Multi-person multi-machine interaction station disassembly line balance design method

Abstract

The invention belongs to the field of disassembly production line balance design in the recovery process of waste electrical and electronic products, and particularly relates to a multi-person multi-machine interaction station disassembly line balance design method which comprises the following steps: S1, counting a master station number started by f1; establishing a mixed integer programming model by taking f1, f2, f3, f4, f5, f6, f7, f7, f8, f8, f8, f8, f8 and f8 as targets; s2, collecting disassembly line data and providing constraint conditions of an objective function to form a disassembly balance design model; s3, on the basis of a mixed integer programming model, domination processing is carried out on the solution set, and an optimal disassembly line balance scheme is obtained; the invention aims to provide a multi-person multi-machine interaction site disassembly line balance design method, which takes the minimum number of workstations, the minimum number of operators, the minimum total disassembly time and the minimum idle balance index as optimization targets, establishes an accurate mixed integer programming model and improves the overall disassembly efficiency.

Description

Technical Field

[0001] The invention belongs to the field of balanced design of disassembly production lines in the process of recycling waste electrical and electronic products, and in particular to a balanced design method of a disassembly line at a multi-person and multi-machine interactive site. Background Art

[0002] In the traditional disassembly line balance design, each workstation adopts a single worker disassembly mode. When dealing with waste electromechanical products with a large number of parts and complex structures, the number of tasks assigned in each station will also increase. If the single worker disassembly mode is still adopted, the disassembly efficiency is extremely low. In this context, a disassembly mode of multiple people sharing the site has emerged, that is, multiple workers are assigned to a site to complete the assigned tasks in the station. With the continuous advancement of science and technology, industrial robots have gradually replaced workers to perform some simple and repetitive operations. Robot operation can not only save costs, but also improve the disassembly speed and accuracy. Therefore, a worker-robot co-station disassembly mode has been proposed. In the research on the disassembly line of human-machine co-station, considering the limitation of the robot's disassembly ability, it is assumed that the robot can complete simple and repetitive disassembly tasks alone, and cannot interact with workers to perform the same disassembly task. Therefore, the existing research on the disassembly line of human-machine co-station cannot handle the disassembly tasks of waste products that require human-machine interaction to complete. Summary of the invention

[0003] The purpose of the present invention is to provide a balanced design method for a disassembly line with multiple people and multiple machines interacting at the site, which takes minimizing the number of workstations, the number of operators, the total disassembly time and the idle balance index as the optimization goal, and establishes an accurate mixed integer programming model to improve the overall disassembly efficiency.

[0004] In order to achieve the above objectives, the technical solution adopted by the present invention is: a multi-person multi-machine interactive site disassembly line balance design method, comprising the following steps:

[0005] S1, with the total number of sites opened by f1, the total number of operators employed by f2, the total operation time of f3 and the idle balance index minimized as the goal, a mixed integer programming model is established; the objective function of the model is as follows:

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[0008] S2, collect disassembly line data and propose constraints of the objective function to form a disassembly balance design model; the constraints are as follows:

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[0033] Where i, j are task indexes, e is site index, w is candidate worker index, and b is candidate robot index; N is the task index set, N = {1, 2, ..., N}, i, j ∈ N; E is the site index set E = {1, 2, ..., E}, e ∈ E; W is the worker index set, W = {1, 2, ..., W}, w ∈ W; B is the robot index set, B = {1, 2, ..., B}, b ∈ B; P i The set of immediate predecessor tasks of task i; t iw The time it takes worker w to perform task i; t ib The time it takes robot r to perform task i; η is a large positive number; m i The interactive properties of the task, m i = 1, when task i needs to be disassembled interactively by a robot and a worker; 0, otherwise; c i The complex properties of the task, c i = 1, task i has complex attributes and can only be performed by workers; 0, otherwise; h i The hazard attribute of the task, h i =1, task i has hazardous attributes and can only be performed by robots; 0, otherwise; CT disassembly line cycle time; CW max The maximum number of workers that can be assigned to each site; CB max The maximum number of robots that can be assigned to each station; t i s The start time of task i; x iew Worker disassembles variable, x 1 =1, task i is executed by worker w in site k; 0, otherwise; x ieb Robot disassembly variable, x 2 =1, task i is performed by robot r in station k; 0, otherwise; y ew Worker allocation variable; y 1 =1, worker w is assigned to site k; 0, otherwise; y eb Robot assigns variable, y 2 =1, robot r is assigned to site k; 0, otherwise; z ijew The variable for the order of tasks in the workers’ hands, z 1 =1, task i and task j are executed by worker w in site k, and i is executed before j; 0, otherwise; z ijeb Task order variable in the robot hand, z 2 =1, task i and task j are executed by robot r in station k, and i is executed before j; 0, otherwise; s e Site start variable, s e =1, site e is enabled; 0, otherwise;

[0034] S3. Based on the mixed integer programming model, perform dominance processing on the solution set to obtain the optimal disassembly line balancing scheme.

[0035] Preferably, S3 uses the GJA algorithm to obtain the optimal disassembly line balancing scheme. The specific steps are as follows:

[0036] Step1: Preset parameters.

[0037] Step2: Initialize the population; design a coding method to generate the initial population and calculate the objective values (f 1 , f 2 , f 3 , f 4 ) corresponding to the individuals in this population.

[0038] Step3: Enter the iterative program, and let l = 1.

[0039] Step4: Select the best individuals in the population to form the mating pool of the algorithm.

[0040] Step5: Make a copy of the new mating pool. Perform crossover operations on all individuals St in the original mating pool, and perform mutation operations on all individuals in the original mating pool; divide the newly copied mating pool into group - a and group - b according to the type differences of So and Ss, and perform crossover operations and mutation operations on these two types of groups respectively.

[0041] Step6: Merge the individuals newly generated in Step5, and further execute the Jaya learning strategy to generate new individuals again.

[0042] Step7: Merge the individuals newly generated in Step6 with the parent population in Step2.

[0043] Step8: Update the population using non - dominated sorting and crowding distance, and calculate the HV index using the non - dominated solution set screened by non - dominated sorting and crowding distance.

[0044] Step9: Determine whether to enter the next iteration. If l < L, let l = l + 1, and go to Step4 to enter the next iteration; otherwise, terminate the iteration. Take the obtained non - dominated solutions as the optimal solutions to the multi - man and multi - machine interactive station disassembly line balancing problem (MMRC - DLBP), and output the non - dominated schemes corresponding to these non - dominated solutions.

[0045] Preferably, the encoding method of Step 2 is as follows: according to the priority constraint, a sequence St containing all disassembly tasks is designed, wherein the subscript "c" indicates a complex task, "m" indicates a human-machine interaction task, "h" indicates a hazardous task, and the other tasks without a subscript are ordinary tasks; then, an operator sequence So containing all candidate workers and candidate robots is designed. To avoid a disassembly task always being assigned to workers or robots in the same site, the sequence So should contain two situations: the worker in front and the robot in the back, and the robot in front and the worker in the back, and the probability of the two situations should be 50%. These two situations are respectively represented by So a and So b Indicates that; considering the uniqueness of worker and robot numbers, the operator numbers at the end of the So sequence need to be adjusted in order to achieve the assignment of operators to sites and match So a and So b Two cases are designed to match So a and So b Site sequence Ss a and Ss b ; in Ss a In the sequence, the site number segment that workers can allocate comes first. This segment is from 1 to the maximum site number that can be opened E according to the worker capacity limit of each site (CW max ) are randomly generated and combined, and the station number that the robot can assign is at the end. This segment is from 1 to E according to the robot capacity limit (CB max ) randomly generated for combination; and So b Similar, Ss b The positions of the worker segment and the robot segment in the sequence are opposite; combined with the designed So a and So b Sequence and Ss a and Ss b The sequence enables the allocation process of candidate workers and robot stations, and then the allocation of tasks to operators within the station is handled by decoding.

[0046] Preferably, the decoding method is as follows: decoding is the execution process of assigning the tasks in the St sequence to the operators in the site one by one according to the beat time constraints of the site. In the assignment process, the assignment object is determined according to the attributes of the currently selected task: complex tasks can only be assigned to candidate workers, hazardous tasks can only be assigned to candidate robots, interactive tasks are assigned to candidate workers and robots in the same site at the same time, and ordinary tasks are randomly assigned to candidate workers or robots. Considering the characteristics of multi-machine sites, that is, a site contains multiple workers and multiple robots, it is inevitable that the specific operator number cannot be selected when assigning tasks. For example, when a complex task is assigned to a worker in the site, it is not certain which worker it is assigned to, which makes decoding impossible to continue. For this reason, a shortest task completion time strategy is proposed, that is, when an operator cannot be selected, the operator with the shortest completion time is selected to perform the task. However, multiple operators performing the current task may also have the shortest completion time at the same time. At this time, the proposed strategy does not work. For this reason, a "selection The method of "selecting the first operator in the So sequence to perform the current task" is used to solve this problem. For interactive tasks, in addition to using the proposed strategy, when there are multiple workers or robots with the same shortest completion time, the method of "selecting the first worker and the first robot in the So sequence" is still required to complete the specific allocation of interactive tasks; in addition, when calculating the completion time of the current task, the constraints (9-13) in the model should be followed; when the maximum remaining time of the operators in the site cannot meet the allocation requirements of the current task, the next site needs to be opened; the waste products are completely disassembled, so the decoding is based on the completion of the allocation of the last task in the St sequence as the exit endpoint. During the decoding process, the following three situations will have infeasible solutions: 1. Complex tasks will be assigned to sites without workers; 2. Hazardous tasks will be assigned to sites without robots; 3. Interactive tasks will be assigned to sites lacking workers or robots. The target values ​​corresponding to these three situations are set to (η,η,η,η), so they can be directly removed by Pareto screening.

[0047] Preferably, the crossover operation is as follows: for the disassembly task sequence St and the operator sequence So, a two-point crossover operation is used, and for the site sequence Ss, an operation of exchanging the number of randomly selected sites is used, and the three newly generated sequences are combined for decoding again to obtain a new solution and disassembly plan.

[0048] Preferably, for the three coding sequences of MMRC-DLBP, single-point mutation is used to perform mutation operations on them with a certain probability. During the mutation, St needs to comply with the priority relationship constraint of waste products, and Ss needs to comply with the operator quantity limit constraint within the site.

[0049] Preferably, the individual update expression of Jaya learning strategy is

[0050]

[0051] In the formula, S l is the individual variable of the continuous problem in the lth iteration process, S best is the individual variable with the best objective function in the lth iteration, S p and S q are two individual variables randomly selected in the lth iteration process, and is a random number between 0 and 1, S l ′ is S l is the updated value;

[0052] In order to match the discrete characteristics of the proposed MMRC-DLBP problem, equation (29) is discretized and the discretized expression is:

[0053]

[0054] In the formula, S l is the population individual sequence (including three sequences St, So, and Ss) obtained after crossover and mutation operations of GJA in the lth iteration, S best is the four single-objective optimal solution sequences of the individuals in the population in the lth iteration, S p and S q are two individuals randomly selected from the new population, ⊕ means performing the operation after the symbol based on the sequence before the symbol, represents the crossover operation, ⊙ represents the reorganization perturbation operation, and sets is a random positive integer, which is a randomly selected individual sequence pair of Sp and Sq;

[0055] Formula (30) means: l Based on the above, the four single-objective optimal solution sequences Sbest and the population individual S generated after crossover and mutation are selected. l Perform a crossover operation to generate new individuals and randomly select The individual sequences Sp and Sq are subjected to a recombination perturbation operation to further produce new individuals S'p and S'q, thereby achieving random perturbation of the population and enhancing the global search capability of the GJA algorithm; the recombination perturbation operation includes three modes: 1) exchanging sequence St; 2) exchanging sequence So for type-a or b respectively; 3) exchanging sequence Ss for type-a or b respectively.

[0056] The technical effects of the present invention are as follows: according to the actual disassembly layout of the disassembly enterprise, a disassembly line with multi-person and multi-robot interactive stations is designed, and the balance of the disassembly is optimized; an accurate MIP model is established for the disassembly line for solving each optimization target; the proposed GJA has a new encoding mode and heuristic decoding strategy as well as a crossover operation, a mutation operation and a Jaya learning strategy that fit the characteristics of the optimized problem, and shows excellent performance in solving MMRC-DLBP; the GJA optimization result can provide decision makers with a variety of alternative optimal disassembly solutions; GJA is applied to the actual disassembly line design of a domestic waste television set, and algorithm comparison shows that the proposed GJA can improve the quality of the solution and accelerate the convergence speed of the algorithm, and also shows the superiority of GJA in solving MMRC-DLBP; the method of obtaining a single biased optimal solution based on the Pareto optimal solution set provides an effective way for decision makers to easily adjust production scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a schematic diagram of the disassembly line of a multi-person and multi-machine interaction site.

[0058] Figure 2 The diagram is the encoding method.

[0059] Figure 3 The decoding method diagram is shown in FIG.

[0060] Figure 4 Schematic diagram of crossover operation.

[0061] Figure 5 Schematic diagram of mutation operation.

[0062] Figure 6 Study strategy map for Jaya.

[0063] Figure 7 This is the flow chart of the GJA algorithm.

[0064] Figure 8 This is a priority relationship diagram for used televisions.

[0065] Fig. 9 This is a view showing the correspondence between the parts of a used TV and the disassembly tasks.

[0066] Fig.10 It is the HV iteration graph.

[0067] Fig.11 It is the HV box diagram.

[0068] Fig.12 The spatial distribution of 29 near-optimal solutions.

[0069] Fig.13 Gantt chart of the disassembly plan corresponding to the single-objective near-optimal solution.

[0070] Fig.14 This is the disassembly line layout of the multi-person and multi-machine interactive site for solution No. 17 (4,11,229,3767). DETAILED DESCRIPTION

[0071] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below in conjunction with the accompanying drawings. The description in this part is only exemplary and explanatory and should not have any limiting effect on the protection scope of the present invention.

[0072] 1. Implementation Plan

[0073] The method for designing a balanced disassembly line of a multi-person multi-machine interactive site includes the following steps:

[0074] S1, with the total number of sites opened by f1, the total number of operators employed by f2, the total operation time of f3 and the idle balance index minimized as the goal, a mixed integer programming model is established; the objective function of the model is as follows:

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[0078] S2, collect disassembly line data and propose constraints of the objective function to form a disassembly balance design model; the constraints are as follows:

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[0103] Where i, j are task indexes, e is site index, w is candidate worker index, and b is candidate robot index; N is the task index set, N = {1, 2, ..., N}, i, j ∈ N; E is the site index set E = {1, 2, ..., E}, e ∈ E; W is the worker index set, W = {1, 2, ..., W}, w ∈ W; B is the robot index set, B = {1, 2, ..., B}, b ∈ B; P i The set of immediate predecessor tasks of task i; t iw The time it takes worker w to perform task i; t ib The time it takes robot r to perform task i; η is a large positive number; m i The interactive properties of the task, m i = 1, when task i needs to be disassembled interactively by a robot and a worker; 0, otherwise; c i The complex properties of the task, c i = 1, task i has complex attributes and can only be performed by workers; 0, otherwise; h i The hazard attribute of the task, h i =1, task i has hazardous attributes and can only be performed by robots; 0, otherwise; CT disassembly line cycle time; CW max The maximum number of workers that can be assigned to each site; CB maxThe maximum number of robots that can be assigned to each station; t i s The start time of task i; x iew Worker disassembles variable, x 1 =1, task i is executed by worker w in site k; 0, otherwise; x ieb Robot disassembly variable, x 2 =1, task i is performed by robot r in station k; 0, otherwise; y ew Worker allocation variable; y 1 =1, worker w is assigned to site k; 0, otherwise; y eb Robot assigns variable, y 2 =1, robot r is assigned to site k; 0, otherwise; z ijew The variable for the order of tasks in the workers’ hands, z 1 =1, task i and task j are executed by worker w in site k, and i is executed before j; 0, otherwise; z ijeb Task order variable in the robot hand, z 2 =1, task i and task j are executed by robot r in station k, and i is executed before j; 0, otherwise; s e Site start variable, s e =1, site e is enabled; 0, otherwise;

[0104] S3, based on the mixed integer programming model, designs the genetic Jaya algorithm (GJA algorithm) to effectively solve the disassembly line balancing problem of large-scale multi-person multi-machine interactive sites (MMRC-DLBP), performs dominant processing on the solution set, and obtains the optimal disassembly line balancing solution.

[0105] 2. Model formula explanation

[0106] Eq.(1)-Eq.(4) represent four optimization objectives: f 1 The total number of sites opened; f 2 ,f 3 and f 4are the total number of operators employed, the total operating time and the idle balance index respectively. Eq.(5) indicates that non-interactive tasks are completely disassembled. Eq.(6) indicates that interactive tasks need to be disassembled by a worker and a robot in the same station in collaboration. Eq.(7) indicates that complex tasks are assigned to workers. Eq.(8) indicates that hazardous and non-complex tasks are performed by robots. Eq.(9) indicates the priority relationship constraints between tasks. Eq.(10)-Eq.(11) indicate that the tasks assigned to workers or robots must wait until the previously scheduled tasks are completed before they can be started. Eq.(12)-Eq.(13) indicate that the start time of any task should be later than the end time of the previously scheduled task, and its end time should be less than the end cycle time of the station where it is located. Eq.(14)-Eq.(17) represent the task execution order constraint, that is, multiple tasks assigned to the same operator must have a sequential execution order. There is no sequential execution order constraint between different tasks assigned to different operators except for the priority relationship. For a certain operator, other tasks not assigned to it have no execution order constraint for him. Eq.(18) indicates that no tasks are assigned to the unopened stations, and the number of tasks assigned to the opened stations is limited to 1 to N. Eq.(19) indicates that the workstations are opened from the front to the back. Eq.(20) and Eq.(23) respectively represent the number of workers or robots that can be accommodated in a single station. Eq.(21) and Eq.(24) respectively indicate that stations without workers and robots are not assigned tasks, and the number of tasks assigned to stations with workers is limited to 1 to N. Eq.(22) and Eq.(25) respectively indicate that candidate workers or robots may be hired or not. Eq. (26) indicates that no operator is assigned to the unactivated site, while the number of operators assigned to the activated site is 1~(CW max +CB max ). Eq.(27) indicates that the total number of operators employed in the entire disassembly line does not exceed the minimum value of the number of tasks and the total number of operations of the product. Eq.(28) indicates the binary variables used in the model.

[0107] 3. Proposed GJA algorithm:

[0108] In order to effectively solve MMRC-DLBP, this application proposes a GJA algorithm based on the constraint characteristics of the problem, the excellent solution performance of NSGA-II and the optimal solution strategy of the JAYA algorithm; first, a three-layer coding sequence is innovatively designed to describe all feasible solution sequences of MMRC-DLBP; for the new coding mode and the solution type of the equilibrium problem (DLBP), a heuristic decoding strategy that depends on the task attributes and the shortest completion time of the candidate operator is designed to achieve a one-to-one mapping of the three-layer coding sequence to a feasible disassembly solution. In order to enable the individuals in the initial population to have the ability to evolve, crossover operations and evolution operations that conform to the three-layer coding sequence are designed. In order to enhance the global search capability of the algorithm and accelerate the convergence speed, the Jaya learning strategy of the JAYA algorithm is discretized to achieve perturbations to the algorithm population, thereby obtaining a better new solution to quickly approach the global optimal solution. When performing multi-objective comparisons, the Pareto dominance method is used to screen non-inferior solutions in the population. Because MMRC-DLBP is a new problem without knowing the true Pareto frontier, and the HV (Hyper-Volume) indicator can evaluate the non-inferior solution without knowing the true Pareto frontier, HV is used as the evaluation indicator to evaluate the quality of the obtained non-inferior solution set. The JAYA algorithm structure includes five important parts: encoding, decoding, crossover operation, mutation operation, and Jaya learning strategy.

[0109] 3.1 Encoding method:

[0110] MMRC-DLBP includes several allocation processes, such as disassembly tasks to stations, candidate workers and robots to stations, and matching of assigned tasks within a station with assigned operators at the same station. To achieve the above objectives, a sequence St containing all disassembly tasks is designed based on its priority relation constraints, such as Figure 2 As shown. Among them, the subscript "c" represents a complex task, "m" represents a human-machine interaction task, "h" represents a hazardous task, and the other tasks without subscripts are ordinary tasks. Then, an operator sequence So containing all candidate workers (4 in number) and candidate robots (3 in number) is designed. In order to avoid that a certain disassembly task is always assigned to workers or robots in the same site, the sequence So should contain two situations: the worker is in front and the robot is behind, and the robot is in front and the worker is behind, and the probability of the two situations should be 50%. These two situations are respectively adopted in So a and So b Note that considering the uniqueness of worker and robot numbers, the operator numbers at the end of the So sequence need to be adjusted, as follows: Figure 2 shown.

[0111] To achieve the assignment of operators to sites and match So a and Sob Two cases are designed to match So a and So b Site sequence Ss a and Ss b In Ss a In the sequence, the site number segment that workers can allocate comes first, and the segment is from 1 to the maximum site number that can be opened E according to the worker capacity limit of each site (CW max ) are randomly generated and combined, and the station number that the robot can assign is at the end. This segment is from 1 to E according to the robot capacity limit (CB max ) are randomly generated and combined. b Similar, Ss b The positions of the worker segment and the robot segment in the sequence are opposite. a and So b Sequence and Ss a and Ss b The sequence can realize the allocation process of candidate workers and robot sites, such as combining So a and Ss a It can be obtained that station 1 contains worker No. 4 and robot No. 1 (5-4=1). Next, the assignment of tasks to operators in the station is handled by decoding.

[0112] 3.2 Decoding method:

[0113] Decoding is the process of assigning tasks in the St sequence to operators in the site one by one according to the takt time constraints of the site. In the assignment process, the assignment object is determined according to the attributes of the currently selected task: complex tasks can only be assigned to candidate workers, hazardous tasks can only be assigned to candidate robots, interactive tasks are assigned to candidate workers and robots in the same site at the same time, and ordinary tasks are randomly assigned to candidate workers or robots. Considering the characteristics of multi-machine sites, that is, a site contains multiple workers and multiple robots, it is inevitable that the specific operator number cannot be selected when assigning tasks. For example, when a complex task is assigned to a worker in the site, it is not certain which worker it is assigned to, which makes decoding impossible to continue. For this reason, the shortest task completion time strategy is proposed, that is, when an operator cannot be selected, the operator with the shortest completion time is selected to perform the task. However, multiple operators performing the current task may also have the shortest completion time at the same time. At this time, the proposed strategy does not work. Therefore, the method of "selecting the first operator in the So sequence to perform the current task" is further proposed to solve this situation. It is worth noting that for interactive tasks, in addition to using the proposed strategy, when there are multiple workers or robots with the same shortest completion time, the method of “selecting the first worker and the first robot in the So sequence” is still required to complete the specific allocation of interactive tasks.

[0114] In addition, when calculating the completion time of the current task, the constraints in the model (9-13) should be followed. When the maximum remaining time of the operators in the site cannot meet the allocation requirements of the current task, the next site needs to be opened. Since this application requires that the scrap products be completely disassembled, the decoding is exited when the last task in the St sequence is assigned. During the decoding process, the following three situations will result in infeasible solutions: 1. Complex tasks will be assigned to sites without workers; 2. Hazardous tasks will be assigned to sites without robots; 3. Interactive tasks will be assigned to sites that lack workers or robots. The target values ​​corresponding to these three situations are set to (η, η, η, η), which can be directly removed by Pareto screening. The specific decoding process is as follows: Figure 3 shown.

[0115] 3.3 Crossover operation:

[0116] The mutation operation of the traditional GA algorithm is a process of exchanging some genes of randomly selected parent individuals from the population to generate new offspring individuals under a certain crossover probability. Taking into account the encoding characteristics of MMRC-DLBP, this application adopts a two-point crossover operation for the disassembly task sequence St and the operator sequence So, and an operation of exchanging the number of randomly selected sites for the site sequence Ss, and combines the three newly generated sequences for re-decoding to obtain a new solution and disassembly plan. The specific execution process of the crossover operation is as follows: Figure 4 shown.

[0117] 3.4 Mutation Operation:

[0118] Mutation operation refers to the operation of mutating the gene position of each individual in the parent generation with a certain mutation probability to generate a new solution. Mutation operation plays an important role in maintaining population diversity and preventing the population from falling into a local optimal solution. For the three coding sequences of MMRC-DLBP, this application uses single-point mutation to mutate them with a certain probability. The specific operation process is as follows Figure 5 As shown, r5~r7 are randomly generated mutation points. During mutation, St needs to comply with the priority constraint of waste products, and Ss needs to comply with the operator quantity limit constraint in the site.

[0119] 3.5Jaya learning strategy

[0120] Formula (29) is the individual update expression of Jaya learning strategy. In order to match the discrete characteristics of the proposed MMRC-DLBP problem, formula (29) is discretized as formula (30), which means: l Based on the above, the four single-objective optimal solution sequences Sbest and the population individual S generated after crossover and mutation are selected. l Perform a crossover operation (as described in Section 3.3) to generate new individuals, and randomly select The individual sequences Sp and Sq are recombined and disturbed to further produce new individuals S'p and S'q, thereby achieving random disturbance of the population and enhancing the global search capability of the GJA algorithm. The recombinant perturbation operation includes three methods: 1) exchanging sequence St; 2) exchanging sequence So for type-a or b respectively; 3) exchanging sequence Ss for type-a or b respectively. The specific exchange process is as follows Figure 6 It is worth noting that the reorganization perturbation operation is designed according to the three-layer coding of MMRC-DLBP, which is a unique population individual operation mode.

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[0122] In the formula, S lis the individual variable of the continuous problem in the lth iteration process, S best is the individual variable with the best objective function in the lth iteration, S p and S q are two individual variables randomly selected in the lth iteration process, and is a random number between 0 and 1, S l ′ is S l is the updated value.

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[0124] In the formula, S l is the population individual sequence (including three sequences St, So, and Ss) obtained after crossover and mutation operations of GJA in the lth iteration, S best is the four single-objective optimal solution sequences of the individuals in the population in the lth iteration, S p and S q are two individuals randomly selected from the new population, ⊕ means performing the operation after the symbol based on the sequence before the symbol, represents the crossover operation, ⊙ represents the reorganization perturbation operation, and sets is a random positive integer, which is a randomly selected individual sequence pair of Sp and Sq.

[0125] 3.6. Algorithm flow:

[0126] The specific process of the GJA algorithm is as follows, and is composed of Figure 7 gives:

[0127] Step 1: Preset parameters.

[0128] Step 2: Population initialization. Use the encoding method designed in Section 3.1 to generate the initial population and calculate the target value (f 1 ,f 2 ,f 3 ,f 4 ).

[0129] Step 3: Enter the iterative process and set l=1.

[0130] Step4: Select the best individuals in the population to form the mating pool of the algorithm.

[0131] Step 5: Copy a new mating pool. Perform a crossover operation on all individuals St in the original mating pool, and perform a mutation operation on all individuals in the original mating pool; divide the newly copied mating pool into type-a groups and type-b groups according to the type differences of So and Ss, and perform crossover and mutation operations on these two types of groups respectively.

[0132] Step 6: Merge the newly generated individuals in Step 5 and further execute the Jaya learning strategy to generate new individuals again.

[0133] Step 7: Merge the newly generated individuals in Step 6 with the parental population in Step 2.

[0134] Step 8: Update the population using non-dominated sorting and crowding distance, and calculate the HV index for the non-dominated solution set screened by non-dominated sorting and crowding distance.

[0135] Step 9: Determine whether to enter the next iteration. If l < L, set l = l + 1, go to Step 4 to enter the next iteration; otherwise, terminate the iteration, take the obtained non-dominated solutions as the optimal solutions of MMRC-DLBP, and output the non-dominated solutions corresponding to these non-dominated solutions.

[0136] 4. Specific implementation cases

[0137] Use the proposed multi-person and multi-robot interactive station disassembly line to disassemble a waste TV set, and give a set of non-dominated optimal disassembly scheduling plans. GJA is programmed using Matlab 2020b, and the computer running environment is Win10 system with CPU i7-8750H and 16G of memory.

[0138] 4.1. Disassembly case data preparation

[0139] Figure 8 The precedence relationship diagram of the disassembly tasks of a domestic waste TV set is given, including four categories: complex, hazardous, interactive, and ordinary, with a total of 36 disassembly tasks. Fig. 9 Figure [ID] is the exploded view of the TV set containing the corresponding disassembly tasks. Table 1 gives a detailed description of the corresponding division relationship between the parts to be disassembled of the TV set and the disassembly tasks. After investigation and measurement, the execution time of each disassembly task in the waste TV set is shown in Appendix 2, and the problem parameters are set as follows: CW max = 3, CB max = 2, CT = 34.

[0140] Table 1 Corresponding relationship table between the part names of waste TV sets and disassembly tasks

[0141]

[0142]

[0143] Table 2 Operation time for each disassembly task of waste TV sets performed by candidate workers and robots

[0144]

[0145] 4.2. Algorithm parameter settings

[0146] In order to verify the effectiveness of GJA in solving the application case of waste TV sets, the original NSGA-II, JAYA and NSGA-III were used together with the improved GJA algorithm to solve the case, and the results were compared and verified. In order to ensure the rationality and fairness of the comparison, the solution results of the four algorithms were compared at the same running time. In order to determine the same running time, the number of iterations L of the four algorithms was set to a large positive number, the population size M = 300, the mutation probability and the crossover probability were set to 0.9 and 0.03 respectively. Since JAYA only has two algorithm parameters, population size and number of iterations, no additional settings are required. In addition, according to the worst case of each optimization objective, the reference point (r 1 * ,r 2 * ,r 3 * ,r 4 * )=(10,14,395,30078), which is used to calculate the HV index of the algorithm to measure the quality of the multi-objective solution.

[0147]

[0148] Next, the four algorithms were run for 500 seconds. Fig.10 The HV index iteration curves of the four algorithms are given. For multi-objective optimization problems, since the larger the HV index, the closer the corresponding multi-objective solution set is to the real Pareto frontier of the optimization problem, Fig.10 It can be seen that the four algorithms are ranked as follows: GJA>NSGA-II>JAYA>NSGA-III, and at 367s, all four algorithms have converged. For convenience, 400s is used as the unified calculation time of the four algorithms. In addition, it is worth mentioning that GJA converges at 367s, while the other three algorithms have converged before this time, which shows that the other three algorithms are more likely to fall into local optimality, while GJA has better global exploration ability, which further illustrates the necessity of algorithm mixing in this paper.

[0149] 4.3. Comparison of solution results

[0150] At the same time, the four algorithms were run 10 times respectively, and the maximum HV index obtained by each algorithm each time was recorded and drawn into a box plot, as shown in Fig.11It can be seen that the smallest of the maximum HVs solved by GJA 10 times is larger than the maximum HV index value solved by the other three algorithms. From the perspective of multi-objective evaluation indicators, this shows that GJA's optimization ability is stronger than the other three algorithms. In addition, GJA's blue box is shorter, which shows that GJA's solution stability is also better than the other three algorithms.

[0151] The four algorithms were run 10 times, and four non-inferior solution sets were obtained, including 22, 22, 19 and 32 non-inferior solutions respectively. The four solution sets were merged and pareto-dominant comparison was performed, and 29 near-optimal solutions were obtained, as shown in Table 3, including 17 solutions of GJA, 6 solutions of NSGA-II, 1 solution of NSGA-III, and 5 solutions of JAYA. The proportion of near-optimal solutions obtained by the four algorithms was 58.62%, 20.69%, 17.24% and 3.45%, respectively, which shows that GJA is more capable of obtaining the optimal solution than the other three original classical algorithms.

[0152] Table 3 29 near-optimal solutions obtained by four comparison algorithms

[0153]

[0154] Fig.12 The spatial distribution of 29 near-optimal solutions obtained by the four algorithms is given. In the figure, the diamond “+” represents f 1 =3 solution, Represents f 1 =4, the colors of GJA solutions are: red, blue, green, NSGA-II's 6 solutions are represented by purple diamonds, NSGA-III's 1 solution is represented by olive diamonds, and JAYA's 5 solutions are represented by yellow plus signs. Fig.12 It can be seen that GJA has found the minimum value of the single objective of the four optimization objectives, namely, f 1min =3,f 2min =9,f 3min =229,f 4min =233, which once again shows that GJA is also very good in obtaining the breadth of solutions.

[0155] 4.4. Analysis of disassembly plan:

[0156] Fig.13 The disassembly schemes corresponding to the four single-objective optimal values ​​obtained by GJA are shown, among which solution No. 14 (4,9,275,233) obtains the optimal values ​​of f2 and f4 at the same time. Fig.13(a) It can be seen that this scheme has opened three stations. The robots employed in station 2 have reached the robot capacity limit CBmax, and the workers employed in station 3 have reached the worker capacity limit CWmax. In addition to the workers 3 and 2 in station 1 needing to perform interactive tasks 6 and 13, the robot 5 in station 3 needs to first cooperate with the worker 1 to perform interactive task 31, and then cooperate with the worker 7 to perform interactive task 26. Fig.13 (b) It can be seen that this scheme opens 4 sites, but the number of workers and robots in each site does not reach CWmax and CBmax. Interaction tasks 6 and 13 are performed by worker No. 1 and robot No. 4 successively, and interaction tasks 26 and 31 are performed by two pairs of workers and robots respectively. Fig.13 The disassembly solution of (c) also opened 4 sites. Except for the robots employed in sites 2 and 3, which reached the robot capacity limit CBmax, the other sites did not reach the maximum capacity of the workers and robots in the site. Interaction tasks 6, 13, 26, and 31 were performed by 4 pairs of workers and robots respectively.

[0157] In the three disassembly schemes shown in the figure, since different operators have different disassembly efficiencies for the same task, the execution time of the same task will also be different. For example, in interactive task 6, Fig.13 The time taken by the worker and the robot to collaborate in (a) and (b) is different. Fig.13 (c) are equal. In addition, when an interactive task is performed by a worker and a robot in collaboration with different execution times, in addition to requiring the start time of the two operators to be consistent, the operator with a shorter execution time still needs to wait for the other operator to complete the interactive task before starting to perform other tasks, such as Fig.13 The interactive tasks 6, 13 and 26 in (a) are handled in this way because when one operator performs an interactive task, the other collaborative operator cannot perform other disassembly tasks by moving or flipping the waste product. Fig.13 Taking the disassembly solution shown in (c) as an example, the layout of stations, workers and robots on the disassembly production line and the scheduling of disassembly tasks are introduced. Fig.14 The corresponding specific production line layout is shown.

[0158] It should be noted that, in this article, the terms "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus.

[0159] This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. The above is only a preferred implementation of the present invention. It should be pointed out that due to the limitations of textual expression and the objective existence of infinite specific structures, ordinary technicians in this technical field can make several improvements, modifications or changes without departing from the principles of the present invention, and can also combine the above technical features in an appropriate manner; these improvements, modifications, changes or combinations, or the direct application of the inventive concept and technical solution to other occasions without improvement, should be regarded as the protection scope of the present invention.

Claims

1. A balanced design method for disassembling lines at multi-person and multi-machine interactive sites, characterized in that: It includes the following steps: S1. Establish a mixed-integer programming model with the goal of minimizing the total number of stations opened at f1, the total number of operators employed at f2, the total operation time at f3, and the idle balance index at f4. The objective function of this model is as follows: S2. Collect disassembly line data and propose the constraints of the objective function to form a disassembly balance design model. The constraints are as follows: Among them, i, j are task indexes, e is site index, w is candidate worker index, b is candidate robot index; N is the task index set, N = {1, 2, ..., N}, i, j ∈ N; E is the site index set E = {1, 2, ..., E}, e∈E; W worker index set, W = {1, 2, ..., W}, w∈W; B robot index set, B = {1, 2, ..., B}, b∈B; P i The set of immediate predecessor tasks of task i; t iw The time it takes worker w to perform task i; t ib The time it takes robot r to perform task i; η is a large positive number; m i The interactive properties of the task, m i =1, when task i needs to be disassembled by a robot and a worker interactively; 0, Otherwise; c i The complex properties of the task, c i = 1, task i has complex attributes and can only be performed by workers; 0, otherwise; h i The hazard attribute of the task, h i =1, task i has hazardous attributes and can only be performed by robots; 0, otherwise; CT disassembly line cycle time; CW max The maximum number of workers that can be assigned to each site; CB max The maximum number of robots that can be assigned to each station; t i s The start time of task i; x iew Worker disassembly variable, x1 = 1, task i is performed by worker w in site k; 0, otherwise; x ieb Robot disassembly variable, x2 = 1, task i is performed by robot r in station k; 0, otherwise; y ew Worker assignment variable; y1 = 1, worker w is assigned to site k; 0, otherwise; y eb Robot assignment variable, y2 = 1, robot r is assigned to site k; 0, otherwise; z ijew The task order variable in the worker’s hand, z1 = 1, task i and task j are executed by worker w in site k, and i is executed before j; 0, otherwise; z ijeb Task order variable in the robot hand, z2 = 1, task i and task j are executed by robot r in station k, and i is executed before j; 0, otherwise; s e Site start variable, s e =1, site e is enabled; 0, otherwise; S3. Based on the mixed-integer programming model, perform dominance processing on the solution set to obtain the optimal disassembly line balance plan.

2. The method for designing a balanced disassembly line for a multi-person multi-machine interactive site according to claim 1, characterized in that: S3 uses the GJA algorithm to obtain the optimal disassembly line balance plan. The specific steps are as follows: Step1: Preset parameters. Step2: Initialize the population; design a coding method to generate the initial population and calculate the objective values (f1, f2, f3, f4) corresponding to the individuals in this population. Step3: Enter the iterative program and set l = 1. Step4: Select the best individuals in the population to form the mating pool of the algorithm. Step5: Make a copy of the new mating pool. Perform crossover operations on all individuals St in the original mating pool and perform mutation operations on all individuals in the original mating pool. Divide the newly copied mating pool into group-a and group-b according to the type differences of So and Ss, and perform crossover operations and mutation operations on these two types of groups respectively. Step6: Merge the individuals newly generated in Step5 and further execute the Jaya learning strategy to generate new individuals again. Step7: Merge the individuals newly generated in Step6 with the parent population in Step2. Step8: Update the population using non-dominated sorting and crowding distance, and calculate the HV index for the non-dominated solution set screened by non-dominated sorting and crowding distance. Step9: Determine whether to enter the next iteration. If l < L, set l = l + 1, go to Step4 to enter the next iteration, otherwise terminate the iteration. Take the obtained non-dominated solutions as the optimal solutions to the multi-operator multi-machine interactive station disassembly line balance problem (MMRC-DLBP), and output the non-dominated plans corresponding to these non-dominated solutions.

3. The method for designing a balanced disassembly line for a multi-person multi-machine interactive site according to claim 2, characterized in that: The coding method of Step 2 is as follows: According to the priority constraint, a sequence St containing all disassembly tasks is designed, where the subscript "c" indicates a complex task, "m" indicates a human-machine interaction task, "h" indicates a hazardous task, and the remaining tasks without a subscript are ordinary tasks; then, an operator sequence So containing all candidate workers and candidate robots is designed. To avoid a disassembly task always being assigned to workers or robots in the same station, the sequence So should contain two situations: the worker in front and the robot in the back, and the robot in front and the worker in the back, and the probability of the two situations should be 50%. These two situations are respectively represented by So a and So b Indicates that; considering the uniqueness of worker and robot numbers, the operator numbers at the end of the So sequence need to be adjusted in order to achieve the assignment of operators to sites and match So a and So b Two cases are designed to match So a and So b Site sequence Ss a and Ss b ; in Ss a In the sequence, the site number segment that workers can allocate comes first. This segment is from 1 to the maximum site number that can be opened E according to the worker capacity limit of each site (CW max ) are randomly generated and combined, and the station number that the robot can assign is at the end. This segment is from 1 to E according to the robot capacity limit (CB max ) randomly generated for combination; and So b Similar, Ss b The positions of the worker segment and the robot segment in the sequence are opposite; combined with the designed So a and So b Sequence and Ss a and Ss b The sequence enables the allocation process of candidate workers and robot stations, and then the allocation of tasks to operators within the station is handled by decoding.

4. The method for designing a balanced disassembly line for a multi-person multi-machine interactive site according to claim 3 is characterized in that: The decoding method is as follows: Decoding is the process of assigning the tasks in the St sequence to the operators in the site one by one according to the beat time constraints of the site. In the assignment process, the assignment object is determined according to the attributes of the currently selected task: complex tasks can only be assigned to candidate workers, hazardous tasks can only be assigned to candidate robots, interactive tasks are assigned to candidate workers and robots in the same site at the same time, and ordinary tasks are randomly assigned to candidate workers or robots. Taking into account the characteristics of multi-machine sites, that is, a site contains multiple workers and multiple robots, it is inevitable that when assigning tasks, it is impossible to select a specific operator number. For example, when a complex task is assigned to a worker in the site, it is not certain which worker it is assigned to, which makes decoding impossible to continue. For this reason, a shortest task completion time strategy is proposed, that is, when an operator cannot be selected, the operator with the shortest completion time is selected to perform the task. However, multiple operators performing the current task There may also be a situation where the shortest completion time exists at the same time. In this case, the proposed strategy will not work. For this reason, the method of "selecting the first operator in the So sequence to perform the current task" is further proposed to solve this situation. For interactive tasks, in addition to using the proposed strategy, when there are multiple workers or robots with the same shortest completion time, the method of "selecting the first worker and the first robot in the So sequence" is still required to complete the specific allocation of interactive tasks; in addition, when calculating the completion time of the current task, the constraints in the model (9-13) should be followed; when the maximum remaining time of the operators in the site cannot meet the allocation requirements of the current task, the next site needs to be opened; the waste products are completely disassembled, so the decoding is exited when the last task in the St sequence is allocated. During the decoding process, the following three situations will have infeasible solutions:

1. Complex tasks will be assigned to sites without workers; 2. Hazardous tasks will be assigned to sites without robots.

3. Interactive tasks will be assigned to sites that lack workers or robots. The target values ​​corresponding to these three situations are set to (η, η, η, η), which can be directly removed by Pareto screening.

5. The method for designing a balanced disassembly line for a multi-person multi-machine interactive site according to claim 4 is characterized in that: The crossover operation is as follows: for the disassembly task sequence St and the operator sequence So, a two-point crossover operation is used, and for the site sequence Ss, an operation of exchanging the number of randomly selected sites is used, and the three newly generated sequences are combined and decoded again to obtain a new solution and disassembly plan.

6. The method for designing a balanced disassembly line for a multi-person multi-machine interactive site according to claim 5, characterized in that: For the three coding sequences of MMRC-DLBP, single-point mutation is used to mutate them with a certain probability. During mutation, St needs to comply with the priority relationship constraint of waste products, and Ss needs to comply with the operator quantity limit constraint within the site.

7. The method for designing a balanced disassembly line for a multi-person multi-machine interactive site according to claim 6, characterized in that: The individual update expression of Jaya learning strategy is: In the formula, S l is the individual variable of the continuous problem in the lth iteration process, S best is the individual variable with the best objective function in the lth iteration, S p and S q are two individual variables randomly selected in the lth iteration process, and is a random number between 0 and 1, S l ′ is S l is the updated value; In order to match the discrete characteristics of the proposed MMRC-DLBP problem, equation (29) is discretized and the discretized expression is: In the formula, S l is the population individual sequence (including three sequences St, So, and Ss) obtained after crossover and mutation operations of GJA in the lth iteration, S best is the four single-objective optimal solution sequences of the individuals in the population in the lth iteration, S p and S q are two individuals randomly selected from the new population, Indicates that the operation after the symbol is performed based on the sequence before the symbol. represents the crossover operation, ⊙ represents the reorganization perturbation operation, and sets is a random positive integer, which is a randomly selected individual sequence pair of Sp and Sq; Formula (30) means: l Based on the above, the four single-objective optimal solution sequences Sbest and the population individual S generated after crossover and mutation are selected. l Perform a crossover operation to generate new individuals and randomly select The individual sequences Sp and Sq are subjected to a recombination perturbation operation to further produce new individuals S'p and S'q, thereby achieving random perturbation of the population and enhancing the global search capability of the GJA algorithm; the recombination perturbation operation includes three modes: 1) exchanging sequence St; 2) exchanging sequence So for type-a or b respectively; 3) exchanging sequence Ss for type-a or b respectively.

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