Optimization Method for Furniture Customized Manufacturing Service System Based on Multi-Objective Grey Wolf Optimization

Abstract

The present invention discloses an optimization method for a furniture customization manufacturing service system based on multi-objective grey wolf optimization, including obtaining customized furniture orders; decomposing the furniture orders into parts of various specifications, and classifying the parts into standardized parts and non-standardized parts; imposing constraints on the makespan and the total cost; improving the search mechanism of the basic grey wolf optimization algorithm; and optimizing the makespan and the total cost based on the improved grey wolf optimization algorithm. By adopting the above method, the present invention uses the grey wolf optimization algorithm, with the minimization of the makespan and the total cost as the optimization objectives, realizes the adjustment of the production scheduling of the hybrid manufacturing workshop, improves the production efficiency and the flexibility of the manufacturing process, and meets the requirements of different customers.

Description

Technical Field

[0001] The present invention relates to the technical field of furniture manufacturing, and in particular to an optimization method for a furniture customization manufacturing service system based on multi-objective grey wolf optimization. Background Art

[0002] Efficient production scheduling strategies can greatly improve efficiency, reduce costs, and shorten delivery cycles. In recent years, research on production scheduling in the furniture manufacturing process has received increasing attention from academia and industry. To effectively solve such problems, various mathematical models and optimization algorithms have been developed to determine the optimal production plan under given constraints and objectives. Kazemi et al. studied an integrated production and distribution scheduling problem using unrelated parallel machines to complete bedroom furniture manufacturing tasks. To solve this problem, a mixed integer linear programming model with the objective of minimizing the total tardiness time and delivery cost was established, and an improved genetic algorithm was proposed as the solution method. Yimer and Demirli (2009) studied a two-stage flow shop scheduling problem for producing a set of customized furniture orders, established a mixed integer fuzzy programming model, and gave a genetic algorithm for minimizing the total weighted flow time.

[0003] By analyzing the relevant literature on production scheduling problems in the furniture industry, it can be found that most studies consider the production scheduling problems of furniture products in a single manufacturing system, including parallel machines, flow shops, hybrid flow shops, job shops, and flexible job shops. Few studies focus on hybrid manufacturing systems composed of multiple types of workshops, although such systems help to improve productivity, enhance flexibility, and meet the requirements of different customers. Summary of the Invention

[0004] The object of the present invention is to provide an optimization method for a furniture customization manufacturing service system based on multi-objective grey wolf optimization. The multi-objective grey wolf optimization algorithm is adopted, and the optimization is carried out with the objectives of minimizing the makespan and the total cost, realizing the adjustment of the production scheduling of the hybrid manufacturing workshop, improving the production efficiency and the flexibility of the manufacturing process, and meeting the requirements of different customers.

[0005] To achieve the above object, the present invention provides an optimization method for a furniture customization manufacturing service system based on multi-objective grey wolf optimization. Based on the furniture customization manufacturing service system, the customization manufacturing service system includes an intelligent order splitting system and an intelligent scheduling system; the intelligent scheduling system includes a distributed flow shop manufacturing unit and a flexible job shop manufacturing unit;

[0006] The steps include:

[0007] S1. Obtain customized furniture orders;

[0008] S2. Decompose the furniture order into parts of various specifications, and divide the parts into standardized parts and non-standardized parts;

[0009] S3. Constrain the makespan and the total cost;

[0010] S4. Improve the search mechanism of the basic Grey Wolf Optimization algorithm;

[0011] S5. Optimize the makespan and the total cost based on the improved Grey Wolf Optimization algorithm.

[0012] Preferably, step S4 includes:

[0013] S41. Define the adaptive selection rate , and its calculation formula is:

[0014]

[0015] In the formula, and respectively represent the current fitness evaluation times and the maximum fitness evaluation times;

[0016] S42. Randomly generate a floating-point number for each solution in the population. When , randomly select a solution , and from the wolves, and perform crossover and mutation operations on the two parents and to generate two new solutions. Otherwise, construct two new solutions by performing crossover and mutation operations on the two parents and and , where is randomly selected from wolves, and the sorting value of is not less than the sorting value of ;

[0017] Preferably, step S5 includes:

[0018] S51. Input the problem parameters and algorithm parameters;

[0019] S52. Encode, decode, and initialize the population;

[0020] S53. Based on the improved Grey Wolf Optimization algorithm, perform crossover and mutation on , , and segments;

[0021] S54. Execute two knowledge-driven local search strategies to update the solution within a fixed number of iterations;

[0022] S55. Merge the new population and the existing population, perform non-dominated sorting on all solutions and calculate their crowding distance values, and select the top solutions as the next generation population according to their sorting and crowding distance values;

[0023] S56. When the termination criterion is met, where the termination criterion is equal to the number of fitness evaluation times, output the obtained non-dominated solution set; otherwise, go to step S53.

[0024] Preferably, in step S51, the problem parameters include the number of factories , the number of machines in the distributed flow shop manufacturing cell , the number of standardized parts , the number of machines in the flexible job shop manufacturing cell , the number of non-standardized parts ; the time for a machine in the flow shop to process a part , the unit cost of processing for a machine in the flow shop , the basic design time of an operation , the personalized design time of an operation , the unit design cost of a part , the degree of personalization of an operation , the basic design time of an operation , the personalized design time of an operation , the unit personalization processing cost of a flexible job shop machine , the unit personalization processing cost of a part , the unit design cost of a part , the degree of personalization of an operation , and the unit personalization processing cost of a flexible job shop machine . The algorithm parameters include the population size and the maximum number of fitness evaluation times . and the maximum number of fitness evaluation times .

[0025] Preferably, in step S52:

[0026] Coding: There are four decoding methods to represent an individual, including the factory segment , the part segment , the operation segment and the machine segment . is represented by an integer string , where is the factory index, representing the factory assignment of standardized parts, ; Indicates the processing sequence of all standardized parts, represented as an integer string , where each digit represents an index of a standardized part; and are integer strings of length , represented by and respectively. Provides the processing sequence of all processes of non-standardized parts, gives the machine allocation for all processes.

[0027] Decoding: Decode according to the allocation of standardized parts among factories, their processing sequences, the processing sequences of all processes of non-standardized parts, and the machine allocation of processes.

[0028] Initializing the population: Randomly generate , and segments, and then generate segments by a hybrid method of randomly generating with a weight of 80%, applying the minimum processing time rule for 10% of the operations, and the global minimum processing time rule for 10%.

[0029] Preferably, step S54 includes:

[0030] First, execute the first local search strategy: Set 7 knowledge-driven local search operators. The first four operators are applied to the distributed flow shop manufacturing cell, and the last three operators are applied to the flexible job shop manufacturing cell. The process is as follows:

[0031] Local search operator 1 ( ), randomly select two key parts in the segment and exchange them; Local search operator 2 ( ): Randomly select two key parts in the segment, and then insert one part in front of the other; Local search operator 3 ( ): Randomly select a key part and a non-key part, exchange them in the segment, and at the same time exchange their factory allocations in the segment; Local search operator 4 ( ): Randomly select a key part and then move it to a non-key factory; Local search operator 5 ( ): Randomly select two key processes in the segment and then exchange them; Local search operator 6 ( ): Randomly select two key processes in the segment, and then insert one process in front of the other; Local search operator 7 ( ):Randomly select a key process, and then randomly change its machine index;

[0032] Secondly, perform the second local search strategy on each updated solution: randomly select a key process, change its machine to the one with the lowest processing cost, compare the advantages of the solution before and after performing the two local search strategies, and save the superior solution to update the population.

[0033] Preferably, the seven knowledge-driven local search operators set by the first local search strategy are set according to the critical path in the distributed flow shop manufacturing cell and the critical path in the flexible job shop manufacturing cell. The critical path refers to the continuous path from the start node to the end node of the solution. The factory where the critical path is located is regarded as the critical factory, and the parts or processes included are defined as critical parts or critical processes.

[0034] Therefore, the present invention adopts the above-mentioned optimization method for the furniture customization manufacturing service system based on multi-objective grey wolf optimization, and has the following beneficial effects:

[0035] (1) Construct a mixed integer mathematical programming model to constrain the makespan and the total cost;

[0036] (2) Improve the grey wolf optimization algorithm, solve the mixed integer programming model through the grey wolf optimization algorithm, solve the optimization problem with the goal of minimizing the makespan and the total cost, realize the adjustment of the production scheduling of the hybrid manufacturing workshop, improve the production efficiency and the flexibility of the manufacturing process, and meet the requirements of different customers.

[0037] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Description of the Drawings

[0038] Figure 1 It is the structure diagram of the intelligent scheduling system according to the embodiment of the present invention;

[0039] Figure 2 It is the four-segment coding method diagram according to the embodiment of the present invention;

[0040] Figure 3 It is the four kinds of crossover operation diagrams according to the embodiment of the present invention;

[0041] Figure 4 It is the three kinds of mutation operation diagrams according to the embodiment of the present invention;

[0042] Figure 5 It is the two kinds of critical path schematic diagrams according to the embodiment of the present invention;

[0043] Figure 6 It is the seven kinds of operation operator schematic diagrams according to the embodiment of the present invention;

[0044] Figure 7Violin plots of six instances of the IGD - metric for embodiments of the present invention;

[0045] Figure 8 Violin plots of six instances of the HV - metric for embodiments of the present invention. Detailed implementation manners

[0046] Embodiment

[0047] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention.

[0048] The present invention provides an optimization method for a furniture customization manufacturing service system based on multi - objective grey wolf optimization. Based on the customization manufacturing service system, it includes an intelligent order - splitting system and an intelligent scheduling system.

[0049] The intelligent order - splitting system decomposes furniture orders into parts of various specifications and classifies the parts into standardized parts and non - standardized parts according to the similarity, commonality and personalization degree of the parts. Standardized parts refer to parts with similar functions, simple structures and can be mass - produced by unified equipment. Non - standardized parts refer to parts with different sizes, different functions and complex structures, which need to be processed using flexible machines.

[0050] Refer to Figure 1 , the intelligent scheduling system includes a distributed flow - shop (DFS) manufacturing unit and a flexible job - shop (FJS) manufacturing unit. The DFS manufacturing unit manufactures standardized parts, and the FJS manufacturing unit manufactures non - standardized parts.

[0051] The steps include:

[0052] S1. Obtain a customized furniture order;

[0053] S2. Decompose the furniture order into parts of various specifications and classify the parts into standardized parts and non - standardized parts;

[0054] S3. Constrain the makespan and the total cost. The constraint formulas are as follows:

[0055] (1)

[0056] (2)

[0057] (3)

[0058] (4)

[0059] (5)

[0060] (6)

[0061] (7)

[0062] (8)

[0063] (9)

[0064] (10)

[0065] (11)

[0066] (12)

[0067] (13)

[0068] (14)

[0069] (15)

[0070] (16)

[0071] (17)

[0072] (18)

[0073] (19)

[0074] (20)

[0075] (21)

[0076] (22)

[0077] (23)

[0078] (24)

[0079] (25) (26)

[0080] In the formula, represents the maximum completion time of all parts; represents the serial number of the flow shop, ; Denote the set of flow shops, ; The set of standardized parts, ; Denote the set of machines in each flow shop, ; Denote the set of non-standardized parts, ; Denote the set of processes, ; The set of machines in each flexible job shop, ; Denote the serial number of standardized parts, Denote the serial number of machines in the flow shop, ; Denote the serial number of non-standardized parts, ; Denote the serial number of processes, ; Denote the serial number of machines in the flexible job shop, ; Denote that non-standardized parts are processed in process ; Denote that non-standardized parts are processed in process ; Denote the flow shop The machine in Process parts Time; Denote the machine in the flow shop Unit cost of processing; Denote the process Personalization degree; Denote the process Basic design time; Denote the process Individual design time; Denote the part Individual design time; Denote the part Unit design cost; Denote the flexible job shop machine Perform the process Basic processing time; Denote the flexible job shop machine Perform the process Individualized processing time; Flexible job shop machine Unit individualized processing cost; A positive number; Denote the flow shop Middle part The workpiece is processed immediately after the machining is completed , with a value of 1, otherwise 0; Flow shop Machining parts , with a value of 1, otherwise 0; Indicates the machine Performs the operation , with a value of 1, otherwise 0; Indicates the machine Completes the operation And immediately performs the operation , with a value of 1, otherwise 0; Indicates the machine Machines the workpiece The completion time of, Indicates the operation The start time of the machining; Indicates the operation The completion time of the machining; Indicates non-standard parts The completion time of the machining.

[0081] Specifically, Equation (1) focuses on minimizing the makespan, and Equation (2) aims to minimize the total cost. Constraints (3) and (4) respectively imply that each standardized part has only one predecessor and one successor on the machine. Constraints (5) and (6) stipulate the continuity of production. Constraint (7) requires that each standardized part can only be assigned to one flow shop. Constraint (8) ensures that each standardized part has no more than one predecessor and one successor on the machine simultaneously. Constraint (9) stipulates the sequential relationship between two standardized parts. Constraint (10) stipulates that it is prohibited to process a standardized part on the next machine before it is completed on the previous machine. Constraint (11) defines that each machine cannot process the next standardized part if the current standardized part on the machine has not been completed. Constraint (12) defines that only one machine is selected for manufacturing each process. Constraint (13) refers to the custom design time for each process of non-standardized parts. Constraint (14) represents the custom design time for each non-standardized part. Constraint (15) ensures that the production start time of non-standardized parts in the manufacturing stage must be greater than their custom design time in the design stage. Constraint (16) defines the custom processing time for each process of each non-standardized part. Constraint (17) indicates that only one process is in progress on each machine at a time. Constraints (18) and (19) respectively limit that each process has only one direct progression and one direct consecutive process. Constraint (20) stipulates that all processes of non-standardized parts are processed according to the given processing route. Constraint (21) calculates the production completion time of the process. Constraint (22) restricts the production completion time of non-standardized parts. Constraints (23) and (24) define the makespan. Constraints (25) and (26) determine the range of variables. Among them, Constraints (1)-(11) are the constraints of the distributed flow shop manufacturing cell, and Constraints (12)-(26) are the constraints of the flexible job shop manufacturing cell.

[0082] S4. Improve the search mechanism of the basic Grey Wolf Optimization Algorithm.

[0083] S41. Define the adaptive selection rate , and its calculation formula is:

[0084] (27)

[0085] In the formula, and respectively represent the current fitness evaluation times and the maximum fitness evaluation times;

[0086] S42. For each solution in the population randomly generate a floating-point number , when , randomly select from , and select a solution from the wolves and perform crossover and mutation operations on two parent generations and to generate two new solutions. Otherwise, construct two new solutions by performing crossover and mutation operations on two parent generations and , where is randomly selected from the wolves, and the sorting value of is not less than the sorting value of .

[0087] S5. Optimize the makespan and total cost based on the improved grey wolf optimization algorithm.

[0088] S51. Input the problem parameters and algorithm parameters.

[0089] The problem parameters include the number of factories , the number of machines in the DFS manufacturing cell , the number of standardized parts , the number of machines in the FJS manufacturing cell , the number of non-standardized parts ; the time it takes for the machine in the flow shop to process the part , the unit cost of processing for the machine in the flow shop , the basic design time of the process , the personalized design time of the process , the unit design cost of the part , the degree of personalization of the process

[0090]

[0091] .

[0090] S52. Encoding, decoding, and initializing the population.

[0091] Encoding: Set four decoding methods to represent individuals, including the factory segment , the part segment , the process segment and the machine segment , which is represented by an integer string denotes, where is the factory index, indicating the factory allocation of standardized parts, ; represents the processing sequence of all standardized parts, represented by an integer string as , where each number represents an index of a standardized part; and are integer strings of length , represented by and respectively, provides the processing sequence of all processes of non-standardized parts, gives the machine allocation for all processes.

[0092] Decoding: Decoding is performed according to the allocation of standardized parts among factories, their processing sequence, the processing sequence of each process of non-standardized parts, and the machine allocation of processes.

[0093] In this embodiment, as Figure 2 shown, it involves nine standardized parts processed by three factories, and nine processes of three non-standardized parts processed on five machines. It is clear that standard parts 4 and 8 are allocated to factory 1, and their processing sequence is: 4 → 8. Standard parts 1, 5, and 7 are allocated to factory 2 and processed in the order of standard part 5 → 1 → 7. The remaining standard parts are produced in factory 3, in the order of 2 → 9 → 6 → 3. The processing sequence of all processes is: , means representing the first process of non-standard part 2, represents listing the first process of part 3, and so on. And the machine selection for each process is given. For example, the first, second, and last processes of non-standard part 1 select machines 2, 1, and 3 respectively for processing. According to this method, 4 key scheduling decisions can be successfully obtained.

[0094] Initialize the population; randomly generate , and segments, and then generate segments by a hybrid method of randomly generating with a weight of 80%, operating the minimum processing time rule with 10%, and the global minimum processing time rule with 10%.

[0095] S53. Based on the search mechanism of the improved grey wolf optimization algorithm, for , , and segments, four crossover operators are applied, including two-point, cycle, order-based, and uniform crossover operators, as Figure 3 shown, representing a descriptive example, where and represents the parent solution, and

[0096] To prevent the algorithm from falling into a local optimal solution, three types of mutation operators are executed on each newly generated solution to explore its neighborhood. Specifically, two factories in the segment are randomly swapped, and between and the elements between two randomly selected points in the segment are reversed. For the segment, a machine for one operation randomly appears, as Figure 4 shown, where represents the new mutation.

[0097] S54. Execute two knowledge-driven local search strategies to update the solution within a fixed number of iterations.

[0098] First, execute the first local search strategy: Set 7 knowledge-driven local search operators according to the critical path in the DFS manufacturing cell and the critical path in the FJS manufacturing cell. The first four operators are applied to the DFS manufacturing cell, and the last three operators are applied to the FJS manufacturing cell. The critical paths in both cases are as Figure 5 shown in the process:

[0099] Local search operator 1( ), randomly selects two critical parts in the segment and swaps them; Local search operator 2( ): Randomly selects two critical parts in the segment, and then inserts one part in front of the other; Local search operator 3( ): Randomly selects a critical part and a non-critical part, swaps them in the segment, and at the same time swaps their factory assignments in the segment; Local search operator 4( ): Randomly selects a critical part and then moves it to a non-critical factory; Local search operator 5( ): Randomly selects two critical processes in the segment and then swaps them; Local search operator 6( ): Randomly selects two critical processes in the segment and then inserts one process in front of the other; Local search operator 7( ): Randomly selects a critical process and then randomly changes its machine index;

[0100] Secondly, perform the second local search strategy on each updated solution: randomly select a critical operation, change its machine to the one with the lowest processing cost, compare the advantages of the solution before and after performing the two local search strategies, and save the superior solution to update the population.

[0101] It should be noted that the critical path refers to the continuous path from the start node to the end node of the solution. The factory where the critical path is located is regarded as the critical factory, and the parts or operations included are defined as critical parts or critical operations.

[0102] Merge the new population and the existing population, perform non-dominated sorting on all solutions and calculate their crowding distance values. According to their sorting and crowding distance values, select the best solutions as the next generation population;

[0103] S56. When the termination criterion is met, and the termination criterion is equal to the number of fitness evaluation times, output the obtained non-dominated solution set; otherwise, go back to step S53.

[0104] To verify the effectiveness of the optimization method in this embodiment, 18 test instances of different scales were generated based on the data of a customized furniture company located in the Pearl River Delta region of South China. Table 1 shows the detailed information of these constructed instances. They are divided into small, medium, and large according to the number of parts. Each scale consists of 6 instances, and each instance has different numbers of factories, machines, and parts. The abbreviations of each instance are shown in Table 1.

[0105] In Table 1, the abbreviation "S11" represents a small-scale instance with 30 parts. The distributed flow shop manufacturing cell contains 2 factories, 4 machines, and 20 standardized parts, and the flexible job shop manufacturing cell contains 4 machines and 10 non-standardized parts. The abbreviation "M14" refers to a medium-scale instance with 60 parts. The DFS manufacturing cell consists of 3 factories, 6 machines, and 40 standardized parts, and the FJS manufacturing cell consists of 6 machines and 20 non-standardized parts. The rest can be explained by analogy. Each non-standardized part contains three operations. Table 2 gives the instance parameters such as the processing time, unit processing cost, basic design processing time, unit design cost, degree of customization of the operation, and unit customization processing cost of the machine for the standardized parts.

[0106] Table 1 Summary of Information of 18 Test Instances

[0107]

[0108] Table 2 Parameters of 18 Test Instances

[0109]

[0110] The MOGWO is compared with two comparative algorithms, NSGAII and MOEA / D, in terms of C - metric, IGD - metric, and HV - metric. Both NSGA - II and MOEA / D are multi - objective evolutionary algorithms and have shown superior capabilities in dealing with various optimization problems, especially job - shop scheduling problems. The comparison results of the three algorithms in terms of C -, IGD -, and HV - metrics are shown in Table 3 - 5.

[0111] Table 3 shows the comparison results of the C - metric, where the symbols " ", " ", and " " are the non - dominated solution sets achieved by MOGWO, NSGA - II, and MOEA / D, respectively. The larger the value, the better the performance of MOGWO. Among the 18 test instances, the value of is greater than in 15 test instances, and the value of is greater than

[0112] in 15 test instances. Therefore, the performance of the MOGWO algorithm is significantly better than that of the similar algorithms. In addition, MOGWO has a larger average value than its two comparative algorithms. Although the average variance value of MOGWO is slightly lower than that of NSGA - II and MOEA / D, the difference is not significant.

[0113] Table 4 provides the comparison results regarding the IGD - metric. The smaller the IGD - metric value, the better the algorithm performance. Compared with NSGA - II, MOGWO shows the best performance on 18 instances and produces better results than MOEA / D on 14 instances. The average mean and average variance of each test instance are also given. The average values of MOGWO, NSGA - II, and MOEA / D are 0.1889, 0.2474, and 0.2046, respectively. Their average variance values are 0.0022, 0.0023, and 0.0026, respectively. Obviously, MOGWO achieves the results with the smallest average mean and the smallest average variance.

[0113] Table 5 lists the comparison results of the HV - metric. From Table 5, we can find that MOGWO is superior to NSGA - II on all test instances and is superior to MOEA / D on 17 out of 18 test instances. In addition, similar conclusions can also be drawn by analyzing the average mean and variance values of MOGWO, NSGA - II, and MOEA / D. Their mean values are 0.7839, 0.6379, and 0.7274, respectively, and the mean variance values are 0.0093, 0.0138, and 0.0109, respectively.

[0114] Table 3 Results of MOGWO and Its Two Comparative Algorithms Regarding the C - metric

[0115]

[0116] Table 4 Results of MOGWO and its two comparison algorithms on IGD-index

[0117]

[0118] Table 5 Results of MOGWO and its two comparison algorithms on HV-index

[0119]

[0120] To show the research results of the three algorithms, violin plots were drawn in six instances of different sizes. Figure 7 and Figure 8 respectively show the violin plots of MOGWO and its comparison algorithms in terms of IGD- and HV-indices. Generally speaking, the results of MOGWO are the best, followed by MOEA / D. On the contrary, the results of NSGA-II are the worst. From Figure 7 it can be seen that in most instances regarding the IGD index, the median of MOGWO is lower than that of its comparison algorithms. Similarly, Figure 8 shows that on each selected HV-index instance, MOGWO exceeds the corresponding value with a higher median. Therefore, the results collected show that MOGWO has obvious advantages compared with its comparison algorithms.

[0121] In summary, the optimization method of the furniture customization manufacturing service system based on multi-objective grey wolf optimization provided by the present invention uses the grey wolf optimization algorithm to optimize the makespan and total cost, realizes the adjustment of the production scheduling of the hybrid manufacturing workshop, improves the production efficiency and the flexibility of the manufacturing process, and meets the requirements of different customers.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A furniture customization manufacturing service system optimization method based on multi-objective gray wolf optimization, characterized by: Based on the furniture customized manufacturing service system, the customized manufacturing service system includes intelligent order splitting system and intelligent scheduling system; The intelligent scheduling system includes distributed flow shop manufacturing units and flexible job shop manufacturing units; The steps include: S1. Obtain customized furniture orders; S2. Decompose the furniture order into parts of various specifications, and divide the parts into standardized parts and non-standardized parts; S3, constrain the maximum completion time and total cost; S4. Improve the search mechanism of the basic grey wolf optimization algorithm, including: S41. Define adaptive selection rate , and its calculation formula is: In the formula, and Respectively represent the current suitable value evaluation times and the maximum suitable value evaluation times; S42, for each solution in the population Generate a random floating point number ,when , randomly from , and Choose a solution from the wolf , and for both parents and Perform crossover and mutation operations to generate two new solutions. Otherwise, and Perform crossover and mutation operations to construct two new solutions, where Random from Choose among the wolves, The ranking value is not less than The sort value of S5. Based on the improved grey wolf optimization algorithm, the maximum completion time and total cost are optimized, including: S51, input problem parameters and algorithm parameters; S52, encoding and decoding and initializing population; Coding: There are four decoding methods to represent individuals, including factory segments , Parts segment , process section and machine segment , By integer string Indicates that is the factory index, indicating the factory assignment of the standardized part, ; Represents the processing order of all standardized parts, expressed as an integer string , where each number represents a standardized part index; and The length is Integer strings, respectively and express, Provides the processing sequence of all processes for non-standard parts. Give the machine allocation for all processes; Decoding: Decoding is performed based on the distribution of standardized parts among various factories and their processing sequence, and the processing sequence of each process of non-standardized parts and the machine allocation of the process; Initialize the population: randomly generate , and The segment is then generated by a mixed method of 80% random generation, 10% operation minimum processing time rule, and 10% global minimum processing time rule. part; S53, based on the improved gray wolf optimization algorithm, , , and Segments are crossovered and mutated; S54, executing two knowledge-driven local search strategies to update the solution in a fixed number of iterations, specifically including; First, the first local search strategy is implemented: 7 knowledge-driven local search operators are set. The first four operators are applied to distributed flow shop manufacturing units, and the last three operators are applied to flexible job shop manufacturing units. The process is as follows: Local search operator 1( ),exist The segment randomly selects two key parts to exchange; local search operator 2 ( ):exist The segment randomly selects two key parts and then inserts one of the parts in front of the other part; the local search operator 3 ( ): Randomly select a key part and a non-key part, Segment exchange, while Segments swap their factory assignments; local search operator 4 ( ): Randomly select a critical part and move it to a non-critical factory; Local search operator 5 ( ):exist The segment randomly selects two key processes and then exchanges them; the local search operator 6 ( ):exist Two key processes are randomly selected in the segment, and then one of the processes is inserted in front of the other process; local search operator 7 ( ): Randomly select a key process and then randomly change its machine index; Secondly, the second local search strategy is executed for each updated solution: randomly select a key process, change its machine to the one with the lowest processing cost, compare the advantages of the solutions before and after executing the two local search strategies, and save the optimal solution to update the population; S55, merge the new population with the existing population, perform non-dominated sorting on all solutions and calculate their crowding distance values, and select the best front based on their sorting and crowding distance values. The solutions are used as the next generation population; S56. When the termination criterion is met, the termination criterion is equal to The number of fitness evaluations is calculated, and the obtained non-dominated solution set is output. Otherwise, the process goes to step S53, where: represents the standardized part quantity, Indicates a non-normalized part quantity.

2. The furniture customized manufacturing service system optimization method based on multi-objective gray wolf optimization according to claim 1 is characterized by: In step S51, the question parameters include the number of factories , the number of machines in distributed assembly line manufacturing units , Standardized number of parts , the number of machines in the flexible job shop manufacturing unit , Non-standardized number of parts ; Assembly line Machines in Processing parts Time , machines in assembly lines Unit cost of processing , Process Basic design time , Process Personalized design time ,Component Unit design cost , Process The degree of personalization and flexible job shop machines Unit personalized processing cost , algorithm parameters include population size and the maximum fitness evaluation times .

3. The furniture customized manufacturing service system optimization method based on multi-objective gray wolf optimization according to claim 1 is characterized by: The seven knowledge-driven local search operators set by the first local search strategy are set according to the critical paths in the distributed assembly line manufacturing unit and the critical paths in the flexible job shop manufacturing unit. The critical path refers to the continuous path from the start node to the end node of the solution. The factory where the critical path is located is regarded as the critical factory, and the parts or processes contained therein are defined as critical parts or critical processes.

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