A scheduling optimization method for hot pressing forming process in aviation composite manufacturing

Abstract

The present invention discloses a scheduling optimization method for the hot press forming process in aviation composite manufacturing, comprising the following steps: Step 1: Based on the hot press forming production plan for aviation composite manufacturing, with the goal of minimizing the total workpiece delay time, a hot press forming production planning scheduling objective function is established; Step 2: A two-dimensional hot press forming process batch scheduling model is established that takes into account the workpiece release time window and machine applicability; Step 3: Using the objective function as the optimization target and the two-dimensional hot press forming process batch scheduling model as the optimization model, a hot press forming production planning scheduling scheme is obtained using a genetic algorithm embedded with an adaptive domain search strategy. This method can significantly reduce the total workpiece delay time while minimizing workpiece processing batches, and reduce the occurrence of prepreg deterioration, creating conditions for improving hot press forming production efficiency and promoting the digital and intelligent transformation and upgrading of composite manufacturing enterprises.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent manufacturing of aviation composites, and in particular relates to a scheduling optimization method for a hot pressing forming process in aviation composite manufacturing. Background Art

[0002] As a vital component of the national economy, the development and progress of the aviation equipment manufacturing industry plays an irreplaceable role in national security, optimizing economic structure, and enhancing international competitiveness. Aviation composites, or aviation composite materials, with their ideal physical and chemical properties, have gradually replaced metal alloys as the primary raw material for aviation equipment manufacturing. The widespread use of composite materials in aviation equipment manufacturing has led to a surge in demand. However, the production characteristics of aviation composites, such as high variety, small batches, and re-entry, result in long production cycles and complex manufacturing processes, leading to a significant imbalance between supply and demand. Traditional composite production management models are unable to meet the demands of current aircraft production, placing higher demands on the production planning and scheduling of composite production systems. As an intermediate step in composite manufacturing, hot press forming (HSP) has the longest processing time, making it a bottleneck process. Traditional process scheduling schemes can easily lead to problems such as insufficient equipment utilization and frequent delays. Therefore, establishing effective scheduling models and algorithms to optimize hot press forming production planning and scheduling is crucial for promoting the transformation and upgrading of aviation composite manufacturing towards digitalization and intelligentization.

[0003] Currently, there is a plethora of research on production scheduling for aviation composite manufacturing. Research on hot press forming scheduling primarily focuses on one-dimensional batch scheduling, which considers variations in workpiece size, workpiece family, and workpiece release time, with the goal of minimizing total completion time. However, existing research often overlooks the limitations of prepreg placement time and machine suitability. Prepreg placement time requires that workpieces be processed in the autoclave before the preforms deteriorate or expire, resulting in variations in workpiece release time windows. Machine suitability means that not all workpieces can be processed in any autoclave model; different workpieces can only be processed on machines that meet their heat treatment parameters and dimensional requirements. Existing technology, such as patent CN118396272A - A Genetic Algorithm-Based Scheduling Optimization Method for Hot Press Forming of Aviation Composites, is only applicable to production scenarios with high requirements for curing process consistency or relatively single-product composite standard parts. In such production scenarios, specific workpiece curing groups can be clearly defined based on the workpiece heat treatment parameters. Each autoclave type processes only one workpiece curing group, and different autoclaves process independent workpieces. Using a single curing group allocation scheme ensures product quality and production efficiency for composite standard parts, while simplifying production management and operations. In terms of the classification criteria for batch scheduling problems, the primary issue addressed is single-machine two-dimensional batch scheduling. Specifically, the production plan for a batch of workpieces processed by a single batch processing machine is determined by the single-machine scheduling problem. The algorithmic approach is to improve population quality using an encoding method and repair operator designed based on the maximum time-compatible workpiece set, and to modify the crossover and mutation operators of the classical genetic algorithm to increase the algorithm's convergence speed and reduce solution time. Summary of the Invention

[0004] In response to the deficiencies of the above-mentioned prior art, the present invention provides a scheduling optimization method for the hot pressing forming process in aviation composite manufacturing, which realizes the optimization of the scheduling scheme for the collaborative processing of multiple non-equivalent batch processing machines in the hot pressing forming and curing process, improves the production efficiency of the hot pressing and curing process, and solves the problems of frequent delays and high workpiece scrap rate in the prior art in the hot pressing forming process.

[0005] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0006] A scheduling optimization method for a hot press forming process in aviation composite manufacturing includes:

[0007] Step 1: Based on the hot press forming production plan for aviation composite manufacturing, the objective function of hot press forming production planning is established with the goal of minimizing the total delay time of the workpiece;

[0008] Step 2: Establish a two-dimensional hot pressing process batch scheduling model considering the workpiece release time window and machine applicability;

[0009] Step 3: Taking the objective function as the optimization target and the two-dimensional hot pressing process batch scheduling model as the optimization model, a genetic algorithm embedded with an adaptive domain search strategy is used to solve and obtain the hot pressing production planning and scheduling solution.

[0010] To optimize the above technical solutions, specific measures taken also include:

[0011] The above step 1 establishes the following hot pressing production scheduling objective function:

[0012] minT(1)

[0013] Where T represents the delay time of all workpieces.

[0014] The two-dimensional hot pressing process batch scheduling model established in step 2 above includes formulas (2) to (27):

[0015] Formula (2) and formula (3) ensure that each workpiece can be allocated only once in the production plan;

[0016] Formula (4) and formula (5) ensure that the release time windows of any two workpieces assigned to a batch of processing are compatible;

[0017] Formula (6) ensures that any workpiece can only be processed by one batch of machines in its applicable set;

[0018] Formula (7) ensures that the workpiece will not be assigned to a machine outside its applicable machine set for processing;

[0019] Formula (8) ensures that workpieces assigned to the same batch must be processed on the same machine;

[0020] Formulas (9) and (10) ensure that any workpiece assigned to a batch of workpieces cannot exceed the edge of the operating platform inside the autoclave;

[0021] Formulas (11) and (12) ensure that any two workpieces assigned to a batch cannot overlap each other;

[0022] Formula (13) is used to ensure the relative positions of any two workpieces assigned to the same batch;

[0023] Through formula (14) and formula (15), it is determined that a batch processing machine can only process one batch of workpieces at a time, and the order of the batches is sorted;

[0024] Determine the delay time of each workpiece using formula (16);

[0025] The total delay time of the allocation scheme is determined by formula (17), where T represents the delay time of all workpieces; the value range of each variable is determined by formula (18)-formula (27), where M is a positive number;

[0026]

[0027]

[0028] The meanings of the variables and parameters in the above model are as follows:

[0029] Collections and Indexes:

[0030] N = {1, 2, ..., n}: represents the set of all workpieces, where n is the number of workpieces;

[0031] M = {1, 2, ..., m}: indicates the machine type, where m indicates the number of machine types.

[0032] B = {1, 2, ..., b}: represents the set of all batches, b is the number of batches;

[0033] i,i′,i″: workpiece index, i,i′,i″∈N;

[0034] j: machine index, j∈M;

[0035] parameter:

[0036] w i ,h i : width and height of the workpiece,

[0037] p i : Processing time of the workpiece,

[0038] d i : expected delivery time of the artifact,

[0039] est i ,lst i : represent the earliest processing time and the latest processing time of the workpiece, i∈N;

[0040] Decision variables:

[0041] u i′i : 0-1 variable, if workpiece i and workpiece i' are assigned to the same batch, it is 1, otherwise it is 0,

[0042] e ii′ : 0-1 variable, if both workpieces i and i′ are critical workpieces and i is processed before i′, then it is 1, otherwise it is 0;

[0043] o i : 0-1 variable, equal to 1 if the height of the i-th workpiece is parallel to the width of the machine (the workpiece is rotated 90°), otherwise equal to 0;

[0044] l i,m : 0-1 variable, which is 1 if the i-th workpiece is processed on the m-th machine, otherwise it is 0;

[0045] a ii′ : 0-1 variable, 1 if the i-th workpiece is to the left of the i′th workpiece, otherwise 0;

[0046] b ii′ : 0-1 variable, 1 if the i-th workpiece is at the bottom of the i′th workpiece, otherwise 0;

[0047] x i : integer variable, the horizontal coordinate of the lower left corner of workpiece i;

[0048] y i : integer variable, the vertical coordinate of the lower left corner of workpiece i;

[0049] c i : integer variable, actual completion time of job i;

[0050] t i : integer variable, the delay time of job i.

[0051] The solution process of the above genetic algorithm embedded with adaptive domain search strategy is as follows:

[0052] (1) Determine the optimization objective and optimization model: take the objective function established in step 1 as the optimization objective, and the model established in step 2 as the optimization model;

[0053] (2) Determine the encoding strategy: Using the integer encoding method, a chromosome is decoded to obtain a solution to the problem. The number of genes on a chromosome is determined by the number of artifacts in the problem. The gene numbers on the chromosome represent different artifact numbers. The order of artifact numbers on the chromosome determines the priority of the artifacts when allocating batches.

[0054] (3) Determine the decoding strategy: Use the earliest completed machine first heuristic decoding strategy EMM to decode the chromosome and obtain the corresponding workpiece scheduling plan;

[0055] (4) Determine the termination condition and fitness function: The termination condition is to determine whether the current number of iterations I is greater than the maximum number of iterations Gen; the fitness function is the total completion time function of the workpiece, and its calculation formula is: f = ∑ i∈N t i , where t iis an integer variable, the delay time of job i;

[0056] (5) Initialize the population and perform fitness evaluation: Generate the initial chromosome coding gene sequence based on the maximum time compatible artifact set segmentation;

[0057] (6) Perform selection, crossover, and mutation operations to calculate the fitness of the new individual;

[0058] (7) Perform adaptive neighborhood search operations to improve population quality.

[0059] The above EMM process is as follows:

[0060] Select a machine to initialize a batch. The machine selection follows the rule of giving priority to the batch machine with the shortest completion time. If the total completion time of all machines is the same, the batch machine with the largest size is given priority. Add workpieces to the batch in order of coding until no new workpieces can be added to the batch. Close the current batch, reselect a machine to initialize a new batch, and repeat the operation until all workpieces are assigned to the batch.

[0061] The crossover strategy adopted by the above crossover operation is: given a crossover probability p c , for a pair of parent chromosomes, randomly generate a probability p, if p≤p c , then select several genes at random positions in the parent chromosome 1. The positions of the genes may not be continuous. Keep the order of the selected genes in chromosome 1 and record them as gene fragment A. Keep the order of all genes in chromosome 2 except gene fragment A. Replace the vacant positions in chromosome 2 according to the gene order in gene fragment A to generate daughter chromosome 1. Select the genes at the same position in chromosome 2 and record them as gene fragment B. Repeat the same operation with chromosome 1 as the base to generate daughter chromosome 2.

[0062] The mutation strategy adopted by the mutation operation is: given a mutation probability p m , for each individual in the current population, randomly generate a probability p, if p≤p m , then perform the mutation operation, the specific operation is: randomly select a time compatible artifact set K s , K s The order of all genes in the chromosome is reversed, and then inserted into the original gene positions in the chromosome in order to generate daughter chromosomes.

[0063] The above adaptive neighborhood search strategy is as follows:

[0064] During the algorithm iteration process, when the crossover and mutation operators of the nth iteration are executed, the roulette wheel is initialized or generated based on the scores of the previous generation of neighborhood search operators. The specific operation is: the selection probability p of the search operator in each field of the current population is generated according to the following formula (ns,n) , using roulette wheel to select a neighborhood search strategy for each individual in the population, where the neighborhood search operator selects the probability p (ns,n) The calculation formula is:

[0065]

[0066] Where w (ns,n-1) It represents the cumulative score weight of the neighborhood search operator ns in the n-1 generation. The score weight calculation formula of each field search operator ns in the nth generation is w (ns,n) for:

[0067]

[0068] Among them, r is a parameter, which indicates the influence of the probability of the previous generation of neighborhood search operators being selected on the next generation; search_time ns Indicates the number of times the neighborhood search operator ns has found a neighborhood solution during the neighborhood search process of the nth generation population; score ns It represents the final score of each neighborhood search operator after the neighborhood search for the nth generation population. The scoring rule is as follows: each individual in the current population is regarded as the current solution. If the neighborhood solution obtained after the neighborhood search is better than the current solution, the corresponding neighborhood search operator score is increased by σ1. If the neighborhood solution is better than the global optimal solution, the corresponding neighborhood search operator score is additionally increased by σ2. If the quality of the neighborhood solution is worse than the current solution, the neighborhood search operator score remains unchanged, and σ1 is less than σ2.

[0069] The adaptive neighborhood search described above is equipped with an adjustment operator MTJ for the maximum delayed workpiece, which is used to insert the workpiece with the largest total delay time into the batch of the same batch processor with better adaptability. The specific process is as follows:

[0070] Record the workpiece i with the longest delay in the entire allocation plan; filter all batches corresponding to all workpieces in the maximum time compatible workpiece set to which workpiece i belongs and select all batches B that meet the machine compatibility of workpiece i. i ; Construct a score function f to evaluate the adaptability of workpieces and batches b ; Generate a roulette wheel based on the scores of each batch to evaluate the adaptability of the workpiece and batch, select a batch according to probability and insert the workpiece into the batch, and adjust the encoding of the chromosome individual; the score function f for evaluating the adaptability of the workpiece and batch b The calculation formula is as follows:

[0071]

[0072] in, Indicates the earliest processing start time est for batch b b and the earliest start processing time est of workpiece i i The difference, The larger it is, the closer the release time of job i is to the earliest processing start time of batch b; Indicates the latest start processing time lst for batch b b and the latest processing start time lst of workpiece i i The difference, The larger it is, the closer the external time of workpiece i is to the latest processing start time of batch b; is a piecewise function, when p b -p i ≥0, that is, when the batch processing time is not less than the workpiece processing time, When p b -p i <0, that is, when the processing time of the workpiece exceeds the processing time of the batch, Used to evaluate the impact of workpiece i on the processing time of batch b before and after insertion. When , it means that after workpiece i is inserted into batch b, the processing time of the entire batch will not increase. When , it means that after workpiece i is added to batch b, the number of workpieces processed in the batch increases to the processing time of the workpiece. At this time, the greater the difference between the processing time of the workpiece and the processing time of the batch, The smaller it is; α represents the degree of influence of the compatibility between the release time window of the workpiece and the time window in which the batch can start processing on the batch adaptability, β represents the influence of the workpiece processing time on the batch adaptability, α+β=1.

[0073] The adaptive neighborhood search described above is equipped with an adjustment operator MTB for the batch with the largest delay on the same batch processing machine, which is used to adjust the batch with the longest total delay time in the solution with other batches on the same batch processing machine. The specific process is as follows:

[0074] Select the batch b1 with the longest total delay time, record the batch processing machine that processes batch b1 as M; select the batches in batch processing machine M that are less than the start processing time of batch b1 to form a set B, and randomly select a batch b2 from the batch set B; take out all the workpieces in batches b1 and b2 to form a workpiece set J, and calculate the workpieces according to the workpiece w i ×h i / d iThe purpose is to prioritize the processing of workpieces with earlier expected delivery time and larger size; replace the gene fragments corresponding to the workpiece set J in the chromosome according to the re-sorted workpiece order, where w i ,h i is the width and height of the workpiece; d i The expected delivery time of the workpiece.

[0075] The adaptive neighborhood search described above is equipped with an adjustment operator MTM for batches between different batch processing machines. This operator is used to adjust the batch with the largest total delay time on a random batch processing machine in the scheme to the batch on a batch processing machine with better adaptability. The specific process is as follows:

[0076] Randomly select a batch machine M1 and record the batch b1 with the largest total delay time on batch machine M1; based on the applicable machine set of all workpieces in batch b1, select the batch machine M2 that is most suitable for adjusting batch b1; select all batches in M2 with a completion time less than that of batch b1 and randomly select a batch b2 as the adjusted batch; merge the workpieces in batches b1 and batch b2, delete the workpieces that cannot be applied to both batch machines M1 and M2, and form a workpiece set J. All workpieces in set J are sorted according to w i ×h i / d i The values ​​of are sorted in descending order to ensure that the workpieces with more urgent delivery tasks and higher space utilization efficiency of batch processing machines are processed first; the gene fragments corresponding to set J in the chromosome are replaced according to the order of the workpieces in set J, where w i ,h i is the width and height of the workpiece; d i The expected delivery time of the workpiece.

[0077] The present invention has the following beneficial effects:

[0078] Based on the existing research on the scheduling problem of hot press molding of aviation composite materials, the present invention studies the two-dimensional batch scheduling problem with the constraints of prepreg external time and machine applicability, targeting the external time of prepreg, the machine applicability of workpieces and the two-dimensional spatial characteristics. A mixed integer programming batch scheduling model for hot press molding process is established with the objective function of minimizing the total delay time of workpieces. In response to the research problem, a genetic algorithm is called to design a genetic algorithm with an adaptive neighborhood search strategy based on the concept of maximum time-compatible workpiece set according to the characteristics of prepreg external time. sets, ANSGA-MTC) is used to solve the model. By applying decoding, crossover and mutation strategies to this problem, the solution accuracy is improved, and the workpiece batching and batch scheduling can be automatically realized to minimize the total delay time of the workpiece. It can significantly reduce the total delay time of the workpiece while minimizing the workpiece processing batches, and reduce the occurrence of prepreg deterioration, creating conditions for improving the production efficiency of hot pressing molding and promoting the digital and intelligent transformation and upgrading of composite manufacturing enterprises. It solves the problem of frequent delays or expired workpieces wasted due to the constraint of prepreg external time in hot pressing molding manufacturing, optimizes the scheduling scheme of hot pressing molding manufacturing, and improves the overall production efficiency of composite manufacturing.

[0079] The present invention is applicable to various production and manufacturing scenarios of composite standard parts. In such production scenarios, order requirements are variable and the types of workpieces are diverse. Therefore, there are many workpiece curing groups divided and the distinction between them is not obvious. In order to make full use of equipment resources, enterprises will use workpiece collaborative processing allocation solutions. The workpieces processed by different autoclaves are neither independent nor completely the same, which limits the applicability of the machines.

[0080] The present invention addresses the production and processing of multiple batch processing machines, a parallel machine scheduling problem. These batch processing machines vary in size, model, and production capacity. Existing technologies address single-machine batch scheduling, which is not equivalent to the two-dimensional batch scheduling problem of identical parallel machines. Single-machine batch scheduling and parallel machine batch scheduling are distinct branches of machine scheduling, and unequal parallel machines represent a more complex aspect of parallel machine scheduling.

[0081] In addition to using the same encoding method to improve population quality, the present invention does not change the crossover and mutation method of the classic genetic algorithm. Instead, it designs three types of neighborhood search actions and an adaptive neighborhood search mechanism based on the concept of the maximum time-compatible artifact set to accelerate the convergence of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0083] Figure 1 A schematic diagram of a method flow chart provided in an embodiment of the present invention;

[0084] Figure 2 An algorithm flow chart of a specific example provided in an embodiment of the present invention;

[0085] Figure 3 Flowchart of NSGA-MTC chromosome decoding (EMM algorithm) provided in an embodiment of the present invention;

[0086] Figure 4 A chromosome encoding flow chart based on a maximum time compatible set design provided by an embodiment of the present invention;

[0087] Figure 5 Flowchart of the NSGA-MTC chromosome crossover (OBX algorithm) provided in an embodiment of the present invention;

[0088] Figure 6 Flowchart of the NSGA-MTC chromosome mutation (MTCIM algorithm) provided in an embodiment of the present invention;

[0089] Figure 7 The MTJ neighborhood search operator provided by the embodiment of the present invention;

[0090] Figure 8 The MTB neighborhood search operator provided by the embodiment of the present invention;

[0091] Figure 9 The MTM neighborhood search operator provided by the embodiment of the present invention;

[0092] Figure 10 Genetic algorithm iteration diagram for a specific example provided for implementation of the present invention;

[0093] Figure 11 A schematic diagram of the device structure provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0094] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0095] Although the steps in the present invention are arranged with numbers, they are not intended to limit the order of the steps. Unless the order of the steps is clearly stated or the execution of a step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" used herein refers to and covers any and all possible combinations of one or more of the associated listed items.

[0096] The embodiment of the present invention provides a scheduling optimization method for the hot pressing forming process of aviation composite manufacturing. An optimization model is established for the scheduling problem of the hot pressing forming process of aviation composites. A mixed integer programming model is established to minimize the total delay time of the workpiece. The effectiveness of the model is verified using the gurobi solver. However, as the scale of the problem increases, the solution efficiency of the gurobi solver obviously cannot meet the requirements of actual production. Therefore, the present invention designs a genetic algorithm to solve the problem according to the actual problem, so as to achieve the overall optimization of the large-scale workpiece batch scheduling scheme and solve the two-dimensional parallel batch scheduling problem of aviation composite hot pressing forming. Figure 1 As shown, specifically including:

[0097] Step 1: Based on the hot press forming production plan for aviation composite manufacturing, the objective function of hot press forming production planning is established with the goal of minimizing the total delay time of the workpiece;

[0098] Step 2: Establish a two-dimensional hot pressing process batch scheduling model considering the workpiece release time window and machine applicability;

[0099] Step 3: Taking the objective function as the optimization target and the two-dimensional hot pressing process batch scheduling model as the optimization model, a genetic algorithm embedded with an adaptive domain search strategy is used to solve and obtain the hot pressing production planning and scheduling solution.

[0100] In the embodiment, step 1 obtains workpiece processing information and autoclave model information of the enterprise's periodic planned order, and determines the objective function of the hot pressing manufacturing scheduling task based on the production plan information and plan requirements, including:

[0101] Collect order information during the scheduling period of the hot pressing process of a composite manufacturing company within a production cycle (month / week / day), as well as the model, size, and processing parameters of the autoclave in the hot pressing process workshop. Combined with the company's needs, determine the objective function for hot pressing workpiece scheduling:

[0102] minT(1)

[0103] Where T represents the delay time of all workpieces.

[0104] The auxiliary material manufacturing production information includes at least: the size information of the workpiece (length and width), the heat treatment processing time required for the workpiece, the expected delivery time of the order to which the workpiece belongs, the set of applicable autoclave models for the workpiece, the workpiece release time window determined by the prepreg, and the size information (length and width) of the internal operating platform of different models of autoclaves, etc.

[0105] Step 2: Establish a two-dimensional batch scheduling model corresponding to the objective function, taking into account the workpiece release time window and machine applicability, including:

[0106] Based on the objective function, a batch scheduling model for the hot press forming process was established, taking into account the workpiece release time window. The model's constraints include: all workpieces must be scheduled for processing; the autoclave can only process one batch of workpieces at a time; workpieces belonging to the same batch must meet time and space constraints; and workpieces can only be processed by the appropriate machine.

[0107] In step 2, the two-dimensional batch scheduling model considering the workpiece release time window and machine applicability requires

[0108] All workpieces can only be assigned to one batch for processing.

[0109] Constraints are imposed on workpieces assigned to the same batch, including: workpieces in each batch cannot be placed overlappingly; they cannot exceed the edge of the operating platform inside the autoclave; and the intersection of the release time windows of each batch of workpieces cannot be an empty set.

[0110] Each workpiece can only be machined by a machine that has the sum of its machine suitability sets.

[0111] In step 2, the two-dimensional batch scheduling model considering the job release time window and machine availability includes:

[0112] Formula (2) to Formula (16):

[0113] Formula (2) and formula (3) ensure that each workpiece can be allocated only once in the production plan;

[0114] Formula (4) and formula (5) ensure that the release time windows of any two workpieces assigned to a batch of processing are compatible;

[0115] Formula (6) ensures that any workpiece can only be processed by one batch of machines in its applicable set;

[0116] Formula (7) ensures that the workpiece will not be assigned to a machine outside its applicable machine set for processing;

[0117] Formula (8) ensures that workpieces assigned to the same batch must be processed on the same machine;

[0118] Formulas (9) and (10) ensure that any workpiece assigned to a batch of workpieces cannot exceed the edge of the operating platform inside the autoclave;

[0119] Formulas (11) and (12) ensure that any two workpieces assigned to a batch cannot overlap each other;

[0120] Formula (13) is used to ensure the relative positions of any two workpieces assigned to the same batch;

[0121] Through formula (14) and formula (15), it is determined that a batch processing machine can only process one batch of workpieces at a time, and the order of the batches is sorted;

[0122] Determine the delay time of each workpiece using formula (16);

[0123] The total delay time of the allocation scheme is determined by formula (17).

[0124] The value range of each variable is determined by formula (18)-formula (27), where M is a sufficiently large positive number.

[0125]

[0126] The meanings of the variables and parameters in the model are as follows:

[0127] (1) Collections and Indexes

[0128] N = {1, 2, ..., n}: represents the set of all workpieces, and n is the number of workpieces.

[0129] M = {1, 2, ..., m}: indicates the machine type, and m indicates the number of machine types.

[0130] B = {1, 2, ..., b}: represents the set of all batches, b is the number of batches.

[0131] i,i′,i″: workpiece index, i,i′,i″∈N.

[0132] j: machine index, j∈M.

[0133] (2) Parameters

[0134] w i ,h i : width and height of the workpiece,

[0135] p i : Processing time of the workpiece,

[0136] d i: expected delivery time of the artifact,

[0137] est i ,lst i : They represent the earliest processing start time and the latest processing start time of the workpiece, i∈N.

[0138] (3) Decision variables

[0139] u i′i : 0-1 variable, if workpiece i and workpiece i' are assigned to the same batch, it is 1, otherwise it is 0,

[0140] e ii′ : 0-1 variable, if both workpieces i and i′ are critical workpieces and i is processed before i′, then it is 1, otherwise it is 0.

[0141] o i : 0-1 variable, equal to 1 if the height of the i-th workpiece is parallel to the width of the machine (the workpiece is rotated 90°), otherwise equal to 0.

[0142] l i,m : A 0-1 variable, which is 1 if the i-th workpiece is processed on the m-th machine, and 0 otherwise.

[0143] a ii′ : 0-1 variable, which is 1 if the i-th workpiece is to the left of the i′th workpiece, and 0 otherwise.

[0144] b ii′ : 0-1 variable, equal to 1 if the i-th workpiece is at the bottom of the i′th workpiece, otherwise equal to 0.

[0145] x i : Integer variable, the horizontal coordinate of the lower left corner of workpiece i.

[0146] y i : Integer variable, the vertical coordinate of the lower left corner of workpiece i.

[0147] c i : integer variable, the actual completion time of job i.

[0148] t i : integer variable, the delay time of job i.

[0149] In step 3, based on the concept of maximum time-compatible job sets, a genetic algorithm with adaptive neighborhood search strategy (ANSGA-MTC) is designed to solve the batch scheduling model of the hot pressing process, and a hot pressing production plan scheduling scheme is generated according to the algorithm solution results.

[0150] In this embodiment, Python programming is used to improve the genetic algorithm, and ANSGA-MTC is used to simulate and analyze the hot pressing batch scheduling model to obtain the minimum total delay time of the workpiece. Figure 2 As shown in Figure 2, the solution process based on ANSGA-MTC is as follows:

[0151] (1) Determine the optimization goal and establish the optimization model;

[0152] (2) Determine the encoding method;

[0153] ANSGA-MTC uses an integer encoding method. After decoding a chromosome, a solution to the problem is obtained. The number of genes on a chromosome is determined by the number of artifacts in the problem. The gene numbers on the chromosome represent different artifact serial numbers. The order of the artifact serial numbers on the chromosome determines the priority of the artifacts when allocating batches.

[0154] (3) Determine the decoding method

[0155] After assigning workpieces a priority order based on the encoding strategy, a decoding process is designed to decode the encoded individuals and obtain the corresponding workpiece scheduling scheme. Based on the two classic production scheduling rules of first-come-first-served and earliest-delivery-due workpieces, this paper designs a heuristic decoding method (earliest makespan machine first, EMM) to decode chromosomes.

[0156] like Figure 3 As shown in Figure 1, the general process of EMM is to select a suitable machine to initialize an empty batch. Machine selection follows the principle of prioritizing the batch machine with the shortest completion time. If the total completion time of all machines is the same, the batch machine with the largest size is selected first. This is done to minimize the number of processing batches and the total planned completion time. After batch initialization is completed, workpieces are added to the batch in order of coding until the batch can no longer contain new workpieces. The current batch is closed, and a new machine is selected to initialize a new batch. This cycle repeats until all workpieces are assigned to the batch.

[0157] (4) Determine the termination condition and fitness function: The termination condition is to determine whether the current number of iterations I is greater than the maximum number of iterations Gen. The fitness value is the total completion time of the workpiece, and its calculation formula is: f = ∑ i∈N t i , where t i is an integer variable, the delay time of job i

[0158] (5) Initialize the population and perform fitness evaluation.

[0159] Because the initial population encoding of the classic genetic algorithm is random, when considering the time window for releasing artifacts, the initial population contains many infeasible individuals and the population quality is very poor. Therefore, this method introduces the concept of a maximum time-compatible artifact set and generates the chromosome encoding gene sequence segmentally based on this set. Figure 4 An example of generating individual chromosomes from a maximum set of time-compatible artifacts is shown.

[0160] (6) Perform selection, crossover and mutation operations and calculate the fitness of the new individual.

[0161] ANSGA-MTC uses the Order-Based Crossover (OBX) crossover method to ensure the global search capability of the algorithm while retaining the excellent gene fragments of the parent chromosome. Figure 5 As shown, given a crossover probability p c , for a pair of parent chromosomes, randomly generate a probability p, if p≤p c , then select several genes at random positions in parent chromosome 1. The gene positions can be discontinuous, and retain the order of the selected genes in chromosome 1, which is recorded as gene segment A. Retain the order of all genes in chromosome 2 except gene segment A, and replace the vacant positions in chromosome 2 according to the gene sequence in gene segment A to generate daughter chromosome 1. Select the gene at the same position in chromosome 2 and record it as gene segment B. Repeat the same operation once with chromosome 1 as the base to generate daughter chromosome 2.

[0162] ANSGA-MTC adopts the Max Time-compatible Job Set Inverse Mutation (MTCIM) strategy to ensure the quality of individual solutions in the population while improving the algorithm's global search capabilities. Figure 6 As shown, given a mutation probability p m For each individual in the current population, a probability p is randomly generated. If p≤p m , then perform the mutation operation. The specific operation is to randomly select a maximum time compatible artifact set K s , K sThe order of all genes in the chromosome is reversed, and then inserted into the original gene positions in the chromosome in order to generate daughter chromosomes.

[0163] (7) Perform adaptive neighborhood search operations to improve population quality. The adaptive neighborhood selection strategy is as follows:

[0164] The adaptive selection mechanism of ANSGA-MTC is that when the crossover and mutation operators of the nth iteration are completed during the algorithm iteration, the roulette wheel is initialized or generated based on the scores of the previous generation of neighborhood search operators. The specific operation is to generate the selection probability p of the search operator in each field of the current population according to the following formula: (ns,n) , using roulette wheel to select the neighborhood search strategy for each individual in the population, the domain search operator selects the probability p (ns,n) The calculation formula is:

[0165]

[0166] where w (ns,n-1) It represents the cumulative score weight of the neighborhood search operator (ns) in the n-1 generation. The score weight calculation formula of each field search operator (ns) in the nth generation is w (ns,n) for:

[0167]

[0168] Among them, r is a parameter, which represents the influence of the probability of the previous generation of neighborhood search operators being selected on the next generation. When r = 0, it means that the probability of the neighborhood search operator being selected is completely determined by the score after the nth generation of neighborhood search. When r = 1, it means that the probability of the neighborhood search operator being selected is determined by the cumulative score of the previous n-1 generations. In general, let r = 0.5. ns Indicates the number of times the neighborhood search operator ns has searched for neighborhood solutions during the neighborhood search process of the nth generation population, score ns It represents the final score of each neighborhood search operator after the neighborhood search for the nth generation population. The scoring rule is as follows: each individual in the current population is regarded as the current solution. If the neighborhood solution obtained after the neighborhood search is better than the current solution, the corresponding neighborhood search operator score is increased by σ1 (the default is 1). If the neighborhood solution is better than the global optimal solution, the corresponding neighborhood search operator score is additionally increased by σ2 (the default is 2). If the quality of the neighborhood solution is worse than the current solution, the neighborhood search operator score remains unchanged.

[0169] The neighborhood search strategies used in this algorithm include three types of operators: adjustment for the maximum delayed workpiece (MTJ), adjustment for the maximum delayed batch on the same batch processor (MTB), and adjustment for batches between different batch processors (MTM). The specific neighborhood search operators are described as follows:

[0170] like Figure 7 As shown in Figure 2, the MTJ neighborhood search operator inserts the workpiece with the largest total delay time into the batch of the same batch processor with better adaptability. The specific process is as follows:

[0171] The first step is line 1 of the code, which is responsible for recording the workpiece i with the longest delay in the entire allocation plan;

[0172] The second step is line 3 of the code, which is responsible for filtering all batches corresponding to all workpieces in the maximum time compatible workpiece set to which workpiece i belongs and filtering out all batches B that meet the machine compatibility of workpiece i. i ;

[0173] The third step is line 4 of the code, which is responsible for constructing the scoring function f to judge the adaptability of the workpiece and batch. b ;

[0174] Finally, in lines 5-6 of the code, we are responsible for generating a roulette wheel based on the fitness scores of each batch, selecting a batch by probability and inserting the artifact into the batch, and adjusting the encoding of the chromosome individuals.

[0175] In the first step, the score function f that evaluates the suitability of artifacts and batches is b The calculation formula is as follows:

[0176]

[0177] in, Indicates the earliest processing start time est for batch b b and the earliest start processing time est of workpiece i i The difference, The larger it is, the closer the release time of job i is to the earliest processing start time of batch b; Indicates the latest start processing time lst for batch b b and the latest processing start time lst of workpiece i i The difference, similarly, The larger it is, the closer the external time of workpiece i is to the latest processing start time of batch b; is a piecewise function, when p b -p i ≥0, that is, when the batch processing time is not less than the workpiece processing time, When p b -p i <0, that is, when the processing time of the workpiece exceeds the processing time of the batch, Used to evaluate the impact of workpiece i on the processing time of batch b before and after insertion. When , it means that after workpiece i is inserted into batch b, the processing time of the entire batch will not increase. When , it means that after workpiece i is added to batch b, the number of workpieces processed in the batch increases to the processing time of the workpiece. At this time, the greater the difference between the processing time of the workpiece and the processing time of the batch, The smaller the value, the smaller the impact. α represents the degree of compatibility between the workpiece release window and the batch processing start window on batch adaptability, while β represents the impact of the workpiece processing time on batch adaptability, with α + β = 1. When α = 1 and β = 0, the feasibility of inserting a workpiece into a batch is evaluated based solely on whether the workpiece's insertion into the batch affects the batch processing start window. When α = 0 and β = 1, the feasibility of inserting a workpiece into the batch is evaluated based solely on whether the workpiece's insertion into the batch affects the batch processing time. Generally, α = 0.5 and β = 0.5 are used.

[0178] like Figure 8 As shown in Figure 2, the MTB neighborhood search operator adjusts the solution with the longest total delay time with other batches in the same batch of processors. The specific process is as follows:

[0179] The first step is lines 2-3 of the code, which is responsible for selecting the batch b1 with the longest total delay time and recording the batch processing machine that processed batch b1, denoted by M;

[0180] The second step is lines 4-5 of the code, which is responsible for screening the batches in batch machine M that have a processing time less than that of batch b1 to form a set B, and randomly selects a batch b2 from the batch set B;

[0181] The third step is line 6 of the code, which is responsible for taking out all the workpieces in batches b1 and b2 to form a workpiece set J, and then i ×h i / d i The purpose is to prioritize the processing of workpieces with earlier expected delivery time and larger size, where w i ,h i is the width and height of the workpiece; d i The expected delivery time of the workpiece.

[0182] Finally, in line 7 of the code, the gene segments corresponding to the artifact set J in the chromosome are replaced according to the reordered artifact sequence.

[0183] like Figure 9 As shown in Figure 2, the MTM neighborhood search operator adjusts the batch with the largest total delay time on a random batch processing machine in the solution with the batch on a batch processing machine with better adaptability. The specific process is as follows:

[0184] The first step is lines 2-3 of the code, which randomly selects a batch processing machine M1 and records the batch b1 with the largest total delay time on batch processing machine M1;

[0185] The second step is lines 4-5 of the code, which is responsible for selecting the batch processing machine M2 that is most suitable for adjusting batch b1 based on the applicable machine set of all workpieces in batch b1;

[0186] The third step is line 6 of the code, which is responsible for filtering out all batches in M2 whose completion time is less than batch b1 and randomly selecting a batch b2 as the adjusted batch;

[0187] The fourth step is to merge the workpieces in batches b1 and b2, delete the workpieces that cannot be used by batch machines M1 and M2 at the same time, and form a workpiece set J. All workpieces in set J are sorted according to w i ×h i / d i The values ​​are sorted in descending order to ensure that workpieces with more urgent delivery tasks and higher space utilization efficiency of batch processing machines are processed first;

[0188] Finally, the gene segments corresponding to set J in the chromosome are replaced according to the order of the artifacts in set J.

[0189] Below, we construct an example of scheduling a hot press forming process, using the ANSGA-MTC algorithm of our invention to solve it. We optimize the production plan for a specific day at Factory M, where the planned workpiece dimensions are shown in Table 1. The factory has three types of autoclaves, with their dimensions shown in Table 2.

[0190] Table 1 Weekly plan workpiece information for hot pressing process of a certain curing group

[0191]

[0192]

[0193] Table 2 Dimensions of operating platforms for different types of autoclaves

[0194]

[0195] The above processing information is input into the ANSGA-MTC of the present invention, and the crossover probability cr=0.9 and the mutation probability mr=0.1 are set, the population size pop=100, and the maximum number of iterations maxgen=100.

[0196] Using ANSGA-MTC, we can repeat the solution 10 times and take the average value. The algorithm iteration diagram is shown as follows: Figure 10 As shown in Figure 2, it can be seen that the algorithm can converge after 40 iterations, with fast convergence speed and short solution time.

[0197] The workpiece batching scheme generated by ANSGA-MTC is shown in Table 3, and the factory's original production plan is shown in Table 4. A comparison of the two plans shows that the ANSGA-MTC solution significantly improves delays, reducing the total workpiece delay from 43 hours in the original solution to 9 hours, a 79% reduction, significantly improving the production efficiency of hot press forming.

[0198] Table 3 ANSGA-MTC solution schedule

[0199]

[0200]

[0201] Table 4 Factory original plan

[0202]

[0203] like Figure 11 As shown, the present invention also designs an aviation composite hot pressing forming process scheduling system, which can be embedded in the MES system of the composite manufacturing enterprise, including:

[0204] Production information collection module, used for workpiece processing information and autoclave model information of enterprise cycle planning orders;

[0205] The planning and demand analysis module is used to set the hot pressing molding scheduling objective function based on the preset production plan information and scheduling requirements;

[0206] A planning and scheduling module, configured to establish a two-dimensional parallel machine batch scheduling model associated with the objective function;

[0207] The information processing module is used to solve the two-dimensional parallel machine batch scheduling model using ANSGA-MTC to obtain a workpiece production plan scheduling solution.

[0208] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0209] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A scheduling optimization method for hot pressing forming process in aviation composite manufacturing, characterized in that: include: Step 1: Based on the hot press forming production plan for aviation composite manufacturing, the objective function of hot press forming production planning is established with the goal of minimizing the total delay time of the workpiece; Step 2: Establish a two-dimensional hot pressing process batch scheduling model considering the workpiece release time window and machine applicability; Step 3: Taking the hot press forming production planning and scheduling objective function as the optimization target and the two-dimensional hot press forming process batch scheduling model as the optimization model, a genetic algorithm embedded with an adaptive neighborhood search strategy is used to solve the hot press forming production planning and scheduling solution; Adaptive neighborhood search is equipped with an adjustment operator MTJ for the maximum delayed workpiece, which is used to insert the workpiece with the largest total delay time into the batch of the same batch processor with better adaptability: Record the workpiece i with the longest delay in the entire allocation plan; filter all batches corresponding to all workpieces in the maximum time compatible workpiece set to which workpiece i belongs and select all batches B that meet the machine compatibility of workpiece i. i ; Construct a score function f to evaluate the adaptability of workpieces and batches b ; Generate a roulette wheel based on the scores of each batch to evaluate the adaptability of the workpiece and batch, select a batch according to probability and insert the workpiece into the batch, and adjust the encoding of the chromosome individual; the score function f that evaluates the adaptability of the workpiece and batch b The calculation formula is as follows: ； , which means the earliest processing start time est of batch b b and the earliest start processing time est of workpiece i i The difference, The larger it is, the closer the release time of job i is to the earliest processing start time of batch b; , indicating the latest start processing time lst of batch b b and the latest processing start time lst of workpiece i i The difference, The larger it is, the closer the external time of workpiece i is to the latest processing start time of batch b; is a piecewise function, when p b -p i ≥0, that is, when the batch processing time is not less than the workpiece processing time, When p b -p i <0, that is, when the processing time of the workpiece exceeds the processing time of the batch, ; Used to evaluate the impact of workpiece i on the processing time of batch b before and after insertion. When , it means that after workpiece i is inserted into batch b, the processing time of the entire batch will not increase. When , it means that after workpiece i is added to batch b, the number of workpieces processed in the batch increases to the processing time of the workpiece. At this time, the greater the difference between the processing time of the workpiece and the processing time of the batch, The smaller it is; α represents the degree of influence of the compatibility between the release time window of the workpiece and the start processing time window of the batch on the batch adaptability, β represents the influence of the workpiece processing time on the batch adaptability, α+β=1; Adaptive neighborhood search has an adjustment operator MTB for the maximum delayed batch on the same batch processing machine, which is used to adjust the batch with the longest total delay time in the solution with other batches in the same batch processing machine: Select the batch b1 with the longest total delay time, record the batch processing machine that processes batch b1 as M; select the batches in batch processing machine M that are less than the start processing time of batch b1 to form a set B, and randomly select a batch b2 from the batch composition set B; take out all the workpieces in batches b1 and b2 to form a workpiece set J, and sort them according to the workpiece The purpose is to prioritize the processing of workpieces with earlier expected delivery time and larger size; replace the gene fragments corresponding to the workpiece set J in the chromosome according to the re-sorted workpiece order, where w i ,h i is the width and height of the workpiece; d i The expected delivery time of the workpiece; Adaptive neighborhood search has an adjustment operator MTM for batches between different batch processing machines, which is used to adjust the batch with the largest total delay time on a random batch processing machine in the scheme with the batch on a batch processing machine with better adaptability: Randomly select a batch machine M1 and record the batch b1 with the largest total delay time on batch machine M1; based on the applicable machine set of all workpieces in batch b1, select the batch machine M2 that is most suitable for adjusting batch b1; select all batches in M2 with a completion time less than that of batch b1 and randomly select a batch b2 as the batch to be adjusted; merge the workpieces in batches b1 and batch b2, delete the workpieces that cannot be applied to both batch machines M1 and M2, and form a workpiece set J. All workpieces in set J are sorted according to The values ​​of are sorted in descending order to ensure that the workpieces with more urgent delivery tasks and higher space utilization efficiency of batch processing machines are processed first; the gene fragments corresponding to set J in the chromosome are replaced according to the order of the workpieces in set J, where w i ,h i is the width and height of the workpiece; d i The expected delivery time of the workpiece.

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