A second-type balance optimization method for a variable-rhythm synchronous hybrid flow multi-person co-station assembly line

Abstract

The present application belongs to the technical field of assembly line balancing, and particularly relates to a second-type balancing optimization method for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, which comprises the following steps: setting relevant parameters of a second-type balancing optimization problem of the variable-rhythm synchronous mixed-flow multi-person co-station assembly line; solving the second-type balancing optimization problem of the variable-rhythm synchronous mixed-flow multi-person co-station assembly line by using an improved genetic algorithm to obtain an optimal solution; and modeling and designing an intelligent optimization method genetic algorithm for solving by comprehensively arranging the mixed-flow assembly, multi-person co-station operation and variable-rhythm synchronous conveying line, so as to provide an optimization scheme for the production and assembly of products with large volume, complex types and no shaking operation, and to be beneficial to improving the production efficiency of the products and reducing the production cost.

Description

Technical Field

[0001] This invention belongs to the field of assembly line balancing technology, specifically relating to a two-class balancing optimization method for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line. Background Technology

[0002] The variable-rhythm synchronous mixed-flow multi-person co-station assembly line combines the features of mixed-flow assembly, multi-person collaborative co-station operation, and variable-rhythm synchronous conveying. It is highly flexible, efficient, and cost-effective, and is suitable for mass production of large-scale, large-volume products. It is commonly used in production scenarios with large product sizes and diverse models, such as automobiles, trucks, and home appliances.

[0003] Assembly lines, as dynamic flow systems, play a crucial role in manufacturing. How to allocate all processes to various workstations while meeting assembly task constraints and ensuring the continuity of production along the entire assembly line is the primary assembly line balancing problem to consider when designing an assembly line. The second type of assembly line balancing problem is an optimization problem aimed at minimizing the production cycle time given a certain number of workstations and assembly line layout. Considering the characteristic of multiple workers sharing a workstation, the optimization objective is expanded to minimize the production cycle time as the primary objective and minimize the total number of workers as a secondary objective.

[0004] In recent years, the design and modeling of assembly line balancing problems have become increasingly realistic and closer to the actual production environment of factories, considering balancing problems such as mixed-flow assembly lines, dual-side lines, multi-person co-station lines, U-shaped lines, and parallel assembly lines. The optimization objectives have also become increasingly diversified, from simply minimizing the number of workstations for a given production cycle time (Type I balancing problem) and minimizing the production cycle time for a given number of workstations (Type II balancing problem), to cost-oriented approaches that aim to minimize unit production costs, and even considering multi-objective balancing problems. However, balancing methods for variable-rhythm synchronous mixed-flow multi-person co-station assembly lines have not yet been addressed.

[0005] Methods for solving assembly line balancing problems include exact algorithms, heuristic algorithms, and metaheuristic algorithms. Since it has been proven to be an NP-hard problem, metaheuristic algorithms such as genetic algorithms, ant colony optimization, particle swarm optimization, and simulated annealing are widely accepted and applied, and have been adapted for specific problems. Among these, genetic algorithms, employing a population search strategy and a flexible fitness function construction method, can handle various types of optimization criteria and constraints. Therefore, it is suitable for solving assembly line balancing problems of various types and scenarios. This invention addresses the second type of balancing problem in variable-rhythm synchronous mixed-flow multi-person co-station assembly lines and designs a solution method based on a genetic algorithm. Summary of the Invention

[0006] To address the second type of equilibrium optimization problem in a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, this invention provides a method for the second type of equilibrium optimization in such a line. The method includes constructing the second type of equilibrium optimization problem for the variable-rhythm synchronous mixed-flow multi-person co-station assembly line; employing an improved genetic algorithm to solve the second type of equilibrium optimization problem for the variable-rhythm synchronous mixed-flow multi-person co-station assembly line; and finally obtaining the optimal solution.

[0007] The improved genetic algorithm is used to solve the second type of equilibrium optimization problem in a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, including the following steps:

[0008] S1. Calculate the lower bound LB for the second type of equilibrium problem applicable to a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, and perform population initialization based on the lower bound LB;

[0009] S2. Decode each chromosome in the population to obtain the corresponding production rhythm;

[0010] S3. Obtain the value assessment results for each chromosome based on the production cycle;

[0011] S4. Based on the value assessment results, the population is screened, crossovered, and mutated until the maximum number of iterations is reached to obtain the optimal solution.

[0012] The beneficial effects of this invention are:

[0013] This invention is the first to consider a mixed-flow, multi-person co-station assembly line under variable-rhythm synchronous conveying, and provides a solution for its second type of equilibrium problem, which is beneficial to the design of solution methods for other types of equilibrium problems of this type of assembly line.

[0014] This invention integrates mixed-flow assembly, multi-person co-working, and variable-rhythm synchronous conveyor lines into a unified model and designs an intelligent optimization method using a genetic algorithm to solve the problem. It provides an optimization solution for the production and assembly of large, complex products that require no shaking, which helps to improve the production efficiency and reduce the production cost of such products. Attached Figure Description

[0015] Figure 1 This is a flowchart of the second type of intelligent balancing optimization method for variable-rhythm synchronous mixed-flow multi-person co-station assembly line of the present invention;

[0016] Figure 2 This is a flowchart of the population initialization process based on the lower bound (LB) of this invention.

[0017] Figure 3 This is a flowchart illustrating the decoding process for each chromosome within a population according to the present invention.

[0018] Figure 4 This is a schematic diagram of chromosome encoding according to an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] This invention provides a second-class equilibrium optimization method for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line. The method includes constructing a second-class equilibrium optimization problem for the variable-rhythm synchronous mixed-flow multi-person co-station assembly line; using an improved genetic algorithm to solve the second-class equilibrium optimization problem for the variable-rhythm synchronous mixed-flow multi-person co-station assembly line; and finally obtaining the optimal solution.

[0021] Specifically, the relevant parameters for the second type of equilibrium optimization problem in a variable-rhythm synchronous mixed-flow multi-person co-station assembly line are set, including:

[0022] S001. Set the product production sequence Q, the number of multi-person workstations Ns, and the worker density ω. max Simultaneously, the sequential relationship between assembly tasks is set to obtain the pre-order task set and post-order task set for each assembly task; worker density refers to the maximum number of workers that can be allocated in each multi-person workstation.

[0023] S002. Define a task time matrix TTM of size Nt×|M|, where Nt is the number of assembly tasks, |M| is the number of product model types, and the element t in the i-th row and m-th column of the task time matrix TTM is... im This represents the completion time of the i-th assembly task under the m-th product model;

[0024] S003. Define an average task time matrix (ATM) of size 1×Nt, where the i-th element ATM(i) is calculated using the following formula:

[0025]

[0026] ATM(i) represents the average operation time for all types of product models under the i-th assembly task.

[0027] Specifically, in this invention, the working time refers to the time period required to complete the assembly task, and the completion time refers to the moment when the assembly task is completed.

[0028] Preferably, an improved genetic algorithm is used to solve the second type of equilibrium optimization problem in a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, such as... Figure 1 As shown, it includes the following steps:

[0029] S1. Calculate the lower bound LB for the second type of equilibrium problem applicable to a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, and perform population initialization based on the lower bound LB.

[0030] Specifically, step S1 calculates the lower bound LB applicable to the second type of equilibrium problem in a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, expressed as:

[0031]

[0032]

[0033] LB = max{LBS1, LBS2}

[0034] LBS1 and LBS2 are two theoretically effective boundary values ​​for the objective value (i.e., the solution objective of the second type of equilibrium problem in a variable-rhythm synchronous mixed-flow multi-person co-station assembly line). Let ω represent the smallest integer greater than x, Ns represent the number of multi-user workstations, and ω represent the number of multi-user workstations. max Indicates worker density; The weighted average completion time of the i-th assembly task is represented by the following formula:

[0035]

[0036] Where |M| represents the number of product model types, and t im k represents the completion time required for the i-th assembly task under the m-th product model; m Let |Q| represent the proportion of the m-th product model in the product production sequence Q, and |Q| represent the total number of models in the product production sequence.

[0037] Specifically, such as Figure 2 As shown, population initialization includes:

[0038] S11. Set a 1×Nt string as a chromosome Chrom, and the chromosome Chrom carries a workstation counter with a counting range of 1 to Ns. The workstation counter is used to indicate which multi-user workstation is currently assigning tasks; initially, all elements in the chromosome Chrom are empty, and the current count value of the workstation counter is Cs. 1 =1; Ns represents the number of multi-person workstations, and Nt represents the number of assembly tasks; set an average task completion time matrix Tc of size 1×Nt, and a matrix of size 1×ω maxThe average worker end time matrix Sc is used to record the average task completion time of all types of product models under each assembly task, and the average worker end time of each worker for producing all types of product models. Initially, the average task completion time matrix Tc and the average worker end time matrix Sc are both zero matrices. Define the set S0;

[0039] S12. Put the assembly tasks without pre-order tasks and the assembly tasks for which all pre-order tasks have been assigned into the set S0;

[0040] S13. Randomly select an assembly task i from the empty set S0, find the task j with the maximum average task completion time in the pre-order task set of the assembly task i, and record its average task completion time as Tc(j). At the same time, obtain the worker r with the minimum average worker end time in the Cs 1 th multi-worker workstation, and record its average worker end time as Sc(r);

[0041] S14. Judge whether the condition Cs 1 = Ns is satisfied, that is, judge whether the current multi-worker workstation for task assignment is the last multi-worker workstation. If not, go to step S15. If satisfied, go to step S16;

[0042] S15. Judge whether the inequality max(Tc(j), Sc(r)+ATM(i)) < LB×σ is satisfied. If not, remove the assembly task i from the empty set S0 and judge whether the current empty set S0 is empty. If so, let Cs 1 = Cs 1 +1, clear the matrices Tc and Sc, and return to step S12. If not, return to step S12. If satisfied, go to step S16; ATM(i) represents the average operation time of all types of product models under the i-th assembly task, and σ is the LB control parameter. It should be noted that for each multi-worker workstation during task assignment, there are its own matrices Tc and Sc for recording; S16. Let Tc(j) = max(Tc(j), Sc(r)+ATM(i)), and Sc(r) = max(Tc(j), Sc(r)+ATM(i)). At the same time, let the i-th element of the chromosome Chrom be Cs 1 , mark that the i-th assembly task has been assigned to the Cs 1 th multi-worker workstation, and judge whether the condition Cs 1 = Ns is satisfied. If not, return to step S12. If satisfied, go to step S17

[0043] S17. Copy the configured chromosome Chrom to obtain chromosome Chrom_cp, decode chromosome Chrom_cp to obtain its minimum production cycle CT; determine whether CT is less than LB, if so, update the value of LB to CT; if not, do not update the value of LB.

[0044] In the initialization of the population, chromosome replication and decoding are performed to obtain the production beat CT and update the LB, because the LB plays a key role in the entire initialization process and needs to be dynamically updated.

[0045] S18. Repeat steps S11-S17 until the population size reaches PopSize, then end the initialization of the population.

[0046] Specifically, the initialization process of each chromosome is the process of assigning appropriate assembly tasks to each multi-person workstation in sequence. When the workstation counter has reached its maximum value and all assembly tasks have been assigned, the initialization of the chromosome is completed.

[0047] In one embodiment, let the number of assembly tasks Nt = 20, the number of multi-person workstations Ns = 5, and the allocation of each multi-person workstation as follows: Figure 4 As shown in (a), the chromosome coding is as follows: Figure 4 As shown in (b), each cell represents an assembly task, and the element value of each cell represents a multi-person workstation.

[0048] S2. Decode each chromosome in the population to obtain the corresponding production rhythm.

[0049] Specifically, the decoding operation here is used to solve for the target value and update iteratively to obtain the globally optimal solution, such as... Figure 3 As shown, decoding any chromosome includes:

[0050] S21. Based on the order of assembly tasks, calculate the position weight of each assembly task to form a task position weight matrix TWM; define a product processing time matrix PTT of size Ns×|M|, where the element in the i-th row and j-th column represents the time for the i-th multi-person workstation to process the j-th product model; simultaneously set a workstation counter from 1 to Ns and a counter from 1 to ω max The worker density counter, also known as the workstation counter, indicates which multi-person workstation is currently operating. The worker density counter is used for surface analysis. Initially, the current count value Cs of the workstation counter is... 2 =1, the current count value of the worker density counter is Cw=1; and the variable Wn is used to count the total number of workers assigned assembly tasks in all multi-person workstations.

[0051] Specifically, the formula for calculating the position weight of each assembly task in step S21 is as follows:

[0052]

[0053] Where Succ(j) represents the j-th assembly task in the set of subsequent tasks of assembly task i, and |Succ| represents the number of assembly tasks in the set of subsequent tasks of assembly task i.

[0054] S22. Determine whether condition Cs is satisfied. 2 If Ns is true, proceed to step S28; otherwise, proceed to step S23.

[0055] S23. Define a task model operation time matrix TCM of size Nt×|M|, where the element in the i-th row and j-th column represents the completion time of the i-th assembly task under the j-th product model; define a matrix of size 1×ω max The matrix MWCM, where MWCM(i) represents the Cs-th matrix. 2 In a multi-workstation network, the average task completion time of the i-th worker is defined; a matrix MTCM of size 1×Nt is defined, where MTCM(i) represents the average operation time of all product models under the i-th assembly task; a matrix of size ω is defined. max The matrix ARM is a ×|M| matrix, where the element in the i-th row and j-th column represents the element in the Cs-th column when the worker density is i. 2 The operation time of multiple workstations on the j-th product model; then, with a maximum worker density of Cw, the operation time of the cs-th product model. 2 Multiple workstations are used to precisely allocate assembly tasks.

[0056] S24. Define a set S1, obtain all assembly tasks in the chromosome whose element value is equal to Cs, and filter out assembly tasks with no prior tasks or whose prior tasks have all been assigned and put them into set S1.

[0057] S25. Determine if set S1 is empty. If set S1 is not empty, select the assembly task with the largest position weight in set S1 based on the task position weight matrix TWM, and assign it to the worker who can execute the assembly task earliest. At the same time, mark the assembly task as assigned. Update the values ​​of the corresponding elements in the MTCM matrix, MWCM matrix and TCM matrix, and then return to step S25. If set S1 is empty, execute step S26.

[0058] S26. End this task assignment and, based on the characteristics of the variable-rhythm synchronous second-type equilibrium problem (variable output, and strong dependence on the model sequence and its execution, workstations and their number, and processing time caused by task assignment), determine whether this assignment is valid. If the assignment is valid, let Wn = Wn + Cw, Cs 2 =Cs 2+1, and return to step S23; if the allocation is illegal, fill all the element values in the Cs-th row of the PTT matrix into the Cw-th row of the ARM matrix in sequence, and clear the Cs-th row of the PTT matrix, then execute step S27. 2 The Cs-th row of the PTT matrix, and then clear the Cs-th row of the PTT matrix, and then execute step S27. 2 row, and then execute step S27.

[0059] Specifically, step S26 determines whether this allocation is legal according to the characteristics of the variable rhythm synchronous second-class balance problem, including:

[0060] If max(MWCM) < LB×σ and max(MWCM) < LB new ×σ, then this allocation is legal; where, max(MWCM) represents the maximum average task end time in the matrix MWCM, and LB new represents the new lower bound for further judging the legality of the allocation;

[0061] LB new is calculated as follows: fill the maximum element value of each column of the TCM matrix into the Cs-th row of the PTT matrix in sequence, and calculate the production rhythm Ct of the production line composed of the first Cs multi-person workstations according to the rhythm calculation method of the characteristics of the variable rhythm synchronous second-class balance problem. The value of this production rhythm Ct is the value of LB 2 row, and calculate the production rhythm Ct of the production line composed of the first Cs multi-person workstations according to the rhythm calculation method of the characteristics of the variable rhythm synchronous second-class balance problem. The value of this production rhythm Ct is the value of LB 2 value, which is expressed as: new value, which is expressed as:

[0062]

[0063]

[0064] μ ∈ (1, 2,..., |Q|)

[0065] Among them, the product production sequence Q is divided into |Q| production line states, and Ct is expressed as the weighted average of the output rhythms of these |Q| production line states. ts μ represents the output rhythm of the μ-th production line state, and Q q represents the q-th product in the product production sequence Q; q = μ + Ns ± Δ·Nq-s is the relationship expression between the multi-person workstations, product production sequence and production line states of the variable rhythm synchronous assembly line, which means that the q-th product in the product production sequence Q is produced in the s-th multi-person workstation of the μ-th production line state. Δ is an arbitrary positive integer, so that the parameter q satisfies q = 1, 2,..., |Q|.

[0066] S27. Judge whether the condition Cw = ω max is satisfied. If it is satisfied, calculate the row sum value of each row of the ARM matrix, and fill all the element values of the row corresponding to the minimum row sum value into the Cs-th row of the PTT matrix in sequence 2Okay, let Wn = Wn + Cw, Cs 2 =Cs 2 +1, Cw = 1, then return to step S22; if not satisfied, let Cw = Cw + 1, and proceed to step S23.

[0067] S28. Obtain the complete PTT matrix, calculate the production beat CT of the entire assembly line including all multi-person workstations according to the beat calculation method of the second type of equilibrium problem of variable rhythm synchronization, that is, the beat when Cs = Ns, output CT and Wn as the final decoding result, and end the decoding operation of the chromosome individual.

[0068] S3. Obtain the value assessment results for each chromosome based on the production cycle.

[0069] Specifically, the value assessment results for each chromosome are obtained based on the production cycle, and are expressed as follows:

[0070]

[0071] Where obj represents the value assessment result of the j-th chromosome, CT represents the production cycle time, Wn represents the sum of the total number of workers in all multi-person workstations, Ns represents the number of multi-person workstations, and ω max Indicates worker density.

[0072] S4. Based on the value assessment results, the population is screened, crossovered, and mutated until the maximum number of iterations is reached to obtain the optimal solution.

[0073] Specifically, the screening operation includes: following the design principle that the smaller the value assessment result, the better the fitness of the individual chromosome, the value assessment result of each chromosome in the population is reverse normalized to obtain the fitness value of each chromosome; then, based on the fitness value of each chromosome, the survival probability of each chromosome is calculated, and the population is screened using a roulette wheel betting method with the GGap generation gap, eliminating individuals with low survival probability and re-initializing some new chromosome individuals to maintain the PopSize population size.

[0074] The crossover operation includes: selecting a pair of parent chromosomes X and Y from the population with probability Cr; generating a random number r from 1 to Nt; copying genes with values ​​from 1 to r from parent chromosome X to offspring chromosome O1; copying genes with values ​​from r+1 to Nt from parent chromosome Y to empty gene loci in offspring chromosome O1; marking the still empty gene loci in offspring chromosome O1 and filling them in using task redistribution; and swapping the roles of X and Y to generate offspring chromosome O2 in the same way.

[0075] The mutation operation includes: selecting chromosomes from the population with probability Mr and performing mutation operations, randomly selecting several genes of the chromosome, clearing them and marking them, and then filling them back into the chromosome using task redistribution to obtain a new chromosome.

[0076] Specifically, the population iteration process includes:

[0077] S41. Randomly select a chromosome from the initial population as the globally optimal chromosome Chrom_Best;

[0078] S42. In each iteration, obtain the value evaluation results of all chromosomes in the population of this iteration, and take the chromosome with the minimum value evaluation result as the local optimal chromosome chrom_best for this iteration; compare Chrom_Best and chrom_best, and take the minimum value of the two as the new global optimal chromosome.

[0079] S43. In each iteration, the chromosomes after the genetic operations are randomly sorted to generate a new population as the search solution for the next iteration. Simultaneously, the currently globally optimal chromosome is inserted into the population for the next iteration.

[0080] S44. Set the termination conditions for the algorithm. You can set the CPU running time and the maximum number of iterations to terminate the algorithm.

[0081] S45. Output the globally optimal chromosome information stored at the end of the iteration as the optimal solution to the second type of equilibrium problem of the variable-rhythm synchronous mixed-flow multi-person co-station assembly line, and output the minimum cycle time and the minimum total number of workers.

[0082] In one embodiment, a mixed-flow assembly line with three multi-workstation workstations is used to illustrate two types of products, product A and product B. The maximum number of workers that can be assigned to one workstation is 3, the production sequence is Q = [A,A,A,B,B,B,B], and the number of assembly tasks is 8. The specific information is shown in the table below:

[0083] Table 1 shows the assembly task information entered.

[0084] Task Number Product A working time Product B working time Subsequent tasks 1 1 9 2 2 5 4 3,4 3 8 0 5,6 4 5 2 6 5 0 5 7 6 8 6 8 7 6 9 - 8 2 2 -

[0085] After executing and implementing this case, the final sequence of tasks assigned to workstations is [1,2,2,2,2,3,3,3], the sequence of tasks assigned to workers is [1,1,1,2,1,1,2,1], the maximum operating time of product A in the two workstations is [1,13,10], the maximum operating time of product B in the two workstations is [9,9,9], the minimum production cycle time is 10.857, and the minimum number of workers is 5.

[0086] Verification showed that the output followed the input data and conditions; the optimal value of 10.857 was less than the maximum value of 13 in the workstation cycle time, which is consistent with the typical characteristics of the solution to the second type of equilibrium problem in a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, and the result is valid.

[0087] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "setting," "connection," "fixing," "rotation," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal connection of two components or the interaction between two components. Unless otherwise explicitly limited, those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0088] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A two-class equilibrium optimization method for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, characterized in that, A second-type equilibrium optimization problem for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line is constructed; an improved genetic algorithm is used to solve the second-type equilibrium optimization problem for the variable-rhythm synchronous mixed-flow multi-person co-station assembly line and obtain the optimal solution; The improved genetic algorithm is used to solve the second type of equilibrium optimization problem in a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, including the following steps: S1. Calculate the lower bound LB for the second type of equilibrium problem applicable to a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, and perform population initialization based on the lower bound LB; Step S1 calculates the lower bound LB for the second type of equilibrium problem applicable to a variable-rhythm synchronous mixed-flow multi-person co-station assembly line, expressed as: Wherein, LBS1 and LBS2 are two theoretical effective boundary values ​​of the target value. Let x represent the smallest integer greater than x, and Ns represent the number of multi-user workstations. Indicates worker density; The weighted average completion time of the i-th assembly task is represented by the following formula: Where |M| represents the number of product model types, and t im This represents the completion time of the i-th assembly task under the m-th product model; Let |Q| represent the proportion of the m-th product model in the product production sequence Q, and |Q| represent the total number of models in the product production sequence. S2. Decode each chromosome in the population to obtain the corresponding production rhythm; S3. Obtain the value assessment results for each chromosome based on the production cycle, expressed as follows: Where obj represents the value assessment result of the j-th chromosome, CT represents the production cycle time, Wn represents the sum of the total number of workers in all multi-person workstations, and Ns represents the number of multi-person workstations. Indicates worker density; S4. Based on the value assessment results, the population is screened, crossovered, and mutated until the maximum number of iterations is reached to obtain the optimal solution.

2. The two-class balance optimization method for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line according to claim 1, characterized in that, The relevant parameters for the second type of equilibrium optimization problem in a variable-rhythm synchronous mixed-flow multi-person co-station assembly line are set, including: S001. Set the number of assembly tasks Nt, the number of product model types |M|, the product production sequence Q, the number of multi-person workstations Ns, and the worker density. Simultaneously, the sequential relationship between assembly tasks is defined to obtain the pre-order task set and post-order task set for each assembly task. S002. Define a task time matrix TTM of size Nt×|M|, where the element t in the i-th row and m-th column of the task time matrix TTM is... im This represents the completion time of the i-th assembly task under the m-th product model; S003. Define an average task time matrix ATM of size 1×Nt, where the i-th element... This represents the average operation time for all types of product models under the i-th assembly task.

3. The two-class balance optimization method for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line according to claim 1, characterized in that, Population initialization includes: S11. Set a 1×Nt string as a chromosome Chrom, and the chromosome Chrom carries a station counter with a counting range of 1~Ns; initially, all elements in the chromosome Chrom are empty, and the current count value of the station counter is Cs. 1 =1; Ns represents the number of multi-person workstations, and Nt represents the number of assembly tasks; set an average task completion time matrix Tc of size 1×Nt, and a matrix of size 1× The average worker completion time matrix Sc; initially, both the average task completion time matrix Tc and the average worker completion time matrix Sc are zero matrices; define a set S0; S12. Place assembly tasks without prerequisite tasks, and assembly tasks for which all prerequisite tasks have been assigned, into set S0. S13. Randomly select an assembly task i from set S0, find the maximum average task completion time Tc(j) in the pre-order task set of assembly task i, and simultaneously obtain the Cs-th task. 1 The minimum average worker finish time Sc(r) in a multi-person workstation; S14. Determine if condition Cs is satisfied. 1 =Ns, if not satisfied, proceed to step S15; if satisfied, proceed to step S16. S15. Determine whether the inequality is satisfied. If the condition is not met, then remove assembly task i from set S0 and check if the current set S0 is empty. If it is, then let Cs... 1 =Cs 1 +1, clear matrices Tc and Sc, and return to step S12. If not, return to step S13; if satisfied, proceed to step S16. This represents the average operation time for all types of product models under the i-th assembly task. For LB control parameters; S16. Let Tc(j) = And Sc(r) = Meanwhile, let the i-th element of chromosome Chrom be Cs. 1 And mark that assembly task i has been assigned, and determine whether condition Cs is met. 1 =Ns, if not satisfied, return to step S12; if satisfied, proceed to step S17. S17. Copy the configured chromosome Chrom to obtain chromosome Chrom_cp, decode chromosome Chrom_cp to obtain its production beat CT; determine whether CT is less than LB, if so, update the value of LB to CT; if not, do not update the value of LB. S18. Repeat steps S11-S17 until the population size reaches PopSize, then end the initialization of the population.

4. The two-class balance optimization method for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line according to claim 1, characterized in that, Step S2 decodes any chromosome in the population, including: S21. Based on the order of assembly tasks, calculate the position weight of each assembly task to form a task position weight matrix TWM; define a product processing time matrix PTT of size Ns×|M|, where the element in the i-th row and j-th column represents the time for the i-th multi-person workstation to process the j-th product model; simultaneously set a workstation counter from 1 to Ns and a counter from 1 to Ns. The worker density counter, initially, has a current count value Cs. 2 =1, the current count value of the worker density counter Cw=1; define variable Wn to count the total number of workers assigned assembly tasks in all multi-person workstations; S22. Determine whether condition Cs is satisfied. 2 If Ns is true, proceed to step S28; otherwise, proceed to step S23. S23. Define a task model operation time matrix TCM of size Nt×|M|, where the element in the i-th row and j-th column represents the completion time of the i-th assembly task under the j-th product model; define a matrix of size 1× The matrix MWCM, where MWCM(i) represents the Cs-th matrix. 2 The average task completion time of the i-th worker in a multi-person workstation; define a matrix MTCM of size 1×Nt, where MTCM(i) represents the average operation time of all product models under the i-th assembly task; define a matrix of size Nt. The matrix ARM is a ×|M| matrix, where the element in the i-th row and j-th column represents the element in the Cs-th column when the worker density is i. 2 The operation time of a multi-user workstation on the j-th product model; S24. Define a set S1, obtain all assembly tasks in the chromosome whose element value is equal to Cs, and filter out assembly tasks with no prior tasks or whose prior tasks have all been assigned and put them into set S1. S25. Determine if set S1 is empty. If set S1 is not empty, select the assembly task with the largest position weight in set S1 based on the task position weight matrix TWM, and assign it to the worker who can execute the assembly task earliest. At the same time, mark the assembly task as assigned. Update the values ​​of the corresponding elements in the MTCM matrix, MWCM matrix and TCM matrix, and then return to step S25. If set S1 is empty, proceed to step S26. S26. End this task assignment and determine whether the assignment is valid according to the characteristics of the second type of equilibrium problem with variable rhythm synchronization. If the assignment is valid, let Wn = Wn + Cw, Cs 2 =Cs 2 +1, and return to step S23; if the allocation is invalid, then the Cs-th element of the PTT matrix is ​​incremented. 2 All element values ​​of the row are sequentially filled into the Cw-th row of the ARM matrix, and the Cs-th row of the PTT matrix is ​​cleared. 2 Okay, then proceed to step S27; S27. Determine if condition Cw= is satisfied. If satisfied, calculate the row sum of each row in the ARM matrix, and then fill the Cs-th row of the PTT matrix with all the element values ​​of the row corresponding to the smallest row sum. 2 Okay, let Wn = Wn + Cw, Cs 2 =Cs 2 +1, Cw=1, then return to step S22; if not satisfied, let Cw=Cw+1, and proceed to step S23; S28. Obtain the complete PTT matrix, calculate the production cycle time CT of the entire assembly line including all multi-person workstations, output CT and Wn as the final decoding results, and end the decoding operation for individual chromosomes.

5. The two-class balance optimization method for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line according to claim 4, characterized in that, The formula for calculating the position weight of each assembly task in step S21 is as follows: in, Let |Succ| represent the j-th assembly task in the set of subsequent tasks of assembly task i, and let |Succ| represent the number of assembly tasks in the set of subsequent tasks of assembly task i.

6. The two-class balance optimization method for a variable-rhythm synchronous mixed-flow multi-person co-station assembly line according to claim 4, characterized in that, Step S26 determines whether the allocation is valid based on the characteristics of the second type of equilibrium problem with variable rhythm synchronization, including: like and If so, then this allocation is legal; among them, This represents the maximum average task completion time in the MWCM matrix. This represents a new lower bound used to further determine the legality of the allocation, and its calculation formula is as follows: Here, the production sequence Q is divided into |Q| production line states, and Ct is represented as the weighted average of the output cycle times of these |Q| production line states. Indicates the first Output cycle time of various production line states This represents the q-th product in the product production sequence Q; It is an expression relating workstations, production sequences, and production line states in a variable-rhythm synchronous assembly line, denoted as the first... In the s-th multi-person workstation of the production line state, the product being produced is the q-th product in the product production sequence Q. Let q be any positive integer such that the parameter q satisfies q=1,2,…,|Q|.

Images