Aircraft pulsation assembly line balancing method considering complex constraints and medium

Abstract

The invention relates to an aircraft pulsation assembly line balancing method considering complex constraints and a medium. The aircraft pulsation assembly line balancing method comprises the following steps that S1, a process priority relation matrix and a process information matrix are established; s2, generating a feasible sequence and a parallel sequence, expressing the feasible sequence and the parallel sequence in a matrix form, and completing a coding process; s3, in combination with a local splitting strategy, splitting the parallel sequence matrix to each station in a balanced manner; s4, performing line-by-line decoding to obtain a feasible balance scheme corresponding to the sequence, and expressing the feasible balance scheme in a matrix form to complete a decoding process; s5, constructing an optimized feasible balance scheme set through an internal and external double-layer genetic algorithm; and S6, using a fuzzy analytic hierarchy process to calculate the final weight of each index which most accords with the current production demand, and according to the weight, using a sorting method approaching an ideal value to decide an optimal feasible balance scheme in the feasible balance scheme set. Compared with the prior art, the method can further improve the efficiency and result of aircraft assembly pulsation line balance optimization.

Description

Technical Field

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

[0002] Aircraft assembly is a complex systematic project and the most important part of aircraft manufacturing. It involves a large number of processes, materials, resources and personnel. With the introduction of lean manufacturing ideas, various aircraft manufacturers have gradually established pulsating assembly lines to solve the problems of low assembly efficiency, unstable quality, chaotic site and difficult management brought about by the traditional fixed hangar assembly mode.

[0003] The pulsating assembly line transforms the concentrated assembly at a single location into the coordinated assembly of multiple stations. After completing the specified assembly process within a fixed pulsating beat, the aircraft to be assembled enters the next station in turn at the same time point to complete the processing of the assembly process within the next pulsating beat, which can realize the synchronous production of multiple aircraft at multiple stations. However, only by reasonably allocating resources such as materials, workers and assembly processes to the corresponding stations according to production goals to achieve continuous and balanced production can the advantages of high efficiency and low cost of the aircraft assembly pulsating line be highlighted. Different beats, number of stations and process allocation will lead to great differences in the production capacity and economic benefits of each assembly line scheme. Therefore, how to arrange the completion order of the assembly process and reasonably allocate it to each station to achieve the balance of the assembly line is a key issue that needs to be solved in the construction of the aircraft assembly pulsating line.

[0004] In the existing research on the balance problem of the aircraft assembly pulse line, most of the meta-heuristic methods are used to adjust the completion order and distribution of the assembly process to balance the workload of each station and optimize the pulse beat or reduce the number of stations. For example, the Chinese invention patent with the publication number CN110991056A proposes an aircraft assembly line operation scheduling method based on the genetic variable neighborhood algorithm, which takes minimizing the total construction period of the assembly operation as the optimization goal, while considering the close front and close back constraints, resource constraints and space constraints, constructs an aircraft assembly line segment operation scheduling model, adopts an improved genetic variable neighborhood algorithm for solution, and constructs a neighborhood structure to ensure that a legal solution is generated during the search process, improves the search ability, avoids the algorithm from falling into the local optimum, and can shorten the total assembly operation cycle. The Chinese invention patent with the publication number CN114004008A proposes an aircraft assembly line resource allocation optimization method based on neural networks and genetic algorithms. The resource allocation plan, production goals, and resource constraint information are input into this method. The fast non-dominated sorting genetic algorithm is used to autonomously search for the best in the overall solution space, and the population objective function is calculated in combination with the neural network. After iterative optimization, the optimal resource allocation plan is output. However, in actual production, the aircraft assembly line process is large-scale, with multiple areas of parallel processing in each station and multiple types of work working together. Directly using metaheuristic methods to solve the problem is difficult to solve complex constrained optimization. In existing studies, the use of mechanism knowledge has not been considered, and there is a lack of methods for optimizing the static balance of aircraft assembly pulsation lines. Therefore, it is necessary to redesign a balancing method for aircraft pulsation assembly production lines that can generate a feasible balancing solution that is more in line with actual production needs and improve the efficiency and results of aircraft assembly pulsation line balance optimization. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a balancing method and medium for an aircraft pulsating assembly production line taking into account complex constraints. A new encoding and decoding scheme based on mechanism knowledge is introduced, and a double-layer genetic algorithm and a multi-objective fuzzy comprehensive evaluation decision-making method are designed. A feasible balancing scheme that is more in line with actual production needs can be generated, thereby improving 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 pulsation assembly production line considering 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 area, process completion time and corresponding assembly specialty;

[0009] S2. Generate a feasible sequence including the linear completion order of all processes and a parallel sequence reflecting the parallel assembly relationship of all processes according to the process priority relationship matrix and the process information matrix and express them in the form of a matrix to complete the encoding process;

[0010] S3, calculate the pre-completion time and initial benchmark splitting time of the parallel sequence, combine the local splitting strategy, split the parallel sequence matrix station by station, recalculate the benchmark time according to the splitting result and split the sequence again, and after multiple iterations, evenly split the parallel sequence matrix to each station;

[0011] S4. According to the matrix representation of the parallel sequence and its split results, a feasible balance solution corresponding to the sequence is obtained by decoding row by row and represented 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.

[0012] S5. Constructing an optimized feasible balance solution set through an inner-outer double-layer genetic algorithm, wherein the outer layer balances the initial weights of each optimization target according to the process data set and the assembly line layout information, and 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 target weights. After the outer layer updates the weights of each optimization target, the inner layer continues to solve, and after multiple iterations, the optimal feasible balance solution under different indicator weights is obtained, thereby obtaining a feasible balance solution set;

[0013] S6. According to different production demands, the fuzzy analytic hierarchy process is used to calculate the final weights of various indicators that best meet the current production demands, and based on the weights, a sorting method close to the ideal value is used to decide the best feasible balance solution from 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 processes one by one, the i-th row represents the relevant process constraints of process i, the i-th row and the first column represent the completion time of process i, the i-th row and the second column represent the assembly specialty corresponding to process i, the i-th row and the third column represent the number of workers required to complete the assembly of process i, the i-th row and the fourth column represent the assembly area where process i is assembled, and the i-th row and the fifth column represent 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, performing an initial classification of the processes according to the process priority relationship matrix, wherein the classification categories include an allocatable process set, a to-be-allocated process set, and an allocated process set, wherein the initial allocatable process set is a process set without priority relationship constraints, the initial to-be-allocated process set is the full set of process sets, and the initial allocated process set is an empty set;

[0022] 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 process set to be allocated, and update the allocable process set according to 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 yes, 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, judging 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 of P, u and v are the row and column indices of the last non-zero element of 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 in processing order, obtain the processing start time matrix S, processing end time matrix E, completion order matrix R and completion time matrix T, and calculate the estimated completion time t of the parallel sequence P ;

[0031] S312, set 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 Assign 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 decoding the processing order, 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 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 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, we get the benchmark splitting time t 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 label or process number corresponding to T before sorting; 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 order matrix R is output. The decoding of the processing order 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] According to the decoding result of the process processing sequence of the corresponding parallel sequence matrix, the number of workers of each assembly specialty 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, it is judged one by one whether there is a conflict in the processing time according to the processing sequence to complete the calculation of the number of workers of each specialty and the calculation of the working time consumption, and the worker configuration matrix W = [w i j] c×1 's construction.

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

[0040] S511, allocating weights of various optimization indicators according to different production requirements, and constructing an indicator weight set, wherein the indicator weight set includes weights of various 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 is composed 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 according to the weight, and the inner layer uses the genetic algorithm to solve the optimal feasible balance plan 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 plan under all indicator weights in the indicator weight set is obtained, and a set of feasible balance plans is obtained.

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

[0044] S611. According to the current production demand, the indicators are compared with each other in terms of their importance 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.

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

[0046] S613, calculating the attribute values ​​of each optimization index of all solutions in the feasible equilibrium solution set, forming a decision matrix, combining the final weight set of each optimization index, and calculating a weighted normalized decision matrix based on the decision matrix;

[0047] S614, dividing the indicator attribute values ​​into cost-type indicators and benefit-type indicators, and determining 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 of each indicator attribute value in each feasible solution to 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 determined by the decision.

[0049] The present invention also provides a computer-readable storage medium on which a computer program is stored, and 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. The present invention proposes a balancing method for an aircraft pulse assembly production line under complex constraints, introduces a new encoding and decoding scheme based on mechanism knowledge, and effectively solves the limitations of existing methods in dealing with complex constraints such as multi-region 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 It 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 embodiments. DETAILED DESCRIPTION

[0057] The present invention is described in detail below in conjunction with 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 pulsation assembly production 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 processes one by one, the i-th row represents the relevant process constraints of process i, the i-th row and the first column represent the completion time of process i, the i-th row and the second column represent the assembly specialty corresponding to process i, the i-th row and the third column represent the number of workers required to complete the assembly of process i, the i-th row and the fourth column represent the assembly area where process i is assembled, and the i-th row and the fifth column represent 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 an allocatable process set, a to-be-allocated process set, and an allocated process set. The initial allocatable process set is a process set without priority relationship constraints, the initial to-be-allocated process set is the full set of process sets, and the initial allocated process set is an empty set.

[0071] S212: After randomly selecting a process from the current allocatable process set and adding it to the current allocatable process set, the process is deleted from the current process set to be allocatable, and the allocatable process set is updated 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 yes, output the set of assigned processes and express it as a feasible sequence F=[f ij ] n×1 .

[0073] The specific process of generating parallel sequences 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, judging 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, and u and v are the row and column indices of the last non-zero element of 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 pre-completion time and initial benchmark split time of the parallel sequence, combine the local splitting strategy, split the parallel sequence matrix station by station, recalculate the benchmark time according to the splitting result and split the sequence again, and after multiple iterations, evenly split the parallel sequence matrix to each station. The specific process is as follows:

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

[0080] S312, set 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 Assign 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 decoding the processing order, 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 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 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, we get the benchmark splitting time t 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 After initializing all matrix elements to zero, 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 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.

[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 label or process number corresponding to T before sorting; 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 order matrix R is output. The decoding of the processing order 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, the feasible balance scheme corresponding to the sequence is obtained by decoding row by row and represented in matrix form to complete the decoding process. The feasible balance scheme includes a process allocation scheme, a process completion sequence and a worker configuration scheme.

[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 result of the process processing sequence of the corresponding parallel sequence matrix, the number of workers of each assembly specialty 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 calculation of the working time consumption are completed, and the worker configuration matrix W = [w i j] c×1 's construction.

[0089] S5. Construct an optimized feasible equilibrium solution set through an 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 according to the process data set and assembly line layout information. The inner layer operation takes the outer layer information as input. After the genetic algorithm is applied 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, 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 various optimization indicators according to different production demands, and construct an indicator weight set, wherein the indicator weight set includes weights of various indicators under multiple different production demands 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 according to the weight, and the inner layer uses the genetic algorithm to solve the optimal feasible balance plan 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 plan under all indicator weights in the indicator weight set is obtained, and a set of feasible balance plans is obtained.

[0095] S6. According to different production requirements, the final weights of each indicator that best meets the current production requirements are calculated using the fuzzy analytic hierarchy process (FAHP), and the optimal feasible balance solution is determined from the feasible balance solution set using the technique for order preference by similarity to ideal solution (TOPSIS) based on the weights. 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. Using the analytic hierarchy process, the weight of each indicator is calculated based on the triangular fuzzy judgment matrix, and the final weight set of all indicators is obtained after normalization.

[0098] S613. Calculate the attribute values ​​of each optimization index of all solutions in the set of feasible equilibrium solutions to form a decision matrix. Combine the final weight set of each optimization index 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 of each indicator attribute value in each feasible solution to 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 determined by the decision.

[0101] This embodiment uses an example of an aircraft pulse assembly production line of an aircraft company to verify the above method. This example meets the basic problem assumptions of multi-region, multi-professional, and multi-person cooperation in the balance problem of aircraft assembly pulse line. There are 76 assembly processes in total. Workers are divided into 7 assembly professions according to different process categories. Each station is divided into 11 assembly areas according to the assembly position. The specific process information table is shown in Table 1.

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

[0103]

[0104] The optimization method is adopted, which specifically includes the following steps:

[0105] Step 1: Generate the indicator weight set W. Generate 30 indicator weights based on the possible production demand orientation and then randomly generate 270 indicator weights to complete the construction of the indicator weight set W. Each indicator weight consists 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 feasible balance solution set B. Use DGA to traverse the indicator weight set. The relevant parameters are shown in Table 2. Output the feasible balance solution set 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 Partial display of attribute values ​​of decision matrix D indicators

[0111]

[0112] Step 3: Use the fuzzy hierarchical analysis method to calculate the weight of each indicator according to the fuzzy production requirements. According to 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. According to 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 a ranking 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 as shown in Table 5 = [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 every feasible equilibrium solution B i The closeness to the optimal solution D i .

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

[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 =The optimal solution under (w1, w2, w3, w4), the optimal solution decided 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 balance 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 process allocation Gantt chart of the feasible balancing solution 49 shown in the figure intuitively reflects the sequence of process assembly and the parallel relationship between the processes. The decoded worker quantity configuration and station allocation scheme are shown in Table 10.

[0131] Table 10 Feasible balance solution 49 Configuration and allocation of the number of workers in each team

[0132]

[0133] DGA solves the model according to the indicator weight set and obtains a set of feasible balance solutions; FAHP calculates the weights between the four indicators according to 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 according to the weights between the indicators, that is, the feasible balance solution49.

[0134] Depend on Figure 3As shown in Table 10, the process allocation scheme of feasible balancing scheme 49 meets the production characteristics of aircraft pulse assembly line with multi-area parallel operation and multi-worker cooperative assembly, and there are a large number of parallel processes. When constructing a feasible balancing scheme, it is necessary to reasonably allocate the processes to each station and determine the specific processing sequence within the station according to production needs to achieve the balance of the production line. Finally, the number of team workers is configured according to the process allocation results.

[0135] In addition, the FAHP-TOPSIS method can determine different optimal solutions in the feasible equilibrium solution set around different production requirements. As shown in Table 11, the optimal solution determined meets the corresponding production requirements, which verifies 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, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform 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 codes.

[0140] The above description of the embodiments is to facilitate the understanding and use of the invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to these embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments, and 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 in that: 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 area, process completion time and corresponding assembly specialty; S2. Generate a feasible sequence including the linear completion order of all processes and a parallel sequence reflecting the parallel assembly relationship of all processes according to the process priority relationship matrix and the process information matrix and express them in the form of a matrix to complete the encoding process; S3, calculate the pre-completion time and initial benchmark splitting time of the parallel sequence, combine the local splitting strategy, split the parallel sequence matrix station by station, recalculate the benchmark time according to the splitting result and split the sequence again, and after multiple iterations, evenly split the parallel sequence matrix to each station; S4. According to the matrix representation of the parallel sequence and its split results, a feasible balance solution corresponding to the sequence is obtained by decoding row by row and represented 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. S5. Constructing an optimized feasible balance solution set through an inner-outer double-layer genetic algorithm, wherein the outer layer balances the initial weights of each optimization target according to the process data set and the assembly line layout information, and 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 target weights. After the outer layer updates the weights of each optimization target, the inner layer continues to solve, and after multiple iterations, the optimal feasible balance solution under different indicator weights is obtained, thereby obtaining a feasible balance solution set; S6. According to different production demands, the fuzzy analytic hierarchy process is used to calculate the final weights of various indicators that best meet the current production demands, and based on the weights, a sorting method close to the ideal value is used to decide the best feasible balance solution from 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 processes one by one, the i-th row represents the relevant process constraints of process i, the i-th row and the first column represent the completion time of process i, the i-th row and the second column represent the assembly specialty corresponding to process i, the i-th row and the third column represent the number of workers required to complete the assembly of process i, the i-th row and the fourth column represent the assembly area where process i is assembled, and the i-th row and the fifth column represent 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, performing an initial classification of the processes according to the process priority relationship matrix, wherein the classification categories include an allocatable process set, a to-be-allocated process set, and an allocated process set, wherein the initial allocatable process set is a process set without priority relationship constraints, the initial to-be-allocated process set is the full set of process sets, and the initial allocated process set is an empty set; 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 process set to be allocated, and update the allocable process set according to the priority relationship of the process; 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 assigned process 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, judging 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 of P, u and v are the row and column indices of the last non-zero element of 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 in processing order, obtain the processing start time matrix S, processing end time matrix E, completion order matrix R and completion time matrix T, and calculate the estimated completion time t of the parallel sequence P ; S312, set 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 Assign 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 decoding the processing order, 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 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 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, we get the benchmark splitting time t 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 label or process number corresponding to T before sorting; 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 order matrix R; complete the decoding of the processing order 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 allocation plan is as follows: According to the decoding result of the process processing sequence of the corresponding parallel sequence matrix, the number of workers of each assembly specialty 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, it is judged one by one whether there is a conflict in the processing time according to the processing sequence to complete the calculation of the number of workers of each specialty and the calculation of the working time consumption, 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 for each index, 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 between each pair of indexes and represent the comparison result with a triangular fuzzy number, and use a triangular fuzzy judgment matrix composed of triangular fuzzy numbers to represent the comparison result of the importance between 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 on the basis of 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 degree of each plan to the optimal plan. The plan with the maximum closeness degree 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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