often deviates from the process set value due to factors such as uneven temperature and pressure distribution inside the machine and changes in material state, and the degree of deviation cannot be determined before processing is completed, thus exhibiting significant uncertainty. Traditional scheduling methods are mostly designed based on deterministic processing times, which leads to significant schedule deviations from the plan during implementation, thus affecting the practical value of the scheme. Given the significant impact of processing time uncertainty on the formulation and execution of scheduling schemes, how to obtain the optimal production scheduling scheme under uncertain time scheduling environments to effectively alleviate production delays has become an important problem that urgently needs to be solved. Therefore, there is an urgent need for a scheduling method that fully considers the dynamic transmission mechanism of workpiece processing time uncertainty, which is of great engineering significance for improving the practical applicability of scheduling schemes and production management efficiency. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention proposes a production scheduling method for composite material hot pressing molding based on a dynamic transmission mechanism of time uncertainty. This method comprehensively considers the uncertainty of workpiece processing time, the applicability relationship between workpiece and machine, and the relationship between machine capacity and workpiece size to obtain the optimal scheduling scheme. The aim is to reduce the impact of uncertainty on the design of production scheduling scheme and improve the scheduling efficiency and stability of composite material hot pressing molding process.

[0004] To achieve the above-mentioned technical objectives, the present invention proposes the following technical solution: A production scheduling method for hot pressing molding of composite materials based on a dynamic transmission mechanism of time uncertainty, specifically including: Based on a non-parallel machine environment, batch hot pressing forming of workpieces is performed, and a dynamic transmission mechanism for time uncertainty is constructed: the batch processing time is determined by the processing time of all workpieces in the batch, and the batch start processing time is determined by the completion time of the previous batch on the same machine and the release time of the workpieces in this batch. The workpiece processing time is an uncertain time. According to the dynamic transmission mechanism for time uncertainty, the uncertainty of workpiece processing time is transmitted from the workpiece layer to the batch layer and the machine layer, and the completion time of each batch on a single machine and the maximum completion time of the processing task are obtained. Based on the dynamic transmission mechanism of time uncertainty, a scheduling optimization model is established under constraints including equipment capacity constraints, workpiece allocation and matching constraints, batch sequence constraints, and workpiece release time constraints, with the optimization objective of minimizing the maximum completion time of processing tasks; the scheduling optimization model is represented using a three-field representation method. Based on the scheduling optimization model, optimization and adjustment strategies for scheduling schemes are formulated; A hybrid heuristic algorithm is designed and combined with an optimization adjustment strategy to solve the scheduling optimization model and obtain the optimal scheduling scheme. The optimal scheduling scheme is then applied to the hot pressing production of the workpiece to complete the processing task.

[0005] Furthermore, the specific process for obtaining the completion time of each batch on a single machine and the maximum completion time of the processing task is as follows: For any workpiece, its processing time is expressed as an interval gray number to characterize the uncertainty; For any batch on any machine, its completion time is the sum of the batch processing time and the batch start processing time, and both the batch processing time and the batch start processing time are in the form of interval gray numbers. The batch processing time is the maximum value of the processing time of the workpieces within that batch; The lower bound of the batch start processing time is the larger of the lower bound of the previous batch completion time and the current batch release time; the upper bound of the batch start processing time is the larger of the upper bound of the previous batch completion time and the current batch release time; the batch release time is the maximum value of the workpiece release time within the batch. The maximum completion time of the processing task is expressed as an interval gray number, taking the maximum value of the completion time of each batch on each machine.

[0006] Furthermore, the constraints, including equipment capacity constraints, workpiece allocation and matching constraints, batch sequence constraints, and workpiece release time constraints, are specifically as follows: Each workpiece must be assigned to one machine in one batch for processing, and can only be assigned to one machine from its applicable set of machines; On the same machine, the sum of the dimensions of all workpieces processed in each batch does not exceed the capacity of the machine; If a workpiece is assigned to a batch on a machine for processing, then the batch on that machine is marked as used; otherwise, it is marked as unused. For batches on the same machine, they are processed sequentially according to the batch number. If a later batch is marked as used, then its preceding batch must also be marked as used, and the start time of the later batch is no earlier than the completion time of the preceding batch. The lower limit of the start processing time for each batch shall not be less than the lower limit of the release time of any workpiece in the batch and the completion time of the previous batch, and the upper limit of the start processing time for each batch shall not be less than the upper limit of the release time of any workpiece in the batch and the completion time of the previous batch. The completion time of each batch shall not be earlier than the start time of the batch plus the processing time of any workpiece in the batch; If a batch of a machine is not used, then the start time and completion time of that batch are both zero. The maximum completion time of a processing task is not less than the completion time of any batch on any machine; the start time, completion time of all batches, and the maximum completion time of the processing task are all non-negative values.

[0007] Furthermore, the optimization and adjustment strategy specifically includes: Optimization and adjustment strategy 1: Under the premise of meeting the equipment capacity constraints, move the workpiece with the longest processing time in the last batch on the same machine to another batch on the same machine. The other batch must meet the following conditions: the maximum processing time of the workpieces in this batch is not less than the processing time of the workpiece being moved, and the maximum release time of the workpieces in this batch is not less than the release time of the workpiece being moved. Optimization and adjustment strategy 2: If two adjacent batches on the same machine meet the following conditions: the difference between the release time of the current batch and the release time of the next batch is not less than the lower bound of the processing time of the next batch; at the same time, the release time of the current batch is greater than the lower bound of the completion time of the previous batch; then all workpieces in the two adjacent batches on the same machine are swapped.

[0008] Furthermore, the design of the hybrid metaheuristic algorithm combined with the optimization adjustment strategy to solve the scheduling optimization model and obtain the optimal scheduling scheme specifically includes: P1. Initialize algorithm parameters, including: current algebra Population size Maximum number of iterations Crossover probability and mutation probability ; P2, Generated using a hybrid heuristic method Individuals, forming the initial population Each individual represents a scheduling scheme; the fitness of individuals in the population is calculated through decoding. P3. Determine if the maximum number of iterations has been reached. If so, output the optimal scheduling scheme; otherwise, proceed to P4. P4. Perform population mating operations to generate... Initial offspring individuals And decode to calculate fitness; P5. If the current algebra exceeds the preset algebra threshold, then execute P6; otherwise, execute P7. P6. For all initial offspring individuals Perform local search optimization to obtain optimized offspring individuals. ; P7. Merge the current population And offspring individuals, retaining the ones with the lowest fitness values. Each individual receives the next generation of the population. And continue executing P3.

[0009] More specifically, the hybrid metaheuristic algorithm adopts a two-dimensional coding scheme: the number of genes on each individual's chromosome is consistent with the number of workpieces in the processing task, and each gene contains two dimensions: the workpiece number and the machine number assigned to the workpiece.

[0010] More specifically, the decoding process of the hybrid metaheuristic algorithm is as follows: Starting with the first gene, the workpiece dimension codes that are consistent with the machine dimension codes are sorted according to their order on the chromosome; all workpiece dimension codes corresponding to all machine dimension codes are traversed, and the workpiece processing order of each batch of each machine is obtained according to the equipment capacity constraints, thus obtaining a scheduling scheme; the maximum completion time of the processing tasks in each scheduling scheme is calculated according to the dynamic transmission mechanism of time uncertainty, which is used as the fitness of each individual.

[0011] Furthermore, the method of generating using a hybrid heuristic approach... Individuals, forming the initial population Specifically, it includes: For each individual, generate a random number within the interval [0,1]. ; Determine whether the random number is not greater than the preset random number threshold. If it is not greater, use a heuristic method to generate the workpiece dimension code and the machine dimension code; otherwise, randomly shuffle the workpiece set to obtain the workpiece dimension code, and randomly select a machine from the set of machines that can be used for the workpiece to obtain the machine dimension code. The workpiece dimension code and machine dimension code are combined into an individual, and the above process is repeated to generate... Individuals, forming the initial population ; The sorting heuristic rule based on non-ascending processing time is as follows: Sort the set of workpieces according to the non-ascending order of their processing time to generate workpiece dimensional codes; Randomly select a machine from the set of applicable machines corresponding to each workpiece to generate machine dimensional codes. The sorting heuristic rule based on non-decreasing release time is as follows: Sort the set of workpieces according to the non-decreasing order of their release time to generate workpiece dimensional codes; Randomly select a machine from the set of applicable machines corresponding to each workpiece to generate machine dimensional codes. Based on the heuristic rule of compact workpiece size arrangement: Sort the workpiece set in non-ascending order according to workpiece size, and generate workpiece dimension codes by alternately selecting elements from the sorted workpiece sequence at the beginning and end; generate machine dimension codes as follows: For the first workpiece in the workpiece dimension code, randomly select a machine from its applicable machine set; for each subsequent workpiece, first try to reuse the machine assigned to the previous workpiece, if reuse fails, randomly select a machine from the applicable machine set of the current workpiece for allocation; allocate machines to all workpieces in turn, and generate machine dimension codes.

[0012] Furthermore, the execution of the population mating operation generates... Initial offspring individuals Specifically, it includes: Selected using a tournament selection method For the parent generation; A random number is generated for each pair of parent individuals. random numbers within ; right Each pair of parent chromosomes undergoes an ERX crossover operation to produce a daughter chromosome; right Each pair of parent chromosomes undergoes an IM mutation operation to produce a daughter chromosome, wherein the IM mutation operation occurs randomly on one of the chromosomes in that pair of parent chromosomes. A daughter chromosome is produced by performing a replication operation on the remaining parent chromosome pair, wherein the replication operation occurs randomly on one of the chromosomes in the parent chromosome pair; The above Each offspring chromosome is converted into an initial offspring individual, decoded, and output.

[0013] Furthermore, the above applies to all initial offspring individuals. Perform local search optimization to obtain optimized offspring individuals. Specifically: For each initial offspring individual Obtain its corresponding scheduling scheme. And calculate the fitness value. The fitness value is the maximum completion time of the processing task in the scheduling scheme; Randomly select an optimization and adjustment strategy and try it on the scheduling scheme. Optimize; if an optimized scheduling scheme is obtained Then, based on the dynamic transmission mechanism of time uncertainty, the calculation is performed. Maximum completion time If an optimized scheduling scheme is not obtained Then this step is performed on the next initial offspring individual; Will and Compare: If satisfied This will optimize the scheduling scheme. The corresponding new individuals are added. Otherwise, add the original individual directly. .

[0014] Based on the above technical solution, the present invention has at least the following beneficial effects: For the hot pressing and forming of aerospace composite materials in small batches and with diverse product types, a dynamic mechanism for the transmission of time uncertainty is constructed. A scheduling model is built with the goal of minimizing the maximum completion time, comprehensively considering the applicability relationship between workpieces and machines, as well as the relationship between machine capacity and workpiece size. Based on this, two scheduling optimization theorems are derived, and a hybrid metaheuristic algorithm is designed to solve the scheduling problem, obtaining the optimal scheduling scheme for the processing tasks. This ensures the reasonable allocation of workpieces, batches, and machines, thereby effectively mitigating production delays.

[0015] The method proposed in this invention employs a hybrid metaheuristic algorithm and a two-dimensional coding scheme, which can effectively handle the complex relationships between workpiece, batch, and machine allocation, improving the algorithm's adaptability to multi-dimensional problems. By combining crossover, mutation, replication, and local search operations, it can better explore the solution space and avoid getting trapped in local optima. Through optimization, this algorithm not only obtains a better solution in a shorter time but also exhibits high stability, effectively improving scheduling efficiency. Under the premise of satisfying various constraints, the optimal scheduling scheme obtained considering uncertain processing times is applied to the aerospace composite hot pressing process to improve production efficiency. Attached Figure Description

[0016] Figure 1 The flowchart shows a production scheduling method for hot pressing of composite materials based on a dynamic transmission mechanism of time uncertainty proposed in this invention. Figure 2 This is a flowchart illustrating the execution of the hybrid metaheuristic algorithm in this embodiment. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention.

[0019] To overcome the limitations of existing scheduling schemes for hot pressing processes in aerospace composite materials, in this embodiment, as follows: Figure 1 As shown, this invention proposes a production scheduling method for hot pressing molding of composite materials based on a dynamic transmission mechanism of time uncertainty, which specifically includes the following steps: S1. Based on a non-parallel machine environment, batch hot pressing forming of workpieces is performed, and a dynamic transmission mechanism for time uncertainty is constructed: in the machine... The uncertainty of workpiece processing time leads to batch processing... The uncertainty of processing time leads to the uncertainty of the completion time of this batch; the current batch The uncertainty of the completion time will affect the next batch The uncertainty of the start processing time is transmitted batch by batch, ultimately affecting the uncertainty of the maximum completion time. That is, under a given scheduling scheme, the batch processing time is determined by the processing time of all workpieces in the batch, and the batch start processing time is determined by the completion time of the previous batch on the same machine and the release time of the workpieces in this batch. The workpiece processing time is an uncertain working time. According to the dynamic transmission mechanism of working time uncertainty, the uncertainty of workpiece processing time is transmitted from the workpiece layer to the batch layer and the machine layer to obtain the completion time of each batch on a single machine and the maximum completion time of the processing task. In a preferred embodiment, the specific process for obtaining the completion time of each batch on a single machine and the maximum completion time of the processing task is as follows: For any workpiece, its processing time is expressed as an interval gray number to characterize the uncertainty; For any batch on any machine, its completion time is the sum of the batch processing time and the batch start processing time, and both the batch processing time and the batch start processing time are in the form of interval gray numbers. The batch processing time is the maximum value of the processing time of the workpieces within that batch; The lower bound of the batch start processing time is the larger of the lower bound of the previous batch completion time and the current batch release time; the upper bound of the batch start processing time is the larger of the upper bound of the previous batch completion time and the current batch release time; the batch release time is the maximum value of the workpiece release time within the batch. The maximum completion time for a processing task is expressed as an interval gray number, taking the maximum value of the completion time for each batch on each machine; the formula for the above process is expressed as: ; ; ; in, Indicates the maximum completion time for the processing task; For machines Previous batch Completion time; For machines Previous batch Start processing time; Let be the processing time for workpiece j; Represented as machines Previous batch The lower and upper bounds of the completion time; For machines Previous batch Release time, ,in This refers to the release time of the workpiece, which is a fixed value; it is marked with a superscript. The variables are uncertainties represented by interval gray numbers; This indicates that workpiece j is assigned to machine m for batch k processing.

[0020] S2. Based on the dynamic transmission mechanism of time uncertainty, under the constraints including equipment capacity constraints, workpiece allocation and matching constraints, batch sequence constraints, and workpiece release time constraints, a scheduling optimization model is established with the optimization objective of minimizing the maximum completion time of the processing task. In this embodiment, the scheduling optimization model is represented using a three-field notation (machine environment | constraints | optimization objective): ; in, This indicates that the machine environment is a non-equivalent parallel machine environment; This represents the maximum completion time for the processing task, used to evaluate the optimization objective; These are constraints; , They represent the machine and the workpiece, respectively. This indicates that the production mode of this process is batch processing, that is, several workpieces that meet the constraints are grouped into a batch, and the processing starts and ends simultaneously. Used to evaluate workpieces The two-dimensional projected area, i.e., the workpiece size; For workpiece The set of applicable machines (i.e., the set of machines that can be used to process workpiece j). Used to evaluate machines The maximum cross-sectional projected area, i.e., the machine capacity; The optimization objective is to minimize the maximum completion time of the processing task, i.e. .

[0021] In a preferred embodiment, the constraints, including equipment capacity constraints, workpiece allocation and matching constraints, batch sequence constraints, and workpiece release time constraints, are specifically as follows: Each workpiece must be assigned to one machine in one batch for processing, and can only be assigned to one machine from its applicable set of machines; the formula is expressed as: Constraint 1: ; Constraint 2: ; in, For 0-1 decision variables, if the workpiece Assigned to machine On the batch Once the processing is completed, then Otherwise, it is 0; workpiece set By index Represents a single workpiece or a set of machines. By index Represents a single machine; a batch set By index Indicates a single batch; , These represent the number of workpieces and the number of machines, respectively; (in special cases, each workpiece is processed in a batch, in which case the batch quantity equals the number of workpieces). On the same machine, the sum of the dimensions of all workpieces processed in each batch shall not exceed the capacity of the machine; the formula is expressed as: Constraint 3: ; Constraint 3 is the equipment capacity constraint; workpieces exceeding the capacity of the current batch will be processed in the next batch.

[0022] If a workpiece is assigned to a batch on a machine for processing, then that batch on that machine is marked as used; otherwise, it is marked as unused. For batches on the same machine, processing is done sequentially according to batch number. If a later batch is marked as used, then its preceding batch must also be marked as used, and the start time of the later batch cannot be earlier than the completion time of the preceding batch. The formula is expressed as: Constraint 4: ; Constraint 5: ; Constraint 6: ; Constraint 7: ; Constraint 8: ; Among them, For 0-1 decision variables, if the machine... On the batch If the status is "used", then Otherwise, it is 0; , For machines Previous batch The upper and lower bounds of the start time, , For machines Previous batch -1 Upper and lower bounds of completion time; where This describes a modeling technique for relaxing partial constraints, as shown in this embodiment. The value is the sum of the processing time and release time of all workpieces, ensuring the effectiveness of this modeling technique in the constraint transformation process.

[0023] The lower bound of the start processing time for each batch shall not be less than the lower bound of the release time of any workpiece within that batch and the completion time of the previous batch; the upper bound of the start processing time for each batch shall not be less than the upper bound of the release time of any workpiece within that batch and the completion time of the previous batch; the formula is expressed as: Constraint 9: ; Constraint 10: ; The completion time of each batch shall not be earlier than the start time of that batch plus the processing time of any workpiece within that batch; the formula is expressed as: Constraint 11: ; By applying the constraints 7-11 above, the batch start time and completion time satisfy the dynamic transmission mechanism of time uncertainty proposed in this invention.

[0024] If a batch of a machine is not used, then the start time and completion time of that batch are both zero; the formula is as follows: Constraint 12: ; Constraint 13: ; The maximum completion time of a processing task is no less than the completion time of any batch on any machine; the start time, completion time, and maximum completion time of all batches, as well as the maximum completion time of the processing task, are all non-negative values; the formula is expressed as: Constraint 14: ; Constraint 15: ; Constraint 16: ; Constraint 17: ; Constraint 14 is also to ensure that the maximum completion time of the processing task satisfies the dynamic transmission mechanism of time uncertainty; in addition, this embodiment also provides corresponding constraints on the decision variables, namely: ; ; This is to ensure that the decision variables are within a feasible range.

[0025] S3. Based on the scheduling optimization model, formulate optimization and adjustment strategies for the scheduling scheme; As a preferred embodiment, the optimization and adjustment strategy specifically includes: Optimization and adjustment strategy 1: Under the premise of meeting equipment capacity constraints, the same machine The last batch The workpiece with the longest processing time Moved to another batch on the machine, said other batch Must meet: , ; That is, batch The maximum processing time for the intermediate workpiece shall not be less than that for the moved workpiece. Processing time ,batch The maximum release time of the middle workpiece shall not be less than that of the moved workpiece. Release time This optimized scheduling strategy achieves the effect of shortening the completion time by reducing the completion time of the last batch on a certain machine.

[0026] Optimization and adjustment strategy 2: If two adjacent batches on the same machine meet the following conditions: current batch release time With the release time of the next batch The difference is not less than the lower bound of the processing time of the next batch. Meanwhile, the release time of the current batch The lower bound of the completion time of the previous batch The formula is expressed as: , ; Then, all workpieces in two adjacent batches on the same machine are swapped; this optimization adjustment strategy is based on the idea of ​​optimizing the scheduling scheme by processing the workpieces that arrive first.

[0027] In this embodiment, the valid solution of the scheduling optimization model that satisfies all constraints is denoted as the scheduling scheme. The new scheduling scheme obtained after optimizing strategy 1 or 2 is denoted as... ,but The maximum completion time of the processing task will not exceed the maximum completion time of the processing task in the original scheduling scheme.

[0028] S4. Design a hybrid heuristic algorithm and combine it with an optimization adjustment strategy to solve the scheduling optimization model and obtain the optimal scheduling scheme; apply the optimal scheduling scheme to the hot pressing production of the workpiece to complete the processing task. The model constructed in S2 of this invention is a variant of the batch scheduling problem for non-equivalent parallel machines, belonging to a typical NP-hard problem. Therefore, as a preferred implementation of step S4, this embodiment uses a hybrid metaheuristic algorithm to solve this NP-hard problem, such as... Figure 2 As shown, it specifically includes: P1. Initialize algorithm parameters, including: current algebra Population size Maximum number of iterations Crossover probability and mutation probability ; P2, Generated using a hybrid heuristic method Individuals, forming the initial population Each individual represents a scheduling scheme; the fitness of individuals in the population is calculated through decoding. The encoding scheme serves as a bridge connecting the model and the algorithm. Considering the characteristics of the production scheduling model for the hot pressing process of aerospace composites based on uncertain working hours in this invention, this embodiment proposes an effective two-dimensional encoding scheme, specifically: The number of genes on each individual's chromosome is consistent with the number of workpieces in the processing task. Each gene contains two dimensions: the workpiece number and the machine number assigned to the workpiece. As shown in Table 1, taking a scheduling problem involving 10 workpieces to be processed and 3 available machines as an example, this embodiment uses a two-dimensional coding method to construct a chromosome structure. Each chromosome consists of 10 genes in sequence, and each gene corresponds to the scheduling decision information of a workpiece and the assigned machine. Specifically, the first dimension of the gene is used to represent the workpiece number, with a value range of 1 to 10; the second dimension of the gene is used to represent the machine number assigned to the workpiece, with a value limited to the machine number (1 to 3) within the set of available machines for that workpiece. For example, when the first gene in the chromosome is (1, 1), it means that workpiece 1 is assigned to machine 1 for processing.

[0029] Table 1 Examples of chromosome structures

[0030] The decoding method is a method in genetic algorithms that maps individuals to scheduling schemes and the objective function of the scheduling model. Considering the constraints of the production scheduling model for the hot pressing process of aerospace composites based on uncertain working hours in this invention, this embodiment proposes a decoding method, specifically: Starting with the first gene, the workpiece dimension codes that are consistent with the machine dimension codes are sorted according to their order on the chromosome; all workpiece dimension codes corresponding to all machine dimension codes are traversed, and the workpiece processing order of each batch of each machine is obtained according to the equipment capacity constraints, thus obtaining a scheduling scheme; the maximum completion time of the processing tasks in each scheduling scheme is calculated according to the dynamic transmission mechanism of time uncertainty, which is used as the fitness of each individual.

[0031] As shown in Table 2, based on the aforementioned scheduling problem parameters and the individual chromosome structure shown in Table 1, the corresponding scheduling results, including the scheduling scheme and its fitness evaluation, can be obtained according to the decoding method described in this embodiment of the invention. The specific scheduling scheme mapped by this chromosome is as follows: workpiece 1 and workpiece 10 are assigned to batch 1 of machine 1 for processing; workpiece 9 is assigned to batch 2 of machine 1 for processing; workpiece 8 and workpiece 4 are assigned to batch 1 of machine 2 for processing; workpiece 5 and workpiece 2 are assigned to batch 2 of machine 2 for processing; workpiece 3 and workpiece 6 are assigned to batch 1 of machine 3 for processing; and workpiece 7 is assigned to batch 2 of machine 3 for processing. The maximum completion time calculated according to this scheduling scheme is... This serves as the fitness value for that individual.

[0032] Table 2. Examples of scheduling problem parameters and decoding results

[0033] In addition to the encoding and decoding methods described above, this embodiment also uses a hybrid heuristic method to increase the proportion of superior individuals in the initial population. The hybrid heuristic method is used to generate... Individuals, forming the initial population The specific process is as follows: For each individual, generate a random number within the interval [0,1]. ; Determine whether the random number is not greater than a preset random number threshold (in this embodiment, the random number threshold is set to 0.2). If it is not greater than the threshold, a heuristic method is used to generate the workpiece dimension code and the machine dimension code; otherwise, the workpiece dimension code is obtained by randomly shuffling the workpiece set, and the machine dimension code is obtained by randomly selecting a machine from the set of machines that can be used for the workpiece. The workpiece dimension code and machine dimension code are combined into an individual, and the above process is repeated to generate... Individuals, forming the initial population ; The method of generating workpiece dimension code and machine dimension code using heuristics includes: The sorting heuristic rule based on non-ascending processing time is as follows: Sort the set of workpieces according to the non-ascending order of their processing time to generate workpiece dimensional codes; Randomly select a machine from the set of applicable machines corresponding to each workpiece to generate machine dimensional codes. The sorting heuristic rule based on non-decreasing release time is as follows: Sort the set of workpieces according to the non-decreasing order of their release time to generate workpiece dimensional codes; Randomly select a machine from the set of applicable machines corresponding to each workpiece to generate machine dimensional codes. Based on the heuristic rule of compact workpiece size arrangement: Sort the workpiece set in non-ascending order according to workpiece size, and generate workpiece dimension codes by alternately selecting elements from the sorted workpiece sequence at the beginning and end; generate machine dimension codes as follows: For the first workpiece in the workpiece dimension code, randomly select a machine from its applicable machine set; for each subsequent workpiece, first try to reuse the machine assigned to the previous workpiece. If reuse fails (the machine assigned to the previous workpiece is not in the applicable machine set of the current workpiece), then randomly select a machine from the applicable machine set of the current workpiece for allocation; repeat the above method to allocate machines to all workpieces in turn, and generate machine dimension codes.

[0034] P3. Determine if the maximum number of iterations has been reached. If so, output the optimal scheduling scheme; otherwise, proceed to P4. P4. Perform population mating operations to generate... Initial offspring individuals And decode to calculate fitness; In a preferred embodiment, step P4 specifically includes: P41. Selected using a tournament selection method. For the parent generation; P42. Randomly generate one for each pair of parent individuals. random numbers within ; P43, Yes Each pair of parent chromosomes undergoes an ERX crossover operation to produce a daughter chromosome; P44, Yes Each pair of parent chromosomes undergoes an IM mutation operation to produce a daughter chromosome, wherein the IM mutation operation occurs randomly on one of the chromosomes in that pair of parent chromosomes. P45. Perform a replication operation on the remaining parent chromosome pairs to produce a daughter chromosome, wherein the replication operation randomly occurs on one of the chromosomes in the parent chromosome pair; P46, the above Each offspring chromosome is converted into an initial offspring individual, decoded, and output.

[0035] P5. If the current algebra exceeds the preset algebra threshold (set to [value] in this embodiment), If the condition is met, then execute P6; otherwise, execute P7. P6. For all initial offspring individuals Perform local search optimization to obtain optimized offspring individuals. ; In a preferred embodiment, step P6 specifically includes: For each initial offspring individual Obtain its corresponding scheduling scheme. And calculate the fitness value. The fitness value is the maximum completion time of the processing task in the scheduling scheme; Randomly select an optimization and adjustment strategy and try it on the scheduling scheme. Optimization is performed (since not all scheduling schemes can meet the previous optimization conditions, optimization is attempted); if an optimized scheduling scheme is obtained... Then, based on the dynamic transmission mechanism of time uncertainty, the calculation is performed. Maximum completion time If an optimized scheduling scheme is not obtained Then this step is performed on the next initial offspring individual; Will and Compare: If satisfied This will optimize the scheduling scheme. The corresponding new individuals are added. Otherwise, add the original individual directly. Optimizing the strategy can yield a non-deteriorating scheduling scheme. However, considering that the maximum completion time of processing tasks remains the same before and after optimization, only the scheduling scheme with the shorter maximum completion time is retained as the optimized scheduling scheme.

[0036] P7. Merge the current population And offspring individuals, retaining the ones with the lowest fitness values. Each individual receives the next generation of the population. And continue executing P3.

[0037] This concludes the description of the entire process of the method proposed in this invention. Furthermore, this embodiment further illustrates the superiority and feasibility of the composite material hot pressing molding production scheduling method based on a dynamic transmission mechanism of time uncertainty proposed in this invention through the following processing task examples.

[0038] Example of a processing task: The processing task includes 50 workpieces to be processed and 3 available machines; the capacity parameters of each machine are listed in Table 3; the uncertain processing time, size, set of available machines and release time of the workpieces are listed in Table 4; and the specific parameters used are detailed in Table 5, taking into account the algorithm's solving ability and speed. The genetic algorithm involved in the method proposed in this invention is implemented based on the Pymoo framework and the Python language, and runs on a macOS computer equipped with an Apple M1 Max processor and 32 GB of memory.

[0039] Table 3 Case Machine Information

[0040] Table 4 Case Study Workpiece Information

[0041] Table 5 Algorithm parameters and their values

[0042] For the above case, the method proposed in this invention was used for solution. The algorithm ran for 18.70 seconds and converged in the 46th generation, indicating that the proposed method can effectively explore the solution space and quickly approach the optimal solution under the above parameter settings. Based on the solution results shown in Table 6, the 50 workpieces were divided into 17 batches for processing, and all workpieces were completed no earlier than 75.24 and no later than 82.52. The processing time information for each batch is detailed in Table 7. The usage status of the three machines was relatively balanced, and there were no cases of large differences in completion time. Overall, this invention can provide a reliable scheduling scheme for the production scheduling task of the aerospace composite hot pressing forming process with uncertain processing time within an acceptable time.

[0043] Table 6. Case Solution Results

[0044] Table 7. Work Hour Information for Each Batch in the Case Scheduling Plan

[0045] In summary, this invention proposes a production scheduling method for the hot pressing process of composite materials, based on a dynamic transmission mechanism of time uncertainty, for multi-variety, small-batch hot pressing processing tasks of aerospace composites. Based on this, a hybrid meta-heuristic algorithm is used for optimization. Case results show that the proposed scheduling method can provide a reliable scheduling scheme within an acceptable time. The scheduling scheme obtained by this invention can ensure the reasonable allocation of workpieces, batches, and machines, thereby effectively mitigating production delays. Under the premise of satisfying various constraints, the optimal scheduling scheme obtained considering uncertain processing time is applied to the hot pressing process of aerospace composites to improve production efficiency.

[0046] In this specification, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to at least one embodiment or example described in connection with a specific feature, structure, material, or characteristic. These specific features, structures, materials, or characteristics may be combined in a suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples and their features described in this specification.

[0047] The logic and / or steps shown in the flowchart or otherwise described can be viewed as a sequence of executable instructions for implementing logical functions. These instructions may be implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device. Such systems, apparatus, or devices include processor systems or other systems capable of receiving and executing instructions.

[0048] The above embodiments detail the principles and implementation methods of the present invention, and illustrate its working principle using specific examples. These examples are only used to help understand the method and core ideas of the present invention. Furthermore, based on the ideas of the present invention, actual implementation methods and application scope may vary. Therefore, the content of this specification should not be construed as limiting the present invention.

Claims

1. A production scheduling method for hot pressing molding of composite materials based on a dynamic transmission mechanism of time uncertainty, characterized in that, Specifically, the following steps are included: Based on a non-parallel machine environment, batch hot pressing forming of workpieces is performed, and a dynamic transmission mechanism for time uncertainty is constructed: the batch processing time is determined by the processing time of all workpieces in the batch, and the batch start processing time is determined by the completion time of the previous batch on the same machine and the release time of the workpieces in this batch. The workpiece processing time is an uncertain time. According to the dynamic transmission mechanism for time uncertainty, the uncertainty of workpiece processing time is transmitted from the workpiece layer to the batch layer and the machine layer, and the completion time of each batch on a single machine and the maximum completion time of the processing task are obtained. Based on the dynamic transmission mechanism of time uncertainty, a scheduling optimization model is established under constraints including equipment capacity constraints, workpiece allocation and matching constraints, batch sequence constraints, and workpiece release time constraints, with the optimization objective of minimizing the maximum completion time of processing tasks; the scheduling optimization model is represented using a three-field representation method. Based on the scheduling optimization model, optimization and adjustment strategies for scheduling schemes are formulated; A hybrid heuristic algorithm is designed and combined with an optimization adjustment strategy to solve the scheduling optimization model and obtain the optimal scheduling scheme. The optimal scheduling scheme is then applied to the hot pressing production of the workpiece to complete the processing task.

2. The composite material hot pressing production scheduling method based on a dynamic transmission mechanism of time uncertainty as described in claim 1, characterized in that, The specific process for obtaining the completion time of each batch and the maximum completion time of the processing task on a single machine is as follows: For any workpiece, its processing time is expressed as an interval gray number to characterize the uncertainty; For any batch on any machine, its completion time is the sum of the batch processing time and the batch start processing time, and both the batch processing time and the batch start processing time are in the form of interval gray numbers. The batch processing time is the maximum value of the processing time of the workpieces within that batch; The lower bound of the batch start processing time is the larger of the lower bound of the previous batch completion time and the current batch release time; the upper bound of the batch start processing time is the larger of the upper bound of the previous batch completion time and the current batch release time; the batch release time is the maximum value of the workpiece release time within the batch. The maximum completion time of the processing task is expressed as an interval gray number, taking the maximum value of the completion time of each batch on each machine.

3. The composite material hot pressing production scheduling method based on a dynamic transmission mechanism of time uncertainty as described in claim 1, characterized in that, The constraints, including equipment capacity constraints, workpiece allocation and matching constraints, batch sequence constraints, and workpiece release time constraints, are specifically as follows: Each workpiece must be assigned to one machine in one batch for processing, and can only be assigned to one machine from its applicable set of machines; On the same machine, the sum of the dimensions of all workpieces processed in each batch does not exceed the capacity of the machine; If a workpiece is assigned to a batch on a machine for processing, then the batch on that machine is marked as used; otherwise, it is marked as unused. For batches on the same machine, they are processed sequentially according to the batch number. If a later batch is marked as used, then its preceding batch must also be marked as used, and the start time of the later batch is no earlier than the completion time of the preceding batch. The lower limit of the start processing time for each batch shall not be less than the lower limit of the release time of any workpiece in the batch and the completion time of the previous batch, and the upper limit of the start processing time for each batch shall not be less than the upper limit of the release time of any workpiece in the batch and the completion time of the previous batch. The completion time of each batch shall not be earlier than the start time of the batch plus the processing time of any workpiece in the batch; If a batch of a machine is not used, then the start time and completion time of that batch are both zero. The maximum completion time of a processing task is not less than the completion time of any batch on any machine; the start time, completion time of all batches, and the maximum completion time of the processing task are all non-negative values.

4. The composite material hot pressing production scheduling method based on a dynamic transmission mechanism of time uncertainty as described in claim 1, characterized in that, The optimization and adjustment strategies specifically include: Optimization and adjustment strategy 1: Under the premise of meeting the equipment capacity constraints, move the workpiece with the longest processing time in the last batch on the same machine to another batch on the same machine. The other batch must meet the following conditions: the maximum processing time of the workpieces in this batch is not less than the processing time of the workpiece being moved, and the maximum release time of the workpieces in this batch is not less than the release time of the workpiece being moved. Optimization and adjustment strategy 2: If two adjacent batches on the same machine meet the following conditions: the difference between the release time of the current batch and the release time of the next batch is not less than the lower bound of the processing time of the next batch; at the same time, the release time of the current batch is greater than the lower bound of the completion time of the previous batch; then all workpieces in the two adjacent batches on the same machine are swapped.

5. A method for scheduling composite material hot pressing production based on a dynamic transmission mechanism of time uncertainty, as described in claim 4, is characterized in that... The design of the hybrid metaheuristic algorithm, combined with optimization and adjustment strategies, to solve the scheduling optimization model and obtain the optimal scheduling scheme specifically includes: P1. Initialize algorithm parameters, including: current algebra Population size Maximum number of iterations Crossover probability and mutation probability ; P2, Generated using a hybrid heuristic method Individuals, forming the initial population Each individual represents a scheduling scheme; the fitness of individuals in the population is calculated through decoding. P3. Determine if the maximum number of iterations has been reached. If so, output the optimal scheduling scheme; otherwise, proceed to P4. P4. Perform population mating operations to generate... Initial offspring individuals And decode to calculate fitness; P5. If the current algebra exceeds the preset algebra threshold, then execute P6; otherwise, execute P7. P6. For all initial offspring individuals Perform local search optimization to obtain optimized offspring individuals. ; P7. Merge the current population And offspring individuals, retaining the ones with the lowest fitness values. Each individual receives the next generation of the population. And continue executing P3.

6. A method for scheduling composite material hot pressing production based on a dynamic transmission mechanism of time uncertainty, as described in claim 5, is characterized in that... The hybrid metaheuristic algorithm adopts a two-dimensional coding scheme: the number of genes on each individual's chromosome is consistent with the number of workpieces in the processing task, and each gene contains two dimensions: the workpiece number and the machine number assigned to the workpiece.

7. A method for scheduling composite material hot pressing production based on a dynamic transmission mechanism of time uncertainty, as described in claim 6, is characterized in that... The decoding process of the hybrid meta-heuristic algorithm is as follows: Starting with the first gene, the workpiece dimension codes that are consistent with the machine dimension codes are sorted according to their order on the chromosome; all workpiece dimension codes corresponding to all machine dimension codes are traversed, and the workpiece processing order of each batch of each machine is obtained according to the equipment capacity constraints, thus obtaining a scheduling scheme; the maximum completion time of the processing tasks in each scheduling scheme is calculated according to the dynamic transmission mechanism of time uncertainty, which is used as the fitness of each individual.

8. A method for scheduling composite material hot pressing production based on a dynamic transmission mechanism of time uncertainty, as described in claim 6, is characterized in that... The method uses a hybrid heuristic to generate Individuals, forming the initial population Specifically, it includes: For each individual, generate a random number within the interval [0,1]. ; Determine whether the random number is not greater than the preset random number threshold. If it is not greater, use a heuristic method to generate the workpiece dimension code and the machine dimension code; otherwise, randomly shuffle the workpiece set to obtain the workpiece dimension code, and randomly select a machine from the set of machines that can be used for the workpiece to obtain the machine dimension code. The workpiece dimension code and machine dimension code are combined into an individual, and the above process is repeated to generate... Individuals, forming the initial population ; The method of generating workpiece dimension code and machine dimension code using heuristics includes: The sorting heuristic rule based on non-ascending processing time is as follows: Sort the set of workpieces according to the non-ascending order of their processing time to generate workpiece dimensional codes; Randomly select a machine from the set of applicable machines corresponding to each workpiece to generate machine dimensional codes. The sorting heuristic rule based on non-decreasing release time is as follows: Sort the set of workpieces according to the non-decreasing order of their release time to generate workpiece dimensional codes; Randomly select a machine from the set of applicable machines corresponding to each workpiece to generate machine dimensional codes. Based on the heuristic rule of compact workpiece size arrangement: Sort the workpiece set in non-ascending order according to workpiece size, and generate workpiece dimension codes by alternately selecting elements from the sorted workpiece sequence at the beginning and end; generate machine dimension codes as follows: For the first workpiece in the workpiece dimension code, randomly select a machine from its applicable machine set; for each subsequent workpiece, first try to reuse the machine assigned to the previous workpiece, if reuse fails, randomly select a machine from the applicable machine set of the current workpiece for allocation; allocate machines to all workpieces in turn, and generate machine dimension codes.

9. A method for scheduling composite material hot pressing production based on a dynamic transmission mechanism of time uncertainty, as described in claim 5, is characterized in that... The process of performing population mating operations generates Initial offspring individuals Specifically, it includes: Selected using a tournament selection method For the parent generation; A random number is generated for each pair of parent individuals. random numbers within ; right Each pair of parent chromosomes undergoes an ERX crossover operation to produce a daughter chromosome; right Each pair of parent chromosomes undergoes an IM mutation operation to produce a daughter chromosome, wherein the IM mutation operation occurs randomly on one of the chromosomes in that pair of parent chromosomes. A daughter chromosome is produced by performing a replication operation on the remaining parent chromosome pair, wherein the replication operation occurs randomly on one of the chromosomes in the parent chromosome pair; The above Each offspring chromosome is converted into an initial offspring individual, decoded, and output.

10. A method for scheduling production of composite material hot pressing based on a dynamic transmission mechanism of time uncertainty, as described in claim 5, is characterized in that... The first offspring individuals Perform local search optimization to obtain optimized offspring individuals. Specifically: For each initial offspring individual Obtain its corresponding scheduling scheme. And calculate the fitness value. The fitness value is the maximum completion time of the processing task in the scheduling scheme; Randomly select an optimization and adjustment strategy and try it on the scheduling scheme. Optimize; if an optimized scheduling scheme is obtained Then, based on the dynamic transmission mechanism of time uncertainty, the calculation is performed. Maximum completion time If an optimized scheduling scheme is not obtained Then this step is performed on the next initial offspring individual; Will and Compare: If satisfied This will optimize the scheduling scheme. The corresponding new individuals are added. ; Otherwise, add the original individual directly. .

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