A multi-constrained aircraft assembly scheduling method based on multi-objective transfer learning

Abstract

The application provides a multi-constraint aircraft assembly scheduling method based on multi-target migration learning, and relates to the technical field of assembly scheduling. Firstly, task decomposition is performed on assembly list requirements in the aircraft scheduling process, an operation station adjustment mechanism is designed, and reconfiguration operation of operation stations corresponding to assembly tasks is completed; then, operation station types required by the assembly tasks are updated, an aircraft scheduling problem is mathematically modeled, a multi-constraint multi-target aircraft assembly scheduling problem model is constructed, an initial task sequence of the tasks is determined, a non-dominated fast sorting genetic algorithm optimization framework with a multi-target elite gene reservation strategy is established, a multi-target migration strategy is established, and a migratable solution set is obtained; finally, a Pareto front solution set is obtained, one solution with the minimum value in the Pareto front 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 application relates to the technical field of assembly scheduling, in particular to a multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning. BACKGROUND

[0002] The flexibility of aircraft assembly stations plays a crucial role in modern aviation manufacturing. With the continuous advancement of aviation technology and the diversification of market demand, assembly production lines need to have higher adaptability to cope with the rapid switching of different types of aircraft and customized needs. Traditional fixed assembly mode has been unable to meet the current production challenges, therefore, using more flexible assembly stations has become the solution. By improving the modular design and automation level of the workstation, not only can the production cycle be shortened, the production efficiency can be improved, but also the manufacturing cost can be reduced, and the quality control can be improved. Flexible assembly stations not only can cope with changing production tasks, but also can better support the further development of intelligent manufacturing, providing a strong competitive advantage for the aviation manufacturing industry.

[0003] Aircraft assembly scheduling involves a large number of complex task queues, resource constraints and strict time constraints, production rhythm rapid switching, while meeting time utilization and resource cost balance and other multiple assembly targets. Traditional manual scheduling methods often have difficulty coping with multi-constrained and multi-objective scheduling problems. Therefore, the ability of evolutionary algorithms to enhance global search and good robustness in high dynamic scheduling environments can quickly generate high-quality scheduling schemes. Therefore, how to achieve assembly process scheduling agility and improve assembly process robustness becomes particularly important. A multi-constraint multi-objective assembly scheduling method based on transfer learning is proposed to reduce the consumption of human resources in the assembly process and reduce the assembly completion time, while achieving flexible use between assembly stations, achieving the goal of green production and manufacturing. SUMMARY

[0004] In view of the deficiencies of the prior art, the present application 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, comprising the following steps:

[0006] Step 1: task decomposition of assembly directory requirements in aircraft scheduling process;

[0007] Task decomposition specifically includes decomposing the whole component wing in the assembly directory into wing spar, stringer, wing rib, skin and longitudinal wall through task decomposition, the order of assembly tasks is wing spar, wing rib, stringer, longitudinal wall, skin, and assembly resources are configured according to the order;

[0008] Step 2: design operation station adjustment mechanism, complete reconfiguration operation of operation station corresponding to assembly task.

[0009] The operator station adjustment mechanism is specifically as follows: if the current operator station Unavailable, and the task set at this operator station is Find the task set Each assembly task As well as the job type corresponding to the task, assembly tasks are randomly assigned. Go to an operator station of the same job type; if the current operator station task set The number of assembly tasks is less than Then all assembly tasks in this workstation Randomly assign them to workstations of the same job type; update all workstations sequentially and merge the update results into the workstation set. middle;

[0010] Let the number of assembly tasks be... The number of operator stations is , For the current operator station and operator station set , For assembly tasks and , For assembly tasks Required workstation For the need in operator station type The task set for the above operation, This is the minimum assembly task limit for the operator station.

[0011] Step 3: Update the type of operator station required for the assembly task based on the results in Step 2, and mathematically model the aircraft scheduling problem to construct a multi-constraint, multi-objective aircraft assembly scheduling problem model.

[0012] The model for the multi-constraint, multi-objective aircraft assembly scheduling problem 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] where, is the maximum completion time of all assembly tasks; is the maximum number of workers required during assembly; is the number of assembly tasks; the number of operation stations is ; the number of skill sets; is the time instant; is the current task index, is the task immediately preceding the task index and ; when is 1, it is the task must be executed after the task ; is the start time of the current task ; when is 0, it is the task has no preceding task ; has a start time of 0; is the end time of the current task ; is the execution time of the current task ; is the number of workers required for the current task ; is the number of workers at time instant ; is the maximum number of workers at time instant ; represents the set of skill sets ; represents the set of operation station types ; represents the set of tasks that require skill set at time instant , represents the set of tasks that require operation station at time instant ; represents the set of tasks that require operation station The number of workers on duty; It is a moment At the workstation Maximum number of employees allowed on the job Described as a task It was assigned to the workstation with index k. Describe the task Assigned to index The type of work performed;

[0026] Step 4: Based on the multi-constraint, multi-objective aircraft assembly scheduling problem model The preceding and following relationships are constrained to determine the initial task sequence of the task;

[0027] Specifically, randomly select a task number from all assembly tasks that has no preceding task as the starting task; set the current task as... Seeking satisfaction Task As a subsequent task, until all conditions are met. The task number is used to obtain the task queue, which is a chromosome that satisfies the task priority relationship; step 4 is repeated to obtain a set of multiple chromosomes.

[0028] Step 5: Based on the multiple chromosomes obtained in Step 4, i.e., the initial task sequence, calculate the maximum completion time for each chromosome. and maximum number of employees , to obtain first fitness and second fitness .

[0029] Step 5-1: Traverse each task in the chromosome, assuming the current task's number is... ,and When a certain task Once selected, set a time. The end time of all preceding tasks of the current task;

[0030] Step 5-2: Assuming the current task If there are no prerequisite tasks, then Otherwise, calculate the current task. The end times of all prerequisite tasks are calculated until the end time of the last prerequisite task is found and assigned a value. ;

[0031] Step 5-3: Set one The matrix serves as a spatial constraint on the number of people; current task The required number of operators is Find out no more than Number of people limited the maximum value of the end time of the number of workers , compare and , take the maximum value of the two as the start time of the current task , that is ; calculate the end time of the current task , is the execution time of the current task ;

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

[0033] Step 5-5: According to the assembly sequence of each task , calculate the number of people needed for each assembly task at each time ; calculate the total number of people at each time , get the second fitness .

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

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

[0036] (13) ;

[0037] Wherein the weight value satisfies , and are the mean or maximum value of the first fitness and the second fitness respectively;

[0038] Introduce the tournament selection method, randomly compare two individuals in the current population, and keep the individual with small front; if the front is equal, select the individual with higher crowding distance, until the number of individuals in the entire population is selected;

[0039] Step 6-2: Complete the crossover and mutation process by using two-point crossover and single-point mutation that meet the task priority relationship;

[0040] ​Step 6-3: Assume that the initial population is , the maximum number of iterations is , and the multi-objective elitist strategy is adopted: first, the initial population is calculated according to the multi-objective selection strategy , the minimum value of the fitness is , the current number of iterations is , and the initial population after iteration is updated to , the mean, maximum, and minimum values of the fitness of this population are , , respectively;

[0041] Step 6-3-1: When , and , find all chromosomes in that are less than to form a set , and randomly extract a chromosome from the set to replace the chromosome with the maximum fitness in . If , do not replace the chromosomes in the population , then execute step 6-3-3;

[0042] Step 6-3-2: When , and , find the chromosome with the minimum fitness in , and replace the chromosome with the maximum fitness in . If , do not replace the chromosomes in the population , then execute step 6-3-3;

[0043] Step 6-3-3: After step 6-3-1 or 6-3-2, update the population , and use the updated population as the new input to initialize the population , until iterations are completed;

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

[0045] Step 7-1: Establish problem 1: two short assembly schemes FS1 and FS2, add or delete the head and tail of part tasks, or problem 2: three assembly schemes FS1, FS2, and FS3 through intersection, generate an assembly scheme set that meets the new assembly task requirements, denoted as FL1; the solution of FL1 is to retain part of the assembly tasks and calculate the optimal solution as the assembly scheme;

[0046] Step 7-2: The generated assembly scheme FL1 first executes step 2, determines the availability of the workstation, and completes the site adjustment and worker reconfiguration; each assembly task in scheme FL1 corresponds to the execution time, worker type, number of workers, and workstation type; at the same time, scheme FL1 is deduplicated, and the remaining solution set is denoted as FL2;

[0047] Step 7-3: Select a subset of solutions from solution set FL2 as the transferable solution set. :

[0048] (14);

[0049] in and These represent the mean values ​​of the two fitness values ​​in the solution set FL2; and This represents the minimum of two fitness values; and express and The span; where the parameters satisfy Choose two fitness values ​​from the solution set FL2. and The solutions that satisfy formula (14) are considered as the transferable solution set. ;

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

[0051] (15);

[0052] in It is the mean of the transferable solution set; It is to initialize the population. The mean, and The two means are calculated using formula (13); and It is the number of tasks for the reserved portions of FS1 and FS2 in the two short assembly schemes; , , and The number of tasks added and deleted in FS1 and FS2 respectively; and These represent the shortage and redundant tasks at the intersection of the three assembly schemes FS1, FS2, and FS3, respectively. This refers to the number of tasks in FL1; , , , It is a positive constant and satisfies , ; the parameter relationship satisfies: and ; if the value of function SI is greater than 70%, the solution set can be used for migration; otherwise, when , is true, there will be a negative migration case;

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

[0054] (16);

[0055] wherein:

[0056] (17);

[0057] The parameters , , , are normal numbers and satisfy , , and have and ; if , the maximum value of is 4; similarly, , then the maximum value of is 8; is the minimum value of the initial population calculated by formula (13); is the span size of [3%, 5%];

[0058] Step 7-4-2: If , the initial population needs to be reinitialized; until is satisfied;

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

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

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

[0062] Step 8: The final Pareto front solution set is obtained by iteratively optimizing the migratable solution set obtained in step 7 and the initial task sequence generated in step 4 through the non-dominated fast sorting genetic algorithm optimization framework using the multi-objective elitist genetic reservation strategy established in step 6, one solution with the minimum value in the Pareto front solution set is selected, the corresponding specific assembly scheme Gantt chart is obtained according to the selected solution, the assembly scheduling table is made, and thus the assembly process of the aircraft is guided;

[0063] The beneficial effects generated by the above technical solutions are as follows:

[0064] The application provides a multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning, which is used for solving the problems that aircraft assembly tasks are complex and changeable, uncontrollable assembly resource failures occur, assembly tasks are complex and changeable, high requirements are required for assembly cycle and resource utilization, traditional optimization cannot extract and use historical assembly experience, and a new assembly task needs to be explicitly modeled, the method migrates historical aircraft assembly experience to a new task through transfer learning, significantly reduces training time and calculation cost in a new scene, quickly generates a high-quality scheduling scheme, sufficiently fuses information of assembly task data and assembly resource data, avoids repeatedly searching for task assembly features, reduces unnecessary workload, and speeds up the assembly optimization process. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 A multi-constraint assembly scheduling intelligent method flowchart based on multi-objective transfer learning is provided for the application.

[0066] Figure 2 A schematic diagram of an aircraft assembly adjustable process is provided for the embodiment of the application.

[0067] Figure 3 A schematic diagram of an assembly task queue is provided for the embodiment of the application.

[0068] Figure 4 A schematic diagram of a multi-objective transfer process is provided for the embodiment of the application.

[0069] Figure 5 A schematic diagram of a transfer process is provided for the embodiment of the application.

[0070] Figure 6 A schematic diagram of the Pareto optimization result of problem 1 is provided for the embodiment of the application.

[0071] Figure 7 A schematic diagram of assembly time optimization of problem 1 is provided for the embodiment of the application.

[0072] Figure 8 A schematic diagram of assembly number optimization of problem 1 is provided for the embodiment of the application. DETAILED DESCRIPTION

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

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

[0075] Step 1: The aircraft assembly scheduling process with adaptive operation station adjustment is shown in Figure 2 . The assembly catalog requirements in the aircraft scheduling process are task decomposed; in this embodiment, the information and constraint relationships of known assembly task data are fully utilized to complete the reconfiguration of scheduling resources through the assembly station regulation mechanism, which informationizes and datafies the entire assembly task, simplifies the resource configuration preprocessing in the mathematical modeling process of the assembly problem, thereby speeding up the optimization process of the algorithm.

[0076] Task decomposition specifically refers to decomposing the whole component wing in the assembly catalog into wing spar, stringer, wing rib, skin, and longitudinal wall through task decomposition. Here, the assembly task sequence is wing spar, wing rib, stringer, longitudinal wall, and skin, and the assembly resources are configured according to this sequence;

[0077] The aircraft scheduling problem includes multiple operation stations, and each operation station can complete multiple assembly tasks. This means that assembly tasks can be transferred between multiple operation stations. Therefore, in Figure 2 operation station adjustment, operation station 3 indicates that the workstation cannot complete task processing, and the assembly task is integrated into workstation 1. Operation station 2 means that only a small amount of assembly tasks are executed at the 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 different types of assembly personnel, multiple types of operation stations, and other assembly resources to meet assembly requirements. The complex and variable operation 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 , the operation station with a cross indicates that the operation station is not available, so an operation station adjustment mechanism needs to be designed to complete the reconfiguration of the operation station corresponding to the assembly task.

[0079] The operation station adjustment mechanism specifically refers to: if the current operation station is not available, and the task set at the operation station is , find each assembly task in the task set and the type of work corresponding to the task, and randomly assign the assembly task to the operation station of the same work type; if the current operation station the task set of the operation station If the number of assembly tasks in the operation station is less than , all assembly tasks in the operation station are randomly assigned to the operation stations of the same type; sequentially update all operation stations and merge the update results into the operation station set

[0080] Let the number of assembly tasks be , the number of operation stations be , be the current operation station and the operation station set , be the assembly task and , be the assembly task required workstations, be the task set that needs to be operated on the operation station type , be the minimum assembly task limit of the operation station.

[0081] Step 3: Update the operation station type required by the assembly task according to the result in step 2, mathematically model the aircraft scheduling problem, and construct a multi-constraint multi-objective aircraft assembly scheduling problem model;

[0082] The multi-constraint 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] where, is the maximum completion time of all assembly tasks; is the maximum number of workers required for assembly; is the number of assembly tasks; the number of operation stations is ; the number of worker qualifications; is the time instant; is the current task index, is the task immediately preceding the task index and ; when is 1, it is the task that needs to be executed after the task ; is the start time of the current task ; when is 0, it is the task that has no preceding task ; has a start time of 0; is the end time of the current task ; is the execution time of the current task ; is the number of workers required for the current task ; is the number of workers at time instant ; is the maximum number of workers at time instant ; represents the set of worker qualifications ; represents the set of operation station types ; denotes the set of tasks that require worker qualification at time instant , denotes the set of tasks that require operation station at time instant ; denotes the number of workers working at workstation at time instant t, is the maximum number of workers limit at workstation at time instant , describes that task is assigned to the workstation with index k, describes that task is assigned to the worker with index ;

[0096] Step 4: Based on the multi-constraint, multi-objective aircraft assembly scheduling problem model The preceding and following relationships are constrained to determine the initial task sequence of the task;

[0097] Specifically, randomly select a task number from all assembly tasks that has no preceding task as the starting task; set the current task as... Seeking satisfaction Task As a subsequent task, until all conditions are met. 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 a set of multiple chromosomes.

[0098] Step 5: Based on the multiple chromosomes obtained in Step 4, i.e., the initial task sequence, calculate the maximum completion time for each chromosome. and maximum number of employees , to obtain first fitness and second fitness .

[0099] Step 5-1: Traverse each task in the chromosome, assuming the current task's number is... ,and When a certain task Once selected, set a time. The end time of all preceding tasks of the current task;

[0100] Step 5-2: Assuming the current task If there are no prerequisite tasks, then Otherwise, calculate the current task. The end times of all prerequisite tasks are calculated until the end time of the last prerequisite task is found and assigned a value. ;

[0101] Step 5-3: Set one The matrix serves as a spatial constraint on the number of people; current task The required number of operators is Find out no more than Number of people limited The maximum number of workers' end times ,Compare and The size of the two values ​​is taken as the current task. The start 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 obtain the start time and end time of all tasks, and obtain the total completion time , obtain the first fitness , and generate each assembly task sequence according to the size of the start time and end time of the task ;

[0103] Step 5-5: According to each task assembly sequence , calculate the number of people needed by each assembly task at each time ; calculate the total number of people at each time , obtain the second fitness .

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

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

[0106] (13);

[0107] Wherein the weight value satisfies , and are the mean or maximum value of the first fitness and the second fitness respectively;

[0108] In the selection process of algorithm iteration, the tournament selection method is introduced, and two individuals in the current population are randomly compared to retain the individual with small front. If the front is equal, select the individual with higher crowding distance, until the number of individuals in the entire population is selected;

[0109] Step 6-2: Complete the crossover and mutation process by using two-point crossover and single-point mutation that meet the task priority relationship;

[0110] Step 6-3: Assuming that the initial population is , the maximum number of iterations is , and the multi-objective elite reservation strategy is adopted: first, calculate the minimum value of the initial population fitness according to the multi-objective selection strategy , the current iteration number is , and the updated initial population after iteration is The mean, maximum and minimum of the fitness of the population are , and ;

[0111] The initial population in this embodiment is set to 100, and the maximum number of iterations is set to 200.

[0112] Step 6-3-1: When , and , find all chromosomes in that are less than to form a set , and randomly extract a chromosome from the set to replace the chromosome with the maximum fitness in . If , do not replace the chromosome in the population , and then execute step 6-3-3.

[0113] Step 6-3-2: When , and , find the chromosome with the minimum fitness in , and replace the chromosome with the maximum fitness in . If , do not replace the chromosome in the population , and then execute step 6-3-3.

[0114] Step 6-3-3: After step 6-3-1 or 6-3-2, the update of the population is completed, and the updated population is used as the new input to initialize the population , until the number of iterations is completed.

[0115] Step 7: Establish a multi-objective migration strategy.

[0116] In this embodiment, the goal is to solve the three important problems of transfer learning, i.e., as shown in Figure 4 : what to transfer? How to transfer? When to transfer? The main transfer in aircraft assembly scheduling is the past assembly experience, i.e., selecting excellent assembly scheduling schemes with small fitness values from mature assembly scheduling schemes. However, these scheduling schemes cannot be used directly and require certain processing and judgment. According to the requirements of the new assembly task, certain task addition or task fusion operations are performed on the existing assembly scheduling schemes. The assembly scheduling schemes that meet the requirements of the new assembly task can be transferred by adding or subtracting tasks from the existing assembly scheduling schemes, as shown in Figure 5 .

[0117] ​​​Step 7-1: Establish Problem 1: Using two known short assembly schemes FS1 and FS2, add or delete the head and tail of some tasks, or Problem 2: Using three known short assembly schemes FS1, FS2 and FS3, generate an assembly scheme set that meets the requirements of the new assembly task through the intersection, denoted as FL1; The solution of FL1 is to retain some assembly tasks and calculate and select the optimal solution as the assembly scheme according to formula (14). For example: FS1: ①→②→③; FS2: ⑥→⑦→⑧; Add task: ④→⑤; ​​Reduce task: ①→⑧; FL1: ②→③→④→⑤→⑥→⑦;

[0118] Step 7-2: The generated assembly scheme FL1 first executes step 2, determines the availability of the workstation, and completes the site adjustment and worker reconfiguration; each assembly task in scheme FL1 corresponds to the execution time, worker type, number of workers, and workstation type; at the same time, scheme FL1 is deduplicated, and the remaining solution set is denoted as FL2;

[0119] In this embodiment, 5000 solutions FL1 are generated. First, step 2 is executed to determine the availability of the workstation and complete the site adjustment and worker reconfiguration. Each assembly task in solution FL1 corresponds to the execution time, worker type, number of workers and workstation type. At the same time, duplicate individuals in solution FL1 are deduplicated, leaving 3772 solutions FL2.

[0120] Step 7-3: Select a subset of solutions from solution set FL2 as the transferable solution set. :

[0121] (14);

[0122] in and These represent the mean values ​​of the two fitness values ​​in the solution set FL2; and This represents the minimum of two fitness values; and express and The span; where the parameters satisfy Choose two fitness values ​​from the solution set FL2. and The solutions that satisfy formula (14) are considered as the transferable solution set. ;

[0123] In this embodiment, parameters are set. Calculations show that: and They were 70.69 and 78.39 respectively. and 54 and 67, respectively, and 67.16 and 72.90, respectively. The selected solution FL2 in the FL1 solution set is 105;

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

[0125] (15);

[0126] wherein is the mean value of the migratable solution set; is the mean value of the initialization population , and The calculation of the two mean values uses formula (13); and are the number of tasks in the reserved parts of FS1 and FS2 in the two short assembly schemes; , , and are the number of added and deleted tasks of FS1 and FS2, respectively; and respectively represent the short tasks and redundant tasks at the intersection of the three assembly schemes FS1, FS2 and FS3; is the number of tasks in FL1; , , , is a normal number 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 , is true, there will be a negative migration case;

[0127] In this embodiment, the fitness value is calculated, wherein the parameter . The mean value of the migratable solution set ; the mean value of the initialization population M Pop is ; n1=115, n2=85; add1=5, add2=5, del1=10, del2=11; the number of tasks in FL1 is ; 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 for migration to problem 1;

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

[0129] (16);

[0130] in

[0131] (17);

[0132] parameter , , , It is a positive constant and satisfies , And there are and Valid; if ,but The maximum value is 4; similarly, At that time, The maximum value is 8; It is the initial population The minimum value can be calculated using formula (13); yes The span is [3%, 5%];

[0133] Step 7-4-2: If Then the initial population Reinitialization is required; until the condition is met. until;

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

[0135] when At that time, the migration rate was [12%, 27%].

[0136] when At that time, if The migration rate is [27%, 50%]); if The migration rate is [50%, 98%]); when At that time, the migration rate was [98%, 100%].

[0137] This embodiment conforms to ,and The migration rate falls within the range of [27%, 50%].

[0138] Parameters λ3=4.1, λ4=3.9, initial population minimum value =55.5, Δ=3%, therefore, the migration ratio is obtained. The number of migration solutions in the initial population is 34.

[0139] Step 8: The migratable solution obtained in step 7 is iteratively optimized with the initial population composed of chromosomes generated in step 4 by using the non-dominated sorting genetic algorithm II (NSGA-II) optimization framework established in step 6 based on the multi-objective elitist genetic reservation strategy, to obtain the final Pareto frontier solution set. The value of the selected one in the Pareto frontier solution set is selected by formula (13), and the corresponding specific assembly scheme Gantt chart is obtained according to the selected solution. Thus, the aircraft assembly process is guided, and the aircraft assembly scheduling is realized.

[0140] In this embodiment X = 34 and the number of the initial population generated in step 4 is - 34, which is iteratively optimized to obtain the final Pareto frontier solution set.

[0141] In this embodiment, an example problem 1 is selected, as shown in Figure 5 , Figure 6 , Figure 7 and Figure 8 , wherein FS1 in problem 1 has 115 assembly tasks and FS2 has 85 assembly tasks. Table 1 below is the assembly data and required resource data of the assembly tasks. Each assembly task contains a plurality of preceding tasks , the worker type is represented by , and the operation station type is represented by . The completion time of each task is represented by t, , and the operation station personnel limit is represented by . The number of workers required for each task is represented by

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

[0143] ;

[0144] The data of task in Table 1 has been desensitized. At the same time, in order to facilitate subsequent algorithm processing, it is necessary to encode the worker type and operation station type, and generate the preceding task limit, worker number, worker type, worker type, operation station type, operation station number limit matrix to enable the computer to recognize and process.

[0145] The data of all assembly tasks after fusion of assembly resource data and constraints is as follows:

[0146] =[2 3 1 2 2 3 1 1 …];

[0147] T=[4 8 2 4 4 8 2 2 …];

[0148] Operation station types Weizhi 01, 02, 03, 04, 05, 06 and 07 are numbered as 1, 2, 3, 4, 5, 6 and 7 respectively, and the operation station type set is generated as follows:

[0149] =[1 2 3 4 1 2 2 4 …];

[0150] Worker types: ID, JG and SD are numbered as 1, 2 and 3, and the worker type set is generated as follows:

[0151] =[1 2 1 1 3 2 3 3 …];

[0152] Operation station number limit is as follows:

[0153] =[10 10 10 10 10 10 10 10 …];

[0154] From the above table, it is found that the assembly task No. 1 process must be operated after the completion of assembly tasks No. 3 and No. 23, and the pre-task limit is empty, and the pre-task limit does not need to be considered, and the assembly operation can be directly performed. By analogy, the initialization is completed.

[0155] The number of workers, worker types and required man-hours correspond to each task one by one.

[0156] Each worker type can operate multiple tasks at the same time, but the number of each worker type is unlimited.

[0157] Each operation station can provide operation space for multiple tasks at the same time, but the personnel limit of each operation station is 10 people.

[0158] The above description is only a preferred embodiment of the present disclosure and a description of the technical principles applied. Those skilled in the art should understand that the scope of the application involved in the embodiments of the present disclosure is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by any combination of the above technical features or equivalent features without departing from the above inventive concept. For example, the above features are replaced with technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) to form technical solutions.

Claims

1. A multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning, characterized in that, Includes the following steps: Step 1: Decompose the assembly catalog requirements in the aircraft scheduling process into tasks. Step 2: Design an operator station adjustment mechanism to complete the reconfiguration operation of the operator station corresponding to the assembly task; Step 3: Update the type of operator station required for the assembly task, mathematically model the aircraft scheduling problem, and construct a multi-constraint, multi-objective aircraft assembly scheduling problem model; Step 4: Determine the initial task sequence based on the pre- and post-task constraints in the multi-constraint, multi-objective aircraft assembly scheduling problem model. Step 5: Based on the multiple chromosomes obtained in Step 4, i.e., the initial task sequence, calculate the maximum completion time for each chromosome. and maximum number of employees to obtain first fitness and second fitness ; Step 6: Establish an optimization framework for a non-dominated quicksort genetic algorithm with a multi-objective elite gene preservation strategy; Step 7: Establish a multi-objective migration strategy and obtain a set of transferable solutions; Step 7-1: For Problem 1: Two short assembly schemes FS1 and FS2, add or delete the head and tail of some tasks, or for Problem 2: Three assembly schemes FS1, FS2 and FS3, generate a set of assembly schemes that meet the requirements of the new assembly task by taking their intersection, denoted as FL1; The solution of FL1 is to retain some assembly tasks and calculate and select the optimal solution as the assembly scheme. Step 7-2: The generated assembly scheme FL1 first executes step 2, determines the availability of the workstation, and completes the site adjustment and worker reconfiguration; each assembly task in scheme FL1 corresponds to the execution time, worker type, number of workers, and workstation type; at the same time, scheme FL1 is deduplicated, and the remaining solution set is denoted as FL2; Step 7-3: Select a subset of solutions from solution set FL2 as the transferable solution set. : （14）； in and These represent the mean values ​​of the two fitness values ​​in the solution set FL2; and This represents the minimum of two fitness values; and express and The span; where the parameters satisfy Choose two fitness values ​​from the solution set FL2. and The solutions that satisfy formula (14) are considered as the transferable solution set. ; Step 7-4: Transfer Detection: The similarity function SI is defined as follows: （15）； in It is the mean of the transferable solution set; It is to initialize the population. The mean; and It is the number of tasks for the reserved portions of FS1 and FS2 in the two short assembly schemes; , , and The number of tasks added and deleted in FS1 and FS2 respectively; and These represent the shortage and redundant tasks at the intersection of the three assembly schemes FS1, FS2, and FS3, respectively. This refers to the number of tasks in FL1; , , , It is a positive constant and satisfies , The parameter relationships satisfy: and ; If the value of function SI is greater than 70%, then the solution set... It can be used for migration; otherwise, when hour, If this is true, then negative migration will occur; Step 8: Using the non-dominated fast sorting genetic algorithm optimization framework of the multi-objective elite gene preservation 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 scheme Gantt chart is obtained based on the selected solution. An assembly schedule is then created to guide the aircraft assembly process.

2. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1, characterized in that, The task decomposition mentioned in step 1 specifically involves dividing the overall component wing in the assembly catalog into wing spars, longitudinal spars, wing ribs, skin, and longitudinal walls through task decomposition. The assembly task sequence is wing spars, wing ribs, longitudinal spars, longitudinal walls, and skin, and the assembly resources are configured according to this sequence.

3. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1, characterized in that, The operator station adjustment mechanism described in step 2 is specifically as follows: if the current operator station Unavailable, and the task set at this operator station is Find the task set Each assembly task As well as the job type corresponding to the task, assembly tasks are randomly assigned. Go to an operator station of the same job type; if the current operator station task set The number of assembly tasks is less than Then all assembly tasks in this workstation Randomly assigned to workstations of the same job type; Update all operator stations sequentially and merge the update results into the operator station set. middle; Let the number of assembly tasks be... The number of operator stations is , For the current operator station and operator station set , For assembly tasks and , For assembly tasks Required workstation For the need in operator station type The task set for 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, characterized in that, The multi-constraint, 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; The number of assembly tasks; the number of operator stations is... ; Number of job qualifications; For a specific moment; For the current task index, For the task Preceding task index and ;when If it is 1, then it is a task. Need to be in the task Execute after; For the current task The start time; when A value of 0 indicates 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 any moment The number of workers; At any moment The maximum number of workers; Representative job qualification collection ; Representative operator station type set ; Indicates at time Requires job qualification The task set Indicates at time Requires an operating station The task set; This indicates that at time t, at the workstation The number of workers on duty; It is a moment At the workstation Maximum number of employees allowed on the job Described as a task It was assigned to the workstation with index k. Describe the task Assigned to index The job duties performed.

5. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1, characterized in that, Step 4 specifically involves randomly selecting a number from all assembly tasks that has no preceding task as the starting task; and setting the current task as... Seeking satisfaction Task As a subsequent task, until all conditions are met. The task number is used to obtain the task queue, which is a chromosome that satisfies the task priority relationship; step 4 is repeated to obtain a set of multiple chromosomes.

6. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1, characterized in that, Step 5 specifically includes the following steps: Step 5-1: Traverse each task in the chromosome, assuming the current task number is... ,and When a certain task Once selected, set a time. The end time of all preceding tasks of the current task; Step 5-2: Assuming the current task If there are no prerequisite tasks, then Otherwise, calculate the current task. The end times of all prerequisite tasks are calculated until the end time of the last prerequisite task is found and assigned a value. ; Step 5-3: Set one The matrix serves as a spatial constraint on the number of people; current task The required number of operators is Find out no more than Number of people limited The maximum end time of a number of workers ,Compare and The size of the two values ​​is taken as the current task. The start 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 obtain the start and end times of all tasks, and then obtain the total completion time. , obtain first fitness Simultaneously, each assembly task sequence is generated by sorting the tasks according to their start and end times. ; Step 5-5: Assemble according to the task sequence Calculate each assembly task at each time step. Number of people needed ; Calculate the total number of people at each time point The second fitness is obtained. .

7. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1, characterized in that, Step 6 specifically includes the following steps: Step 6-1: Based on the initial task sequence obtained in Step 4 and the first fitness obtained in Step 5... and second fitness Set up a multi-objective selection strategy: （13）； Among them, the weight value satisfy , and These are the mean or maximum values ​​of the first fitness and the second fitness, respectively; A tournament selection method is introduced, which randomly compares two individuals in the current population and retains 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 that satisfy the task priority relationship to complete the crossover and mutation process; Step 6-3: Assume the initial population is The maximum number of iterations is A multi-objective elite retention strategy is adopted: First, the initial population is calculated according to the multi-objective selection strategy. Minimum fitness The current iteration number is The initial population after iteration is updated to The mean, maximum, and minimum fitness of this population are respectively , and ; Step 6-3-1: When At that time, and At that time, searching All less than The chromosomes form a set And randomly select a chromosome replacement from this set. The chromosome with the highest fitness, if At that time, the population is not replaced. If the chromosome is in the sequence, then proceed to step 6-3-3; Step 6-3-2: When At that time, and At that time, searching Replace the chromosome with the lowest fitness. The chromosome with the highest fitness; if At that time, the population is not replaced. If the chromosome is in the sequence, then proceed to step 6-3-3; Step 6-3-3: After step 6-3-1 or 6-3-2, the population is complete. The update, the updated population As a new input to initialize the population until completion The next iteration.

8. The multi-constraint aircraft assembly scheduling method based on multi-objective transfer learning according to claim 1, characterized in that, Step 7-4 specifically includes the following steps: Step 7-4-1: Introduce a new migration ratio : （16）； in: （17）； parameter , , , It is a positive constant and satisfies , And there are and Valid; if ,but The maximum value is 4; similarly, At that time, The maximum value is 8; It is the initial population The minimum value; yes The span is [3%, 5%]; Step 7-4-2: If Then the initial population Reinitialization is required; until the condition is met. until; Step 7-4-3: When hour: when At that time, the migration rate was [12%, 27%]. when At that time, if The migration rate is [27%, 50%]); if The migration rate is [50%, 98%]); when At that time, the migration rate was [98%, 100%].

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