Multi-constraint aircraft assembly scheduling method based on multi-target transfer learning

Abstract

The invention provides a multi-constraint aircraft assembly scheduling method based on multi-target transfer learning, and relates to the technical field of assembly scheduling. The method comprises the following steps: firstly, performing task decomposition on an assembly directory demand in an aircraft scheduling process, designing an operation station adjusting mechanism, and completing an operation station reconfiguration operation corresponding to an assembly task; then, updating the type of an operation station required by an assembly task, carrying out mathematical modeling on an aircraft scheduling problem, constructing a multi-constraint multi-target aircraft assembly scheduling problem model, determining an initialized task sequence of the task, establishing a non-dominated rapid sorting genetic algorithm optimization framework with a multi-target elite gene retention strategy, and establishing a multi-target migration strategy; obtaining a transferable solution set; finally, a Pareto frontier solution set is obtained, the solution with the minimum value in the Pareto frontier solution set is selected, a corresponding specific assembly scheme Gantt chart is obtained, an assembly scheduling table is made, and the assembly process of the aircraft is guided.

Description

Technical Field

[0001] The present invention relates to the technical field of assembly scheduling, and in particular to a multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning. Background Art

[0002] The flexibility of aircraft assembly workstations plays a vital role in the modern aviation manufacturing industry. With the continuous advancement of aviation technology and the diversification of market demands, assembly lines need to be more adaptable to meet the rapid switching and customization requirements of different aircraft models. Traditional fixed assembly models are no longer able to meet current production challenges, so the adoption of more flexible assembly workstations has become a solution. By improving the modular design and degree of automation of workstations, not only can production cycles be shortened and production efficiency improved, but manufacturing costs can also be reduced and quality control enhanced. Flexible assembly workstations can not only cope with ever-changing production tasks but also better support the further development of intelligent manufacturing, providing the aviation manufacturing industry with a strong competitive advantage.

[0003] Aircraft assembly scheduling involves a large number of complex task queues, resource limitations, and strict time constraints. The production rhythm switches rapidly, and multiple assembly objectives such as time utilization and resource cost balance need to be met. Traditional manual scheduling methods often have difficulty coping with multi-constraint and multi-objective scheduling problems. Therefore, the evolutionary algorithm's ability to enhance global search and good robustness in a highly dynamic scheduling environment can quickly generate high-quality scheduling solutions. Therefore, how to achieve assembly process scheduling agility and improve assembly process robustness becomes particularly important. A multi-constraint and multi-objective assembly scheduling method based on transfer learning is proposed to reduce the human resource consumption of the assembly process and shorten the assembly completion time, while achieving flexible use between assembly stations and achieving the goal of green production and manufacturing. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the present invention provides a multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning;

[0005] A multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning includes the following steps:

[0006] Step 1: Decompose the assembly catalog requirements during aircraft scheduling.

[0007] Specifically, the wing component in the assembly catalog is divided into wing spars, longitudinal beams, ribs, skins, and longitudinal walls through task decomposition. The order of assembly tasks is wing spars, ribs, longitudinal beams, longitudinal walls, and skins. Assembly resources are allocated according to this order.

[0008] Step 2: Design an operation station adjustment mechanism to complete the reconfiguration of the operation station corresponding to the assembly task.

[0009] The operation station adjustment mechanism is specifically as follows: if the current operation station Unavailable, and the task set at this operator station is , find the task set Each assembly task And the type of work corresponding to the task, randomly assign assembly tasks Go to the same type of operation station; if the current operation station Task set The number of assembly tasks is less than , then all assembly tasks in this operation station Randomly assign them to the same type of operation stations; update all the operation stations in turn and merge the update results into the operation station set middle;

[0010] Assume the number of assembly tasks is , the number of operating stations is , is the current operator station and the operator station set , For assembly tasks and , For assembly tasks Required workstations, For operation station type The task set of the above operation, This is the minimum assembly task limit for the operator station.

[0011] Step 3: Update the type of operating stations required for the assembly task based on the results of step 2, mathematically model the aircraft scheduling problem, and construct a multi-constraint and multi-objective aircraft assembly scheduling problem model;

[0012] The multi-constraint and multi-objective aircraft assembly scheduling problem model is as follows:

[0013] (1);

[0014] (2);

[0015] (3);

[0016] (4);

[0017] (5);

[0018] (6);

[0019] (7);

[0020] (8);

[0021] (9);

[0022] (10);

[0023] (11);

[0024] (12);

[0025] in, The maximum completion time for all assembly tasks; The maximum number of workers required for assembly; is the number of assembly tasks; the number of operation stations is ; Number of job qualifications; For the moment; is the current task index, For the task Predecessor index and ;when If it is 1, it is a task Need to be in the task Post-execution; For the current task The start time of If it is 0, it is a task No prerequisite tasks ; The start time is 0; For the current task End time; For the current task Execution time; For the current task the number of workers required; At the moment the number of workers; At the moment the maximum number of workers; Representative job qualification collection ; Represents a collection of operation station types ; Indicates at time Required job qualification The task set, Indicates at time Operator station required The task set; Indicates that at time t at the workstation the number of workers employed; It's time At the workstation The maximum number of people working, Describe as a task is assigned to the workstation with index k, Describe the task Assigned to index Type of work performed;

[0026] Step 4: Based on the multi-constraint and multi-objective aircraft assembly scheduling problem model The context constraints determine the initialization task sequence of the task;

[0027] Specifically, randomly search for the number of all assembly tasks that have no predecessor tasks as the starting task; set the current task to , looking for satisfaction Mission As a post-task, until all the The task number is obtained to obtain a task queue, that is, a chromosome that satisfies the task priority relationship; repeat step 4 to obtain multiple chromosome sets.

[0028] Step 5: Based on the multiple chromosomes obtained in step 4, that is, the initialization task sequence, calculate the maximum completion time of each chromosome and the maximum number of workers , get the first fitness And the second fitness .

[0029] Step 5-1: Traverse each task in the chromosome, assuming that the number of the current task is ,and , when a task After being selected, set a time The end time of all predecessor tasks of the current task;

[0030] Step 5-2: If the current task If there is no predecessor task, ; Otherwise, calculate the current task The end time of all predecessor tasks until the end time of the last predecessor task is found and assigned to ;

[0031] Step 5-3: Set up a The matrix is ​​used as the space number constraint; the current task The number of operators required is , find no more than Limited number of people The maximum end time of a number of workers ,Compare and The maximum value of the two is taken as the current task The starting time is ; Calculate the current task End time , For the current task Execution time;

[0032] Step 5-4: Repeat steps 5-1 to 5-3 to get the start and end times of all tasks and the total completion time. , and the first fitness is At the same time, the assembly task sequence is generated according to the size of the task start time and end time ;

[0033] Step 5-5: Assemble the sequence according to each task , calculate the assembly tasks at each moment Number of people required ; Calculate the total number of people at each moment , and the second fitness is .

[0034] Step 6: Establish a non-dominated quick sorting genetic algorithm NSGA-II optimization framework with a multi-objective elite gene retention strategy;

[0035] Step 6-1: Initialize the task sequence obtained in step 4 and the first fitness obtained in step 5 And the second fitness , set up a multi-objective selection strategy:

[0036] (13);

[0037] The weight value satisfy , and are the mean or maximum values ​​of the first fitness and the second fitness respectively;

[0038] A tournament selection method is introduced to randomly compare two individuals in the current population and retain the individual with the smaller frontier. If the frontiers are equal, the individual with the higher crowding distance is selected until the entire population is selected.

[0039] Step 6-2: Use two-point crossover and single-point mutation to complete the crossover and mutation process;

[0040] Step 6-3: Assume that the initial population is , the maximum number of iterations is , adopting a multi-objective elite retention strategy: First, calculate the initial population according to the multi-objective selection strategy Minimum fitness , the current number of iterations is , the initial population after iteration is updated to , the mean, maximum and minimum values ​​of the fitness of the population are 、 and ;

[0041] Step 6-3-1: When When, and When looking for All less than The chromosomes form a set , and randomly extract a chromosome from the set to replace The chromosome with the highest fitness among When , the population is not replaced If the chromosome is in , execute step 6-3-3;

[0042] Step 6-3-2: When When, and When looking for The chromosome with the smallest fitness is replaced The chromosome with the largest fitness among When , the population is not replaced If the chromosome is in , execute step 6-3-3;

[0043] Step 6-3-3: After step 6-3-1 or 6-3-2, the population is completed The updated population Initialize the population as new input , until completion iterations;

[0044] Step 7: Establish a multi-target migration strategy;

[0045] Step 7-1: Create two short assembly solutions FS1 and FS2 for Problem 1, adding or deleting the head and tail of some tasks, or Problem 2: generate a set of assembly solutions that meet the new assembly task requirements through the intersection of three assembly solutions FS1, FS2, and FS3, denoted as FL1. The solution to FL1 is to retain some assembly tasks and calculate and select the optimal solution as the assembly solution.

[0046] Step 7-2: The generated assembly solution FL1 first executes Step 2 to determine the availability of the operation stations and complete the station adjustment and worker reconfiguration. Each assembly task in solution FL1 corresponds to the execution time, worker type, number of workers, and operation station type. At the same time, solution FL1 is deduplicated, and the remaining solution set is recorded as FL2.

[0047] Step 7-3: Select some solutions in solution set FL2 as transferable solution sets :

[0048] (14);

[0049] in and Respectively represent the means of the two fitness values ​​in the solution set FL2; and Represents the minimum of two fitness values; and express and The span of ; Select two fitnesses in solution set FL2 and The solution that satisfies formula (14) is regarded as the transferable solution set. ;

[0050] Step 7-4: Migration judgment: The similarity function SI is defined as follows:

[0051] (15);

[0052] in is the mean of the set of transferable solutions; is the initial population The mean of and The two means are calculated using formula (13); and is the number of tasks in the retained parts of FS1 and FS2 in the two short assembly schemes; 、 、 and The number of tasks added and deleted by FS1 and FS2 respectively; and They represent the shortage tasks and redundant tasks at the intersection of the three assembly schemes FS1, FS2 and FS3 respectively; is the number of tasks for FL1; 、 、 、 is a positive constant and satisfies , ; The parameter relationship satisfies: and ; If the value of the function SI is greater than 70%, the solution set Can be used for migration; otherwise, when hour, If it is established, negative migration will occur;

[0053] Step 7-4-1: Introduce a new migration ratio :

[0054] (16);

[0055] in:

[0056] (17);

[0057] parameter 、 、 、 is a positive constant and satisfies , , and there are and Established; if ,but The maximum value of is 4; similarly, When The maximum value of is 8; is the initial population The minimum value of is calculated by formula (13); yes The span size is [3%, 5%];

[0058] Step 7-4-2: If , then the initial population Need to reinitialize; until satisfied until;

[0059] Step 7-4-3: When hour:

[0060] when When , the migration rate is [12%, 27%);

[0061] when When, if , the migration rate is [27%, 50%); if , then the migration rate is [50%,98%); when When , the migration rate is [98%, 100%).

[0062] Step 8: Using the non-dominated quick sort genetic algorithm optimization framework with the multi-objective elite gene retention strategy established in Step 6, the transferable solution set obtained in Step 7 and the initialization task sequence generated in Step 4 are iteratively optimized to obtain the final Pareto front solution set. The solution with the smallest value in the Pareto front solution set is selected. Based on the selected solution, a Gantt chart of the corresponding specific assembly plan is obtained, and an assembly schedule is created to guide the aircraft assembly process.

[0063] The beneficial effects of adopting the above technical solution are:

[0064] The present invention provides a multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning. Aiming at the complex and changeable aircraft assembly tasks, uncontrollable assembly resource failures, complex and changeable assembly tasks, high requirements on assembly cycle and resource utilization, traditional optimization cannot complete the extraction and use of historical assembly experience, and there is a clear need for modeling new assembly tasks. The method of the present invention transfers historical aircraft assembly experience to new tasks through transfer learning, significantly reduces training time and computing costs in new scenarios, quickly generates high-quality scheduling solutions, fully integrates information of assembly task data and assembly resource data, avoids repeated searches for task assembly features, reduces unnecessary workload, and speeds up the assembly optimization process. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A flow chart of the multi-constraint assembly scheduling intelligent method based on multi-objective transfer learning provided by the present invention;

[0066] Figure 2 A schematic diagram of an adjustable aircraft assembly process according to an embodiment of the present invention;

[0067] Figure 3 A schematic diagram of an assembly task queue provided by an embodiment of the present invention;

[0068] Figure 4 A schematic diagram of a multi-target migration process provided by an embodiment of the present invention;

[0069] Figure 5 A schematic diagram of the migration process provided by an embodiment of the present invention;

[0070] Figure 6 A schematic diagram of the Pareto optimization results of Problem 1 is provided for an embodiment of the present invention;

[0071] Figure 7 A schematic diagram of optimizing assembly time for Problem 1 is provided for an embodiment of the present invention;

[0072] Figure 8 A schematic diagram of optimizing the number of assembly personnel for Problem 1 is provided for an embodiment of the present invention. DETAILED DESCRIPTION

[0073] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0074] A multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning, such as Figure 1 As shown, the following steps are included:

[0075] Step 1: By Figure 2 The aircraft assembly scheduling process with adaptive operation station adjustment is shown. Assembly catalog requirements during aircraft scheduling are broken down into tasks. This embodiment fully leverages the information and constraints of known assembly task data to reconfigure scheduling resources through an assembly station control mechanism. This digitizes the entire assembly task and simplifies the mathematical modeling of the assembly problem through preprocessing resource allocation, thereby accelerating the algorithm's optimization process.

[0076] Specifically, the wing component in the assembly catalog is divided into several parts through task decomposition: wing spars, longitudinal beams, ribs, skins, and longitudinal walls. The order of assembly tasks is wing spars, ribs, longitudinal beams, longitudinal walls, and skins. Assembly resources are allocated according to this order.

[0077] The aircraft scheduling problem involves multiple operating stations, each of which can complete multiple assembly tasks. This means that assembly tasks can be transferred between multiple operating stations. Figure 2 During the operation station adjustment, operation station 3 indicates that the workstation is unable to complete task processing, and the assembly task is integrated into workstation 1. Operation station 2 means that only a small number of assembly tasks are performed at this station, so it can be replaced by operation station 1 to save assembly resources. It is worth noting that assembly tasks require the configuration of assembly personnel with different types of qualifications, multiple types of operation stations, and other assembly resources to meet assembly requirements. The complex and changing operating environment requires timely adjustment of the configuration of operation stations, and the adjustment of operation stations is accompanied by the reconfiguration of personnel and materials;

[0078] Step 2: According to Figure 2 In the above content, the operation station with a cross indicates that the operation station is unavailable, so it is necessary to design an operation station adjustment mechanism to complete the reconfiguration operation of the operation station corresponding to the assembly task.

[0079] The operation station adjustment mechanism is specifically as follows: if the current operation station Unavailable, and the task set at this operator station is , find the task set Each assembly task And the type of work corresponding to the task, randomly assign assembly tasks Go to the same type of operation station; if the current operation station Task set The number of assembly tasks is less than , then all assembly tasks in this operation station Randomly assign them to the same type of operation stations; update all the operation stations in turn and merge the update results into the operation station set middle;

[0080] Assume the number of assembly tasks is , the number of operating stations is , is the current operator station and the operator station set , For assembly tasks and , For assembly tasks Required workstations, For operation station type The task set of the above operation, This is the minimum assembly task limit for the operator station.

[0081] Step 3: Update the type of operating stations required for the assembly task based on the results of step 2, mathematically model the aircraft scheduling problem, and construct a multi-constraint and multi-objective aircraft assembly scheduling problem model;

[0082] The multi-constraint and multi-objective aircraft assembly scheduling problem model is as follows:

[0083] (1);

[0084] (2);

[0085] (3);

[0086] (4);

[0087] (5);

[0088] (6);

[0089] (7);

[0090] (8);

[0091] (9);

[0092] (10);

[0093] (11);

[0094] (12);

[0095] in, The maximum completion time for all assembly tasks; The maximum number of workers required for assembly; is the number of assembly tasks; the number of operation stations is ; Number of job qualifications; For the moment; is the current task index, For the task Predecessor index and ;when If it is 1, it is a task Need to be in the task Post-execution; For the current task The start time of If it is 0, it is a task No prerequisite tasks ; The start time is 0; For the current task End time; For the current task Execution time; For the current task the number of workers required; At the moment the number of workers; At the moment the maximum number of workers; Representative job qualification collection ; Represents a collection of operation station types ; Indicates at time Required job qualification The task set, Indicates at time Operator station required The task set; Indicates that at time t at the workstation the number of workers employed; It's time At the workstation The maximum number of people working, Describe as a task is assigned to the workstation with index k, Describe the task Assigned to index Type of work performed;

[0096] Step 4: Based on the multi-constraint and multi-objective aircraft assembly scheduling problem model The context constraints determine the initialization task sequence of the task;

[0097] Specifically, randomly search for the number of all assembly tasks that have no predecessor tasks as the starting task; set the current task to , looking for satisfaction Mission As a post-task, until all the The task number is obtained Figure 3 The task queue shown is a chromosome that satisfies the task priority relationship; repeat step 4 to obtain multiple chromosome sets.

[0098] Step 5: Based on the multiple chromosomes obtained in step 4, that is, the initialization task sequence, calculate the maximum completion time of each chromosome and the maximum number of workers , get the first fitness And the second fitness .

[0099] Step 5-1: Traverse each task in the chromosome, assuming that the number of the current task is ,and , when a task After being selected, set a time The end time of all predecessor tasks of the current task;

[0100] Step 5-2: If the current task If there is no predecessor task, ; Otherwise, calculate the current task The end time of all predecessor tasks until the end time of the last predecessor task is found and assigned to ;

[0101] Step 5-3: Set up a The matrix is ​​used as the space number constraint; the current task The number of operators required is , find no more than Limited number of people The maximum end time of a number of workers ,Compare and The maximum value of the two is taken as the current task The starting time is ; Calculate the current task End time , For the current task Execution time;

[0102] Step 5-4: Repeat steps 5-1 to 5-3 to get the start and end times of all tasks and the total completion time. , and the first fitness is At the same time, the assembly task sequence is generated according to the size of the task start time and end time ;

[0103] Step 5-5: Assemble the sequence according to each task , calculate the assembly tasks at each moment Number of people required ; Calculate the total number of people at each moment , and the second fitness is .

[0104] Step 6: Establish a non-dominated quick sorting genetic algorithm NSGA-II optimization framework with a multi-objective elite gene retention strategy;

[0105] Step 6-1: Initialize the task sequence obtained in step 4 and the first fitness obtained in step 5 And the second fitness , set up a multi-objective selection strategy:

[0106] (13);

[0107] The weight value satisfy , and are the mean or maximum values ​​of the first fitness and the second fitness respectively;

[0108] In the algorithm's iterative selection process, a tournament selection method is introduced to randomly compare two individuals in the current population and retain the individual with the smaller frontier. If the frontiers are equal, the individual with the higher crowding distance is selected until the entire population is selected.

[0109] Step 6-2: Use two-point crossover and single-point mutation to complete the crossover and mutation process;

[0110] Step 6-3: Assume that the initial population is , the maximum number of iterations is , adopting a multi-objective elite retention strategy: First, calculate the initial population according to the multi-objective selection strategy Minimum fitness , the current number of iterations is , the initial population after iteration is updated to , the mean, maximum and minimum values ​​of the fitness of the population are 、 and ;

[0111] In this embodiment, the initial population is set 100, the maximum number of iterations is 200;

[0112] Step 6-3-1: When When, and When looking for All less than The chromosomes form a set , and randomly extract a chromosome from the set to replace The chromosome with the highest fitness among When , the population is not replaced If the chromosome is in , execute step 6-3-3;

[0113] Step 6-3-2: When When, and When looking for The chromosome with the smallest fitness is replaced The chromosome with the largest fitness among When , the population is not replaced If the chromosome is in , execute step 6-3-3;

[0114] Step 6-3-3: After step 6-3-1 or 6-3-2, the population is completed The updated population Initialize the population as new input , until completion iterations;

[0115] Step 7: Establish a multi-target migration strategy;

[0116] The goal of this embodiment is to solve three important problems of transfer learning, namely Figure 4 As shown in the figure: What to migrate? How to migrate? When to migrate? Three key questions. In aircraft assembly scheduling, the main thing to migrate is past assembly experience, that is, to select excellent assembly sorting schemes with small fitness values ​​from mature assembly scheduling schemes. However, these sorting schemes cannot be used directly and require certain processing and judgment. According to the requirements of the new assembly task, certain task addition and subtraction operations or task fusion operations are performed on the existing assembly sorting schemes. By adding and subtracting tasks of the existing assembly sorting schemes, an assembly sorting scheme that meets the requirements of the new assembly task and can be migrated is obtained, such as Figure 5 shown.

[0117] Step 7-1: Establish Problem 1: Using two known short assembly solutions FS1 and FS2, add or delete the head and tail of some tasks, or Problem 2: Using three known short assembly solutions FS1, FS2, and FS3, generate a set of assembly solutions that meet the requirements of the new assembly task in the form of intersection, denoted as FL1; the solution of FL1 is to retain some assembly tasks and select the optimal solution as the assembly solution according to formula (14). For example: FS1: ①→②→③; FS2: ⑥→⑦→⑧; adding tasks: ④→⑤; ​​reducing tasks: ①→⑧; FL1: ②→③→④→⑤→⑥→⑦;

[0118] Step 7-2: The generated assembly solution FL1 first executes Step 2 to determine the availability of the operation stations and complete the station adjustment and worker reconfiguration. Each assembly task in solution FL1 corresponds to the execution time, worker type, number of workers, and operation station type. At the same time, solution FL1 is deduplicated, and the remaining solution set is recorded as FL2.

[0119] In this example, 5,000 solutions FL1 were generated. First, step 2 was executed to determine the availability of the operation stations, and to complete station adjustments and worker reconfiguration. Each assembly task in solution FL1 corresponded to an execution time, worker type, number of workers, and operation station type. At the same time, duplicate individuals in solution FL1 were removed, leaving a solution set FL2 with 3,772 solutions.

[0120] Step 7-3: Select some solutions in solution set FL2 as transferable solution sets :

[0121] (14);

[0122] in and Respectively represent the means of the two fitness values ​​in the solution set FL2; and Represents the minimum of two fitness values; and express and The span of ; Select two fitnesses in solution set FL2 and The solution that satisfies formula (14) is regarded as the transferable solution set. ;

[0123] In this embodiment, the parameters are set . Calculation yields: and They are 70.69 and 78.39 respectively. and 54 and 67 respectively, and They are 67.16 and 72.90 respectively. After selecting solution set FL2 as the transferable solution set is 105;

[0124] Step 7-4: Migration judgment: The similarity function SI is defined as follows:

[0125] (15);

[0126] in is the mean of the set of transferable solutions; is the initial population The mean of and The two means are calculated using formula (13); and is the number of tasks in the retained parts of FS1 and FS2 in the two short assembly schemes; 、 、 and The number of tasks added and deleted by FS1 and FS2 respectively; and They represent the shortage tasks and redundant tasks at the intersection of the three assembly schemes FS1, FS2 and FS3 respectively; is the number of tasks for FL1; 、 、 、 is a positive constant and satisfies , ; The parameter relationship satisfies: and ; If the value of the function SI is greater than 70%, the solution set Can be used for migration; otherwise, when hour, If it is established, negative migration will occur;

[0127] In this embodiment, the fitness value is calculated, where the parameter The mean of the set of transferable solutions ; Initialize population M Pop The mean ; n1 = 115, n2 = 85; add1 = 5, add2 = 5, del1 = 10, del2 = 11; the number of tasks for FL1 ; The parameter relationship satisfies: h1=0.32, h2=0.68. The value of the function SI is 89.83%, so the solution set Can be used to migrate to question 1;

[0128] Step 7-4-1: Introduce a new migration ratio :

[0129] (16);

[0130] in

[0131] (17);

[0132] parameter 、 、 、 is a positive constant and satisfies , , and there are and Established; if ,but The maximum value of is 4; similarly, When The maximum value of is 8; is the initial population The minimum value of is calculated by formula (13); yes The span size is [3%, 5%];

[0133] Step 7-4-2: If , then the initial population Need to reinitialize; until satisfied until;

[0134] Step 7-4-3: When hour:

[0135] when When , the migration rate is [12%, 27%);

[0136] when When, if , the migration rate is [27%, 50%); if , then the migration rate is [50%,98%); when When , the migration rate is [98%, 100%).

[0137] In this embodiment, ,and , the migration rate belongs to [27%,50%);

[0138] Parameters λ3=4.1, λ4=3.9, initial population Minimum value of =55.5, Δ=3%, so the migration ratio is It is 34%, and the number of migration solutions in the initial population is 34.

[0139] Step 8: Using the non-dominated rapid sorting genetic algorithm (NSGA-II) optimization framework with a multi-objective elite gene retention strategy established in Step 6, the transferable solution obtained in Step 7 and the initial population of chromosomes generated in Step 4 are iteratively optimized to obtain the final Pareto front solution set. The solution with the smallest value in the Pareto front solution set is selected using Formula (13). Based on the selected solution, a Gantt chart of the corresponding specific assembly plan is obtained. This guides the aircraft assembly process and achieves aircraft assembly scheduling.

[0140] In this embodiment × =34 and the number of partial populations generated in step 4 is -34, forming an initial population and performing iterative optimization to obtain the final Pareto front solution set.

[0141] In this embodiment, an example problem 1 is selected, such as Figure 5 、 Figure 6 、 Figure 7 as well as Figure 8 As shown, FS1 in Problem 1 has 115 assembly tasks and FS2 has 85 assembly tasks. Table 1 below shows the assembly data and required resource data of the assembly tasks. Contains several pre-tasks , worker type Indicates that the operator station category is The completion time of each task is represented by t. Indicates the number of people in the operation station. The number of workers required for each task is ,Table 1 shows some data of the assembly task.

[0142] Table 1. Partial data of assembly tasks: ;

[0143] Table 1 has been assigned to the tasks Perform data desensitization. At the same time, to facilitate subsequent algorithm processing, it is necessary to encode the worker type and operation station type, and generate a matrix of pre-task restrictions, number of workers, working hours, worker type, job type limit, operation station type, and operation station limit so that the computer can recognize and process it.

[0144] The data after integrating assembly resource data and constraints for all assembly tasks are as follows:

[0145] =[2 3 1 2 2 3 1 1 …];

[0146] T=[4 8 2 4 4 8 2 2 …];

[0147] The operation station types Weizhi 01, 02, 03, 04, 05, 06 and 07 are numbered 1, 2, 3, 4, 5, 6 and 7 respectively, and the generation station operation station type set is as follows:

[0148] =[1 2 3 4 1 2 2 4 …];

[0149] Worker type: ID, JG and SD are numbered 1, 2 and 3, generating the worker type set:

[0150] =[1 2 1 1 3 2 3 3 …];

[0151] Limit on the number of people at the operation station as follows:

[0152] =[10 10 10 10 10 10 10 10 …];

[0153] From the above table, we can conclude that the assembly task The process number 1 must be in the assembly task The operation can only be performed after the completion of tasks No. 3 and 23. If the constraint is empty, you don't need to consider the constraints of the previous task and can directly perform the assembly operation. And so on, to complete the initialization.

[0154] Number of workers, worker types, and required work hours associated with each task One to one correspondence.

[0155] Each job type can perform multiple tasks simultaneously , but there is no limit on the number of each worker type.

[0156] Each operating station can perform multiple tasks simultaneously Operating space is provided, but the number of people at each operating station is limited to 10.

[0157] The above description is merely an illustration of the preferred embodiments of the present disclosure and the technical principles employed. Those skilled in the art should understand that the scope of the invention encompassed by the embodiments of the present disclosure is not limited to technical solutions formed by specific combinations of the aforementioned technical features. It also encompasses other technical solutions formed by any combination of the aforementioned technical features or their equivalents, without departing from the aforementioned inventive concept. For example, a technical solution formed by replacing the aforementioned features with (but not limited to) technical features with similar functions disclosed in the embodiments of the present disclosure.

Claims

1. A multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning, characterized in that: The following steps are involved: Step 1: Decompose the assembly catalog requirements during aircraft scheduling. Step 2: Design an operation station adjustment mechanism to complete the reconfiguration of the operation station corresponding to the assembly task; Step 3: Update the operation station type required for the assembly task, mathematically model the aircraft scheduling problem, and construct a multi-constraint and multi-objective aircraft assembly scheduling problem model; Step 4: Based on the multi-constraint and multi-objective aircraft assembly scheduling problem model The context constraints determine the initialization task sequence of the task; Step 5: Based on the multiple chromosomes obtained in step 4, that is, the initialization task sequence, calculate the maximum completion time of each chromosome and the maximum number of workers , get the first fitness And the second fitness ; Step 6: Establish a non-dominated quick sort genetic algorithm optimization framework with a multi-objective elite gene retention strategy; Step 7: Establish a multi-objective migration strategy and obtain a set of transferable solutions; Step 8: By using the non-dominated quick sorting genetic algorithm optimization framework with the multi-objective elite gene retention strategy established in step 6, the transferable solution set obtained in step 7 and the initialization task sequence generated in step 4 are iteratively optimized to obtain the final Pareto front solution set. The solution with the smallest value in the Pareto front solution set is selected, and the corresponding specific assembly plan Gantt chart is obtained based on the selected solution. An assembly schedule is made to guide the assembly process of the aircraft.

2. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1 is characterized in that: The task decomposition described in step 1 is specifically to decompose the wing component in the assembly catalog into wing spars, longitudinal beams, ribs, skins, and longitudinal walls through task decomposition. The order of assembly tasks is wing spars, ribs, longitudinal beams, longitudinal walls, and skins. Assembly resources are configured according to this order.

3. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1 is characterized in that: The specific adjustment mechanism of the operation station in step 2 is: if the current operation station Unavailable, and the task set at this operator station is , find the task set Each assembly task And the type of work corresponding to the task, randomly assign assembly tasks Go to the same type of operation station; if the current operation station Task set The number of assembly tasks is less than , then all assembly tasks in this operation station Randomly assigned to operating stations of the same type of work; Update all operation stations in sequence and merge the updated results into the operation station set middle; Assume the number of assembly tasks is , the number of operating stations is , is the current operator station and the operator station set , For assembly tasks and , For assembly tasks Required workstations, For operation station type The task set of the above operation, This is the minimum assembly task limit for the operator station.

4. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1 is characterized in that: The multi-constraint and multi-objective aircraft assembly scheduling problem model described in step 3 is as follows: （1）； （2）； （3）； （4）； （5）； （6）； （7）； （8）； （9）； （10）； （11）； （12）； in, The maximum completion time for all assembly tasks; The maximum number of workers required for assembly; is the number of assembly tasks; the number of operation stations is ; Number of job qualifications; For the moment; is the current task index, For the task Predecessor index and ;when If it is 1, it is a task Need to be in the task Post-execution; For the current task The start time of If it is 0, it is a task No prerequisite tasks ; The start time is 0; For the current task End time; For the current task Execution time; For the current task the number of workers required; At the moment the number of workers; At the moment the maximum number of workers; Representative job qualification collection ; Represents a collection of operation station types ; Indicates at time Required job qualification The task set, Indicates at time Operator station required The task set; Indicates that at time t at the workstation the number of workers employed; It's time At the workstation The maximum number of people working, Describe as a task is assigned to the workstation with index k, Describe the task Assigned to index Type of work performed.

5. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1 is characterized in that: Specifically, step 4 is to randomly find the number of all assembly tasks that do not have a predecessor task as the starting task; set the current task to , looking for satisfaction Mission As a post-task, until all the The task number is obtained to obtain a task queue, that is, a chromosome that satisfies the task priority relationship; repeat step 4 to obtain multiple chromosome sets.

6. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1 is characterized in that: The step 5 specifically includes the following steps: Step 5-1: Traverse each task in the chromosome, assuming that the number of the current task is ,and , when a task After being selected, set a time The end time of all predecessor tasks of the current task; Step 5-2: If the current task If there is no predecessor task, ; Otherwise, calculate the current task The end time of all predecessor tasks until the end time of the last predecessor task is found and assigned to ; Step 5-3: Set up a The matrix is ​​used as the space number constraint; the current task The number of operators required is , find no more than Limited number of people The maximum end time of a number of workers ,Compare and The maximum value of the two is taken as the current task The starting time is ; Calculate the current task End time , For the current task Execution time; Step 5-4: Repeat steps 5-1 to 5-3 to get the start and end times of all tasks and the total completion time. , and the first fitness is At the same time, the assembly task sequence is generated according to the size of the task start time and end time ; Step 5-5: Assemble the sequence according to each task , calculate the assembly tasks at each moment Number of people required ; Calculate the total number of people at each moment , and the second fitness is .

7. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1 is characterized in that: The step 6 specifically includes the following steps: Step 6-1: Initialize the task sequence obtained in step 4 and the first fitness obtained in step 5 And the second fitness , set up a multi-objective selection strategy: （13）； The weight value satisfy , and are the mean or maximum values ​​of the first fitness and the second fitness respectively; A tournament selection method is introduced to randomly compare two individuals in the current population and retain the individual with the smaller frontier. If the frontiers are equal, the individual with the higher crowding distance is selected until the entire population is selected. Step 6-2: Use two-point crossover and single-point mutation to complete the crossover and mutation process; Step 6-3: Assume that the initial population is , the maximum number of iterations is , adopting a multi-objective elite retention strategy: First, calculate the initial population according to the multi-objective selection strategy Minimum fitness , the current number of iterations is , the initial population after iteration is updated to , the mean, maximum and minimum values ​​of the fitness of the population are 、 and ; Step 6-3-1: When When, and When looking for All less than The chromosomes form a set , and randomly extract a chromosome from the set to replace The chromosome with the highest fitness among When , the population is not replaced If the chromosome is in , execute step 6-3-3; Step 6-3-2: When When, and When looking for The chromosome with the smallest fitness is replaced The chromosome with the largest fitness among When , the population is not replaced If the chromosome is in , execute step 6-3-3; Step 6-3-3: After step 6-3-1 or 6-3-2, the population is completed The updated population Initialize the population as new input , until completion Iterations.

8. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1 is characterized in that: The step 7 specifically includes the following steps: Step 7-1: Create two short assembly solutions FS1 and FS2 for Problem 1, adding or deleting the head and tail of some tasks, or Problem 2: generate a set of assembly solutions that meet the new assembly task requirements through the intersection of three assembly solutions FS1, FS2, and FS3, denoted as FL1. The solution to FL1 is to retain some assembly tasks and calculate and select the optimal solution as the assembly solution. Step 7-2: The generated assembly solution FL1 first executes Step 2 to determine the availability of the operation stations and complete the station adjustment and worker reconfiguration. Each assembly task in solution FL1 corresponds to the execution time, worker type, number of workers, and operation station type. At the same time, solution FL1 is deduplicated, and the remaining solution set is recorded as FL2. Step 7-3: Select some solutions in solution set FL2 as transferable solution sets : （14）； in and Respectively represent the means of the two fitness values ​​in the solution set FL2; and Represents the minimum of two fitness values; and express and The span of ; Select two fitnesses in solution set FL2 and The solution that satisfies formula (14) is regarded as the transferable solution set. ; Step 7-4: Migration judgment: The similarity function SI is defined as follows: （15）； in is the mean of the set of transferable solutions; is the initial population The mean of and The two means are calculated using formula (13); and is the number of tasks in the retained parts of FS1 and FS2 in the two short assembly schemes; 、 、 and The number of tasks added and deleted by FS1 and FS2 respectively; and They represent the shortage tasks and redundant tasks at the intersection of the three assembly schemes FS1, FS2 and FS3 respectively; is the number of tasks for FL1; 、 、 、 is a positive constant and satisfies , ; The parameter relationship satisfies: and ; If the value of the function SI is greater than 70%, the solution set Can be used for migration; otherwise, when hour, If it is established, negative migration will occur; Step 7-4-1: Introduce a new migration ratio : （16）； in: （17）； parameter 、 、 、 is a positive constant and satisfies , , and there are and Established; if ,but The maximum value of is 4; similarly, When The maximum value of is 8; is the initial population The minimum value of is calculated by formula (13); yes The span size is [3%, 5%]; Step 7-4-2: If , then the initial population Need to reinitialize; until satisfied until; Step 7-4-3: When hour: when When , the migration rate is [12%, 27%); when When, if , the migration rate is [27%, 50%); if , then the migration rate is [50%,98%); when When , the migration rate is [98%, 100%).

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