Electronic product flexible installation and adjustment station construction and scheduling method

Abstract

The invention discloses an electronic product flexible installation and adjustment station construction and scheduling method, and belongs to the field of production scheduling. According to the method, the problems of multiple product types, batch change, limited number of test instruments, time-consuming repeated construction of workbenches and the like in an electronic product radio frequency line test stage are considered, a flexible station construction and scheduling integration method is researched, and a flexible station construction and scheduling model of a complex electronic product under resource limitation is established; the invention aims to minimize the maximum completion time so as to improve the production efficiency and the resource utilization rate. The model is solved by designing an improved adaptive large neighborhood search algorithm, a backward insertion heuristic algorithm considering time point constraint is innovatively proposed to generate a high-quality initial solution, and two destruction operators and repair operators are designed for problem features. The solution is accepted by adopting an algorithm combining a threshold value accepting algorithm and a simulated annealing algorithm, and the effectiveness of the algorithm is proved through a numerical experiment.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling, and in particular to a method for constructing and scheduling a flexible assembly station for electronic products. Background Art

[0002] Radio frequency line testing is an important stage in the manufacturing process of electronic information countermeasure equipment. This stage is responsible for detecting the performance of products under normal and extreme conditions. Generally, multiple instruments are required to conduct multiple tests such as electrical testing, signal testing, vibration testing, and temperature testing at the same time. The testing is less time-consuming and stable. However, since the construction of the test bench in the test phase is time-consuming, that is, the number of various instruments required for testing, such as signal sources and spectrum analyzers, is limited, and the product types are large and the batches are unstable, the test bench needs to be frequently built according to different test requirements. If the product test sequence is not properly allocated, it will not only increase the worker's operation time, but also reduce the test efficiency. Therefore, the testing process has difficulties in resource allocation and production planning, and resource allocation conflicts and coordination difficulties, resulting in slow response to external demand and long production cycle. However, the computing power of human beings is limited and it is impossible to comprehensively consider multiple constraints. The scheduling results are likely to ignore global optimization, resulting in a low plan completion rate, and it is urgent to optimize it.

[0003] With the intensification of market competition and the diversification of consumer demand, enterprises need to quickly adjust production lines, improve production efficiency, and flexibly produce a variety of products. The emergence of flexible manufacturing has greatly promoted the development of enterprises. However, existing research rarely considers the flexible configuration and scheduling integration of electronic product assembly stations, and there is also little research on parallel machine problems under heterogeneous resources in multi-variety variable batch production modes. Summary of the invention

[0004] The present invention provides a method for constructing and scheduling a flexible assembly station for electronic products, so as to solve the problem that the existing research rarely considers the flexible configuration and scheduling integration of assembly stations for electronic products, and the parallel machine problem under the resource heterogeneity of multi-variety variable batch production mode is also rarely studied.

[0005] The embodiment of the present invention provides a method for constructing and scheduling a flexible assembly station for electronic products, comprising the following steps:

[0006] Construct a flexible workstation construction and scheduling model for electronic products under resource constraints;

[0007] An improved adaptive large neighborhood search algorithm is used to solve the flexible workstation construction and scheduling model for electronic products. The backward insertion heuristic algorithm considering time constraints constructs the initial solution. In the iterative process, the destruction operator and the repair operator are used to generate new solutions respectively. The TA-SA acceptance algorithm combining the threshold acceptance algorithm and the simulated annealing algorithm is used to update the solution, and the flexible workstation construction and scheduling plan for electronic products is obtained.

[0008] Optionally, in one embodiment of the present invention, the construction resource-constrained electronic product flexible workstation construction and scheduling model is:

[0009] minimise C max

[0010] st

[0011]

[0012] In the formula, C max is the maximum completion time, M is the set of workstations, M∈m, N is the set of workpieces, I,j,o∈N, K is the set of instrument types, k∈K, T is the set of time periods, t∈t; p j is the processing time of workpiece j, d k is the number of instruments of type k, n jk The number of instruments k required to complete workpiece j, ST ij is the time required to rebuild the workbench after workpiece i, L is a large positive integer; x ijm is a 0-1 variable. If workpiece j is scheduled to be tested after workpiece i at workstation m, x ijm =1, S j is the start time of job j, z tj is a 0-1 variable. If workpiece j is occupying the instrument at time t, z tj =1; define the set N0 = N∪{0}, N v+1 =N∪{v+1}, between N0 and N v+1 In the set, 0 and v+1 are virtual workpieces. All workstations start from workpiece 0 and end at workpiece v+1. Let p0 = n 0k =n v+1,k =p v+1 =0,

[0013] Constraint (1.1) indicates that at each workstation m, each workpiece j has a preceding workpiece; constraint (1.2) indicates that at each workstation m, each workpiece i has a succeeding workpiece; constraint (1.3) ensures that any non-virtual workpiece has only a preceding workpiece and a succeeding workpiece at the same workstation; constraint (1.4) avoids the situation where the preceding and succeeding workpieces are the same; constraints (1.5) and (1.6) constrain the virtual process 0 to ensure that all workstations start processing from the virtual process 0; constraints (1.7) and (1.8) constrain the virtual process v+1 to ensure that all workstations The processing is finished at the virtual v+1 process; Constraint (1.9) prevents two workpieces from being closely preceded or followed by each other at the same time; Constraint (1.10) is a constraint on the start time between workpieces, indicating that if workpiece j is the close successor of workpiece i, then the start time of j must be greater than or equal to the sum of the start time of i and the test time and the instrument installation and commissioning time; Constraint (1.11) defines the maximum completion time; Constraint (1.12) constrains whether the instrument is occupied by workpiece j at time t to ensure that when time t is between the time when the workpiece starts using the instrument and the time when the workpiece ends processing, z tj is 1, that is, the instrument required by the workpiece is occupied; constraint (1.13) ensures that the number of instruments k used at time t does not exceed d k ; Constraints (1.14) and (1.15) constrain the decision variables.

[0014] Optionally, in one embodiment of the present invention, an auxiliary variable is introduced to perform a linear transformation on constraint (1.12). First, the auxiliary variable is set b j =S j +p j , at this time a j represents the time when the instrument associated with workpiece j begins to be occupied, b j represents the time when the instrument associated with j ends its occupation, when time t is between a j With b j When the time is between, it means that the instrument is occupied; introduce the auxiliary variable u tj represents that time t is greater than the earliest starting occupancy time of workpiece j, and introduces auxiliary variable w tj represents that time t is less than the latest occupancy time of workpiece j, only when u tj and w tj When both are 1, workpiece j will occupy the instrument at time t; therefore, constraint (1.12) can be linearized as:

[0015]

[0016] Among them, constraints (1.16) and (1.17) on the auxiliary variable u tj and w tjConstraints (1.18), (1.19), (1.20) and (1.21) are used to construct the relationship between the four newly added auxiliary variables to ensure that when time t is between a j With b j When and only when u tj and w tj When all are 1, workpiece j will occupy the instrument at time t; constraints (1.22), (1.23) and (1.24) are used to impose the final constraint on whether the instrument is occupied by workpiece j at time t.

[0017] Optionally, in one embodiment of the present invention, a backward insertion heuristic algorithm considering time point constraints is used to construct an initial solution, including:

[0018] Step 1: Set m integer arrays as workstation sets, where each array has n positions, each position of the array stores a job number, initialize each element in the array to 0, and construct a two-dimensional array W[i,j], where each element β ij Represents the transition value between workpieces, that is, each element β in the two-dimensional array W[i,j] ij Defined as:

[0019] β ij =St ij +p j

[0020] The installation and debugging time ST required for workpiece i to workpiece j ij and the processing time p of workpiece j j sum;

[0021] Step 2: Randomly select m workpieces from the workpiece set, insert them into each workstation set as the first workpiece on each workstation, calculate the processing time on each workstation, and delete the corresponding rows and columns of the assigned workpieces from the two-dimensional array W[i,j];

[0022] Step 3: According to the processing time of the scheduled jobs at each workstation, for the first workpiece at the workstation with the shortest current processing time, select the workpiece with the smallest transition value from the corresponding row of the two-dimensional array W[i,j] as its next job and insert it into the workstation set, and delete the corresponding row and column of the assigned workpiece from the two-dimensional array W[i,j];

[0023] Step 4: Repeat step 3, calculate the processing time of each station, and insert the workpiece with the smallest transition value next to the station with the shortest processing time in turn; and perform a feasibility check. If the constraint cannot be met, select the next smallest transition value and execute steps 3 and 4;

[0024] Step 5: If the remaining allocatable workpieces do not satisfy the constraints of the workstation, reselect the initial workpiece of the workstation and execute steps 2, 3 and 4 until no workpiece can be inserted into the workstation;

[0025] Step 6: If no workpiece can be inserted, the obtained set of m workstations is used as the initial solution.

[0026] Optionally, in one embodiment of the present invention, the destruction operator includes: a workpiece random destruction operator and a Shaw destruction operator;

[0027] The process of the random destruction operator is as follows: randomly select a workstation m in the existing sequence, where m∈{1,2,...,M}, and randomly select a workpiece j at a position on the randomly selected workstation, where j∈{1,2,...,N}, and delete the randomly selected workpiece;

[0028] The process of Shaw's destruction operator is: randomly select a workpiece j, and then delete workpiece j and the most related workpiece in its workstation sequence together.

[0029] Optionally, in one embodiment of the present invention, the repair operator includes a workpiece random repair operator and a greedy repair operator;

[0030] The process of the random workpiece repair operator is as follows: first randomly select a deleted workpiece j from the list of damaged workpieces, then randomly select any position of a station m in the current workpiece sequence, m∈{1,2,...,M}, insert workpiece j into this position, and determine whether the station constraint is satisfied. If the station constraint is satisfied, the repair of workpiece j is completed until all removed workpieces are allocated;

[0031] The process of the greedy repair operator is as follows: in the assigned sequence, calculate the increment of the objective function value ΔC after inserting workpiece j max size, choose to make the objective function increment ΔC max The smallest workpiece is inserted into its corresponding position and a check is made to see whether the workstation constraints are met. If so, the repair is completed until all removed workpieces are allocated.

[0032] Optionally, in one embodiment of the present invention, a TA-SA acceptance algorithm combining a threshold acceptance algorithm and a simulated annealing algorithm is used to update the solution, including the following steps:

[0033] Define the initial temperature and cooling rate: Set the initial temperature T0 in the simulated annealing algorithm, the current temperature after the εth iteration Where epochs is the maximum number of iterations given in advance;

[0034] Define the threshold of the threshold acceptance algorithm: Set the weight adjustment step size M. In each iteration of the adaptive large neighborhood search algorithm, determine the threshold T of the threshold acceptance algorithm according to the quality of the current solution and the number of iterations. After each search ends, update the threshold through a threshold change coefficient α ∈ (0, 1).

[0035] Combine the threshold acceptance algorithm and the simulated annealing algorithm: Before each iteration, judge the threshold and temperature simultaneously. In the iterative process within the given weight adjustment step size M, calculate the energy values F of the new solution S′, the current solution S, and the optimal solution S e and make a judgment. The judgment process is as follows:

[0036] If F(S′) < F(S), then the adaptive large neighborhood search algorithm accepts the new solution S′ as the current solution S;

[0037] If F(S′) < F(S e ), then the adaptive large neighborhood search algorithm accepts the new solution S′ as the optimal solution S e ;

[0038] Otherwise, calculate the energy difference ΔE = F(S′) - F(S) between the new solution S′ and the current solution S, calculate the acceptance probability of the solution

[0039] Generate a random number r between 0 and 1, and compare the random number r with the acceptance probability to determine whether to finally accept the new solution S ′ , and update the operator weights, the current temperature, and the threshold.

[0040] A method for constructing and scheduling a flexible assembly and adjustment station for electronic products according to an embodiment of the present invention considers problems such as a large variety of products, batch changes, limited number of test instruments, and time-consuming repeated setup of workbenches during the radio frequency line testing stage of electronic products. It studies the integrated method for constructing and scheduling a flexible station, establishes a complex electronic product flexible station construction and scheduling model under resource constraints, aims to minimize the makespan, and improve production efficiency and resource utilization. Design an improved adaptive large neighborhood search algorithm to solve the model, innovatively propose a backward insertion heuristic algorithm considering time point constraints to generate more effective initial solutions, design two destruction operators and repair operators according to the problem characteristics, and use an algorithm combining the threshold acceptance algorithm and the simulated annealing algorithm to accept the solution. The effectiveness of the algorithm is proved through numerical experiments.

[0041] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0043] Figure 1 A flowchart of a method for constructing and scheduling a flexible assembly and adjustment station for electronic products according to an embodiment of the present invention;

[0044] Figure 2 A flowchart of the construction and scheduling of a flexible assembly and adjustment station according to an embodiment of the present invention;

[0045] Figure 3 This is a flow chart of the construction and scheduling algorithm of the flexible assembly and adjustment station of electronic products according to an embodiment of the present invention;

[0046] Figure 4 This is a result diagram after destruction by the destruction operator of an embodiment of the present invention;

[0047] Figure 5 This is a result diagram after repair by the repair operator of an embodiment of the present invention;

[0048] Figure 6 A comparison diagram of algorithm effects of a medium-to-large-scale example of an embodiment of the present invention;

[0049] Figure 7 This is another comparison diagram of algorithm effects for a medium to large-scale example of an embodiment of the present invention. DETAILED DESCRIPTION

[0050] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0051] This paper takes the RF line test of a company's complex electronic products as the research background, considers the direct coupling relationship between the installation and debugging of equipment and scheduling in the scheduling process of the production mode of multiple varieties and variable batches, and focuses on the problem of flexible station construction and scheduling integration under resource constraints. Through careful analysis of the problem, a flexible station construction and scheduling model for electronic products is established, and an effective optimization algorithm is designed to reduce the production cycle and improve production capacity.

[0052] Figure 1 The present invention is a flowchart of a method for constructing and scheduling a flexible assembly station for electronic products according to an embodiment of the present invention.

[0053] like Figure 1 As shown, the method for constructing and scheduling the flexible assembly and adjustment station of electronic products includes the following steps:

[0054] Construct a flexible workstation construction and scheduling model for electronic products under resource constraints;

[0055] An improved adaptive large neighborhood search algorithm is used to solve the flexible workstation construction and scheduling model for electronic products. The backward insertion heuristic algorithm considering time constraints constructs the initial solution. In the iterative process, the destruction operator and the repair operator are used to generate new solutions respectively. The TA-SA acceptance algorithm combining the threshold acceptance algorithm and the simulated annealing algorithm is used to update the solution, and the flexible workstation construction and scheduling plan for electronic products is obtained.

[0056] The present invention mainly studies the flexible workstation construction and scheduling problems in the RF line testing stage of complex electronic products. This stage is responsible for detecting the performance of the product under normal and extreme conditions. Generally, multiple instruments are required to perform multiple tests such as electrical testing, signal testing, vibration testing, and temperature testing at the same time. The testing is less time-consuming and stable. The construction of flexible workstations for electronic products is reflected in the construction of multiple workbenches at the test site. However, due to the limited number of various instruments required for testing, such as signal sources, spectrum analyzers, etc., and the large variety of products, it is necessary to frequently disassemble the instruments on the workbenches according to different testing requirements. Therefore, these workbenches can be simulated as parallel machines, and this problem can be refined into the problem of flexible workstation construction and scheduling under resource constraints. The scheduling process is as follows: Figure 2 shown.

[0057] During the manufacturing process of the day, all the planned types and corresponding quantities of products that need to be tested on the day have been obtained. The test items and the number of test instruments for each product can be different. During the test process, because the same process involves multiple types of products that need to be tested, the test instruments need to be converted, but the installation and debugging time of each instrument is a certain value and will not change due to the different types of tested products. If you want to minimize the overall test time, you need to ensure that the time for replacing the instrument installation and debugging is as short as possible, that is, the number of instrument changes is as short as possible. Each product is tested separately at the workstation, and there will be no phenomenon of testing several products at the same time at one workstation.

[0058] In summary, this problem can be expressed as follows: before the overall product production starts, the testing department has obtained the test product plan to be completed today, that is, there is a known product set N. All tasks need to be completed on m workbenches, the workbench set M, m∈M, there are K different test instruments available on site {k|k=1,2,...,K}, and the number of each test instrument is known, which is (d1,d2,...,d k ), and the inspection time required for product j can be calculated as p j Whenever different types of products are processed continuously on a workbench, the instrument needs to be replaced. Depending on the type of instrument, the time required to rebuild the workbench after workpiece j is produced after workpiece i can be calculated as STij Therefore, the maximum completion time is determined by the sum of the workpiece testing time at the relatively more time-consuming workstation and the time to rebuild the workbench between different workpieces. The final scheduling task is to arrange the testing of N products on these m workbenches, determine the products to be processed on each workbench and the product processing order, and achieve the goal of minimizing the maximum completion time, considering the limited number of workbenches and test instruments at the test site.

[0059] In one embodiment of the present invention, a flexible workstation construction and scheduling model for electronic products under resource constraints is constructed. Considering the complexity of the actual problem, the model established for this problem needs to meet the following assumptions:

[0060] (1) The test task data required to be completed on the day is known before the production and processing begins on the day.

[0061] (2) A full range of instruments are available, and no instrument failure will occur during the test, and the product testing process will not be interrupted.

[0062] (3) The test time for each instrument is the same and will not change due to changes in product types.

[0063] (4) Each instrument can be used multiple times.

[0064] (5) Since the instrument needs to be debugged when installed at the workstation, this article only considers the time for setting up the workbench, and the time for disassembling the instrument is negligible.

[0065] (6) Each product will be tested after all the necessary instruments have been installed and debugged, and all test items will be debugged in parallel.

[0066] In an embodiment of the present invention, the construction and scheduling model of the flexible workstation for electronic products under resource constraints is:

[0067] minimise C max

[0068] st

[0069]

[0070]

[0071] In the formula, C max is the maximum completion time, M is the set of workstations, m∈M, N is the set of workpieces, i,j,o∈N, K is the set of instrument types, k∈K, T is the set of time periods, t∈T; p j is the processing time of workpiece j, d k is the number of instruments of type k, n jk The number of instruments k required to complete workpiece j, ST ijis the time required to rebuild the workbench after workpiece i, L is a large positive integer; x ijm is a 0-1 variable. If workpiece j is scheduled to be tested after workpiece i at workstation m, x ijm =1, S j is the start time of job j, z tj is a 0-1 variable. If workpiece j is occupying the instrument at time t, z tj =1; define the set N0 = N∪{0}, N v+1 =N∪{v+1}, between N0 and N v+1 In the set, 0 and v+1 are virtual workpieces. All workstations start from workpiece 0 and end at workpiece v+1. Let p0 = n 0k =n v+1,k =p v+1 =0,

[0072] Constraint (1.1) indicates that at each workstation m, each workpiece j has a preceding workpiece; constraint (1.2) indicates that at each workstation m, each workpiece i has a succeeding workpiece; constraint (1.3) ensures that any non-virtual workpiece has only a preceding workpiece and a succeeding workpiece at the same workstation; constraint (1.4) avoids the situation where the preceding and succeeding workpieces are the same; constraints (1.5) and (1.6) constrain the virtual process 0 to ensure that all workstations start processing from the virtual process 0; constraints (1.7) and (1.8) constrain the virtual process v+1 to ensure that all workstations The processing is finished at the virtual v+1 process; Constraint (1.9) prevents two workpieces from being closely preceded or followed by each other at the same time; Constraint (1.10) is a constraint on the start time between workpieces, indicating that if workpiece j is the close successor of workpiece i, then the start time of j must be greater than or equal to the sum of the start time of i and the test time and the instrument installation and commissioning time; Constraint (1.11) defines the maximum completion time; Constraint (1.12) constrains whether the instrument is occupied by workpiece j at time t to ensure that when time t is between the time when the workpiece starts using the instrument and the time when the workpiece ends processing, z tj is 1, that is, the instrument required by the workpiece is occupied; constraint (1.13) ensures that the number of instruments k used at time t does not exceed d k ; Constraints (1.14) and (1.15) constrain the decision variables.

[0073] Since there are minimum and maximum functions in constraint (1.12), this constraint is defined as a nonlinear constraint. In order to facilitate the solution, constraint (1.12) is linearized by introducing auxiliary variables. First, let the auxiliary variable a j =S j - bj =S j +p j , at this time a j represents the time when the instrument associated with workpiece j begins to be occupied, b j represents the time when the instrument associated with j ends its occupation, when time t is between a j With b j In between, it indicates that the instrument is occupied. In addition, the auxiliary variable u is introduced tj represents that time t is greater than the earliest starting occupancy time of workpiece j, and introduces auxiliary variable w tj represents that time t is less than the latest occupancy time of workpiece j, only when u tj and w tj When both are 1, workpiece j will occupy the instrument at time t. Therefore, constraint (1.12) can be linearized as:

[0074]

[0075]

[0076] Among them, constraints (1.16) and (1.17) on the auxiliary variable u tj and w tj Constraints (1.18), (1.19), (1.20) and (1.21) are used to construct the relationship between the four newly added auxiliary variables to ensure that when time t is between a j With b j When and only when u tj and w tj When all are 1, workpiece j will occupy the instrument at time t; constraints (1.22), (1.23) and (1.24) are used to impose the final constraint on whether the instrument is occupied by workpiece j at time t.

[0077] The Adaptive Large Neighborhood Search (ALNS) algorithm is an effective tool for solving the problem of flexible workstation scheduling. It can dynamically adjust the search strategy according to the system status to find a better scheduling solution. The Adaptive Large Neighborhood Search algorithm was proposed by Ropke and Pisinger in 2006 and is an extension of the large-scale neighborhood search algorithm. Its core idea is to use different neighborhood structures (i.e., the way the solution changes) to search the solution space to find a better solution. The algorithm can dynamically adjust the search strategy during the search process to better explore the solution space.

[0078] The adaptive large neighborhood search algorithm (ALNS) adds a measure of the effect of the operator on the basis of the neighborhood search. It has better adaptability and can accelerate the generation of better solutions. It is especially suitable for large-scale examples and easy to meet the actual situation of the enterprise. The present invention designs an improved adaptive large neighborhood search algorithm (Modified ALNS, M-ALNS) to solve the problem. According to the characteristics of the problem, a time-constrained backward insertion (Time Considering Backwardinsertion method, TC-BIM) heuristic algorithm is designed to construct the initial solution. In the iterative process, two types of destruction operators and repair operators are used to generate new solutions, and the TA-SA acceptance algorithm that combines the threshold acceptance algorithm with the simulated annealing algorithm is used to update the solution. The process of the above-mentioned algorithm is as follows: Figure 3 shown.

[0079] In one embodiment of the present invention, as a heuristic search algorithm, the M-ALNS algorithm needs to be given an initial solution, and then iteratively search it in the neighborhood space. A good initial solution can reduce the computing time consumption and improve the quality of the solution. The insertion method is a commonly used method for generating an initial solution. Combined with the characteristics of the problem, the time-constrained backward insertion (TC-BIM) heuristic algorithm is used to construct an initial solution for the problem design. The specific process is as follows:

[0080] Step 1: Set m integer arrays as workstation sets, where each array has n positions, each position of the array stores a job number, initialize each element in the array to 0, and construct a two-dimensional array W[i,j], where each element β ij Represents the transition value between workpieces, that is, each element β in the two-dimensional array W[i,j] ij Defined as:

[0081] β ij =ST ij +p j

[0082] The installation and debugging time required for workpiece i to workpiece j is ST ij and the processing time p of workpiece j j sum;

[0083] Step 2: Randomly select m workpieces from the workpiece set, insert them into each workstation set as the first workpiece on each workstation, calculate the processing time on each workstation, and delete the corresponding rows and columns of the assigned workpieces from the two-dimensional array W[i,j];

[0084] Step 3: According to the processing time of the scheduled jobs at each workstation, for the first workpiece at the workstation with the shortest current processing time, select the workpiece with the smallest transition value from the corresponding row of the two-dimensional array W[i,j] as its next job and insert it into the workstation set, and delete the corresponding row and column of the assigned workpiece from the two-dimensional array W[i,j];

[0085] Step 4: Repeat step 3, calculate the processing time of each station, and insert the workpiece with the smallest transition value next to the station with the shortest processing time in turn; and perform a feasibility check. If the constraint cannot be met, select the next smallest transition value and execute steps 3 and 4;

[0086] Step 5: If the remaining allocatable workpieces do not satisfy the constraints of the workstation, reselect the initial workpiece of the workstation and execute steps 2, 3 and 4 until no workpiece can be inserted into the workstation;

[0087] Step 6: If no workpiece can be inserted, the obtained set of m workstations is used as the initial solution.

[0088] Optionally, in one embodiment of the present invention, the destruction operator includes: a workpiece random destruction operator and a Shaw destruction operator;

[0089] The process of the random destruction operator is as follows: randomly select a workstation m in the existing sequence, where m∈{1,2,...,M}, and randomly select a workpiece j at a position on the randomly selected workstation, where j∈{1,2,...,N}, and delete the randomly selected workpiece;

[0090] The process of Shaw's destruction operator is: randomly select a workpiece j, and then delete workpiece j and the most related workpiece in its workstation sequence together.

[0091] Optionally, in one embodiment of the present invention, the repair operator includes a workpiece random repair operator and a greedy repair operator;

[0092] The process of the random workpiece repair operator is as follows: first randomly select a deleted workpiece j from the list of damaged workpieces, then randomly select any position of a station n in the current workpiece sequence, n∈{1,2,...,M}, insert workpiece j into this position, and determine whether the station constraint is satisfied. If the station constraint is satisfied, the repair of workpiece j is completed until all removed workpieces are assigned;

[0093] The process of the greedy repair operator is as follows: in the assigned sequence, calculate the increment of the objective function value ΔC after inserting workpiece j max size, choose to make the objective function increment ΔC maxThe smallest workpiece is inserted into its corresponding position, and it is judged whether the station constraints are met. If the station constraints are met, this repair is completed until all the removed workpieces are allocated.

[0094] As Figure 4 and Figure 5 shown, it shows the destruction and repair processes of a destruction operator and a repair operator.

[0095] Optionally, in an embodiment of the present invention, the TA-SA acceptance algorithm combining the threshold acceptance algorithm and the simulated annealing algorithm is used to update the solution, including the following steps:

[0096] Define the initial temperature and the cooling rate: Set the initial temperature T0 in the simulated annealing algorithm, and the current temperature after the ε-th iteration where epochs is the maximum number of iterations given in advance;

[0097] Define the threshold of the threshold acceptance algorithm: Set the weight adjustment step size M. In each iteration of the adaptive large neighborhood search algorithm, determine the threshold T of the threshold acceptance algorithm according to the quality of the current solution and the number of iterations. After each search ends, update the threshold through a threshold change coefficient α∈(0,1);

[0098] Combine the threshold acceptance algorithm and the simulated annealing algorithm: Before each iteration, judge the threshold and the temperature at the same time. In the iterative process within the given weight adjustment step size M, calculate the energy values F of the new solution S′, the current solution S and the optimal solution S e and make a judgment. The judgment process is as follows:

[0099] If F(S′)<F(S), then the adaptive large neighborhood search algorithm accepts the new solution S′ as the current solution S;

[0100] If F(S′)<F(S e ), then the adaptive large neighborhood search algorithm accepts the new solution S′ as the optimal solution S e ;

[0101] Otherwise, calculate the energy difference ΔE = F(S′)-F(S) between the new solution S′ and the current solution S, and calculate the acceptance probability of the solution

[0102] Generate a random number r between 0 and 1, and compare the random number r with the acceptance probability to determine whether to finally accept the new solution S′, and update the operator weight, the current temperature and the threshold.

[0103] The following uses specific embodiments to illustrate the flexible assembly and adjustment station construction and scheduling method of the electronic product of the invention.

[0104] The test cases are generated with reference to the data of a company's complex electronic product RF line test task. In order to verify the performance of the M-ALNS algorithm designed above, three scale cases of small scale, medium scale and large scale are randomly generated. The case types are shown in Table 1. There are 9 small scale cases, 9 medium scale cases, 9 large scale cases, and a total of 27 cases. For the convenience of representation, the following experimental example of 3 workstations and 15 workpieces is represented as "3-15". The basic data in the example includes the available number of various instruments, the installation and debugging time of each instrument, the workpiece test time, the test instrument requirements for each workpiece, etc. Part of the above information is shown in Table 2, Table 3, Table 4, and Table 5. The following data can guarantee the normal processing requirements of the workpiece.

[0105] Table 1 Example scale

[0106]

[0107] Table 2 Available quantity of each instrument

[0108]

[0109] Table 3 Workpiece test time

[0110]

[0111] Table 4 Instruments required for workpiece testing

[0112]

[0113] Table 5 Instrument installation and debugging time

[0114]

[0115] At the same time, through the data in Table 4 and Table 5, the debugging time of the reconstruction station required when switching the test instrument between workpieces with a close relationship can be calculated. The calculation results are shown in Table 6.

[0116] Table 6 Reconfiguration time of workstations between workpieces

[0117]

[0118] Comparative analysis between M-ALNS algorithm and Gurobi:

[0119] First, the algorithm performance analysis is performed based on a small-scale example. For each problem size, 10 runs are performed to obtain the average value. max (Gurobi) means using the Gurobi solver to find the optimal solution of the model proposed in this paper, C max(MALNS) represents the average target value obtained by the algorithm proposed in this paper according to the number of runs. The algorithm solution time is (s), and Gpa represents the relative error between the algorithm and the optimal solution, and the formula is as follows:

[0120]

[0121] It can be seen from Table 7 that the average relative error between the M-ALNS algorithm and the optimal solution is 0.3%, and its average solution time is much shorter than Gurobi. As the scale of the workpiece increases, the solution time of Gurobi increases greatly, especially when the number of workpieces reaches 15, Gurobi cannot find the optimal solution within 3600s, while the M-ALNS algorithm can still find the corresponding solution quickly in a short time, which is enough to reflect the advantages of the M-ALNS algorithm in performance and solution speed.

[0122] Table 7 Comparison of the optimal solutions of M-ALNS and Gurobi

[0123]

[0124]

[0125] Comparative analysis between M-ALNS algorithm and ALNS algorithm:

[0126] For large-scale examples, Gurobi has difficulty in obtaining the optimal solution, so the M-ALNS and ALNS algorithms are compared for medium- and large-scale examples. ALNS(a) is the ALNS algorithm that uses TC-BIM to generate the initial solution based on ALNS, and ALNS(b) is the ALNS algorithm that uses the TA-SA acceptance algorithm based on ALNS. For medium-scale examples, the solution time (s) and objective function value of each algorithm are recorded, and the results obtained by the MALNS algorithm are used as the benchmark. The relative error is calculated as follows:

[0127]

[0128] Among them C max (X) represents the target value obtained by using the basic ALNS algorithm, ALNS (a) and ALNS (b) algorithm, C max (MALNS) represents the average target value obtained by the proposed algorithm according to the number of runs. For each problem size, 5 experiments are run to get the average value. The experimental results are shown in Tables 8 and 9.

[0129] It can be seen from Table 8 that in the medium-scale example, the MALNS algorithm is better than the ALNS algorithm, ALNS(a) and ALNS(b) algorithms in terms of average solution performance; the average target value obtained by the MALNS algorithm is improved by an average of 19.6% compared with the ALNS algorithm, and is improved by an average of 2.3% and 10.8% compared with ALNS(a) and ALNS(b).

[0130] Table 8 Comparison results of algorithms for large-scale examples

[0131]

[0132] Table 9 shows that in large-scale examples, the average solution speed of the MALNS algorithm is better than that of the ALNS algorithm, ALNS(a) and ALNS(b); the average solution time of the MALNS algorithm is reduced by 73.3% on average compared with the ALNS algorithm, and by 70.7% and 23.3% on average compared with ALNS(a) and ALNS(b). In addition, except for example "6-75", the solution results of the MALNS algorithm are better than those of the other three algorithms; the average value obtained by the MALNS algorithm is improved by 57.6% on average compared with the ALNS algorithm, and by 1.0% and 40.4% on average compared with ALNS(a) and ALNS(b). It can be seen that the MALNS algorithm has good results in terms of performance and speed.

[0133] Table 9 Comparison results of large-scale example algorithms

[0134]

[0135] Depend on Figure 7 It can be seen that for different part sizes, the average completion time solved by MALNS is better than that of ALNS algorithm, ALNS(a) and ALNS(b). Figure 7 It can be seen that in the box plots of the four algorithms for all examples, MALNS has a smaller degree of dispersion than the other three algorithms.

[0136] The embodiment of the present invention first describes in detail the problems existing in the testing phase of a company's complex electronic products, and makes corresponding assumptions on the requirements of the test instruments, etc., defines the problem-related parameters and the decision variables to be solved, and takes minimizing the maximum completion time as the goal, considering resource constraints, and constructing a flexible workstation construction and scheduling model for electronic products. There are nonlinear constraints in the model, so by introducing new variables to linearize this nonlinear constraint, the purpose of facilitating the solution is achieved. After the model is built, the Gurobi algorithm is called by Python to verify the model, which proves the correctness and rationality of the model.

[0137] ALNS adds a measure of the effect of operators on the basis of neighborhood search, has better adaptability, can accelerate the generation of better solutions, is especially suitable for large-scale examples, and is easy to meet the actual situation of enterprises. In order to solve the model more efficiently, an improved adaptive large-scale search M-ALNS algorithm is designed. In the design process of the algorithm, an innovative backward insertion heuristic TC-BIM algorithm considering time constraints is proposed to generate a more effective initial solution. Then, two destruction operators and repair operators are designed according to the characteristics of the problem. Then, the TA-SA algorithm combining the threshold acceptance algorithm and the simulated annealing algorithm is used to accept the solution to improve the convergence speed and stability of the algorithm. After the algorithm design is completed, in order to verify the effectiveness and superiority of the M-ALNS algorithm, multiple groups of small-scale examples, medium-scale examples and large-scale examples constructed with reference to the actual production situation of the enterprise are used for numerical experiments. The experiment proves that the M-ALNS algorithm can still obtain the corresponding solution quickly in a short time, which is enough to reflect the advantages of the M-ALNS algorithm in performance and solution speed.

[0138] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0139] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0140] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present invention belong.

Claims

1. A method for constructing and scheduling a flexible assembly station for electronic products, characterized in that: The following steps are involved: Construct a flexible workstation construction and scheduling model for electronic products under resource constraints; An improved adaptive large neighborhood search algorithm is used to solve the flexible workstation construction and scheduling model for electronic products. The backward insertion heuristic algorithm considering time constraints constructs the initial solution. In the iterative process, the destruction operator and the repair operator are used to generate new solutions respectively. The TA-SA acceptance algorithm combining the threshold acceptance algorithm and the simulated annealing algorithm is used to update the solution, and the flexible workstation construction and scheduling plan for electronic products is obtained.

2. The method according to claim 1, characterized in that: The construction and scheduling model of flexible workstations for electronic products under resource constraints is as follows: In the formula, C max is the maximum completion time, M is the set of workstations, m∈M, N is the set of workpieces, i, j, o∈N, K is the set of instrument types, k∈K, T is the set of time periods, t∈T; p j is the processing time of workpiece j, d k is the number of instruments of type k, n jk The number of instruments k required to complete workpiece j, ST ij is the time required to rebuild the workbench after workpiece i, L is a large positive integer; x ijm is a 0-1 variable. If workpiece j is scheduled to be tested after workpiece i at workstation m, x ijm =1, S j is the start time of job j, z tj is a 0-1 variable. If workpiece j is occupying the instrument at time t, z tj =1; define the set N0 = N∪{0}, N v+1 =N∪{v+1}, between N0 and N v+1 In the set, 0 and v+1 are virtual workpieces. All workstations start from workpiece 0 and end at workpiece v+1. Let p0 = n 0k =n v+1，k =p v+1 =0, Constraint (1.1) indicates that at each workstation m, each workpiece j has a preceding workpiece; constraint (1.2) indicates that at each workstation m, each workpiece i has a succeeding workpiece; constraint (1.3) ensures that any non-virtual workpiece has only a preceding workpiece and a succeeding workpiece at the same workstation; constraint (1.4) avoids the situation where the preceding and succeeding workpieces are the same; constraints (1.5) and (1.6) constrain the virtual process 0 to ensure that all workstations start processing from the virtual process 0; constraints (1.7) and (1.8) constrain the virtual process v+1 to ensure that all workstations The processing is finished at the virtual U+1 process. Constraint (1.9) prevents two workpieces from being closely preceded or followed by each other at the same time. Constraint (1.10) is a constraint on the start time between workpieces, which means that if workpiece j is the close successor of workpiece i, then the start time of j must be greater than or equal to the sum of the start time of i and the test time and the instrument installation and commissioning time. Constraint (1.11) defines the maximum completion time. Constraint (1.12) constrains whether the instrument is occupied by workpiece j at time t to ensure that when time t is between the time when the workpiece starts using the instrument and the time when the workpiece ends processing, z tj is 1, that is, the instrument required by the workpiece is occupied; constraint (1.13) ensures that the number of instruments k used at time t does not exceed d k ; Constraints (1.14) and (1.15) constrain the decision variables.

3. The method according to claim 2, characterized in that Auxiliary variables are introduced to linearize constraint (1.12). First, let the auxiliary variables b j =S j +p j , at this time a j represents the time when the instrument associated with workpiece j begins to be occupied, b j represents the time when the instrument associated with j ends its occupation, when time t is between a j With b j When the time is between, it means that the instrument is occupied; introduce the auxiliary variable u tj represents that time t is greater than the earliest starting occupancy time of workpiece j, and introduces auxiliary variable w tj represents that time t is less than the latest occupancy time of workpiece j, only when u tj and w tj When both are 1, workpiece j will occupy the instrument at time t; Therefore, constraint (1.12) can be linearized as: Among them, constraints (1.16) and (1.17) on the auxiliary variable u tj and w tj Constraints (1.18), (1.19), (1.20) and (1.21) are used to construct the relationship between the four newly added auxiliary variables to ensure that when time t is between a j With b j When and only when u tj and w tj When all are 1, workpiece j will occupy the instrument at time t; constraints (1.22), (1.23) and (1.24) are used to impose the final constraint on whether the instrument is occupied by workpiece j at time t.

4. The method according to claim 1, characterized in that: The backward insertion heuristic algorithm considering the time point constraints constructs the initial solution, including: Step 1: Set m integer arrays as workstation sets, where each array has n positions, each position of the array stores a job number, initialize each element in the array to 0, and construct a two-dimensional array W[i, j], where each element β ij Represents the transition value between workpieces, that is, each element β in the two-dimensional array W[i, j] ij Defined as: β ij =ST ij +p j The installation and debugging time ST required for workpiece i to workpiece j ij and the processing time p of workpiece j j sum; Step 2: Randomly select m workpieces from the workpiece set, insert them into each workstation set as the first workpiece on each workstation, calculate the processing time on each workstation, and delete the corresponding rows and columns of the assigned workpieces from the two-dimensional array W[i, j]; Step 3: According to the processing time of the scheduled jobs at each workstation, for the first workpiece at the workstation with the shortest current processing time, select the workpiece with the smallest transition value from the corresponding row of the two-dimensional array W[i, j] as its next job and insert it into the workstation set, and delete the corresponding row and column of the assigned workpiece from the two-dimensional array W[i, j]; Step 4: Repeat step 3, calculate the processing time of each station, and insert the workpiece with the smallest transition value next to the station with the shortest processing time in turn; and perform a feasibility check. If the constraint cannot be met, select the next smallest transition value and execute steps 3 and 4; Step 5: If the remaining allocatable workpieces do not satisfy the constraints of the workstation, reselect the initial workpiece of the workstation and execute steps 2, 3 and 4 until no workpiece can be inserted into the workstation; Step 6: If no workpiece can be inserted, the obtained set of m workstations is used as the initial solution.

5. The method according to claim 1, characterized in that The destruction operators include: random destruction operator of workpiece and Shaw destruction operator; The process of the random destruction operator is as follows: randomly select a workstation m in the existing sequence, where m∈{1, 2, ..., M}, and randomly select a workpiece j at a position on the randomly selected workstation, where j∈{1, 2, ..., N}, and delete the randomly selected workpiece; The process of Shaw's destruction operator is: randomly select a workpiece j, and then delete workpiece j and the most related workpiece in its workstation sequence together.

6. The method according to claim 1, characterized in that The repair operators include the random repair operator and the greedy repair operator; The process of the random workpiece repair operator is as follows: first randomly select a deleted workpiece j from the list of damaged workpieces, then randomly select any position of a workstation m in the current workpiece sequence, m∈{1, 2, ..., M}, insert workpiece j into this position, and determine whether the workstation constraint is satisfied. If the workstation constraint is satisfied, the repair of workpiece j is completed until all removed workpieces are assigned; The process of the greedy repair operator is as follows: in the assigned sequence, calculate the increment of the objective function value ΔC after inserting workpiece j max size, choose to make the objective function increment ΔC max The smallest workpiece is inserted into its corresponding position and a check is made to see whether the workstation constraints are met. If so, the repair is completed until all removed workpieces are allocated.

7. The method according to claim 1, characterized in that The TA-SA acceptance algorithm, which combines the threshold acceptance algorithm with the simulated annealing algorithm, is used to update the solution, including the following steps: Define the initial temperature and cooling rate: Set the initial temperature T0 in the simulated annealing algorithm, the current temperature after the εth iteration Where epochs is the maximum number of iterations given in advance; Define the threshold of the threshold acceptance algorithm: set the weight adjustment step size M. In each iteration of the adaptive large neighborhood search algorithm, determine the threshold T of the threshold acceptance algorithm according to the quality of the current solution and the number of iterations. After each search, update the threshold by a threshold change coefficient α∈(0,1); Combine the threshold acceptance algorithm with the simulated annealing algorithm: before each iteration, the threshold and temperature are judged at the same time, and the new solution S′, the current solution S and the optimal solution S are calculated during the iteration process within the given weight adjustment step size M. e The energy value F is determined and judged. The judgment process is as follows: If F(S′)<F(S), the adaptive large neighborhood search algorithm accepts the new solution S′ as the current solution S; If F(S′)<F(S e ), then the adaptive large neighborhood search algorithm accepts the new solution S′ as the optimal solution S e ; Otherwise, calculate the energy difference ΔE=F(S′)-F(S) between the new solution S′ and the current solution S, and calculate the acceptance probability of the solution Generate a random number r between 0 and 1, and compare the random number r and the acceptance probability Compare to determine whether to accept the new solution S′ and update the operator weight, current temperature and threshold.

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