Aircraft pulsation assembly line balancing method and medium considering complex constraints

Abstract

The present invention relates to a method and medium for balancing an aircraft pulse assembly production line under complex constraints, comprising the following steps: S1. Establishing a process priority relationship matrix and a process information matrix; S2. Generating feasible sequences and parallel sequences and expressing them in matrix form to complete the encoding process; S3. Incorporating a local splitting strategy, evenly splitting the parallel sequence matrix into various stations; S4. Decoding the sequence row by row to obtain the feasible balance solution corresponding to the sequence and expressing it in matrix form to complete the decoding process; S5. Constructing an optimized set of feasible balance solutions using an inner and outer double-layer genetic algorithm; S6. Using a fuzzy hierarchical analysis method to calculate the final weights of each indicator that best meets current production requirements, and using a ranking method that approximates ideal values ​​based on the weights to determine the optimal feasible balance solution from the set of feasible balance solutions. Compared with existing technologies, the present invention can further improve the efficiency and results of aircraft final assembly pulse line balancing optimization.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft assembly and manufacturing, and in particular relates to a balancing method and medium for an aircraft pulsating assembly production line under complex constraints. Background Art

[0002] Aircraft final assembly is a complex, systematic project and the most crucial part of aircraft manufacturing. It involves numerous processes and a vast amount of materials, resources, and personnel. With the introduction of lean manufacturing, aircraft manufacturers have gradually established pulsating final assembly lines to address the low efficiency, inconsistent quality, chaotic on-site operations, and difficult management associated with the traditional fixed hangar assembly model.

[0003] The pulsating assembly line transforms centralized assembly at a single location into collaborative assembly across multiple stations. After completing a specific assembly process within a fixed pulsating cycle, aircraft undergoing assembly simultaneously enter the next station to complete the next assembly process within the next pulsating cycle. This allows for the simultaneous production of multiple aircraft at multiple stations. However, the efficiency and cost-effectiveness of the pulsating assembly line can only be realized by rationally allocating resources—such as materials, workers, and assembly processes—to the corresponding stations based on production goals, achieving continuous and balanced production. Different cycle times, number of stations, and process allocations result in significant differences in production capacity and economic benefits across various assembly line options. Therefore, arranging the order in which assembly processes are completed and rationally allocating them to stations to achieve a balanced assembly line is a key issue that needs to be addressed in the construction of pulsating assembly lines.

[0004] Existing research on balancing problems in aircraft assembly pulse lines mostly uses metaheuristic methods to adjust the completion order and distribution of assembly processes to balance the workload of each station and optimize the pulse beat or reduce the number of stations. For example, Chinese invention patent publication number CN110991056A proposes a method for scheduling aircraft assembly line operations based on a genetic variable neighborhood algorithm. Minimizing the total assembly duration is the optimization objective, while considering top-to-bottom constraints, resource constraints, and space constraints. A sub-segment scheduling model for aircraft assembly line operations is constructed, using an improved genetic variable neighborhood algorithm for the solution. A neighborhood structure is constructed to ensure that legitimate solutions are generated during the search process, improving search capabilities, preventing the algorithm from falling into local optimality, and shortening the total assembly cycle. Chinese invention patent publication number CN114004008A proposes a resource allocation optimization method for aircraft assembly lines based on neural networks and genetic algorithms. The method inputs resource allocation plans, production goals, and resource constraints. A fast non-dominated sorting genetic algorithm autonomously searches within the overall solution space, combined with a neural network to calculate the population objective function. After iterative optimization, the optimal resource allocation plan is output. However, in actual production, aircraft assembly lines involve a large scale, with multiple areas of parallel processing within each station and multiple types of work performed collaboratively. Directly applying metaheuristic methods to solve complex constrained optimization problems presents difficulties. Previous research has not considered the use of mechanistic knowledge, and lacks methods for optimizing the static balance of aircraft assembly lines. Therefore, a new balancing method for aircraft assembly lines is needed that can generate feasible balancing solutions that better meet actual production needs and improve the efficiency and results of aircraft assembly line balancing optimization. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies and provide a balancing method and medium for aircraft pulsating assembly production lines under complex constraints. It introduces a new encoding and decoding scheme based on mechanism knowledge, and designs a two-layer genetic algorithm and a multi-objective fuzzy comprehensive evaluation decision-making method. It can generate a feasible balancing scheme that is more in line with actual production needs, and improve the efficiency and results of aircraft assembly pulsating line balancing optimization.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] The present invention provides a balancing method for an aircraft pulsating assembly line under complex constraints, comprising the following steps:

[0008] S1. Obtain process information and assembly constraints, and establish a process priority relationship matrix and a process information matrix. The process information includes the priority relationship between processes, process assembly areas, process completion time, and corresponding assembly specialties.

[0009] S2. Based on the process priority relationship matrix and the process information matrix, a feasible sequence including the linear completion order of all processes and a parallel sequence reflecting the parallel assembly relationship of all processes are generated and expressed in the form of a matrix, thereby completing the encoding process;

[0010] S3. Calculate the pre-completion time and initial benchmark split time of the parallel sequence. Combined with the local splitting strategy, split the parallel sequence matrix station by station. Recalculate the benchmark time based on the splitting results and split the sequence again. After multiple iterations, split the parallel sequence matrix evenly to each station.

[0011] S4. Based on the matrix representation of the parallel sequence and its split results, decode row by row to obtain a feasible balance solution corresponding to the sequence and express it in matrix form, completing the decoding process. The feasible balance solution includes a process allocation solution, a process completion sequence, and a worker configuration solution.

[0012] S5. Constructing an optimized set of feasible balance solutions using an inner-outer double-layer genetic algorithm. In the inner-outer double-layer genetic algorithm, the outer layer balances the initial weights of each optimization objective based on the process data set and assembly line layout information. The inner layer calculates the outer layer information as input and applies the genetic algorithm to solve the optimal feasible balance solution under the current objective weights. The outer layer updates the weights of each optimization objective and the inner layer continues to solve. After multiple iterations, the optimal feasible balance solution under different indicator weights is obtained, thereby obtaining a set of feasible balance solutions.

[0013] S6. According to different production needs, the fuzzy hierarchical analysis method is used to calculate the final weights of each indicator that best meets the current production needs, and based on the weights, a sorting method close to the ideal value is used to decide the best feasible balance solution in the set of feasible balance solutions.

[0014] Furthermore, the specific expression of the process priority relationship matrix is:

[0015]

[0016] Where n is the number of processes;

[0017] The specific expression of the process information matrix is:

[0018] C=[c ij ] n×m

[0019] Among them, m is the number of stations, the number of matrix rows corresponds to the process one by one, the i-th row represents the relevant process constraints of process i, the i-th row and column 1 represents the completion time of process i, the i-th row and column 2 represents the assembly specialty corresponding to process i, the i-th row and column 3 represents the number of workers required to complete the assembly of process i, the i-th row and column 4 represents the assembly area where process i is assembled, and the i-th row and column 5 represents the capacity limit of the assembly area where process i is located.

[0020] Furthermore, the specific generation process of the feasible sequence is as follows:

[0021] S211. Initially classify the processes according to the process priority relationship matrix. The classification categories include an allocable process set, a to-be-assigned process set, and an allocated process set. The initial allocable process set is a process set without priority relationship constraints, the initial to-be-assigned process set is the entire set of process sets, and the initial allocated process set is an empty set.

[0022] S212. After randomly selecting a process from the current set of allocable processes and adding it to the current set of allocated processes, delete the process from the current set of processes to be allocated, and update the set of allocable processes based on the priority relationship of the process;

[0023] S213. Determine whether the current set of processes to be assigned is an empty set. If not, go to step S212. If so, output the set of assigned processes and represent it as a feasible sequence in matrix form.

[0024] Furthermore, the specific generation process of the parallel sequence is as follows:

[0025] S221, construct parallel sequence matrix P = [p ij ] n×n , and initialize the matrix elements to zero, where n is the number of processes;

[0026] S222, obtain the feasible sequence matrix F = [f ij ] n×1 , let p 11 =f 11 ;

[0027] S223, judgment process f s1 and process f s+11 The feasibility of parallel assembly, if feasible, then let p uv+1 =f s+11 , otherwise let p u+11 =f s+11 , where s is the sum of the number of non-zero elements in P, u and v are the row and column indices of the last non-zero element in the parallel sequence matrix P respectively;

[0028] S224: If s+1<n, go to step S223; if s+1=n, complete the construction of the parallel sequence and output it.

[0029] Furthermore, the specific process of evenly splitting the parallel sequence matrix to each station is as follows:

[0030] S311, decode the parallel sequence matrix P to obtain the processing start time matrix S, processing end time matrix E, completion sequence matrix R and completion time matrix T, and calculate the pre-completion time t of the parallel sequence P ;

[0031] S312, let the initial benchmark split time t b =t P ÷m, according to t b Split the parallel sequence matrix P into sub-parallel sequence matrices P that meet the benchmark time 11 And the sub-parallel sequence matrix P that does not meet the benchmark time 12 , P 11 Assigned to station 1; parallel sequence matrix P 12 After decoding the process sequence, P 12 Split into sub-parallel sequence matrices P that meet the benchmark time 21 And the sub-parallel sequence matrix P that does not meet the benchmark time 22 , P 21 Assign to station 2; continue to parallel sequence matrix P 22 After processing sequence decoding, split it again until it is split into a sub-parallel sequence matrix P that meets the benchmark time m-11 And the sub-parallel sequence matrix P that does not meet the benchmark time m-12 , P m-11 Assign to station m-1, and P m-12 Assigned to station m;

[0032] S313. According to the sequence splitting result, each station decodes the processing order of the assigned parallel sequence matrix and calculates the completion time T of each station. j1 , j = 1, 2...m, and update the benchmark split time According to t b1 Re-split the parallel sequence matrix P, and after splitting, decode the process sequence to obtain the completion time T of each station j2 , j = 1, 2...m, and update the benchmark split time After iterating u times, the benchmark splitting time t is obtained bu , according to t bu Complete the balanced splitting of the parallel sequence matrix P, and the splitting result is {P 11 ;P21 ;P 31 ...P m-11 ;P m-12}.

[0033] Furthermore, the specific process of step S311 is as follows:

[0034] S321, parallel sequence matrix P = [p ij ] n×n Delete all zero rows and columns to get P′=[p′ ij ] a×b , according to P′ and process information matrix C=[c ij ] n×m , construct the processing start time matrix S = [s ij ] a×b , processing end time matrix E = [e ij ] a×b , completion sequence matrix R = [r ij ] c×n and the completion time matrix T = [t ij ] n×m , initialize all matrix elements to zero and let t ij+2 =c ij , j=1,2,...m-2, i=1,2,...n, n is the number of processes, m is the number of stations;

[0035] S322, traverse P', when p' ij ≠0, let u=p′ ij , calculate the optional processing start time range of process u, and decide the processing start time t of process u according to the priority relationship and process constraints of process u u，s , and let s ij =t u，s , e ij =t u，s +t u ; Traverse P' in turn to determine the processing start time and processing end time of each process in P', and output the processing start time matrix S and processing end time matrix E;

[0036] S323, traverse S and E, when s ij ≠0, let v=p ij , t v1 =s ij , t v2 =e ij After the traversal is completed, the completion time matrix t is output and t is sorted from small to large according to the processing start time of each process to obtain the process sorting result P″=[p″ ij ] n×1 , p″ ijis the row number corresponding to T before sorting, i.e. the process number; traverse P″ and let h=p″ ij , q=c h That is, the assembly specialty corresponding to process h is q, let r qz = h, where z is the column index of the first zero element in the qth row of R. After traversing P″, the completion sequence matrix R is output. The decoding of the processing sequence of each process in the sequence is completed and the completion time t of P′ is calculated. P =maxE-minS.

[0037] Furthermore, the decoding process of the worker configuration scheme is as follows:

[0038] The number of workers of each assembly specialty required to complete the parallel sequence assembly is calculated based on the decoding results of the process processing sequence of the corresponding parallel sequence matrix. According to the process processing sequence and processing time of each assembly specialty represented by the completion sequence matrix R and the completion time matrix T, whether there is a conflict in the processing time is determined one by one according to the processing sequence. The calculation of the number of workers of each specialty and the working time consumption is completed, and the worker configuration matrix W = [w i j] c×1 's construction.

[0039] Furthermore, the process of constructing a set of feasible equilibrium solutions through the inner and outer double-layer genetic algorithm is as follows:

[0040] S511. Allocate weights of the optimization indicators according to different production requirements and construct an indicator weight set, wherein the indicator weight set includes weights of the indicators under multiple different production requirements and a series of random weights;

[0041] S512. Randomly generate a certain number of feasible sequences and construct a parallel sequence matrix to complete population initialization. Each individual consists of a feasible sequence and its parallel sequence matrix.

[0042] S513. The outer layer inputs the process data set and the indicator weight set of each optimization indicator, selects an unused indicator weight, determines the optimization target based on the weight, and the inner layer uses a genetic algorithm to solve the optimal feasible balance solution under the current optimization target. After the outer layer updates the indicator weight set, the inner layer continues to solve. After multiple iterations, the optimal feasible balance solution under all indicator weights in the indicator weight set is obtained, and a set of feasible balance solutions is obtained.

[0043] Furthermore, the specific process of step S6 is as follows:

[0044] S611. Based on current production requirements, subjective comparisons of the importance of each pair of indicators are performed and the comparison results are expressed using triangular fuzzy numbers. The triangular fuzzy numbers are used to form a triangular fuzzy judgment matrix to express the comparison results of the importance of each indicator.

[0045] S612, using the hierarchical analysis method, calculate the weight of each indicator according to the triangular fuzzy judgment matrix, and obtain the final weight set of all indicators after normalization;

[0046] S613. Calculate the attribute values ​​of each optimization indicator of all solutions in the set of feasible equilibrium solutions to form a decision matrix. Combine the final weight set of each optimization indicator and calculate a weighted normalized decision matrix based on the decision matrix.

[0047] S614. Classify the indicator attribute values ​​into cost-type indicators and benefit-type indicators, and determine the positive and negative ideal solutions of the attribute values ​​of each indicator in the weighted normalized decision matrix, wherein the positive ideal solution is the minimum value of the cost-type indicator and the maximum value of the benefit-type indicator, and the negative ideal solution is the maximum value of the cost-type indicator and the minimum value of the benefit-type indicator;

[0048] S615. After calculating the Euclidean distance between the attribute value of each indicator in each feasible solution and the positive and negative ideal solutions, the closeness of each solution to the optimal solution is obtained. The solution with the largest closeness is the optimal balance solution under the current production demand.

[0049] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the program implements the above method when executed by a processor.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] 1. This paper proposes a balancing method for aircraft pulse assembly lines under complex constraints. It introduces a new encoding and decoding scheme based on mechanism knowledge, which effectively addresses the limitations of existing methods in dealing with complex constraints such as multi-area parallel processing and multi-worker collaborative assembly.

[0052] 2. The present invention designs an inner and outer double-layer genetic algorithm to construct an optimized set of feasible balancing solutions. The algorithm combines the multiple decoding strategies of the aircraft assembly pulse line balancing problem under complex constraints with the genetic algorithm optimization to solve the aircraft assembly pulse line balancing problem model under complex constraints. The inner layer obtains the optimal individual under one indicator weight in the indicator weight set, and the outer layer outputs the optimal individual set under different indicator weights and decodes it into a set of feasible balancing solutions, which effectively expresses the assembly constraints and priority relationships, and improves the efficiency and results of aircraft assembly pulse line balancing optimization.

[0053] 3. The present invention designs a multi-objective fuzzy comprehensive evaluation decision-making method, which uses the fuzzy hierarchical analysis method to calculate the final weights of each indicator that best meets the current production needs, and uses a sorting method close to the ideal value based on the weight to decide the optimal feasible balance plan from the set of feasible balance plans, thereby improving the efficiency and accuracy of decision-making and generating a feasible balance plan that better meets actual production needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of the method of the present invention;

[0055] Figure 2 This is the flow chart of the inner and outer double-layer genetic algorithm (DGA);

[0056] Figure 3 49 Gantt charts of feasible balancing solutions for example. DETAILED DESCRIPTION

[0057] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0058] Example:

[0059] This embodiment provides a method for balancing an aircraft pulsating assembly line under complex constraints, such as Figure 1 As shown, the following steps are included:

[0060] S1. Obtain process information and assembly constraints, and establish a process priority relationship matrix and a process information matrix.

[0061] Process information includes the priority relationship between processes, process assembly area, process completion time and corresponding assembly specialty.

[0062] The specific expression of the process priority relationship matrix A is:

[0063]

[0064] Where n is the number of processes.

[0065] The specific expression of the process information matrix C is:

[0066] C=[c ij ] n×m

[0067] Among them, m is the number of stations, the number of matrix rows corresponds to the process one by one, the i-th row represents the relevant process constraints of process i, the i-th row and column 1 represents the completion time of process i, the i-th row and column 2 represents the assembly specialty corresponding to process i, the i-th row and column 3 represents the number of workers required to complete the assembly of process i, the i-th row and column 4 represents the assembly area where process i is assembled, and the i-th row and column 5 represents the capacity limit of the assembly area where process i is located.

[0068] S2. Based on the process priority relationship matrix and the process information matrix, a feasible sequence containing the linear completion order of all processes and a parallel sequence reflecting the parallel assembly relationship of all processes are generated and expressed in the form of a matrix to complete the encoding process.

[0069] The specific process of generating a feasible sequence is as follows:

[0070] S211. Perform an initial classification of the processes according to the process priority relationship matrix A. The classification categories include the assignable process set, the to-be-assigned process set, and the assigned process set. The initial assignable process set is a process set without priority relationship constraints, the initial to-be-assigned process set is the full set of process sets, and the initial assigned process set is an empty set.

[0071] S212. After randomly selecting a process from the current allocable process set and adding it to the current allocated process set, delete the process from the current set of processes to be allocated, and update the allocable process set according to the priority relationship of the process.

[0072] S213, determine whether the current set of processes to be assigned is an empty set. If not, go to step S212; if so, output the set of assigned processes and express it as a feasible sequence F=[f ij ] n×1 .

[0073] The specific generation process of the parallel sequence is as follows:

[0074] S221, construct parallel sequence matrix P = [p ij ] n×n , and initialize the matrix elements to zero.

[0075] S222, obtain the feasible sequence matrix F = [f ij ] n×1 , let p 11 =f 11 .

[0076] S223, judgment process f s1 and process f s+11 The feasibility of parallel assembly, if feasible, then let p uv+1 =f s+11 , otherwise let p u+11 =f s+11 , where s is the sum of the number of non-zero elements in P, u and v are the row and column indices of the last non-zero element in the parallel sequence matrix P, respectively.

[0077] S224: If s+1<n, go to step S223; if s+1=n, complete the construction of the parallel sequence and output it.

[0078] S3: Calculate the parallel sequence's pre-completion time and initial benchmark split time. Combined with the local splitting strategy, split the parallel sequence matrix station by station. Recalculate the benchmark time based on the split results and split the sequence again. After multiple iterations, split the parallel sequence matrix evenly to each station. The specific process is as follows:

[0079] S311, decode the parallel sequence matrix P to obtain the processing start time matrix S, processing end time matrix E, completion sequence matrix R and completion time matrix T, and calculate the pre-completion time t of the parallel sequence P .

[0080] S312, let the initial benchmark split time t b =t P ÷m, according to t b Split the parallel sequence matrix P into sub-parallel sequence matrices P that meet the benchmark time 11 And the sub-parallel sequence matrix P that does not meet the benchmark time 12 , P 11 Assigned to station 1; parallel sequence matrix P 12 After decoding the process sequence, P 12 Split into sub-parallel sequence matrices P that meet the benchmark time 21 And the sub-parallel sequence matrix P that does not meet the benchmark time 22 , P 21 Assign to station 2; continue to parallel sequence matrix P 22 After processing sequence decoding, split it again until it is split into a sub-parallel sequence matrix P that meets the benchmark time m-11 And the sub-parallel sequence matrix P that does not meet the benchmark time m-12 , P m-11 Assign to station m-1, and P m-12 Assigned to station m.

[0081] S313. According to the sequence splitting result, each station decodes the processing order of the assigned parallel sequence matrix and calculates the completion time T of each station. j1 , j = 1, 2...m, and update the benchmark split time According to t b1 Re-split the parallel sequence matrix P, and after splitting, decode the process sequence to obtain the completion time T of each station j2 , j = 1, 2...m, and update the benchmark split time After iterating u times, the benchmark splitting time t is obtained bu , according to t bu Complete the balanced splitting of the parallel sequence matrix P, and the splitting result is {P 11 ;P21 ;P 31 ...P m-11 ;P m-12}.

[0082] The specific steps for decoding the process sequence are as follows:

[0083] S321, parallel sequence matrix P = [p ij ] n×n Delete all zero rows and columns to get P′=[p′ ij ] a×b According to P′ and process information matrix c=[c ij ] n×m , construct the processing start time matrix S = [s ij ] a×b , processing end time matrix E = [e ij ] a×b , completion sequence matrix R = [r ij ] c×n and the completion time matrix T = [t ij ] n×m . Initialize all matrix elements to zero and let t ij+2 =c ij , j=1,2,...m-2, i=1,2,...n.

[0084] S322, traverse P', when p' ij ≠0, let u=p′ ij , calculate the optional processing start time range of process u, and decide the processing start time t of process u according to the priority relationship and process constraints of process u u，s , and let s ij =t u，s , e ij =t u，s +t u Traverse P′ in sequence to determine the processing start time and processing end time of each process in P′, and output the processing start time matrix S and processing end time matrix E.

[0085] S323, traverse S and E, when s ij ≠0, let v=p ij , t v1 =s ij , t v2 =e ij After the traversal is completed, the completion time matrix T is output and T is sorted from small to large according to the processing start time of each process to obtain the process sorting result P″=[p″ ij ] n×1 , p″ ijis the row number corresponding to T before sorting, i.e. the process number; traverse P″ and let h=p″ ij , q=c h That is, the assembly specialty corresponding to process h is q, let r qz = h, where z is the column index of the first zero element in the qth row of R. After traversing P″, the completion sequence matrix R is output. The decoding of the processing sequence of each process in the sequence is completed and the completion time t of P′ is calculated. P =maxE-minS.

[0086] S4. According to the matrix representation of the parallel sequence and its split results, decode row by row to obtain a feasible balance solution corresponding to the sequence and express it in matrix form to complete the decoding process. The feasible balance solution includes a process allocation solution, a process completion sequence, and a worker configuration solution.

[0087] The completion sequence matrix R records the processing sequence of each process within each assembly specialty, and the completion time matrix T records the processing start time, processing end time, completion time, assembly specialty and the number of workers required for each process. The completion sequence matrix R and the completion time matrix T can comprehensively and clearly represent the processing time and processing sequence of each process after the current individual decoding.

[0088] The decoding process of the worker configuration scheme is as follows: according to the decoding results of the process processing sequence of the corresponding parallel sequence matrix, the number of assembly professionals required to complete the parallel sequence assembly is calculated; according to the process processing sequence and processing time of each assembly specialty represented by the completion sequence matrix R and the completion time matrix T, whether there is a conflict in the processing time is determined one by one according to the processing sequence; the calculation of the number of workers of each specialty and the working time consumption is completed, and the worker configuration matrix W = [w i j] c×1 's construction.

[0089] S5. Construct an optimized feasible equilibrium solution set through the inner and outer double-layer genetic algorithm.

[0090] In the inner-outer double-layer genetic algorithm (DGA), the outer layer balances the initial weights of each optimization objective based on the process data set and assembly line layout information. The inner layer uses the outer layer information as input and applies the genetic algorithm to solve the optimal feasible balance solution under the current objective weights. After the outer layer updates the weights of each optimization objective, the inner layer continues to solve. After multiple iterations, the optimal feasible balance solution under different indicator weights is obtained, and a set of feasible balance solutions is obtained.

[0091] The flowchart of the inner and outer double-layer genetic algorithm (DGA) is as follows: Figure 2 As shown, the specific process is as follows:

[0092] S511. Allocate weights of the optimization indicators according to different production requirements, and construct an indicator weight set, where the indicator weight set includes weights of indicators under multiple different production requirements and a series of random weights.

[0093] S512. Randomly generate a certain number of feasible sequences and construct a parallel sequence matrix to complete population initialization. Each individual consists of a feasible sequence and its parallel sequence matrix.

[0094] S513. The outer layer inputs the process data set and the indicator weight set of each optimization indicator, selects an unused indicator weight, determines the optimization target based on the weight, and the inner layer uses a genetic algorithm to solve the optimal feasible balance solution under the current optimization target. After the outer layer updates the indicator weight set, the inner layer continues to solve. After multiple iterations, the optimal feasible balance solution under all indicator weights in the indicator weight set is obtained, and a set of feasible balance solutions is obtained.

[0095] S6. Based on different production requirements, the Fuzzy Analytic Hierarchy Process (FAHP) is used to calculate the final weights of each indicator that best meets the current production requirements. Based on the weights, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is used to determine the optimal feasible balance solution from the set of feasible balance solutions. The specific process is as follows:

[0096] S611. According to the current production demand, the importance of each indicator is subjectively compared and the comparison results are expressed by triangular fuzzy numbers. The triangular fuzzy numbers are used to form a triangular fuzzy judgment matrix to express the comparison results of the importance of each indicator.

[0097] S612. Use the hierarchical analysis method to calculate the weight of each indicator based on the triangular fuzzy judgment matrix, and obtain the final weight set of all indicators after normalization.

[0098] S613. Calculate the attribute values ​​of each optimization indicator of all solutions in the set of feasible equilibrium solutions to form a decision matrix. Combine the final weight set of each optimization indicator and calculate a weighted normalized decision matrix based on the decision matrix.

[0099] S614. Divide the indicator attribute values ​​into cost-type indicators and benefit-type indicators, and determine the positive and negative ideal solutions of the attribute values ​​of each indicator in the weighted normalized decision matrix, where the positive ideal solution is the minimum value of the cost-type indicator and the maximum value of the benefit-type indicator, and the negative ideal solution is the maximum value of the cost-type indicator and the minimum value of the benefit-type indicator.

[0100] S615. After calculating the Euclidean distance between the attribute value of each indicator in each feasible solution and the positive and negative ideal solutions, the closeness of each solution to the optimal solution is obtained. The solution with the largest closeness is the optimal balance solution under the current production demand.

[0101] This example verifies the aforementioned method using an aircraft assembly line at an aircraft manufacturer. This example meets the fundamental assumptions of multi-area, multi-disciplinary, and multi-person collaboration in aircraft assembly line balancing. There are 76 assembly processes, with workers divided into seven assembly specialties based on process categories. Stations are divided into 11 assembly areas based on assembly locations. Specific process information is shown in Table 1.

[0102] Table 1 Partial process information of 76 process examples

[0103]

[0104] The optimization method includes the following steps:

[0105] Step 1: Generate the indicator weight set W. 30 indicator weights are generated based on possible production demand orientations, and 270 indicator weights are randomly generated to complete the construction of the indicator weight set W. Each indicator weight is composed of the weights of four optimization indicators: pulse beat (CT), balance index (BI), total number of workers (WN), and standard deviation of idle time (SDI) of workers in each team.

[0106] Step 2: Use DGA to generate a set of feasible balance solutions B. Use DGA to traverse the indicator weight set. The relevant parameters are shown in Table 2. Output the set of feasible balance solutions B. The set has a total of 300 feasible balance solutions. The i-th feasible balance solution B i (i=1,2,…300) is the corresponding indicator weight W i The optimal balance solution under (i=1,2,…300). According to the feasible balance solution set B, the decision matrix D=[b ij ] 300×4 , some of which are shown in Table 3.

[0107] Table 2 DGA algorithm parameters

[0108]

[0109]

[0110] Table 3 shows some of the attribute values ​​of the decision matrix D indicator

[0111]

[0112] Step 3: Use the fuzzy analytic hierarchy process to calculate the weight of each indicator based on the fuzzy production requirements. Based on the actual production requirements, the fuzzy ranking of the importance of the indicators CT, BI, WN, and SDI is subjectively given. The importance ranking assumed in this experiment is: CT = BI > WN > SDI. Based on the comparison of the importance of each indicator, the triangular fuzzy number is obtained and the triangular fuzzy judgment matrix Y = [y ij ] 4×4 :

[0113]

[0114] Calculate the final weight W of each index after normalization as shown in Table 4 f =(w1,w2,w3,w4).

[0115] Table 4 Fuzzy weights of indicators

[0116]

[0117] Step 4: Use the sorting method close to the ideal value to evaluate the set of feasible equilibrium solutions. According to the decision matrix D = [b ij ] 300×4 and the weight of each indicator W f =(w1,w2,w3,w4) to construct the weighted normalized decision matrix V = [v ij ] 300×4 And determine the positive ideal solution B under each index as shown in Table 6 + and negative ideal solution B - The corresponding feasible balance solutions and weighted normalized decision matrix attribute values ​​are calculated as shown in Table 7. i To the positive ideal solution B + The distance scale D i + To the negative ideal solution B - The distance scale D i - and each feasible equilibrium solution B i The closeness D to the optimal solution i .

[0118] Table 5 Partial display of attribute values ​​of weighted normalized decision matrix V

[0119]

[0120] Table 6 Positive and negative ideal solutions under current indicator weights

[0121]

[0122]

[0123] Table 7 Distance scale D of feasible balance solutions i + 、D i - and closeness D i

[0124]

[0125] Step 5: Scheme evaluation and decision-making. As shown in Table 8, according to the closeness D i Sort the set of feasible equilibrium solutions, and the closeness D i The largest solution is the current indicator weight W f =(w1,w2,w3,w4), the optimal solution determined by the experiment is solution 49, and the indicator attribute values ​​are shown in Table 9.

[0126] Table 8. Results of the closeness ranking of the feasible equilibrium solution set

[0127]

[0128] Table 9 Attribute values ​​of 49 indicators of feasible balance scheme

[0129]

[0130] In order to intuitively display the feasible equilibrium solution obtained by the inner and outer double-layer genetic algorithm (DGA), this embodiment draws the following Figure 3 The Gantt chart for the process allocation of feasible balancing solution 49 shows the order of assembly processes and the parallel relationship between processes. The decoded worker quantity configuration and station allocation solution are shown in Table 10.

[0131] Table 10: Configuration and distribution of workers in each team in the feasible balance plan 49

[0132]

[0133] DGA solves the model based on the indicator weight set to obtain a set of feasible balance solutions; FAHP calculates the weights between the four indicators based on the fuzzy production demand, that is, the fuzzy importance judgment between the indicators (CT = BI > WN > SDI); the TOPSIS method decides the balance solution that best meets the current production demand in the set based on the weights between the indicators, that is, the feasible balance solution49.

[0134] Depend on Figure 3As shown in Table 10, the process allocation scheme for feasible balancing solution 49 meets the production characteristics of the aircraft pulse assembly line, which features multi-area parallel operations and multi-worker collaborative assembly, and involves a large number of parallel processes. When constructing a feasible balancing solution, it is necessary to rationally allocate processes to each station and determine the specific processing sequence within each station based on production requirements to achieve line balance. Finally, the number of workers in each team is configured based on the process allocation results.

[0135] Furthermore, the FAHP-TOPSIS method can determine different optimal solutions from a set of feasible equilibrium solutions based on different production requirements. As shown in Table 11, the optimal solutions determined meet the corresponding production requirements, verifying the effectiveness of the FAHP-TOPSIS method in evaluating decisions.

[0136] Table 11 Optimal solutions under different production requirements

[0137]

[0138]

[0139] If the above method is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, and other media that can store program code.

[0140] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

Claims

1. A balancing method for an aircraft pulsating assembly line under complex constraints, characterized by: The following steps are involved: S1. Obtain process information and assembly constraints, and establish a process priority relationship matrix and a process information matrix. The process information includes the priority relationship between processes, process assembly areas, process completion time, and corresponding assembly specialties. S2. Based on the process priority relationship matrix and the process information matrix, a feasible sequence including the linear completion order of all processes and a parallel sequence reflecting the parallel assembly relationship of all processes are generated and expressed in the form of a matrix, thereby completing the encoding process; S3. Calculate the pre-completion time and initial benchmark split time of the parallel sequence. Combined with the local splitting strategy, split the parallel sequence matrix station by station. Recalculate the benchmark time based on the splitting results and split the sequence again. After multiple iterations, split the parallel sequence matrix evenly to each station. S4. Based on the matrix representation of the parallel sequence and its split results, decode row by row to obtain a feasible balance solution corresponding to the sequence and express it in matrix form, completing the decoding process. The feasible balance solution includes a process allocation solution, a process completion sequence, and a worker configuration solution. S5. Constructing an optimized set of feasible balance solutions using an inner-outer double-layer genetic algorithm. In the inner-outer double-layer genetic algorithm, the outer layer balances the initial weights of each optimization objective based on the process data set and assembly line layout information. The inner layer calculates the outer layer information as input and applies the genetic algorithm to solve the optimal feasible balance solution under the current objective weights. The outer layer updates the weights of each optimization objective and the inner layer continues to solve. After multiple iterations, the optimal feasible balance solution under different indicator weights is obtained, thereby obtaining a set of feasible balance solutions. S6. According to different production needs, the fuzzy hierarchical analysis method is used to calculate the final weights of each indicator that best meets the current production needs, and based on the weights, a sorting method close to the ideal value is used to decide the best feasible balance solution in the set of feasible balance solutions.

2. The aircraft pulsation assembly line balancing method considering complex constraints according to claim 1, characterized in that: The specific expression of the process priority relationship matrix is: Where n is the number of processes; The specific expression of the process information matrix is: C=[c ij ] n×m Among them, m is the number of stations, the number of matrix rows corresponds to the process one by one, the i-th row represents the relevant process constraints of process i, the i-th row and column 1 represents the completion time of process i, the i-th row and column 2 represents the assembly specialty corresponding to process i, the i-th row and column 3 represents the number of workers required to complete the assembly of process i, the i-th row and column 4 represents the assembly area where process i is assembled, and the i-th row and column 5 represents the capacity limit of the assembly area where process i is located.

3. The aircraft pulsation assembly line balancing method considering complex constraints according to claim 1, characterized in that: The specific generation process of the feasible sequence is as follows: S211. Initially classify the processes according to the process priority relationship matrix. The classification categories include an allocable process set, a to-be-assigned process set, and an allocated process set. The initial allocable process set is a process set without priority relationship constraints, the initial to-be-assigned process set is the entire set of process sets, and the initial allocated process set is an empty set. S212. After randomly selecting a process from the current set of allocable processes and adding it to the current set of allocated processes, delete the process from the current set of processes to be allocated, and update the set of allocable processes based on the priority relationship of the process; S213. Determine whether the current set of operations to be assigned is an empty set. If not, go to step S212; if so, output the assigned operation set and represent it as a feasible sequence in matrix form.

4. The aircraft pulsation assembly line balancing method considering complex constraints according to claim 1, characterized in that: The specific generation process of the parallel sequence is as follows: S221, construct parallel sequence matrix P = [p ij ] n×n , and initialize the matrix elements to zero, where n is the number of processes; S222, obtain the feasible sequence matrix F = [f ij ] n×1 , let p 11 =f 11 ; S223, judgment process f s1 and process f s+11 The feasibility of parallel assembly, if feasible, then let p uv+1 =f s+11 , otherwise let p u+11 =f s+11 , where s is the sum of the number of non-zero elements in P, u and v are the row and column indices of the last non-zero element in the parallel sequence matrix P respectively; S224. If s + 1 < n, go to step S223; if s + 1 = n, complete the construction of the parallel sequence and output it.

5. The aircraft pulsation assembly line balancing method considering complex constraints according to claim 1, characterized in that: The specific process of evenly splitting the parallel sequence matrix to each station is as follows: S311, decode the parallel sequence matrix P to obtain the processing start time matrix S, processing end time matrix E, completion sequence matrix R and completion time matrix T, and calculate the pre-completion time t of the parallel sequence P ; S312, let the initial benchmark split time t b =t P ÷m, according to t b Split the parallel sequence matrix P into sub-parallel sequence matrices P that meet the benchmark time 11 And the sub-parallel sequence matrix P that does not meet the benchmark time 12 , P 11 Assigned to station 1; parallel sequence matrix P 12 After decoding the process sequence, P 12 Split into sub-parallel sequence matrices P that meet the benchmark time 21 And the sub-parallel sequence matrix P that does not meet the benchmark time 22 , P 21 Assign to station 2; continue to parallel sequence matrix P 22 After processing sequence decoding, split it again until it is split into a sub-parallel sequence matrix P that meets the benchmark time m-11 And the sub-parallel sequence matrix P that does not meet the benchmark time m-12 , P m-11 Assign to station m-1, and P m-12 Assigned to station m; S313. According to the sequence splitting result, each station decodes the processing order of the assigned parallel sequence matrix and calculates the completion time T of each station. j1 ,j=1,2…m, and update the benchmark split time According to t b1 Re-split the parallel sequence matrix P, and after splitting, decode the process sequence to obtain the completion time T of each station j2 ,j=1,2…m, and update the benchmark split time After iterating u times, the benchmark splitting time t is obtained bu , according to t bu Complete the balanced splitting of the parallel sequence matrix P, and the splitting result is {P 11 ;P 21 ;P 31 …P m-11 ;P m-12 }.

6. The aircraft pulsation assembly line balancing method considering complex constraints according to claim 5, characterized in that: The specific process of step S311 is as follows: S321, parallel sequence matrix P = [p ij ] n×n Delete all zero rows and columns to get P′=[p′ ij ] a×b , according to P′ and process information matrix C=[c ij ] n×m , construct the processing start time matrix S = [s ij ] a×b , processing end time matrix E = [e ij ] a×b , completion sequence matrix R = [r ij ] c×n and the completion time matrix T = [t ij ] n×m , initialize all matrix elements to zero and let t ij+2 =c ij ,j=1,2,…m-2,i=1,2,…n, n is the number of processes, m is the number of stations; S322, traverse P', when p' ij ≠0, let u=p′ ij , calculate the optional processing start time range of process u, and decide the processing start time t of process u according to the priority relationship and process constraints of process u u,s , and let s ij =t u,s , e ij =t u,s +t u ; Traverse P' in turn to determine the processing start time and processing end time of each process in P', and output the processing start time matrix S and processing end time matrix E; S323, traverse S and E, when s ij ≠0, let v=p ij , t v1 =s ij , t v2 =e ij After the traversal is completed, the completion time matrix T is output and T is sorted from small to large according to the processing start time of each process to obtain the process sorting result P″=[p″ ij ] n×1 , p″ ij is the row number corresponding to T before sorting, i.e. the process number; traverse P″ and let h=p″ ij , q=c h That is, the assembly specialty corresponding to process h is q, let r qz =h, where z is the column index of the first zero element in the qth row of R. After traversing P′′, output the completion sequence matrix R; complete the decoding of the processing sequence of each process in the sequence and calculate the completion time t of P′ P =maxE-minS.

7. The aircraft pulsation assembly line balancing method considering complex constraints according to claim 5, characterized in that: The decoding process of the worker configuration plan is as follows: The number of workers of each assembly specialty required to complete the parallel sequence assembly is calculated based on the decoding results of the process processing sequence of the corresponding parallel sequence matrix. According to the process processing sequence and processing time of each assembly specialty represented by the completion sequence matrix R and the completion time matrix T, whether there is a conflict in the processing time is determined one by one according to the processing sequence. The calculation of the number of workers of each specialty and the working time consumption is completed, and the worker configuration matrix W = [w ij ] c×1 's construction.

8. The aircraft pulsation assembly line balancing method considering complex constraints according to claim 1, characterized in that: The process of constructing a set of feasible balance plans through the inner and outer double genetic algorithms is as follows: S511. Allocate the weights of each optimization index according to different production requirements, construct an index weight set, and the index weight set includes the weights of each index under multiple different production requirements and a series of random weights; S512. Randomly generate a certain number of feasible sequences and construct a parallel sequence matrix to complete population initialization. Each individual consists of a feasible sequence and its parallel sequence matrix; S513. The outer layer inputs the process data set and the index weight set of each optimization index, selects an unused index weight, determines the optimization goal according to this weight, the inner layer uses the genetic algorithm to solve the optimal feasible balance plan under the current optimization goal, after the outer layer updates the index weight set, the inner layer continues to solve, and after multiple iterations, the optimal feasible balance plans under all index weights in the index weight set are obtained, and a set of feasible balance plans is obtained.

9. The aircraft pulsation assembly line balancing method considering complex constraints according to claim 1, characterized in that: The specific process of step S6 is as follows: S611. According to the current production requirements, subjectively compare the importance of each pair of indexes and represent the comparison results with triangular fuzzy numbers, and use the triangular fuzzy numbers to form a triangular fuzzy judgment matrix to represent the comparison results of the importance of each index; S612. Use the analytic hierarchy process to calculate the weights of each index according to the triangular fuzzy judgment matrix, and obtain the final weight set of all indexes after normalization; S613. Calculate the attribute values of each optimization index of all plans in the set of feasible balance plans, form a decision matrix, and combine the final weight set of each optimization index to calculate a weighted normalized decision matrix based on the decision matrix; S614. Divide the index attribute values into cost-type indexes and benefit-type indexes, and determine the positive and negative ideal solutions of each index attribute value in the weighted normalized decision matrix. Among them, the positive ideal solution is the minimum value of the cost-type index and the maximum value of the benefit-type index, and the negative ideal solution is the maximum value of the cost-type index and the minimum value of the benefit-type index; S615. Calculate the Euclidean distances from the attribute values of each index in each feasible plan to the positive and negative ideal solutions, and then obtain the closeness of each plan to the optimal plan. The plan with the maximum closeness is the optimal balance plan under the current production requirements determined by the decision.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, it implements the method described in any one of claims 1-8.

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