Methods, systems, terminals, and media for optimizing production scheduling in aluminum alloy aerospace component creep forming production lines.

Abstract

This invention discloses a method, system, terminal, and medium for optimizing the production scheduling of an aluminum alloy aerospace component creep forming production line. The method includes: constructing a multi-dimensional objective function for optimizing the scheduling of the aluminum alloy aerospace component creep forming production line; generating a set of reference points; and initializing a parent population P of size N. t Using genetic operators on P t The operation yields a child population Q of size N. t P t and Q t The mixture yields a population U of size 2N. t From U t N individuals are selected. The selection process involves three stages: first, clustering-based selection; second, non-dominated sorting-based selection; and third, vector angle-based selection. This process is repeated until the iteration termination condition is met. A set of scheduling scheme solutions is obtained, and a fuzzy decision method is applied to select a high-quality production scheduling scheme. This three-stage selection method improves the ability to distinguish non-dominated solutions, strengthens the balance between population convergence and diversity, and yields high-quality production scheduling schemes.

Description

Technical Field

[0001] This invention relates to the field of aluminum alloy component manufacturing technology, and in particular to a method, system, terminal and medium for optimizing production scheduling of an aluminum alloy aerospace component creep forming production line. Background Technology

[0002] Aluminum alloys are among the most widely used non-ferrous metal structural materials in industry. Large aluminum alloy integral structural components, due to their ability to meet the design and manufacturing requirements of light weight and high strength, are widely used in the aerospace industry and are a major structural material, driving the development of the aerospace sector. Currently, creep aging forming technology has become an important manufacturing method for complex aerospace integral components.

[0003] Due to increasingly customized product demands from customers, the production characteristics of aluminum alloy aerospace component creep forming production lines have shifted to multi-variety, small-batch production. This has led to problems such as complex production organization, low production efficiency, and high costs, failing to meet the manufacturing requirements of modern large aluminum alloy aerospace components. Intelligent production scheduling for aluminum alloy creep forming production lines is crucial for improving production efficiency and reducing production costs. Therefore, research on high-dimensional multi-objective intelligent scheduling methods for aluminum alloy component creep forming production lines is necessary. The scheduling optimization problem of aluminum alloy aerospace component creep forming production lines has high-dimensional multi-objective characteristics. To achieve high quality, flexibility, high efficiency, and low consumption in the component manufacturing process, multiple scheduling objectives need to be comprehensively considered and optimized during the scheduling process. As the dimension of the objectives increases, the number of non-dominated individuals in the population of the evolutionary algorithm increases exponentially, thereby reducing the selection pressure of the evolutionary process. This leads to a decrease in the search capability of the evolutionary algorithm, making it difficult to guarantee the convergence and diversity balance of the evolutionary population. Consequently, the optimized production scheduling decision results fail to achieve the goal of cost reduction and efficiency improvement. Therefore, the optimization performance of high-dimensional multi-objective production scheduling decision optimization methods needs to be strengthened.

[0004] Currently, for production scheduling optimization methods in the creep forming production line of aluminum alloy aerospace components, traditional scheduling optimization methods are mainly based on the genetic evolution algorithm of Pareto dominance relationship. These methods have many shortcomings, such as the ability to distinguish solutions to the problem decreases as the number of targets increases, the effect of the strategy to maintain solution diversity is poor, and the computational cost is high. The level of rational allocation of production resources needs to be further improved. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method, apparatus, and medium for optimizing production scheduling in an aluminum alloy aerospace component creep forming production line, so as to rationally allocate production resources, improve the production efficiency of manufacturing enterprises, and reduce production costs.

[0006] Firstly, a method for optimizing production scheduling in an aluminum alloy aerospace component creep forming production line is provided, including the following steps:

[0007] S1: Construct a multi-dimensional objective function for optimizing the scheduling of the aluminum alloy aerospace component creep forming production line;

[0008] S2: Initialize a parent population of size N and generate a set of uniformly distributed reference points; each individual in the population uses a two-layer encoding, with the individual length being the number of components to be processed, the first layer encoding chromosome being the order in which the components are placed in the container, and the second layer encoding chromosome being the placement orientation of each component;

[0009] S3: Use genetic operators to operate on the parent population to obtain a child population of size N, and merge the parent population and the child population to obtain a merged population of size 2N.

[0010] S4: Based on the clustering method, select the individuals with the largest Chebyshev aggregation function value in each class from the merged population to form the first layer of individuals, and the remaining individuals to form the second layer of individuals. Add the individuals in the first layer to the intermediate population.

[0011] S5: Use a non-dominated ranking method to select individuals from the second layer to add to the intermediate population. Assume that the last non-dominated level added to make the size of the intermediate population greater than or equal to N is the l-th non-dominated level F. l Then directly transfer the individuals in the first layer and the first non-dominated level F1 to the (l-1)th non-dominated level F1. l-1 Individuals join the next generation of the parent population;

[0012] S6: Individual selection method based on vector angles from the l-th non-dominated level F l Select individuals to join the next generation of parent populations until the size of the next generation of parent populations is N;

[0013] S7: Determine if the iteration termination condition has been reached. If not, return to step S3; if yes, proceed to step S8.

[0014] S8: Use fuzzy decision-making to find the optimal compromise solution that comprehensively optimizes the multi-dimensional objective function, decode the optimal compromise solution, and obtain the production scheduling optimization scheme.

[0015] Furthermore, in step S1, the multidimensional objective function includes at least three of the following: the autoclave volume utilization function, the completion time function, the delivery delay time function, the equipment utilization function, and the autoclave support number function.

[0016] Furthermore, step S4 specifically includes:

[0017] S41: The population target value is normalized using the adaptive normalization method in the NSGA-Ⅲ algorithm;

[0018] S42: Calculate the PBI distance between the target value normalized vector and the reference vector for each individual in the population, associate each individual with the reference vector corresponding to its smallest PBI distance, and associate individuals under the same reference vector into a class; where the reference vector is the vector formed by the line connecting the reference point and the origin.

[0019] S43: The following improved Chebyshev aggregation function method is used to calculate the Chebyshev aggregation function value for each individual:

[0020]

[0021] In the formula, g te (xλ,z * f represents the Chebyshev aggregation function value of an individual. j (x) represents the j-th objective function value of individual x. Let λ represent the minimum value of the j-th objective function in the population. j This represents the weight of the j-th objective function;

[0022] S44: Extract the individuals with the largest Chebyshev aggregation function value from each class to form the first layer of individuals, and the remaining individuals to form the second layer of individuals. Add the individuals from the first layer to the intermediate population.

[0023] Furthermore, step S5 specifically includes:

[0024] S51: Perform non-dominated ranking on the individuals in the second layer to obtain non-dominated hierarchies F1, F2, ..., F1 from high to low. L L represents the total number of non-dominated levels;

[0025] S52: Add individuals from each non-dominated level to the intermediate population in descending order of non-dominated level, until the size of the intermediate population is greater than or equal to N.

[0026] S53: Assume the last non-dominated level added is the l-th non-dominated level F. l Then directly transfer the individuals in the first layer and the first non-dominated level F1 to the (l-1)th non-dominated level F1. l-1 Individuals join the next generation of the parent population.

[0027] Furthermore, step S6 specifically includes:

[0028] S61: At the l-th non-dominated level F l Select M extreme solutions. The extreme solutions in the solution set are defined as the solutions that have the smallest angle with the M objective vectors (1,0,...), (0,1,...), ..., (0,0,...,1), where M is the number of objective functions.

[0029] S62: Calculate whether the size reaches N when adding M extreme solutions to the next generation of parent population. If it is less than N, then start from the l-th non-dominated level F. l From the remaining individuals, the maximum vector angle retention strategy is used to select individuals to join the next generation parent population until the size of the next generation parent population is N; if it is greater than N, the worst individual deletion strategy based on fitness value is used to delete individuals from the M extreme solutions until the size of the next generation parent population is N.

[0030] Furthermore, in step S8, the optimal compromise solution is obtained through the following method:

[0031] Each objective function is processed using a fuzzy membership function, and the membership degree u of the i-th objective function is... i Its mathematical expression is as follows:

[0032]

[0033] In the formula, F i max and F i min Let represent the maximum and minimum values ​​of the i-th objective function for the N individuals in the final population, respectively;

[0034] The membership degree of the nth individual is standardized using the following formula:

[0035]

[0036] In the formula, u opt This represents the membership degree of the nth individual after standardization. Let M represent the membership degree of the nth individual, and M be the number of all objective functions.

[0037] The individual with the highest membership degree after standardization in the final population is selected as the optimal compromise solution.

[0038] Furthermore, in step S8, decoding the optimal compromise solution includes:

[0039] Based on the order of all the components to be processed into the autoclave and the placement of each component in the optimal compromise solution, the remaining rectangle method is used to develop the autoclave layout plan.

[0040] Based on the autoclave layout plan, the production scheduling of each component in each process is determined from the first process. During the scheduling process, the production of each process is arranged according to the first-come-first-served rule and the allocation rule of the first available equipment.

[0041] Secondly, a production scheduling optimization system for an aluminum alloy aerospace component creep forming production line is provided, including:

[0042] The objective function construction module is used to construct a multi-dimensional objective function for optimizing the scheduling of the aluminum alloy aerospace component creep forming production line.

[0043] The optimization module includes an initialization unit and an iteration unit;

[0044] The initialization unit is used to initialize a parent population of size N and generate a set of uniformly distributed reference points; each individual in the population uses a double-layer encoding, the individual length is the number of components to be processed, the first layer of encoding chromosome is the order in which the components are put into the tank, and the second layer of encoding chromosome is the placement orientation of each component;

[0045] The iterative unit is used to operate on the parent population using genetic operators to obtain a child population of size N, and to merge the parent and child populations to obtain a merged population of size 2N. Based on clustering methods, individuals with the largest Chebyshev aggregation function values ​​in each cluster of the merged population are selected to form the first layer of individuals, and the remaining individuals form the second layer of individuals. The individuals in the first layer are added to the intermediate population. For the individuals in the second layer, a non-dominated sorting method is used to select individuals to add to the intermediate population. It is assumed that the last non-dominated level added to make the size of the intermediate population greater than or equal to N is the l-th non-dominated level F. l Then directly transfer the individuals in the first layer and the first non-dominated level F1 to the (l-1)th non-dominated level F1. l-1 Individuals are added to the next generation of the parent population; the individual selection method based on vector angles starts from the l-th non-dominated level F. l Select individuals to join the next generation of parent populations until the size of the next generation of parent populations is N; iterate the above process until the iteration termination condition is reached.

[0046] The decision module is used to find the optimal compromise solution that comprehensively optimizes the multi-dimensional objective function using fuzzy decision-making methods, and decodes the optimal compromise solution to obtain the production scheduling optimization scheme.

[0047] Thirdly, an electronic terminal is provided, including:

[0048] A memory on which computer programs are stored;

[0049] A processor is used to load and execute the computer program to implement the production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components as described above.

[0050] Fourthly, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components as described above.

[0051] This invention proposes a production scheduling optimization method, system, terminal, and medium for an aluminum alloy aerospace component creep forming production line. Based on a high-dimensional multi-objective evolutionary method with three-stage environmental selection, it improves the ability to distinguish non-dominated solutions and strengthens the balance between population convergence and diversity. This ensures that the aluminum alloy aerospace component creep forming production line obtains a high-quality production scheduling scheme, enabling rational allocation of production resources, improving manufacturing efficiency, reducing production costs, enhancing production management and operation levels, and improving the enterprise's intelligent manufacturing level. Furthermore, it has significant implications for the improvement and development of production scheduling theory. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a flowchart of the production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components provided in this embodiment of the invention;

[0054] Figure 2 This is an xy plan view of the autoclave support provided in an embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram of chromosome encoding provided in an embodiment of the present invention;

[0056] Figure 4 This is a schematic diagram of the remaining rectangle update provided in an embodiment of the present invention;

[0057] Figure 5 This is the evolutionary trajectory of the HV index provided in the embodiments of the present invention;

[0058] Figure 6 This is the evolutionary trajectory of the IGD index provided in the embodiments of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0060] like Figure 1 As shown, this invention provides a production scheduling optimization method for an aluminum alloy aerospace component creep forming production line, comprising the following steps:

[0061] S1: Construct a multi-dimensional objective function for optimizing the scheduling of the aluminum alloy aerospace component creep forming production line.

[0062] The multidimensional objective function includes at least three of the following: autoclave volume utilization rate function, completion time function, delivery delay time function, equipment utilization rate function, and autoclave support number function. In this embodiment, we will use all five objective functions as an example. Let f1 to f5 represent these five optimization objective functions, and thus, we establish a creep aging forming production line full-process production scheduling model F that includes the five optimization objectives, as specifically defined below.

[0063] minF=(-f1,f2,f3,f4,f5) (1)

[0064] The volume utilization rate f1 of the autoclave. Improving the volume utilization rate of the autoclave helps to increase the production capacity of the autoclave equipment, improve the production efficiency of the creep forming production line, and reduce production costs. The volume utilization rate f1 of the autoclave is expressed as follows:

[0065]

[0066] In the formula, m represents the total number of supports in the autoclave planning, and v i The volume utilization rate for each stent.

[0067] Completion time f2. The completion time of the creep aging forming production line refers to the processing time to complete all pending orders. Completion time is one of the important scheduling objectives. Improving production efficiency is an important manifestation of the intelligent scheduling of the entire creep aging forming production line. The completion time f2 is expressed as follows:

[0068] f2 = max(C i |i=1,2,3…P) (3)

[0069] In the formula, C i Let P represent the time it takes for the last process of the i-th component to be completed, and let P represent the total number of components.

[0070] Delay time f3. The scheduling goal based on delay time is to deliver on time and reduce delay time. Delay time f3 is represented as follows:

[0071]

[0072] In the formula, DD i This indicates the delivery date of the i-th component.

[0073] Equipment idle time f4. Reducing equipment idle time can indirectly optimize the utilization rate of production line equipment and reduce the production cost of the aluminum alloy aerospace component creep forming production line. Equipment idle time f4 is expressed as follows:

[0074]

[0075] In the formula, T k The stop time after the k-th device completes order processing. The value can be 0 or 1, representing the process. Is it in machine M? k Upward processing, Indicate process In machine M k Processing time, O represents the j-th process of the i-th component. ij Choose the kth machine M k In the upper processing stage, D represents the total number of machines, and Q represents the upper processing stage. i This represents the total number of processes for the i-th component.

[0076] The number of filling cycles (number of supports) for an autoclave, f5, is represented as follows:

[0077] f5=m (6)

[0078] In the formula, m is the total number of supports in the autoclave planning.

[0079] The constraints of the full-process production scheduling model for the creep aging forming production line of aluminum alloy aerospace components are as follows:

[0080] max(x i1 -x j3 ,x j1 -x i3 ,y i2 -y j4 ,y j2 -y i4 )≥0 (7)

[0081] 0≤x qh ≤W (8)

[0082] 0≤y qh ≤L (9)

[0083] 0≤z q ≤H (10)

[0084] Figure 2 This shows the placement of the component fixture in the xy plane of the autoclave support, x i1 x i3 Let y and y represent the minimum and maximum values ​​of a component on the x-axis in the xy-plane of the autoclave support, respectively. i2 y i4 Let x represent the minimum and maximum values ​​of a component on the x-axis in the xy-plane of the autoclave support; j1 xj3 Let y and y represent the minimum and maximum values ​​of the other component on the x-axis in the xy-plane of the autoclave support, respectively. j2 y j4 Let q represent the minimum and maximum values ​​of the other component on the x-axis in the xy-plane of the autoclave support. Let q be i or j, h be 1, 2, 3, or 4, and z be... q The vertical height of the component is indicated by W, L, and H, which represent the width, length, and height of the autoclave support. Formula (7) indicates that there is no overlap between the positions of the two component fixtures placed on the autoclave support; Formula (8) indicates that the position of the component fixture does not exceed the width of the autoclave support; Formula (9) indicates that the longitudinal position of the component fixture does not exceed the length of the autoclave support; Formula (10) indicates that the vertical position of the component fixture does not exceed the height of the autoclave support; at the same time, the stacking station can only process one component fixture at a time; the creep aging forming process parameters of all components to be processed are known; only components with the same or similar creep aging forming process parameters can be placed in the same autoclave for creep aging forming process; the number of component fixtures in the autoclave is less than the number of vacuum nozzles and thermocouples required.

[0085] S2: Initialize a parent population of size N and generate a set of uniformly distributed reference points; each individual in the population uses a double-layer coding, with the individual length being the number of components to be processed, the first layer coding chromosome being the order in which the components are placed in the container, and the second layer coding chromosome being the placement orientation of each component.

[0086] To effectively solve the full-process production scheduling problem of the aluminum alloy aerospace component creep forming production line, this embodiment adopts a two-layer coding method, such as... Figure 3 As shown. The length of the chromosome represents the number of components to be processed. The first layer of the coded chromosome indicates the order in which the components are placed in the autoclave. The second layer of the coded chromosome indicates the orientation of each component. The orientation of the components determines whether they need to be rotated 90° when placed on the autoclave support.

[0087] Decoding involves converting the encoding scheme into a feasible production scheduling plan. During decoding, the processing sequence of components specified in the encoding chromosome and the placement of each component on the autoclave supports are first determined. The creep forming process is the bottleneck process of the production line; therefore, decoding first requires creating an autoclave layout plan for all components to be processed. Based on the order in which all components enter the autoclaves and their placement positions, the remaining rectangle method is used to create the autoclave layout plan. Based on the autoclave layout plan, the number of times each component is placed in the autoclave, the number of support layers, and its position coordinates can be determined. After completing the autoclave layout plan, the production scheduling of each component in each process is arranged starting from the first process. During production scheduling, the First-In-First-Out (FCFS) rule and the First Idle Equipment Allocation (FAM) rule are used to arrange the production of each process. Based on the above decoding method, the encoding chromosome can be transformed into a production scheduling plan for the creep aging forming production line of aluminum alloy aerospace components.

[0088] S3: Use genetic operators (selection, crossover, mutation) to operate on the parent population to obtain a child population of size N. Merge the parent population and the child population to obtain a merged population of size 2N.

[0089] In practice, the genetic selection operator uses a tournament selection method. The crossover operator for both chromosome layers uses a two-point crossover method. First, the two parent chromosomes are paired. If the random number is less than the crossover probability, crossover is performed on the paired parent chromosomes. Two crossover points are randomly selected on the coding chromosome, and then partial gene segment exchanges are performed. For the first chromosome layer, the crossover segment from the second parent chromosome is placed before the coding string of the first parent chromosome. Then, starting from the initial gene, duplicate component numbers are checked, and the second duplicate component number is deleted. The same process is repeated, placing the crossover segment from the first parent chromosome before the coding string of the second parent chromosome, and then sequentially deleting genes from the second parent chromosome. For the two-point crossover method on the second chromosome layer, two crossover points are randomly set on the individual coding chromosome, and then partial gene segment exchanges are performed, finally forming two offspring individuals. The mutation operator uses a two-point swap mutation method on the chromosome. Two genes are randomly selected on the coding chromosome, and their positions are swapped to generate a new coding chromosome.

[0090] S4: Based on the clustering method, select the individuals with the largest Chebyshev aggregation function value in each class from the merged population to form the first layer of individuals, and the remaining individuals to form the second layer of individuals. Add the individuals in the first layer to the intermediate population.

[0091] Step S4 specifically includes:

[0092] S41: The adaptive normalization method in the NSGA-III algorithm is used to normalize the population target value. Since the dimensions of each target are inconsistent during production scheduling, the adaptive normalization method in NSGA-III is needed to solve this problem. Find the ideal point. Let be the minimum value of the i-th objective function in the population. Then, the objective function can be transformed through the ideal point, and the formula is as follows: f i '(x) is the i-th objective function after transformation.

[0093] Calculate the extreme points according to the following formula (11):

[0094]

[0095] Where, (ω j1 ,ω j2 ,ω j3 ,…ω jM ) T For the target axis f j If the axis direction is ω, then ω ji Satisfies formula (12):

[0096]

[0097] The M extreme points form an M-dimensional linear hyperplane. Therefore, the intercept *a* can be calculated. i If i = 1, ..., M, then the objective function can be normalized to:

[0098]

[0099] In the formula, Let represent the minimum value of the i-th objective function in the population.

[0100] S42: Calculate the PBI distance between the target value normalized vector and the reference vector for each individual in the population. Associate each individual with the reference vector corresponding to its smallest PBI distance. Individuals associated with the same reference vector are classified into the same class. The reference vector is the vector formed by the line connecting the reference point and the origin. Using the PBI distance instead of the vertical distance, which only represents diversity, balances convergence and diversity. j,1 (x) is the projected distance of f(x), d j,2 f(x) is the perpendicular distance from f(x), and its mathematical expression is as follows:

[0101] d j,1 (x)=||(f n (x) T ω ji )|| / ||ω ji|| (14)

[0102] d j,2 (x)=||f n (x)-d j,1 (x)(ω ji / ||ω ji ||)|| (15)

[0103] d j,1 (x) is used to evaluate the convergence of the population, d j,2 d(x) is a method for measuring population diversity. θ is a pre-defined penalty parameter, and the PBI distance can be expressed as d(x) = dθ / θ. j,1 (x)+θd j,2 (x), which can provide a comprehensive measure of x, and this method combines convergence and diversity.

[0104] S43: The improved Chebyshev aggregation function method is used to calculate the Chebyshev aggregation function value for each individual. The main feature of the aggregation function is that it integrates multiple optimization objective values ​​into a single objective function. The improved Chebyshev aggregation function formula is shown in (16). Using the improved Chebyshev aggregation function instead of the original Chebyshev aggregation function as a decomposition method can make the optimization solution uniformly distributed in the objective space. For the Tchebyshev decomposition, the weight vector λ of the subproblem is... j The direction is inconsistent with its optimal solution. However, for the improved Tchebycheff decomposition, the weight vector λ of the subproblem... j It is aligned with the direction of its optimal solution. For the improved Tchebycheff decomposition, it has a weight vector λ. j The optimal solution to the subproblem is precisely the Pareto front (PF) and the weight vector λ. j The intersection of the two, therefore, the weight vector λ in the improved Tchebycheff decomposition. j It can also be seen as a preference direction.

[0105]

[0106] In the formula, g te (xλ,z * f represents the Chebyshev aggregation function value of an individual. j (x) represents the j-th objective function value of individual x. Let λ represent the minimum value of the j-th objective function in the population. j This represents the weight of the j-th objective function;

[0107] S44: Extract the individuals with the largest Chebyshev aggregation function value from each class to form the first layer of individuals, and the remaining individuals to form the second layer of individuals. Add the individuals from the first layer to the intermediate population. The selection method for the first layer of individuals not only focuses on maintaining global diversity, but also prioritizes population convergence when selecting individuals for each class.

[0108] S5: Use a non-dominated ranking method to select individuals from the second layer to add to the intermediate population. Assume that the last non-dominated level added to make the size of the intermediate population greater than or equal to N is the l-th non-dominated level F. l Then directly transfer the individuals in the first layer and the first non-dominated level F1 to the (l-1)th non-dominated level F1. l-1 Individuals join the next generation of the parent population.

[0109] Step S5 specifically includes:

[0110] S51: Perform non-dominated ranking on the individuals in the second layer to obtain non-dominated hierarchies F1, F2, ..., F1 from high to low. L L represents the total number of non-dominated levels;

[0111] S52: Add individuals from each non-dominated level F1, F2, ... to the intermediate population in descending order of non-dominated level, until the size of the intermediate population is greater than or equal to N.

[0112] S53: Assume the last non-dominated level added is the l-th non-dominated level F. l Then directly transfer the individuals in the first layer and the first non-dominated level F1 to the (l-1)th non-dominated level F1. l-1 Individuals join the next generation of the parent population.

[0113] S6: Individual selection method based on vector angles from the l-th non-dominated level F l Individuals are selected to join the next generation of parent populations until the size of the next generation of parent populations is N.

[0114] Step S6 specifically includes:

[0115] S61: At the l-th non-dominated level F l Select M extreme solutions. The extreme solutions in the solution set are defined as the solutions that have the smallest angle with the M objective vectors (1,0,...), (0,1,...), ..., (0,0,...,1), where M is the number of objective functions.

[0116] S62: Calculate whether the size reaches N when adding M extreme solutions to the next generation of parent population. If it is less than N, then start from the l-th non-dominated level F. lThe remaining individuals are selected using the maximum vector angle retention strategy to add individuals to the next generation parent population until the size of the next generation parent population is N. If the size is greater than N, the worst individual deletion strategy based on fitness value is used to delete individuals from the M extreme solutions until the size of the next generation parent population is N. The maximum vector angle retention strategy is as follows: First, obtain the vector angle between the individual to be selected and the individuals in the next generation parent population, calculate the maximum value of the vector angle between the individual and the individuals in the next generation parent population as its vector angle, and then select the individual with the largest vector angle among the individuals to be selected. The worst individual deletion strategy is as follows: Calculate the improved Chebyshev aggregation function value of the M extreme solutions based on equation (16) as its fitness value, and select the individual with the smallest fitness value for deletion.

[0117] S7: Determine whether the iteration termination condition has been reached (such as reaching the preset number of iterations or the preset iteration time). If not, return to step S3; if yes, proceed to step S8.

[0118] S8: Use fuzzy decision-making to find the optimal compromise solution that comprehensively optimizes the multi-dimensional objective function, decode the optimal compromise solution, and obtain the production scheduling optimization scheme.

[0119] In step S8, the optimal compromise solution is obtained through the following method:

[0120] Each objective function is processed using a fuzzy membership function, and the membership degree u of the i-th objective function is... i Its mathematical expression is as follows:

[0121]

[0122] In the formula, F i max and F i min Let represent the maximum and minimum values ​​of the i-th objective function for the N individuals in the final population, respectively;

[0123] The membership degree of the nth individual is standardized using the following formula:

[0124]

[0125] In the formula, u opt This represents the membership degree of the nth individual after standardization. Let M represent the membership degree of the nth individual, and M be the number of all objective functions.

[0126] The individual with the highest membership degree after standardization in the final population is selected as the optimal compromise solution.

[0127] In step S8, decoding the optimal compromise solution includes:

[0128] Based on the order of all the components to be processed into the autoclave and the placement of each component in the optimal compromise solution, the remaining rectangle method is used to develop the autoclave layout plan.

[0129] Based on the autoclave layout plan, the production scheduling of each component in each process is determined from the first process. During the scheduling process, the production of each process is arranged according to the first-come-first-served rule and the allocation rule of the first available equipment.

[0130] To effectively solve the full-process production scheduling model for the creep forming production line of aluminum alloy aerospace components, the problem of autoclave loading must first be addressed. Tooling within the autoclaves must be placed on supports, which have a double-layer structure. The autoclave loading schedule is determined by the component tooling placed on the double-layer supports. Based on the known component tooling entry sequence, the three-dimensional double-layer support loading method needs to determine the number of support layers and the corresponding position for each component tooling entering the autoclave, and consequently, the number of autoclaves required to process the current component order.

[0131] In this embodiment, the residual rectangle method is used to compile the autoclave layout plan. Before layout, the order of the components to be placed and the orientation of each component (whether to rotate 90°) are already determined. B1 = [0 0L1 H1] represents the size information of the first layer of support, which is represented by a rectangle and indicated by the two diagonal points of the rectangle. (0,0) represents the origin, and (L1,H1) represents the diagonal point opposite the origin, where L1 and H1 are the length and width of the first layer of support of the autoclave. Similarly, B2 = [0 0L2H2] represents the size information of the second layer of support. Matrix A stores the coordinates and dimensions of each component.

[0132] The steps of the remaining rectangle method are as follows:

[0133] 1. First, determine whether the component needs to be rotated 90° based on its placement orientation. Components that do not need to be rotated should retain their original length and width dimensions. For components that do need to be rotated, adjust their length and width dimensions. Determine the external dimensions of each component according to the above rules.

[0134] 2. Place the current component i within the remaining rectangles. Find the set of rectangles re that can contain the current component i within the set of remaining rectangles rest. Based on the BL (bottom-up left-justified) condition, determine which rectangle in the set of rectangles re to place component i. At the same time, the information in matrix A needs to be updated.

[0135] 3. Update the number of support layers. If the remaining rectangle set `rest` does not contain a rectangle suitable for placing the current component fixture `i`, then the number of supports needs to be updated. If the first layer of supports has been used to place the fixture, then the placement plan for the second layer of supports needs to be developed; if the second layer of supports has been used to place the fixture, then a new batch needs to be started, and the placement plan for the first layer of supports needs to be developed simultaneously. When starting the placement plan for a new layer of supports, the information in the remaining rectangle set `rest` and matrix A needs to be updated promptly.

[0136] 4. Update the remaining rectangle set `rest`. When placing the current component fixture `i` in remaining rectangle `j`, it's necessary to determine if other remaining rectangles will be generated, and if so, delete remaining rectangle `j`. For example... Figure 4 As shown, when component fixture i is placed in the remaining rectangle j = [x0, y0, x1, y1], remaining rectangles a1 = [x2, y0, x1, y1] and a2 = [x0, y2, x1, y1] will be generated.

[0137] In optimizing high-dimensional multi-objective scheduling models, the NSGA-III algorithm's niche preservation strategy primarily maintains population diversity during each execution, neglecting the balance between population convergence and diversity. Therefore, niche-based environment selection methods are unsuitable for solving the full-process production scheduling problem of aluminum alloy aerospace component creep forming production lines. Consequently, the aforementioned embodiment proposes a three-stage environment selection method for optimizing production scheduling in aluminum alloy aerospace component creep forming production lines. This three-stage method improves the ability to distinguish non-dominated solutions, strengthens the balance between population convergence and diversity, and ensures high-quality production scheduling for aluminum alloy aerospace component creep forming production lines. It enables rational allocation of production resources, improves manufacturing efficiency, reduces production costs, enhances production management and operation, and elevates the level of intelligent manufacturing. Furthermore, it is of significant importance for improving and developing production scheduling theory.

[0138] This invention also provides a production scheduling optimization system for an aluminum alloy aerospace component creep forming production line, comprising:

[0139] The objective function construction module is used to construct a multi-dimensional objective function for optimizing the scheduling of the aluminum alloy aerospace component creep forming production line.

[0140] The optimization module includes an initialization unit and an iteration unit;

[0141] The initialization unit is used to initialize a parent population of size N and generate a set of uniformly distributed reference points; each individual in the population uses a double-layer encoding, the individual length is the number of components to be processed, the first layer of encoding chromosome is the order in which the components are put into the tank, and the second layer of encoding chromosome is the placement orientation of each component;

[0142] The iterative unit is used to operate on the parent population using genetic operators to obtain a child population of size N, and to merge the parent and child populations to obtain a merged population of size 2N. Based on clustering methods, individuals with the largest Chebyshev aggregation function values ​​in each cluster of the merged population are selected to form the first layer of individuals, and the remaining individuals form the second layer of individuals. The individuals in the first layer are added to the intermediate population. For the individuals in the second layer, a non-dominated sorting method is used to select individuals to add to the intermediate population. It is assumed that the last non-dominated level added to make the size of the intermediate population greater than or equal to N is the l-th non-dominated level F. l Then directly transfer the individuals in the first layer and the first non-dominated level F1 to the (l-1)th non-dominated level F1. l-1 Individuals are added to the next generation of the parent population; the individual selection method based on vector angles starts from the l-th non-dominated level F. l Select individuals to join the next generation of parent populations until the size of the next generation of parent populations is N; iterate the above process until the iteration termination condition is reached.

[0143] The decision module is used to find the optimal compromise solution that comprehensively optimizes the multi-dimensional objective function using fuzzy decision-making methods, and decodes the optimal compromise solution to obtain the production scheduling optimization scheme.

[0144] It should be understood that the functional unit modules in the various embodiments of the present invention can be concentrated in one processing unit, or each unit module can exist physically separately, or two or more unit modules can be integrated into one unit module, and can be implemented in hardware or software.

[0145] This invention also provides an electronic terminal, comprising:

[0146] A memory on which computer programs are stored;

[0147] A processor is used to load and execute the computer program to implement the production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components as described in the foregoing embodiments.

[0148] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components as described in the foregoing embodiments.

[0149] It is understood that the same or similar parts in the above embodiments can be referred to each other, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0150] To further illustrate this point, the technical solution of the present invention will be further explained below with reference to specific experiments.

[0151] To verify the efficiency and feasibility of the proposed production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components, 10 benchmark cases (ACF01 to ACF10) were constructed. The benchmark case information is shown in Table 1. The cases were generated with reference to the actual process parameters of each aluminum alloy component.

[0152] Table 1

[0153]

[0154]

[0155] To demonstrate the efficiency of the proposed optimization method (RTEA optimization method) in solving the full-process production scheduling model of the creep forming production line for aluminum alloy aerospace components, T-DEA, SPEA2+SDE, EFR_RR, and NSGA-Ⅲ were used as comparative optimization methods. To ensure fairness in the comparison, the population size, crossover / mutation method, and crossover / mutation probability were kept consistent. Simultaneously, a fixed time was used as the iteration stopping criterion during the comparison process. The RTEA optimization method computed each baseline case 5 times, stopping after 50 iterations per iteration. The average computation time for each case was used as the iteration stopping time, as shown in Table 2.

[0156] Table 2

[0157]

[0158] This experiment uses two performance metrics, IGD (Inverted Generational Distance) and HV (Hypervolume), to verify the superiority of the proposed HMOMA algorithm. Both metrics are comprehensive performance evaluation indicators. The smaller the IGD value, the better the algorithm's diversity and convergence. The larger the HV value, the better the algorithm's diversity and convergence.

[0159] IGD calculates the individuals in the true Pareto optimal solution set P to the non-dominated solution set P obtained by the algorithm. * The average distance.

[0160]

[0161] In the formula, mindis(x,P) represents P * The minimum Euclidean distance from individual x in P to individual p in P.

[0162] Hypervolume can be used to evaluate the quality of a solution set by a single value of its hypervolume. Hypervolume is a comprehensive metric for evaluating the convergence and diversity of approximate solution sets.

[0163]

[0164] In the formula, δ represents the Lebesgue measure, |S| represents the number of non-dominated solution sets, and v i This represents the hypervolume formed by the reference point and the i-th solution in the solution set.

[0165] The parameters were set as follows in this experiment.

[0166] Table 3

[0167]

[0168] Tables 4 and 5 show the average IGD and HV indices and the p-values ​​of the rank-sum test obtained by each algorithm after running 30 times on all benchmark instances. Values ​​that significantly outperform other algorithms are indicated in bold. The RTEA optimization method outperforms other algorithms in IGD and HV indices in most test instances. Based on the experimental results, the efficiency and feasibility of the full-process production scheduling model for aluminum alloy aerospace components and the RTEA optimization method are verified. The application of the RTEA method is beneficial for obtaining high-quality production scheduling schemes.

[0169] Table 4

[0170]

[0171] Table 5

[0172]

[0173] The feasibility and efficiency of the RTEA decision optimization method are analyzed in detail using the ACF01 benchmark case as an example. Figure 5 and Figure 6 This paper depicts the evolutionary trajectories of two performance metrics as the number of function evaluations increases when five optimization methods solve the whole-process production scheduling problem of creep forming production line for aluminum alloy aerospace components. The HV performance metric of the five algorithms gradually increases with the number of function evaluations, while the IGD performance metric gradually decreases, indicating that the convergence performance of the five algorithms is stable. Figure 5 The HV evolution curve of the RTEA algorithm is higher than other curves. Figure 6 The IGD evolution curve of the RTEA algorithm is lower than that of other curves, indicating that the RTEA optimization method has a better evolutionary effect.

[0174] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied 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.

[0175] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0176] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0177] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0178] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for optimizing production scheduling in an aluminum alloy aerospace component creep forming production line, characterized in that, Includes the following steps: S1: Construct a multi-dimensional objective function for optimizing the scheduling of the aluminum alloy aerospace component creep forming production line; S2: Initialize a parent population of size N and generate a set of uniformly distributed reference points; each individual in the population uses a two-layer encoding, with the individual length being the number of components to be processed, the first layer encoding chromosome being the order in which the components are placed in the container, and the second layer encoding chromosome being the placement orientation of each component; S3: Use genetic operators to operate on the parent population to obtain a child population of size N, and merge the parent population and the child population to obtain a merged population of size 2N. S4: Based on the clustering method, select the individuals with the largest Chebyshev aggregation function value in each class from the merged population to form the first layer of individuals, and the remaining individuals to form the second layer of individuals. Add the individuals in the first layer to the intermediate population. S5: Use a non-dominated ranking method to select individuals from the second layer to add to the intermediate population. Assume that the last non-dominated level added to make the size of the intermediate population greater than or equal to N is the l-th non-dominated level F. l Then directly transfer the individuals in the first layer and the first non-dominated level F1 to the (l-1)th non-dominated level F1. l-1 Individuals join the next generation of the parent population; S6: Individual selection method based on vector angles from the l-th non-dominated level F l Select individuals to join the next generation of parent populations until the size of the next generation of parent populations is N; S7: Determine if the iteration termination condition has been reached. If not, return to step S3; if yes, proceed to step S8. S8: Use fuzzy decision-making to find the optimal compromise solution that comprehensively optimizes the multi-dimensional objective function, decode the optimal compromise solution, and obtain the production scheduling optimization scheme; Step S4 specifically includes: S41: The population target value is normalized using the adaptive normalization method in the NSGA-Ⅲ algorithm; S42: Calculate the PBI distance between the target value normalized vector and the reference vector for each individual in the population, associate each individual with the reference vector corresponding to its smallest PBI distance, and associate individuals under the same reference vector into a class; where the reference vector is the vector formed by the line connecting the reference point and the origin. S43: The following improved Chebyshev aggregation function method is used to calculate the Chebyshev aggregation function value for each individual: ； In the formula, g te (xλ,z * f represents the Chebyshev aggregation function value of an individual. j (x) represents the j-th objective function value of individual x. Let λ represent the minimum value of the j-th objective function in the population. j This represents the weight of the j-th objective function; S44: Extract the individuals with the largest Chebyshev aggregation function value from each class to form the first layer of individuals, and the remaining individuals to form the second layer of individuals. Add the individuals from the first layer to the intermediate population. Step S5 specifically includes: S51: Perform non-dominated ranking on the individuals in the second layer to obtain non-dominated hierarchies F1, F2, ..., F from high to low. L L represents the total number of non-dominated levels; S52: Add individuals from each non-dominated level to the intermediate population in descending order of non-dominated level, until the size of the intermediate population is greater than or equal to N. S53: Assume the last non-dominated level added is the l-th non-dominated level F. l Then directly transfer the individuals in the first layer and the first non-dominated level F1 to the (l-1)th non-dominated level F1. l-1 Individuals join the next generation of the parent population; Step S6 specifically includes: S61: At the l-th non-dominated level F l Select M extreme solutions. The extreme solutions in the solution set are defined as the solutions that have the smallest angle with the M objective vectors (1,0,...), (0,1,...), ..., (0,0,...,1), where M is the number of objective functions. S62: Calculate whether the size reaches N when adding M extreme solutions to the next generation of the parent population. If it is less than N, then start from the l-th non-dominated level F. l The remaining individuals are selected using the maximum vector angle retention strategy to add individuals to the next generation parent population until the size of the next generation parent population is N; if it is greater than N, the worst individual deletion strategy based on fitness value is used to delete individuals from the M extreme solutions until the size of the next generation parent population is N, and the fitness value of the M extreme solutions is its improved Chebyshev aggregation function value. The constraints of the full-process production scheduling model for the creep aging forming production line of aluminum alloy aerospace components are as follows: （7）； （8）； （9）； （10）； In the formula, x i1 x i3 Let y and y represent the minimum and maximum values ​​of a component on the x-axis in the xy-plane of the autoclave support, respectively. i2 y i4 Let x represent the minimum and maximum values ​​of a component on the y-axis in the xy-plane of the autoclave support; j1 x j3 Let y and y represent the minimum and maximum values ​​of the other component on the x-axis in the xy-plane of the autoclave support, respectively. j2 y j4 These represent the minimum and maximum values ​​of the other component on the y-axis in the xy-plane of the autoclave support, respectively.

2. The production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components according to claim 1, characterized in that, In step S1, the multidimensional objective function includes at least three of the following: autoclave volume utilization rate function, completion time function, delivery delay time function, equipment utilization rate function, and autoclave support number function.

3. The production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components according to claim 1, characterized in that, In step S8, the optimal compromise solution is obtained through the following method: Each objective function is processed using fuzzy membership functions. The membership degree ui of the i-th objective function is expressed mathematically as follows: ； In the formula, and Let represent the maximum and minimum values ​​of the i-th objective function for the N individuals in the final population, respectively; The membership degree of the nth individual is standardized using the following formula: ； In the formula, u opt This represents the membership degree of the nth individual after standardization. Let M represent the membership degree of the nth individual, and M be the number of all objective functions. The individual with the highest membership degree after standardization in the final population is selected as the optimal compromise solution.

4. The production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components according to claim 1, characterized in that, In step S8, decoding the optimal compromise solution includes: Based on the order of all the components to be processed into the autoclave and the placement of each component in the optimal compromise solution, the remaining rectangle method is used to develop the autoclave layout plan. Based on the autoclave layout plan, the production scheduling of each component in each process is determined from the first process. During the scheduling process, the production of each process is arranged according to the first-come-first-served rule and the allocation rule of the first available equipment.

5. A production scheduling optimization system for an aluminum alloy aerospace component creep forming production line, characterized in that, The method for optimizing the production scheduling of an aluminum alloy aerospace component creep forming production line as described in any one of claims 1-4 includes: The objective function construction module is used to construct a multi-dimensional objective function for optimizing the scheduling of the aluminum alloy aerospace component creep forming production line. The optimization module includes an initialization unit and an iteration unit; The initialization unit is used to initialize a parent population of size N and generate a set of uniformly distributed reference points; each individual in the population uses a double-layer encoding, the individual length is the number of components to be processed, the first layer of encoding chromosome is the order in which the components are put into the tank, and the second layer of encoding chromosome is the placement orientation of each component; The iterative unit is used to operate on the parent population using genetic operators to obtain a child population of size N, and to merge the parent and child populations to obtain a merged population of size 2N. Based on clustering methods, individuals with the largest Chebyshev aggregation function values ​​in each cluster of the merged population are selected to form the first layer of individuals, and the remaining individuals form the second layer of individuals. The individuals in the first layer are added to the intermediate population. For the individuals in the second layer, a non-dominated sorting method is used to select individuals to add to the intermediate population. It is assumed that the last non-dominated level added to make the size of the intermediate population greater than or equal to N is the l-th non-dominated level F. l Then directly transfer the individuals in the first layer and the first non-dominated level F1 to the (l-1)th non-dominated level F1. l-1 Individuals are added to the next generation of the parent population; the individual selection method based on vector angles starts from the l-th non-dominated level F. l Select individuals to join the next generation of parent populations until the size of the next generation of parent populations is N; iterate the above process until the iteration termination condition is reached. The decision module is used to find the optimal compromise solution that comprehensively optimizes the multi-dimensional objective function using fuzzy decision-making methods, and decodes the optimal compromise solution to obtain the production scheduling optimization scheme.

6. An electronic terminal, characterized in that, include: A memory on which computer programs are stored; A processor is configured to load and execute the computer program to implement the production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components as described in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the production scheduling optimization method for the creep forming production line of aluminum alloy aerospace components as described in any one of claims 1 to 4.

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