A method and system for curing scheduling of aerospace composites considering multi-layer space and time window constraints

Abstract

The application discloses a kind of considering multi-layer space and time window constraint's aviation composite curing scheduling method and system, the method is for the space constraint of multi-layer board equipment in aviation composite curing production, workpiece time window limit and batch processing demand, with minimizing maximum completion time as objective function, construct the single machine batch scheduling model of fusion multi-layer space placement, layer board capacity, time window constraint, while solving by using the evolutionary algorithm of combining adaptive neighborhood search, population initialization of time compatibility and random combination is designed for composite curing scheduling characteristics, multi-dimensional neighborhood search operator, double-layer adaptive neighborhood selection and other improvement strategies, improve the global search and local optimization ability of evolutionary algorithm, significantly improve the solution quality and efficiency of composite curing scheduling under complex constraint.The application can be widely applied to aviation composite forming, heat treatment furnace scheduling and other complex manufacturing scenarios with multi-layer processing space, time window constraint and batch processing characteristics.

Description

Technical Field

[0001] This invention relates to the field of curing scheduling technology for aerospace composite materials, and specifically to a curing scheduling method and system for aerospace composite materials that considers multi-layer spatial and temporal window constraints. Background Technology

[0002] Due to their superior comprehensive properties such as lightweight, high strength, and high designability, aerospace composite materials have gradually replaced traditional metal alloys, leading to a widening supply-demand gap. In the manufacturing system of aerospace composite materials, the curing process is a crucial step determining product performance and manufacturing cycle, and is currently a core bottleneck in composite material production. Therefore, achieving scientific and precise production scheduling for the curing process is of significant practical importance for reducing energy costs, improving capacity utilization, and ultimately alleviating the supply-demand imbalance in composite materials.

[0003] Current research on the curing scheduling problem of aerospace composite materials mainly focuses on independent studies of certain scheduling issues within the composite material processing steps, such as the scheduling problems related to workpiece batch loading strategies and batch processing sequencing. Some studies also comprehensively consider the two core issues of workpiece batch loading and batch scheduling; however, due to the complex environment of the workshop, some processes have been simplified, resulting in insufficient model alignment with real-world production scenarios and limited guidance for the actual production scheduling of the curing process.

[0004] Existing methods optimize the utilization efficiency of hot pressing equipment and the workpiece processing sequence based on resource constraints and dual preparation time characteristics in the hot pressing process of aerospace composites. However, these studies typically simplify the workpiece loading process and do not fully consider the geometric differences of workpieces in the spatial dimension and their impact on the feasibility of actual scheduling. Other methods consider workpiece size differences and the external time constraint of prepreg, effectively reducing workpiece delay time and minimizing the risk of material deterioration. However, these studies are based solely on the assumption of a single-layer operating platform, assuming that workpieces are loaded only in a single plane, and do not fully characterize the structural characteristics of multi-layer plate curing equipment in actual production. Therefore, there is an urgent need to construct a single-machine batch scheduling model that considers the spatial structure and time window constraints of multi-layer plates for actual aerospace composite material manufacturing scenarios, and to design an efficient evolutionary algorithm framework to improve the search capability and engineering applicability of scheduling schemes under complex constraints. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a curing scheduling method and system for aerospace composites that considers multi-layer spatial and temporal window constraints. Based on a comprehensive consideration of the spatial characteristics of the workpiece, the processable time window of the material, and the characteristics of multi-layer board curing equipment scenarios, an adaptive neighborhood search evolutionary algorithm is designed. The scheduling scheme is iteratively optimized based on time compatibility and spatial feasibility, aiming to achieve efficient batch scheduling of the curing process, reduce material waste, and improve the production efficiency of aerospace composites.

[0006] To achieve the above-mentioned technical objectives, the present invention provides the following technical solution:

[0007] A method for scheduling the curing of aerospace composites that considers multi-layered spatial and temporal window constraints, specifically includes the following steps:

[0008] Obtain basic information about the aerospace composite curing production workshop, including workpiece information and curing equipment information;

[0009] Based on the basic information, a single-machine batch scheduling model with multi-layer spatial and processing time window constraints is constructed, and the objective function of the model is set to minimize the maximum completion time.

[0010] An evolutionary algorithm combining adaptive neighborhood search is used to solve the single-machine batch scheduling model and obtain the optimal scheduling scheme. The evolutionary algorithm combining adaptive neighborhood search generates the initial population by combining a time-compatible strategy and a completely random strategy, designs a multi-dimensional neighborhood search operator, and dynamically adjusts the search strategy through a two-layer adaptive neighborhood selection mechanism.

[0011] Based on the obtained optimal scheduling scheme, the batch allocation results of workpieces, the placement and orientation of shelves, and the batch processing sequence and time arrangement are visualized.

[0012] Furthermore, the constraints of the single-machine batch scheduling model include:

[0013] Each workpiece must be assigned to and can only be assigned to one batch;

[0014] Each workpiece must be uniquely assigned to a specific layer of a specific batch;

[0015] The batch processing time is determined by the workpiece with the longest processing time within the batch;

[0016] Any two adjacent batches must not overlap in processing time, and batches must be processed sequentially.

[0017] The start time of batch processing must be within the workpiece's processable time.

[0018] For any two different workpieces, if they are in the same batch and on the same layer, the two workpieces cannot overlap.

[0019] For any two different workpieces, if they are in the same batch and the same layer, then at least one of the relative positional relationships between the two workpieces is valid.

[0020] The completion time of each workpiece shall not exceed the maximum completion time.

[0021] Furthermore, the evolutionary algorithm combining adaptive neighborhood search specifically includes:

[0022] P1. Initialize the evolutionary algorithm parameters, including population size. 1. Initialize the population by setting a preset proportion of individuals generated using a time-compatible strategy to the total number of individuals. Crossover probability Probability of mutation Maximum number of iterations in the population ;

[0023] P2. Initialize the population by using a combination of time-compatible and completely random strategies to generate the initial population. Then, decode the individuals, calculate their fitness, and initialize the population to the current iteration number. ;

[0024] P3. Perform selection, crossover, and mutation operations on the initial population, then decode the resulting new individuals and calculate their fitness.

[0025] P4. Perform a two-layer adaptive neighborhood search optimization on each individual after crossover and mutation operations to obtain the optimized individual, and calculate the fitness of the optimized individual.

[0026] P5. Merge the individuals from the parent population with the individuals optimized by the neighborhood search, and sort them according to fitness, selecting the top individuals with high fitness. Individuals form a temporary population; if the current iteration number of the population is... ,but And return to P3; if Output the latest generation of the population and select the individual with the highest fitness as the optimal scheduling scheme.

[0027] Furthermore, the specific steps for generating the initial population by combining a time-compatible strategy with a completely random strategy are as follows:

[0028] According to the preset ratio The total number of individuals generated using the time-compatible strategy One individual is generated, and the remaining individuals are generated using a completely random strategy; the time-compatible strategy is as follows:

[0029] Initialize the time parameters and the workpiece set index synchronously, setting their initial values ​​to 0; then, first calculate the earliest and latest start times for all workpieces, and integrate them into a unique set. Sort by time in ascending order; by The elements in the set are traversed sequentially to update the time parameters. For each time step... Screening out the processing time window coverage All workpieces at any given moment constitute The set of workpieces at time The first set of workpieces obtained is directly retained and denoted as... The workpiece set at subsequent time steps is compared and verified with the previously retained workpiece set, retaining only the workpiece set that is neither a proper subset nor a proper superset of the previously retained workpiece set; this process is repeated for all time steps. The final result is a set of time-compatible workpieces. , for Number of workpiece sets;

[0030] Next, for the time-compatible workpiece set The set of all workpieces in the set is further subdivided, and the set is denoted as set. Any set of workpieces is ; Assemble the workpieces Divided into workpiece sets A subset of identical workpieces and workpiece set A subset of different workpieces Then shuffle The order of the workpieces was shuffled, and all workpieces were extracted as gene fragments, according to... The order of the workpiece set indices is used to concatenate a complete gene, which is the initial individual generated using a time-compatible strategy.

[0031] Furthermore, the decoding strategy of the evolutionary algorithm combined with adaptive neighborhood search is as follows:

[0032] After inputting the encoded sequence, starting from the first workpiece, traverse the entire encoded sequence and filter out all workpieces that are compatible with the time window of the first workpiece, as sub-segments. ; Sub-segment After all workpieces are removed from the encoding sequence, the above operation is repeated for the remaining encoding sequences until all original encoding sequences become empty, resulting in a set of time-compatible segments. Next, iterate through each sub-segment in turn, determine the feasibility of workpiece allocation based on the time window and workpiece size, allocate the workpiece to the batch, and update the batch initialization information after all workpieces have been allocated.

[0033] Furthermore, the fitness is calculated as follows:

[0034] Count the number of batches with time window conflicts in a scheduling scheme, and then compare this number with a preset penalty coefficient. Multiply by the time to obtain the penalty term; then add the penalty term to the completion time of the last batch, and the result is the fitness value of the current scheduling scheme.

[0035] Furthermore, the two-layer adaptive neighborhood search optimization is divided into random exploration neighborhood search optimization and goal-oriented neighborhood search optimization. Each time the two-layer adaptive neighborhood search optimization is performed, the first layer of adaptive selection is performed first, focusing on the category filtering of random exploration neighborhood search optimization and goal-oriented neighborhood search optimization. After determining which type of neighborhood search optimization to select, the second layer of adaptive selection is entered to filter the specific neighborhood search operator to be used.

[0036] For each individual in the evolutionary algorithm population, the algorithm is executed a preset number of times. The process involves a two-layer adaptive neighborhood search. After all individuals have completed neighborhood search optimization in each round of population iteration, the selection probability of the first-layer adaptive selection and the selection probability of the second-layer adaptive selection are updated simultaneously.

[0037] Furthermore, after all individuals in each round of population iteration have completed neighborhood search optimization, the selection probabilities of the first-layer adaptive selection and the second-layer adaptive selection are updated synchronously as follows:

[0038] In each iteration, the relative improvement reward is calculated based on the improvement effect of the individual's fitness value after neighborhood search optimization; let the fitness values ​​of the individual before and after applying the neighborhood search operator x be respectively. and Then the neighborhood search operator Relative improvement reward:

[0039] ;

[0040] If a neighborhood search operator Called in a round of population iteration Then calculate the average reward value. As a relative improvement reward, the formula is expressed as:

[0041] ;

[0042] in, Neighborhood search operator In the The relative improvement reward when the call is repeated;

[0043] Update the neighborhood search operator based on the relative improvement reward. The score in each round of population iteration The formula is expressed as:

[0044] ;

[0045] in, The learning rate parameter; For attenuation parameters; Indicates the current iteration round number of the population;

[0046] After calculating the scores of all neighborhood search operators, the average score of the random exploration type neighborhood search optimization is calculated separately. Average score of goal-oriented neighborhood search optimization :

[0047] ;

[0048] ;

[0049] in, , These represent the sets of strategies for random exploration-type neighborhood search optimization and the sets of strategies for goal-oriented neighborhood search optimization, respectively.

[0050] Based on the average score, the selection probabilities of the first and second layer adaptive selections are updated synchronously.

[0051] The selection probability formula for the first-level adaptive selection is expressed as:

[0052] ;

[0053] ;

[0054] in, This represents the selection probability for neighborhood search optimization in random exploration class. This represents the selection probability for goal-oriented neighborhood search optimization. To optimize the temperature parameters of the category selection layer, the calculation formula is as follows:

[0055] ;

[0056] in, , For the minimum and maximum values ​​of the category layer temperature parameter, The maximum number of iterations for the population. This represents the current iteration number of the population.

[0057] The calculation process of the selection probability in the second-layer adaptive selection uses the neighborhood search operator in random exploration-type neighborhood search optimization. For example, its selection probability is:

[0058] ;

[0059] in The layer temperature parameter is selected for the neighborhood search operator and calculated using the following formula:

[0060] ;

[0061] in, , , These represent the minimum, median, and maximum values ​​of the temperature parameter for the selection layer in the neighborhood search operator; , These are the dividing points between the stages of heating up and cooling down.

[0062] Furthermore, the specific neighborhood search operator includes:

[0063] Neighborhood search operator 1: For two adjacent batches in the scheduling scheme, sort the workpieces within the batch according to their processing time; select the batches with the longest processing time from the previous batches. Long workpieces form a set Select the batches with the longest processing time from the later batches. Short workpieces form a set ; set and set The workpieces in the process are sequentially swapped across batches to obtain a neighborhood search scheme;

[0064] Neighborhood search operator 2: For two adjacent batches in the scheduling scheme, sort the workpieces within the batch according to their density values; select the workpieces with the highest density values ​​from the earlier batches. Large workpieces form a set Select the highest density values ​​from the later batches. Short workpieces form a set ; set and set The workpieces in the process are sequentially exchanged across batches to obtain a neighborhood search scheme; the density value is defined as the ratio of the area of ​​the workpiece to the processing time of the workpiece.

[0065] Neighborhood search operator 3: For all batches in the scheduling scheme, first determine the time-compatible sub-segment corresponding to each batch during the decoding process, then randomly select one layer from the layers involved in that batch, and exchange it with any layer involved in other batches within the same sub-segment to obtain the neighborhood search scheme.

[0066] Neighborhood search operator 4: Randomly select from all batches of the scheduling scheme These batches are arranged in descending order of total processing time. Sort the batches; then, starting from the first sorted batch, select the workpiece with the longest processing time and place it into the remaining batches. Within each batch, a neighborhood search scheme is obtained;

[0067] Neighborhood search operator 5: For all batches in the scheduling scheme, calculate the difference in processing time between the workpiece with the longest processing time and the workpiece with the second longest processing time in each batch. Sort all batches according to the difference and filter out the batch with the largest difference. Then select the workpiece with the longest processing time from the batch, determine the time-compatible set corresponding to the workpiece, and add the workpiece to the batch of other workpieces in its time-compatible set to obtain the neighborhood search scheme.

[0068] Neighborhood search operator 6: For all batches in the scheduling scheme, select the workpieces with the longest processing time in each batch and form a set. From set Select workpieces in sequence In all subsequent batches following the selected workpiece, the workpieces with the closest size are selected to form a set. , will set and set The workpieces in the process are sequentially swapped across batches to obtain a neighborhood search scheme;

[0069] Neighborhood search operator 7: also based on sets From the set Select workpieces sequentially from these. Calculate the density values ​​of all workpieces in the next adjacent batch of the selected batch, sort all workpieces in the next adjacent batch in descending order based on the density values, and then sort the workpieces... The neighborhood search scheme is obtained by exchanging the sorted workpieces with the workpieces in the adjacent batches one by one.

[0070] Neighborhood search operator 8: also based on sets From the set Select workpieces in sequence Determine the time-compatible set and corresponding batch to which each workpiece belongs. Each workpiece must appear only once in each batch within a subset. Divide the entire workpiece set into several subsets, each containing one workpiece. Its corresponding time-compatible set is constituted; then extracted The set is composed of all the workpieces in the same batch. ,Will Time-compatible set elimination set After including all the workpieces, we get the set. If set The processing time of the workpiece with the shortest processing time in the set is greater than or equal to the processing time of the workpiece in the set. If the processing time of the workpiece with the longest processing time is the longest, then skip processing that workpiece. Neighborhood search; otherwise, select a set. The workpiece with the longest processing time is denoted as From the set Selected from those with a processing time of less than Workpiece construction set ; arranging the collections in ascending order of processing time. Try placing and removing the workpieces one by one. In subsequent batches, until the workpieces can no longer be accommodated or assembled. Empty; set Successfully inserted The workpieces belonging to the same batch are removed from their original batch, and finally... Put in From the batch, the neighborhood search scheme is obtained;

[0071] Neighborhood search operator 9: For all batches in the scheduling method, first determine the corresponding time-compatible segment during the decoding process of each batch, and extract all layers of all batches within the time-compatible segment to construct a layer set. and assemble the shelves. The layers are sorted from longest to shortest processing time; the number of layers is determined by the preset quantity of the curing equipment. From the sorted set of shelves Select the first one in order Each layer forms a new first batch, and subsequent layers are grouped in sequence according to this rule to form new batches, thus obtaining the neighborhood search scheme;

[0072] Of the nine neighborhood search operators mentioned above, the first four belong to random exploration-type neighborhood search optimization, while the remaining five belong to goal-oriented neighborhood search optimization. After performing neighborhood search optimization using each operator, the effectiveness of the neighborhood search optimization is determined by whether the fitness of the optimized individual is improved and whether it meets the time window constraint and workpiece size constraint. If it is effective, the optimized individual is output.

[0073] Furthermore, this application also discloses an aerospace composite curing scheduling system that considers multi-layered spatial and temporal window constraints, specifically including:

[0074] The information acquisition unit is used to acquire basic information about the aerospace composite curing process, including workpiece information and curing equipment information;

[0075] The scheduling model construction unit is used to construct a multi-layer spatial and temporal window single-machine batch scheduling model based on the basic information, wherein the model aims to minimize the maximum completion time.

[0076] The scheduling scheme generation unit is used to solve the single-machine batch scheduling model using an evolutionary algorithm that combines adaptive neighborhood search to obtain the optimal scheduling scheme;

[0077] The visualization output unit visualizes the workpiece batch allocation results, shelf placement and orientation, batch processing sequence and time arrangement based on the obtained optimal scheduling scheme.

[0078] Based on the above technical solution, the present invention has at least the following beneficial effects:

[0079] (1) In the production process of curing aerospace composite materials, the present invention constructs a single-machine batch scheduling mathematical model that simultaneously considers multi-layer spatial constraints and material machinability time window constraints. In batch scheduling modeling, the model comprehensively considers the actual production scenarios in the workshop, such as workpiece spatial placement constraints, shelf capacity constraints, workpiece time window constraints, and batch continuous processing constraints.

[0080] (2) This invention proposes an evolutionary algorithm combining adaptive neighborhood search to solve the above-mentioned single-machine batch scheduling problem. By introducing a population initialization method based on a combination of time-compatible and random strategies, and various neighborhood search operators oriented towards batch structure and workpiece characteristics, this algorithm enhances the search diversity and global exploration capability of the algorithm while ensuring the feasibility of the solution, thereby effectively avoiding premature convergence and improving the solution quality of scheduling problems under complex constraints.

[0081] (3) In the evolutionary algorithm framework, the present invention designs a two-layer adaptive neighborhood search mechanism, divides the neighborhood search method into random exploration class and goal-oriented class, and dynamically adjusts the selection probability of different neighborhood search methods through an adaptive probability update strategy, so that the algorithm can adaptively select appropriate neighborhood operations according to the improvement effect of the search stage and the solution, thereby significantly improving the algorithm's ability to escape local optima while ensuring search efficiency.

[0082] (4) The scheduling scheme and system proposed in this invention have good versatility and scalability. They are not only applicable to the production scheduling scenario of multi-layer curing equipment for aerospace composite materials, but can also be extended to other manufacturing systems with multi-layer processing space, time window constraints and batch processing characteristics, such as complex manufacturing environments such as composite material molding and heat treatment furnace scheduling. They have high engineering application value. Attached Figure Description

[0083] Figure 1This is a flowchart of a method for scheduling the curing of aerospace composites that considers multi-layer spatial and temporal window constraints, as proposed in this invention.

[0084] Figure 2 This is a schematic diagram showing the placement of the autoclave and the workpiece in an embodiment of the present invention.

[0085] Figure 3 This is a flowchart of an evolutionary algorithm combining adaptive neighborhood search in an embodiment of the present invention.

[0086] Figure 4 This is a schematic diagram of the decoding of the evolutionary algorithm in an embodiment of the present invention.

[0087] Figure 5 This is a schematic diagram of the time-compatible strategy encoding of the evolutionary algorithm in an embodiment of the present invention.

[0088] Figure 6 This is a Gantt chart of the scheduling results and a partial batch workpiece distribution diagram in an embodiment of the present invention. Detailed Implementation

[0089] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the following description is provided in conjunction with... Figures 1-6 The present invention will be further described in detail below with reference to specific embodiments. This is to ensure that those skilled in the art can fully understand the complete process by which the present application uses technical means to solve technical problems and achieve technical effects, and can implement it according to the process.

[0090] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0091] like Figure 1 As shown, this invention proposes a method for scheduling the curing of aerospace composites that considers multi-layered spatial and temporal window constraints, which specifically includes the following steps:

[0092] S1. Obtain basic information about the aerospace composite material curing production workshop, including workpiece information and curing equipment information;

[0093] In a preferred embodiment, the workpiece information and curing equipment information specifically include:

[0094] The workpiece information includes: the length and width of each workpiece to be processed in the aerospace composite curing process; the required curing time for each workpiece to be processed; the completion layup time for each workpiece to be processed; and the processing time window for each workpiece to be processed.

[0095] The capacity information of the curing equipment includes: the length and width of the shelves in each curing unit; and the number of shelves in each curing unit.

[0096] In this embodiment, the following set of workpieces to be processed in the aerospace composite materials production workshop are provided:

[0097] There are 40 workpieces that need to undergo curing. Each workpiece The width is , length is The processing time is workpiece The processable time window is , , respectively workpiece The earliest and latest start times;

[0098] In this embodiment, the 40 workpieces are numbered 0-39, that is... The specific workpiece information is shown in Table 1 below:

[0099] Table 1 Workpiece Information Table

[0100] Workpiece Number Workpiece width workpiece length Workpiece processing time Start of the workpiece machinable time window End of the workpiece machinability time window 0 33 23 15 0 102 1 28 21 15 22 76 2 15 12 15 32 185 3 14 10 15 30 147 4 21 15 15 51 78 5 24 24 15 119 152 6 27 17 14 8 59 7 11 10 14 69 153 8 20 21 14 126 243 9 15 6 13 41 95 10 11 10 13 48 84 11 25 13 13 61 109 12 36 16 13 79 133 13 32 19 13 94 295 14 13 8 12 33 54 15 16 12 12 82 133 16 31 24 11 1 25 17 17 9 11 0 21 18 14 7 11 12 57 19 37 14 11 49 121 20 16 7 11 50 122 21 20 9 10 51 69 22 17 11 10 59 209 23 10 10 9 50 56 24 38 14 9 99 147 25 22 15 9 123 147 26 40 20 7 2 35 27 17 11 7 12 30 28 26 19 7 22 217 29 15 10 7 45 261 30 34 23 7 70 106 31 29 15 7 113 140 32 34 22 7 115 280 33 16 7 6 13 25 34 14 6 6 32 236 35 19 8 6 51 57 36 26 18 6 58 199 37 20 7 5 0 213 38 13 10 5 52 241 39 10 12 5 61 274

[0101] In this embodiment, the curing equipment in the curing workshop is an autoclave. Only one autoclave is used in this curing workshop to cure the workpiece. A schematic diagram of the autoclave is shown below. Figure 2 As shown, there are two layers of shelves in this autoclave, each measuring 50m x 30m.

[0102] S2. Traditional single-machine batch models often only consider the one-dimensional attributes of the workpiece and ignore the time window attributes of the workpiece, failing to fully consider the real situation of the solidification workshop; while this method constructs a single-machine batch scheduling model based on basic information, which includes multi-layer space and processable time window constraints, and sets the objective function of the model to minimize the maximum completion time.

[0103] In a preferred embodiment, the multi-layer spatial and manufacturable time window constraints include:

[0104] Each workpiece must be assigned to and can only be assigned to one batch:

[0105] ;

[0106] Each workpiece must be uniquely assigned to a specific layer of a specific batch:

[0107] ;

[0108] The batch processing time is determined by the workpiece with the longest processing time within the batch:

[0109] ;

[0110] The completion time of a batch is defined as:

[0111] ;

[0112] Any two adjacent batches must not overlap in processing time, and batches must be processed sequentially.

[0113] ;

[0114] The start time of batch processing must be within the workpiece's processable time:

[0115] ;

[0116] ;

[0117] No workpiece may exceed the edge of the shelf in the curing unit during processing.

[0118] ;

[0119] ;

[0120] For any two different workpieces, if they are in the same batch and on the same layer, then the two workpieces cannot overlap:

[0121]

[0122] ;

[0123]

[0124] ;

[0125] For any two different workpieces, if they are in the same batch and on the same layer, then at least one of the relative positional relationships between the two workpieces holds true:

[0126] ;

[0127] The completion time of each workpiece shall not exceed the maximum completion time:

[0128] ;

[0129] Among them, the workpiece set is recorded. , For the number of workpieces; batch set , Batch quantity; set of layers , The number of layers in the curing equipment; workpiece The width is , length is Processing time is ; workpiece The processable time window is The width of a single layer is , length is ;

[0130] For 0-1 variables, if the workpiece Assigned to The value is 1 if it is in the batch, and 0 otherwise. For 0-1 variables, if the workpiece Assigned to In batch The value is 1 if the layer is layer 1, otherwise it is 0. A 0-1 variable, indicating if the first... If a workpiece is rotated 90° before placement, the value is 1; otherwise, the value is 0. As a continuous variable, representing the workpiece Bottom left x-coordinate; As a continuous variable, representing the workpiece Bottom left ordinate; For variables of 0-1, if in the same batch and the same floor The The workpiece in the first The left side of each workpiece is 1, otherwise it is 0; For variables of 0-1, if in the same batch and the same floor If the first The workpiece in the first The bottom of each workpiece is 1, otherwise it is 0; For continuous variables, representing batches Start time; For continuous variables, representing batches Processing time; An integer variable representing the batch. The completion time. It is a sufficiently large positive number; This is an integer variable representing the maximum completion time of the entire scheduling scheme;

[0131] The objective function is to minimize the maximum completion time, i.e. .

[0132] S3. An evolutionary algorithm combining adaptive neighborhood search is used to solve the single-machine batch scheduling model to obtain the optimal scheduling scheme. The evolutionary algorithm combining adaptive neighborhood search generates the initial population by combining a time-compatible strategy with a completely random strategy, designs a multi-dimensional neighborhood search operator, and dynamically adjusts the search strategy through a two-layer adaptive neighborhood selection mechanism.

[0133] Classical evolutionary algorithms often rely on a single strategy during population initialization, leading to uneven solution distribution. Neighborhood search operators lack targeted design and cannot accurately adapt to requirements such as batch structure optimization and workpiece layer allocation. Furthermore, they lack adaptive adjustment mechanisms based on time-compatible rules and search operations adapted to workpiece characteristics and layer constraints, making them prone to premature convergence and insufficient ability to explore optimal solutions under complex constraints. Therefore, this invention proposes an evolutionary algorithm combining adaptive neighborhood search to solve the aforementioned single-machine batch scheduling problem. This algorithm introduces a population initialization method combining time-compatible and random strategies, and multiple neighborhood search operators oriented towards batch structure and workpiece characteristics. This ensures solution feasibility while enhancing the algorithm's search diversity and global exploration capability, effectively avoiding premature convergence and improving the solution quality for scheduling problems under complex constraints.

[0134] As a preferred embodiment, such as Figure 3 As shown, the evolutionary algorithm combining adaptive neighborhood search includes the following steps:

[0135] P1. Initialize the evolutionary algorithm parameters, including population size. 1. Initialize the population by setting a preset proportion of individuals generated using a time-compatible strategy to the total number of individuals. Crossover probability Probability of mutation Maximum number of iterations in the population ;

[0136] In this embodiment, for the single-machine batch scheduling model that considers multi-layer space and processing time window, a single-layer sequential encoding is adopted. The encoding sequence consists of the serial numbers of all workpieces, indicating the priority order in which workpieces are tried to be assigned to processing batches. Based on the encoding sequence, according to the rule of "checking constraints one by one and prioritizing batch entry", the sorted workpieces are sequentially judged to see if they can be added to the current batch to be filled. If they cannot be added, a new batch is started.

[0137] P2. Initialize the population individuals by combining a time-compatible strategy and a completely random strategy to generate the initial population; in this embodiment, according to a preset ratio. The total number of individuals generated using the time-compatible strategy One individual is generated, and the remaining individuals are generated using a completely random strategy; the time-compatible strategy is as follows:

[0138] Initialize the time parameters and the workpiece set index synchronously, setting their initial values ​​to 0; then, first calculate the earliest and latest start times for all workpieces, and integrate them into a unique set. Sort by time in ascending order; by The elements in the set are traversed sequentially to update the time parameters. For each time step... Screening out the processing time window coverage All workpieces at any given moment constitute The set of workpieces at time The first set of workpieces obtained is directly retained and denoted as... The workpiece set at subsequent time steps is compared and verified with the previously retained workpiece set. Only workpiece sets that are neither a proper subset nor a proper superset of the previously retained workpiece set are retained (workpiece sets at all time steps are not retained). ); Traverse all The final result is a set of time-compatible workpieces. , for Number of workpiece sets;

[0139] Next, for the time-compatible workpiece set The set of all workpieces in the set is further subdivided, and the set is denoted as set. Any set of workpieces is ; Assemble the workpieces Divided into workpiece sets A subset of identical workpieces and workpiece set A subset of different workpieces Then shuffle The order of the workpieces was shuffled, and all workpieces were extracted as gene fragments, according to... The order of the workpiece set indices is used to concatenate a complete gene, which is the initial individual generated using a time-compatible strategy.

[0140] In this embodiment, as Figure 5 As shown, the process of generating initial individuals based on a time-compatible strategy is illustrated. First, all seven artifacts are traversed according to their time nodes, resulting in a set of artifacts that satisfy time compatibility. , , Based on whether each workpiece set contains the same workpiece as the previous workpiece set, each workpiece is grouped into different categories. and That is, you can get , , .Will All the workpieces are taken out and randomly shuffled, used as gene fragments and spliced ​​together to obtain the individuals generated by the time-compatible strategy as {0, 1, 3, 4, 2, 6, 5}.

[0141] After initializing the population individuals, the individuals are decoded. In this embodiment, the decoding strategy is as follows:

[0142] After inputting the encoded sequence (one encoded sequence corresponds to one individual), starting from the first workpiece, traverse the entire encoded sequence and select all workpieces that are compatible with the time window of the first workpiece as sub-segments. ; Sub-segment After all workpieces are removed from the encoding sequence, the above operation is repeated for the remaining encoding sequences until all original encoding sequences become empty, resulting in a set of time-compatible segments. Next, iterate through each sub-segment in turn, determine the feasibility of workpiece allocation based on the time window and workpiece size, allocate the workpiece to the batch, and update the batch initialization information after all workpieces have been allocated.

[0143] The specific decoding results can be seen as follows Figure 4 As shown, the workpieces are attempted to be assigned to batches in the order of 3, 2, 1, 0, 5, 6, 4. The specific allocation logic is as follows: First, workpiece 3 is taken out, and its processing time window, shelf placement rules, and other constraints are checked before creating the first batch and adding it. Next, workpiece 2 is taken out, and it is determined whether it can be batched with workpiece 3. This requires that the start processing time of the batch is within the time window of workpiece 2, and that the workpiece does not overlap or cross the boundary in the shelf after being placed in the batch. If these conditions are met, it is added to the current batch; otherwise, a second batch is created and added. Subsequently, the above-mentioned checks on time windows and size constraints are performed on workpieces 1, 0, 5, 6, and 4 in sequence. If these conditions are met, they are placed in the current batch; otherwise, a new batch is created. Finally, a batch division scheme that meets all constraints is formed.

[0144] Calculate the fitness of each individual and initialize the current iteration number of the population. ;

[0145] In a preferred embodiment, the fitness is calculated as follows:

[0146] Count the number of batches with time window conflicts in a scheduling scheme, and then compare this number with a preset penalty coefficient. Multiply by the time to obtain the penalty term; then add the penalty term to the completion time of the last batch, and the result is the fitness value of the current scheduling scheme.

[0147] P3. Perform selection, crossover, and mutation operations on the initial population, then decode the resulting new individuals and calculate their fitness.

[0148] P4. Perform a two-layer adaptive neighborhood search optimization on each individual after crossover and mutation operations to obtain the optimized individual, and calculate the fitness of the optimized individual.

[0149] It should be noted that this application calculates the fitness of individuals after crossover, mutation, and two-layer adaptive neighborhood search optimization. This is because: firstly, it is necessary to compare the fitness of individuals after neighborhood search optimization with the fitness of individuals before the search to determine whether the neighborhood search is effective; therefore, it is necessary to calculate the fitness of individuals after crossover, mutation, and neighborhood search optimization. Secondly, calculating the fitness of the optimized new individuals is for comparison with the parents' population to select the next generation of individuals.

[0150] In a preferred embodiment, the two-layer adaptive neighborhood search optimization is divided into random exploration neighborhood search optimization and goal-oriented neighborhood search optimization. Each time the two-layer adaptive neighborhood search optimization is performed, a first-layer adaptive selection is first performed, focusing on filtering between random exploration neighborhood search optimization and goal-oriented neighborhood search optimization. After determining which type of neighborhood search optimization to select, the second-layer adaptive selection is entered to filter the specific neighborhood search operator to be used, including:

[0151] Neighborhood search operator 1: For two adjacent batches in the scheduling scheme, sort the workpieces within the batch according to their processing time; select the batches with the longest processing time from the previous batches. Long workpieces form a set Select the batches with the longest processing time from the later batches. Short workpieces form a set ; set and set The workpieces in the process are sequentially swapped across batches to obtain a neighborhood search scheme;

[0152] Neighborhood search operator 2: For two adjacent batches in the scheduling scheme, sort the workpieces within the batch according to their density values; select the workpieces with the highest density values ​​from the earlier batches. Large workpieces form a set Select the highest density values ​​from the later batches. Short workpieces form a set ; set and set The workpieces in the process are sequentially exchanged across batches to obtain a neighborhood search scheme; the density value is defined as the ratio of the area of ​​the workpiece to the processing time of the workpiece.

[0153] Neighborhood search operator 3: For all batches in the scheduling scheme, first determine the time-compatible sub-segment corresponding to each batch during the decoding process, then randomly select one layer from the layers involved in that batch, and exchange it with any layer involved in other batches within the same sub-segment to obtain the neighborhood search scheme.

[0154] Neighborhood search operator 4: Randomly select from all batches of the scheduling scheme These batches are arranged in descending order of total processing time. Sort the batches; then, starting from the first sorted batch, select the workpiece with the longest processing time and place it into the remaining batches. Within each batch, a neighborhood search scheme is obtained;

[0155] Neighborhood search operator 5: For all batches in the scheduling scheme, calculate the difference in processing time between the workpiece with the longest processing time and the workpiece with the second longest processing time in each batch. Sort all batches according to the difference and filter out the batch with the largest difference. Then select the workpiece with the longest processing time from the batch, determine the time-compatible set corresponding to the workpiece, and add the workpiece to the batch of other workpieces in its time-compatible set to obtain the neighborhood search scheme.

[0156] Neighborhood search operator 6: For all batches in the scheduling scheme, select the workpieces with the longest processing time in each batch and form a set. From set Select workpieces in sequence In all subsequent batches following the selected workpiece, the workpieces with the closest size are selected to form a set. , will set and set The workpieces in the process are sequentially swapped across batches to obtain a neighborhood search scheme;

[0157] Neighborhood search operator 7: also based on sets From the set Select workpieces sequentially from these. Calculate the density values ​​of all workpieces in the next adjacent batch of the selected batch, sort all workpieces in the next adjacent batch in descending order based on the density values, and then sort the workpieces... The neighborhood search scheme is obtained by exchanging the sorted workpieces with the workpieces in the adjacent batches one by one.

[0158] Neighborhood search operator 8: also based on sets From the set Select workpieces in sequence Determine the time-compatible set and corresponding batch to which each workpiece belongs. Each workpiece must appear only once in each batch within a subset. Divide the entire workpiece set into several subsets, each containing one workpiece. Its corresponding time-compatible set is constituted; then extracted The set is composed of all the workpieces in the same batch. ,Will Time-compatible set elimination set After including all the workpieces, we get the set. If set The processing time of the workpiece with the shortest processing time in the set is greater than or equal to the processing time of the workpiece in the set. If the processing time of the workpiece with the longest processing time is the longest, then skip processing that workpiece. Neighborhood search; otherwise, select a set. The workpiece with the longest processing time is denoted as From the set Selected from those with a processing time of less than Workpiece construction set ; arranging the collections in ascending order of processing time. Try placing and removing the workpieces one by one. In subsequent batches, until the workpieces can no longer be accommodated or assembled. Empty; set Successfully inserted The workpieces belonging to the same batch are removed from their original batch, and finally... Put in From the batch, the neighborhood search scheme is obtained;

[0159] Neighborhood search operator 9: For all batches in the scheduling method, first determine the corresponding time-compatible segment during the decoding process of each batch, and extract all layers of all batches within the time-compatible segment to construct a layer set. and assemble the shelves. The layers are sorted from largest to smallest according to their processing time (the maximum processing time of all workpieces in the layer); based on the preset number of layers in the curing equipment. From the sorted set of shelves Select the first one in order Each layer forms a new first batch, and subsequent layers are grouped in sequence according to this rule to form new batches, thus obtaining the neighborhood search scheme;

[0160] Of the nine neighborhood search operators mentioned above, the first four belong to random exploration-type neighborhood search optimization, while the remaining five belong to goal-oriented neighborhood search optimization. After performing neighborhood search optimization using each operator, the effectiveness of the neighborhood search optimization is determined by whether the fitness of the optimized individual is improved and whether it meets the time window constraint and workpiece size constraint. If it is effective, the optimized individual is output.

[0161] For each individual in the evolutionary algorithm population, such as Figure 3 As shown, all are executed the preset number of times. The current number of searches is denoted as (times). The system employs a two-layer adaptive neighborhood search. After all individuals complete neighborhood search optimization within each population iteration, the selection probabilities of the first-layer adaptive selection and the second-layer adaptive selection are updated synchronously. In this embodiment, the first layer can be called the optimized category selection layer, and the second layer can be called the neighborhood search operator selection layer. Each layer selects based on its selection probability, which is calculated as follows:

[0162] In each iteration, the relative improvement reward is calculated based on the improvement effect of the individual's fitness value after neighborhood search optimization; let the fitness values ​​of the individual before and after applying the neighborhood search operator x be respectively. and The relative improvement reward for the neighborhood search operator x is:

[0163] ;

[0164] If a neighborhood search operator Called in a round of population iteration Then calculate the average reward value. As a relative improvement reward, the formula is expressed as:

[0165] ;

[0166] in, Neighborhood search operator In the The relative improvement reward when the call is repeated;

[0167] Update the neighborhood search operator based on the relative improvement reward. The score in each round of population iteration The formula is expressed as:

[0168] ;

[0169] in, The learning rate parameter; For attenuation parameters; Indicates the current iteration round number of the population;

[0170] After calculating the scores of all neighborhood search operators, the average score of the random exploration type neighborhood search optimization is calculated separately. Average score of goal-oriented neighborhood search optimization :

[0171] ;

[0172] ;

[0173] in, , These represent the sets of strategies for random exploration-type neighborhood search optimization and the sets of strategies for goal-oriented neighborhood search optimization, respectively.

[0174] Based on the average score, the selection probabilities of the first and second layer adaptive selections are updated synchronously.

[0175] The selection probability formula for the first-level adaptive selection is expressed as:

[0176] ;

[0177] ;

[0178] in, This represents the selection probability for neighborhood search optimization in random exploration class. This represents the selection probability for goal-oriented neighborhood search optimization. To optimize the temperature parameters of the category selection layer, the calculation formula is as follows:

[0179] ;

[0180] in, , For the minimum and maximum values ​​of the temperature parameter of the category layer, The maximum number of iterations for the population. This represents the current iteration number of the population.

[0181] The calculation process of the selection probability in the second-layer adaptive selection uses the neighborhood search operator in random exploration-type neighborhood search optimization. For example, its selection probability is:

[0182] ;

[0183] in The layer temperature parameter is selected for the neighborhood search operator and calculated using the following formula:

[0184] ;

[0185] in, , , These represent the minimum, median, and maximum values ​​of the temperature parameter for the selection layer in the neighborhood search operator; , These are the dividing points between the heating and cooling stages.

[0186] This embodiment uses the above-mentioned two-layer adaptive neighborhood search optimization mechanism to divide the neighborhood search method into random exploration and goal-oriented methods, and dynamically adjusts the selection probability of different neighborhood search methods through an adaptive probability update strategy. This enables the algorithm to adaptively select appropriate neighborhood operations based on the search stage and the improvement effect of the solution, thereby significantly improving the algorithm's ability to escape local optima while ensuring search efficiency.

[0187] The relevant parameter settings for the evolutionary algorithm in this example are shown in Table 2 below:

[0188] Table 2 Evolutionary Algorithm Parameters

[0189]

[0190] P5. Merge the individuals from the parent population with the individuals from the new population, and sort them according to fitness, selecting the individuals with higher fitness. Individuals form a temporary population;

[0191] like ,but And return to step 4.3; if Output the optimal population, i.e., the candidate scheduling method. Calculate the objective function value of each individual in the optimal population, and select the scheme with the lowest objective function value, i.e., the scheme with the smallest maximum completion time, as the final optimal scheduling scheme.

[0192] Table 3 below shows the optimal scheduling scheme results for this example. In Table 3, the "Workpiece ID and Sheet Number" column represents the workpiece ID and the shelf number where the workpiece is located. For example, batch 4 contains three workpieces: workpiece 11, workpiece 30, and workpiece 36. Workpiece 11 and workpiece 36 are located on the first shelf, while workpiece 30 is located on the second shelf. According to the optimal scheduling scheme, this example has a total of 8 batches, with a maximum completion time of 141 seconds.

[0193] Table 3. Results of the scheduling scheme

[0194]

[0195] S4. Finally, based on the obtained optimal scheduling scheme, the batch allocation results of the workpieces, the placement and orientation of the shelves, the batch processing sequence and time arrangement are visualized.

[0196] Figure 6The upper half of the image is a Gantt chart, which visualizes the scheduling results. This chart shows the start time, end time, and processing time for each batch in the scheduling plan. The Gantt chart uses a time axis as the horizontal axis and employs horizontal bars to represent the processing of each batch of workpieces. The starting position of the bar corresponds to the start time of the batch, and the length of the bar corresponds to the processing time of the batch.

[0197] The lower half of the image shows the workpiece layout for a portion of the batch. This image recreates the double-layer structure within the autoclave, as well as the position and orientation of the workpieces on their respective shelves. Each workpiece is represented as a rectangular block, its position determined by the lower-left corner coordinates returned by the bin packing function, ensuring complete consistency with its placement in the actual processing area. Furthermore, the image incorporates the crucial information of workpiece rotation to reflect its posture during placement, providing a visual basis for evaluating space utilization, workpiece interference risk, and the optimization performance of the bin packing algorithm. This image allows direct observation of the spatial distribution density, layout compactness, and rationality of area division for each batch of workpieces, providing a visual reference for further optimization of the spatial layout.

[0198] This concludes the description of the method proposed in this invention. Furthermore, this application also discloses an aerospace composite curing scheduling system considering multi-layered spatial and temporal window constraints, specifically comprising:

[0199] The information acquisition unit is used to acquire basic information about the aerospace composite curing process, including workpiece information and curing equipment information;

[0200] The scheduling model construction unit is used to construct a multi-layered spatial and temporal window single-machine batch scheduling model based on the basic information, the model aiming to minimize the maximum completion time.

[0201] The scheduling scheme generation unit is used to solve the single-machine batch scheduling model using an evolutionary algorithm that combines adaptive neighborhood search to obtain the optimal scheduling scheme;

[0202] The visualization output unit visualizes the workpiece batch allocation results, shelf placement and orientation, batch processing sequence and time arrangement based on the obtained optimal scheduling scheme.

[0203] In summary, this invention proposes a curing scheduling method and system for aerospace composites that considers multi-layered spatial constraints and processable time windows. With minimizing the maximum completion time as the optimization objective, it constructs a targeted single-machine batch scheduling model for multi-layered board curing equipment and time window constraints, thus overcoming the shortcomings of existing research in characterizing spatial dimensions and temporal constraints. This invention also designs an evolutionary algorithm solution framework combining adaptive neighborhood search and integrates diverse neighborhood search operators, which can be specifically described in the following aspects:

[0204] 1) The mathematical model of this invention adopts multi-layer spatial and temporal window fusion modeling: the objective function is constructed with constraints such as workpiece spatial placement, shelf capacity, and time window, abandoning the simplified processing of spatial dimension or time constraints in traditional models, and improving the fit between the model and the real production scenario;

[0205] 2) The evolutionary algorithm of this invention adopts an adaptive neighborhood search evolutionary algorithm to adapt to the aerospace composite solidification scheduling problem:

[0206] a) Population initialization mechanism combining time compatibility and randomness: Time-compatible individuals and random individuals are generated according to a preset ratio to balance the feasibility of solutions and population diversity, and to avoid uneven distribution of initial solutions;

[0207] b) Decoding strategy for time-compatible sub-segments: Sub-segments are formed by iteratively filtering time-window compatible workpieces, and batch allocation is completed in combination with size constraints to ensure that the decoding results meet multi-layer spatial and temporal constraints;

[0208] c) Multi-dimensional neighborhood search operators: Nine neighborhood search methods are designed, covering operations such as workpiece exchange, shelf swapping, and batch reorganization, respectively adapting to workpiece features, batch structure and shelf constraints, and enhancing local search capabilities.

[0209] d) Two-layer adaptive neighborhood selection mechanism: The neighborhood method is divided into random exploration class and goal-oriented class. By dynamically updating the selection probability, it adapts to the needs of different search stages of the algorithm and effectively avoids premature convergence.

[0210] e) Probability update method based on reward and decay: The reward value is calculated by combining the improvement effect of neighborhood search, the learning rate and decay rate are introduced to adjust the score, and the selection probability is dynamically optimized by combining temperature parameters to improve the search efficiency of the algorithm.

[0211] These improvement strategies fully align with the core characteristics and practical needs of multilayer board equipment, time window constraints, and batch processing in aerospace composite curing workshops. They demonstrate that this invention can effectively improve the search efficiency and solution quality of optimal scheduling schemes under complex constraints, significantly optimize the production efficiency of composite curing, and possess good versatility and scalability. It can be extended to complex manufacturing scenarios with multilayer processing space, time window constraints, and batch processing characteristics, such as composite material molding and heat treatment furnace scheduling.

[0212] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0213] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0214] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for scheduling the curing of aerospace composites considering multi-layered spatial and temporal window constraints, characterized in that, Specifically, the steps include the following: Obtain basic information about the aerospace composite curing production workshop, including workpiece information and curing equipment information; Based on the basic information, a single-machine batch scheduling model with multi-layer spatial and processing time window constraints is constructed, and the objective function of the model is set to minimize the maximum completion time. An evolutionary algorithm combining adaptive neighborhood search is used to solve the single-machine batch scheduling model and obtain the optimal scheduling scheme. The evolutionary algorithm combining adaptive neighborhood search generates the initial population by combining a time-compatible strategy and a completely random strategy, designs a multi-dimensional neighborhood search operator, and dynamically adjusts the search strategy through a two-layer adaptive neighborhood selection mechanism. The evolutionary algorithm combining adaptive neighborhood search specifically includes: P1. Initialize the evolutionary algorithm parameters, including population size.

1. Initialize the population by setting a preset proportion of individuals generated using a time-compatible strategy to the total number of individuals. Crossover probability Probability of mutation Maximum number of iterations in the population ; P2. Initialize the population by using a combination of time-compatible and completely random strategies to generate the initial population. Then, decode the individuals, calculate their fitness, and initialize the population to the current iteration number. ; The specific steps for generating the initial population using a combination of time-compatible and completely random strategies are as follows: According to the preset ratio The total number of individuals generated using the time-compatible strategy One individual is generated, and the remaining individuals are generated using a completely random strategy; the time-compatible strategy is as follows: Initialize the time parameters and the workpiece set index synchronously, setting their initial values ​​to 0; then, first calculate the earliest and latest start times for all workpieces, and integrate them into a unique set. Sort by time in ascending order; by The elements in the set are traversed sequentially to update the time parameters. For each time step... Screening out the processing time window coverage All workpieces at any given moment constitute The set of workpieces at time The first set of workpieces obtained is directly retained and denoted as... The workpiece set at subsequent time steps is compared and verified with the previously retained workpiece set, retaining only the workpiece set that is neither a proper subset nor a proper superset of the previously retained workpiece set; this process is repeated for all time steps. The final result is a set of time-compatible workpieces. , for Number of workpiece sets; Next, for the time-compatible workpiece set The set of all workpieces in the set is further subdivided, and the set is denoted as set. Any set of workpieces is , ; Assemble the workpieces Divided into workpiece sets A subset of identical workpieces and workpiece set A subset of different workpieces Then shuffle The order of the workpieces was shuffled, and all workpieces were extracted as gene fragments, according to... The order of the workpiece set indices is used to concatenate a complete gene, which is the initial individual generated using a time-compatible strategy; P3. Perform selection, crossover, and mutation operations on the initial population, then decode the resulting new individuals and calculate their fitness. P4. Perform a two-layer adaptive neighborhood search optimization on each individual after crossover and mutation operations to obtain the optimized individual, and calculate the fitness of the optimized individual. The two-layer adaptive neighborhood search optimization is divided into random exploration neighborhood search optimization and goal-oriented neighborhood search optimization. Each time the two-layer adaptive neighborhood search optimization is performed, the first layer of adaptive selection is performed first, focusing on the category filtering of random exploration neighborhood search optimization and goal-oriented neighborhood search optimization. After determining which type of neighborhood search optimization to select, the second layer of adaptive selection is entered to filter the specific neighborhood search operator to be used. For each individual in the evolutionary algorithm population, the algorithm is executed a preset number of times. This is a two-layer adaptive neighborhood search; After all individuals complete neighborhood search optimization within each round of population iteration, the selection probabilities of the first-level adaptive selection and the selection probabilities of the second-level adaptive selection are updated synchronously, as follows: In each iteration, the relative improvement reward is calculated based on the improvement effect of the individual's fitness value after neighborhood search optimization; the individual's performance in applying the neighborhood search operator is recorded. The fitness values ​​before and after are respectively and Then the neighborhood search operator Relative improvement reward: ； If a neighborhood search operator Called in a round of population iteration Then calculate the average reward value. As a relative improvement reward, the formula is expressed as: ； in, Neighborhood search operator In the The relative improvement reward when the call is repeated; Update the neighborhood search operator based on the relative improvement reward. The score in each round of population iteration The formula is expressed as: ； in, The learning rate parameter; For attenuation parameters; Indicates the current iteration round number of the population; After calculating the scores of all neighborhood search operators, the average score of the random exploration type neighborhood search optimization is calculated separately. Average score of goal-oriented neighborhood search optimization : ； ； in, , These represent the sets of strategies for random exploration-type neighborhood search optimization and the sets of strategies for goal-oriented neighborhood search optimization, respectively. Based on the average score, the selection probabilities of the first and second layer adaptive selections are updated synchronously. The selection probability formula for the first-level adaptive selection is expressed as: ； ； in, This represents the selection probability for neighborhood search optimization in random exploration class. This represents the selection probability for goal-oriented neighborhood search optimization. To optimize the temperature parameters of the category selection layer, the calculation formula is as follows: ； in, , For the minimum and maximum values ​​of the category layer temperature parameter, The maximum number of iterations for the population. This represents the current iteration number of the population. The calculation process of the selection probability in the second-layer adaptive selection uses the neighborhood search operator in random exploration-type neighborhood search optimization. For example, its selection probability is: ； in The layer temperature parameter is selected for the neighborhood search operator and calculated using the following formula: ； in, , , These represent the minimum, median, and maximum values ​​of the temperature parameter for the selection layer in the neighborhood search operator; , These are the dividing points between the heating and cooling stages; P5. Merge the individuals from the parent population with the individuals optimized by the neighborhood search, and sort them according to fitness, selecting the top individuals with high fitness. Individuals form a temporary population; if the current iteration number of the population is... ,but And return to P3; if Output the latest generation of the population and select the individual with the highest fitness as the optimal scheduling scheme; Based on the obtained optimal scheduling scheme, the batch allocation results of workpieces, the placement and orientation of shelves, and the batch processing sequence and time arrangement are visualized.

2. The method for scheduling the curing of aerospace composites considering multi-layered spatial and temporal window constraints according to claim 1, characterized in that, The constraints of the single-machine batch scheduling model include: Each workpiece must be assigned to and can only be assigned to one batch; Each workpiece must be uniquely assigned to a specific layer of a specific batch; The batch processing time is determined by the workpiece with the longest processing time within the batch; Any two adjacent batches must not overlap in processing time, and batches must be processed sequentially. The start time of batch processing must be within the workpiece's processable time. For any two different workpieces, if they are in the same batch and on the same layer, the two workpieces cannot overlap. For any two different workpieces, if they are in the same batch and the same layer, then at least one of the relative positional relationships between the two workpieces is valid. The completion time of each workpiece shall not exceed the maximum completion time.

3. The method for scheduling the curing of aerospace composites considering multi-layered spatial and temporal window constraints according to claim 1, characterized in that, The decoding strategy of the evolutionary algorithm combined with adaptive neighborhood search is as follows: After inputting the encoded sequence, starting from the first workpiece, traverse the entire encoded sequence and filter out all workpieces that are compatible with the time window of the first workpiece, as sub-segments. ; Sub-segment After all workpieces are removed from the encoding sequence, the above operation is repeated for the remaining encoding sequences until all original encoding sequences become empty, resulting in a set of time-compatible segments. Next, iterate through each sub-segment in turn, determine the feasibility of workpiece allocation based on the time window and workpiece size, allocate the workpiece to the batch, and update the batch initialization information after all workpieces have been allocated.

4. The method for scheduling the curing of aerospace composites considering multi-layered spatial and temporal window constraints according to claim 1, characterized in that, The fitness is calculated as follows: Count the number of batches with time window conflicts in a scheduling scheme, and then compare this number with a preset penalty coefficient. Multiply by the time to obtain the penalty term; then add the penalty term to the completion time of the last batch, and the result is the fitness value of the current scheduling scheme.

5. The method for scheduling the curing of aerospace composites considering multi-layered spatial and temporal window constraints according to claim 1, characterized in that, The specific neighborhood search operators include: Neighborhood search operator 1: For two adjacent batches in the scheduling scheme, sort the workpieces within the batch according to their processing time; select the batches with the longest processing time from the previous batches. Long workpieces form a set Select the batches with the longest processing time from the later batches. Short workpieces form a set ; set and set The workpieces in the process are sequentially swapped across batches to obtain a neighborhood search scheme; Neighborhood search operator 2: For two adjacent batches in the scheduling scheme, sort the workpieces within the batch according to their density values; select the workpieces with the highest density values ​​from the earlier batches. Large workpieces form a set Select the highest density values ​​from the later batches. Short workpieces form a set ; set and set The workpieces in the process are sequentially exchanged across batches to obtain a neighborhood search scheme; the density value is defined as the ratio of the area of ​​the workpiece to the processing time of the workpiece. Neighborhood search operator 3: For all batches in the scheduling scheme, first determine the time-compatible sub-segment corresponding to each batch during the decoding process, then randomly select one layer from the layers involved in that batch, and exchange it with any layer involved in other batches within the same sub-segment to obtain the neighborhood search scheme. Neighborhood search operator 4: Randomly select from all batches of the scheduling scheme These batches are arranged in descending order of total processing time. Sort the batches; then, starting from the first sorted batch, select the workpiece with the longest processing time and place it into the remaining batches. Within each batch, a neighborhood search scheme is obtained; Neighborhood search operator 5: For all batches in the scheduling scheme, calculate the difference in processing time between the workpiece with the longest processing time and the workpiece with the second longest processing time in each batch. Sort all batches according to the difference and filter out the batch with the largest difference. Then select the workpiece with the longest processing time from the batch, determine the time-compatible set corresponding to the workpiece, and add the workpiece to the batch of other workpieces in its time-compatible set to obtain the neighborhood search scheme. Neighborhood search operator 6: For all batches in the scheduling scheme, select the workpieces with the longest processing time in each batch and form a set. From set Select workpieces in sequence In all subsequent batches following the selected workpiece, the workpieces with the closest size are selected to form a set. , will set and set The workpieces in the process are sequentially swapped across batches to obtain a neighborhood search scheme; Neighborhood search operator 7: also based on sets From the set Select workpieces sequentially from these. Calculate the density values ​​of all workpieces in the next adjacent batch of the selected batch, sort all workpieces in the next adjacent batch in descending order based on the density values, and then sort the workpieces... The neighborhood search scheme is obtained by exchanging the sorted workpieces with the workpieces in the adjacent batches one by one. Neighborhood search operator 8: also based on sets From the set Select workpieces in sequence Determine the time-compatible set and corresponding batch to which each workpiece belongs. Each workpiece must appear only once in each batch within a subset. Divide the entire workpiece set into several subsets, each containing one workpiece. Its corresponding time-compatible set is constituted; then extracted The set is composed of all the workpieces in the same batch. ,Will Time-compatible set elimination set After including all the workpieces, we get the set. If set The processing time of the workpiece with the shortest processing time in the set is greater than or equal to the processing time of the workpiece in the set. If the processing time of the workpiece with the longest processing time is the longest, then skip processing that workpiece. Neighborhood search; otherwise, select a set. The workpiece with the longest processing time is denoted as From the set Selected from those with a processing time of less than Workpiece construction set ; arranging the collections in ascending order of processing time. Try placing and removing the workpieces one by one. In subsequent batches, until the workpieces can no longer be accommodated or assembled. Empty; set Successfully inserted The workpieces belonging to the same batch are removed from their original batch, and finally... Put in From the batch, the neighborhood search scheme is obtained; Neighborhood search operator 9: For all batches in the scheduling method, first determine the corresponding time-compatible segment during the decoding process of each batch, and extract all layers of all batches within the time-compatible segment to construct a layer set. and assemble the shelves. The layers are sorted from longest to shortest processing time; the number of layers is determined by the preset quantity of the curing equipment. From the sorted set of shelves Select the first one in order Each layer forms a new first batch, and subsequent layers are grouped in sequence according to this rule to form new batches, thus obtaining the neighborhood search scheme; Of the nine neighborhood search operators mentioned above, the first four belong to random exploration-type neighborhood search optimization, while the remaining five belong to goal-oriented neighborhood search optimization. After performing neighborhood search optimization using each operator, the effectiveness of the neighborhood search optimization is determined by whether the fitness of the optimized individual is improved and whether it meets the time window constraint and workpiece size constraint. If it is effective, the optimized individual is output.

6. A curing and scheduling system for aerospace composites considering multi-layered spatial and temporal window constraints, the system being used to execute the curing and scheduling method for aerospace composites according to any one of claims 1-5, characterized in that, Specifically, it includes: The information acquisition unit is used to acquire basic information about the aerospace composite curing process, including workpiece information and curing equipment information; The scheduling model construction unit is used to construct a multi-layer spatial and temporal window single-machine batch scheduling model based on the basic information, wherein the model aims to minimize the maximum completion time. The scheduling scheme generation unit is used to solve the single-machine batch scheduling model using an evolutionary algorithm that combines adaptive neighborhood search to obtain the optimal scheduling scheme; The visualization output unit visualizes the workpiece batch allocation results, shelf placement and orientation, batch processing sequence and time arrangement based on the obtained optimal scheduling scheme.

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