Ship block assembly workshop personnel redistribution method

Abstract

The invention discloses a ship block assembly workshop personnel redistribution method, and belongs to the technical field of personnel distribution. The method specifically comprises the following steps: step 1, constructing a ship block assembly workshop personnel redistribution problem model; and step 2, solving the constructed model based on an improved grey wolf algorithm to obtain an optimal allocation method. According to the method, a ship block assembly workshop personnel redistribution problem model is constructed, and personnel attribute constraints and processing and assembly stage task priority constraints are converted into mathematical model constraints by taking completion time minimization as an optimization target. Based on the characteristics of a ship block assembly workshop personnel redistribution scheduling model, a plurality of improvement strategies are designed on the basis of the grey wolf algorithm, the solving capability of the grey wolf algorithm for the multi-stage collaborative personnel redistribution problem is improved, the ship block assembly workshop personnel redistribution problem is effectively solved, and the ship block assembly workshop personnel redistribution scheduling efficiency is improved. And the method has relatively high solving precision and stability.

Description

Technical Field

[0001] The present invention relates to a personnel reallocation method, in particular to a personnel reallocation method in a ship block assembly workshop, and belongs to the technical field of personnel allocation. Background Art

[0002] The personnel allocation problem is a classic NP-hard problem. This problem involves developing a personnel allocation plan to optimize one or more performance indicators. However, the constraints of personnel allocation often vary with production methods and conditions, making it difficult to integrate theoretical research with actual production. Further mathematical models and optimization of performance indicators are needed, incorporating constraints from actual production. Personnel reallocation is an effective means of addressing workshops' inability to execute project plans due to uncontrollable factors. A reasonable personnel reallocation plan can effectively improve workshop production efficiency. However, ship block assembly workshops employ a hybrid model of block-by-block parallel production. The production process consists of two phases: machining and assembly. Task transfer between phases is not constrained by a fixed cycle time but rather flexibly adjusted based on the process flow and actual production progress. Furthermore, the collaborative work of multiple workers is a key feature of these workshops. The personnel reallocation process must simultaneously consider the multi-skilled nature of workers and their varying skill levels, making the development of a reasonable personnel reallocation plan complex and challenging. Therefore, studying personnel reallocation methods in ship block assembly workshops is of great significance for optimizing resource allocation and improving production efficiency.

[0003] Prior art literature "Human-machine collaborative optimization method for dynamic worker allocation in aircraft final assembly lines.", Wang et al., Computers & Industrial Engineering, 2024, 194:17, focuses on the problem of personnel allocation in aircraft assembly lines, focusing on the differences in personnel skills and the mobility of personnel between workstations, and proposes a human-machine collaborative optimization algorithm to solve the problem. et al., International Journal of Production Economics, 2015, 170:489–500. They address the problem of personnel allocation in an automobile assembly line. They study the mobility of personnel between workstations after completing a task in a hybrid model automobile product assembly environment and propose a heuristic algorithm for optimizing personnel allocation. These methods fail to fully account for the specific characteristics of a ship block assembly shop, including the parallel production of hybrid model sections, the dynamic connection between the processing and assembly phases without a fixed tact time, and the combined impact of personnel multi-skilling and skill efficiency differences. Therefore, these methods have certain limitations when addressing the complex and diverse real-world scenarios of a ship block assembly shop, making them difficult to directly apply.

[0004] Therefore, it is urgent to propose a personnel redistribution method for ship block assembly workshop to solve the above technical problems. Summary of the Invention

[0005] In order to solve the problem of generating a high-quality personnel reallocation plan for a ship block assembly workshop, the present invention further proposes a personnel reallocation method for a ship block assembly workshop.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for redistributing personnel in a ship block assembly workshop is implemented by the following steps:

[0008] S1: Construct a model for personnel redistribution in ship block assembly workshops;

[0009] S2: Solve the model constructed in S1 based on the improved grey wolf algorithm to obtain the optimal allocation method.

[0010] Furthermore, the model for constructing the personnel redistribution problem in the ship block assembly workshop described in S1 includes the following steps:

[0011] S1.1: Construct an optimization objective for redistributing personnel in the assembly workshop to minimize completion time;

[0012] S1.2: Convert personnel attribute constraints into mathematical model constraints;

[0013] S1.3: Convert the task priority constraints of the processing and assembly stages into mathematical model constraints.

[0014] Furthermore, the optimization objectives described in S1.1 are specifically:

[0015]

[0016] In formula (1), f is the optimization target, P is the segment set, p is the segment index value, and B p It represents the completion time of the segment corresponding to p, min represents minimization, and max represents maximization.

[0017] Furthermore, the conversion of personnel attribute constraints into mathematical model constraints described in S1.2 specifically includes:

[0018]

[0019] z wa ≤c wa ,w∈W,a∈T a (5)

[0020]

[0021] In formulas (2) and (3), it is constrained that during the processing and assembly stages, each operator has multiple operating skills and their operating efficiency varies when working on different processing machines or assembly workstations. Here, M is the set of processing machines, m is the machine index value, and T r is the set of workers assigned to the processing stage, r is the index value of the processing worker, W is the set of assembly workstations, w is the workstation index value, T a is the set of workers assigned to the assembly stage, a is the index value of the assembly worker, χ mr is the skill level of the processing operator corresponding to r when processing machine m, χ wa is the skill level of the assembly operator corresponding to a at assembly workstation w. When the skill level is 0, it means that the operator does not master the operation skills of the corresponding equipment or workstation;

[0022] In formula (4) and formula (5), it is constrained that during the processing and assembly stages, workers can only be assigned to machines or workstations with corresponding operating capabilities, where C p is the segmented processing parts set corresponding to p, c is the processing parts index value, O cp For the processing parts set C p Where c corresponds to the process set of the part, o is the process index value, z mr represents the state variable. When the processing worker corresponding to r is assigned to the processing machine m, then z mr is 1, otherwise 0, c mr Represents the state variable. When the processing operator corresponding to r has the ability to operate the processing machine m, then c mr is 1, otherwise 0, z wa represents the state variable. When the assembly worker corresponding to a is assigned to workstation w, then z wa is 1, otherwise 0, c warepresents the state variable. When the assembly worker corresponding to a has the ability to operate workstation w, then c wa is 1, otherwise 0;

[0023] In formula (6) and formula (7), it is constrained that during the processing stage, the processing workers can only perform one task at a time, where K r is the set of tasks executed by the processing personnel corresponding to r, and k is the set of tasks executed K r The location of the event; r Is the maximum index value of the event position in the execution task set. ocprk Represents the state variable. When the operation corresponding to the processing part o corresponding to the segment c corresponding to p is the kth event in the task set executed by the processing personnel corresponding to r, then X ocprk is 1, otherwise it is 0, X ocpr,k+1 Represents the state variable. When the operation corresponding to the processing part o corresponding to the segment c corresponding to p is the k+1th event in the task set executed by the processing personnel corresponding to r, then X ocpr,k+1 is 1, otherwise 0;

[0024] In formula (8) and formula (9), it is constrained that during the assembly phase, the assembly workers can only perform one task at a time, where K a is the set of tasks performed by the assembly personnel corresponding to a, H a is the set of tasks K a The maximum index value of the event position in X pak Represents the state variable. When the segment corresponding to p is the kth event in the set of tasks performed by the assembly personnel corresponding to a, then X pak is 1, otherwise it is 0, X pa,k+1 represents the state variable. When the segment corresponding to p is the k+1th event in the set of tasks performed by the assembly personnel corresponding to a, then X pa,k+1 is 1 if the value is set, otherwise it is 0.

[0025] Furthermore, the conversion of the processing and assembly phase task priority constraints into mathematical model constraints as described in S1.3 specifically includes:

[0026]

[0027] In formula (10), the premise that the assembly workstation can carry out assembly work is that the required parts have been processed. cp | is the process set O cp The last process index value in the assembly process, T is the assembly segment sequence set, t is the assembly segment sequence set index value, b cpw Represents the state variable, when the processing parts set C pWhen the part corresponding to c is assembled on the workstation corresponding to w, then b cpw =1, otherwise b cpw =0, is the process set O cp The process completion time corresponding to o, It indicates the time when the segment corresponding to t starts to be assembled on the workstation corresponding to w;

[0028] In formula (11), the premise for the segment to start the assembly operation at a workstation is that the segment has completed the assembly operation at the previous workstation and no segment has stopped at the workstation. In formula (12), the premise for the segment to transfer between workstations is that the segment has completed the assembly operation at the current workstation and no segment has stopped at the next workstation. N is the maximum index value of the assembly workstation set W, and I is the maximum index value of the assembly segment sequence set T. represents the end time of the assembly segment corresponding to t at the workstation corresponding to w, represents the end time of the assembly segment corresponding to t at the workstation corresponding to w-1; represents the departure time of the assembly segment corresponding to t at the workstation corresponding to w, represents the departure time of the assembly segment corresponding to t-1 at the workstation corresponding to w, It represents the departure time of the assembly segment corresponding to t-1 at the workstation corresponding to w+1.

[0029] Furthermore, solving the constructed model based on the improved grey wolf algorithm described in S2 includes the following steps:

[0030] S2.1: Population initialization; the population initialization includes chromosome coding design, decision parameter setting and initial population construction; the chromosome coding design constructs a double-layer chromosome coding structure suitable for the personnel redistribution problem in the ship segment assembly workshop, which is used to optimize the allocation of workers in the processing stage and the assembly stage; the decision parameter setting is used to improve the solving ability; the initial population is constructed as a hybrid initial population generation method that combines the population initialization strategy of the critical chain progressive mechanism with random initialization.

[0031] S2.2: Population evolution; the population evolution includes global search and local search, and the decision parameters of the global search include the high-amplitude evolution ratio of processing coding, the low-amplitude evolution ratio of processing coding, the high-amplitude evolution ratio of assembly coding and the low-amplitude evolution ratio of assembly coding; the local search is a resource reallocation strategy based on the critical path control mechanism.

[0032] S2.3: Fitness value calculation; the fitness value calculation is based on the decoding strategy, and the fitness value of each chromosome in the population is calculated;

[0033] S2.4: Termination judgment of the algorithm optimization; the termination judgment of the algorithm optimization determines whether the number of iterations has been reached. If so, the optimal solution set is output; otherwise, jump to S2.2.

[0034] Furthermore, the chromosome coding design described in S2.1 constructs a two-layer chromosome coding structure suitable for the personnel reallocation problem in the ship section assembly workshop. The coding idea is as follows: the first layer of coding is used to represent the allocation of workers in the processing stage. The coding length is consistent with the number of processing tasks. Each unit is a set. The set states include the following three types: If the state is "None", it means that the task has been completed or is in progress and no more workers can be assigned; if it is an empty set, it means that no workers have been assigned to the task; if the set contains elements, it means that the elements in the set are specific workers assigned to the task. The second layer of coding is used to represent the allocation of workers in the assembly stage. The coding length is consistent with the number of assembly tasks. Each unit is a set. The set states are consistent with the first layer of coding: If the state is "None", it means that the task has been completed or is in progress and no more workers can be assigned; if it is an empty set, it means that no workers have been assigned to the task; if the set contains elements, it means that the elements in the set are specific workers assigned to the task.

[0035] Furthermore, the specific decision parameters for setting the decision parameters described in S2.1 include: population size, maximum number of algorithm iterations, maximum number of consecutive iterations without change in the optimal solution, population initialization ratio of the critical chain progressive mechanism, high-amplitude evolution ratio of processing coding, low-amplitude evolution ratio of processing coding, high-amplitude evolution ratio of assembly coding, and low-amplitude evolution ratio of assembly coding.

[0036] Furthermore, the hybrid initial population generation method combining the population initialization strategy of the critical chain progressive mechanism for initial population construction described in S2.1 with the random initialization strategy specifically includes:

[0037] Population initialization strategy of critical chain progressive mechanism:

[0038] a. Based on the chromosome codes assigned to operators and combined with the topological sorting of tasks in the processing and assembly stages, identify the critical path task nodes in the processing and assembly stages;

[0039] b. For each task node in the critical path, randomly assign operators or select suitable operators from the previous tasks and transfer them to the critical path node;

[0040] c. Apply conflict resolution mechanisms to eliminate conflicts between personnel and tasks and ensure that the generated chromosomes are encoded as feasible solutions;

[0041] d. Repeat the above steps until there are no more workers to assign to the worker pool;

[0042] Random initialization strategy:

[0043] By randomly selecting available workers from the resource pool and combining it with a conflict resolution algorithm, feasible individuals are quickly generated.

[0044] The population initialization strategy of the critical chain progressive mechanism and the random initialization strategy constitute a mixed initial population.

[0045] Furthermore, the specific process of the global search for population evolution described in S2.2 is as follows: the target wolf of the global search is represented as P1, the gray wolf individual to be evolved is represented as P2, and the evolved gray wolf individual is represented as O1. First, the gene sites to be evolved are randomly selected in the processing code and assembly code; secondly, the gene sites to be evolved of P1 are copied to P2; finally, by combining the conflict resolution algorithm, the offspring O1 individual is generated, thereby completing the evolution process.

[0046] Furthermore, the specific process of the local search of population evolution described in S2.2 is as follows: a resource reallocation strategy based on the critical path control mechanism is introduced in the local search stage. In each iteration, the task nodes on the individual's critical path are first identified, and the idle workers in the resource pool are preferentially allocated to these critical task nodes; at the same time, for workers assigned to non-critical paths, they can also be reallocated to critical tasks through resource adjustment.

[0047] Furthermore, the specific calculation process of the fitness value described in S2.3 is as follows: a semi-active decoding strategy is used to calculate the fitness value of each chromosome, which includes two stages: the first stage is the encoding and decoding of the workers in the processing stage. During this process, the completion time of all parts is calculated in sequence based on the processing personnel assigned to each process; the second stage is the encoding and decoding of the workers in the assembly stage. In this stage, according to the assembly sequence of each segment, when the parts supply, assembly workstation and assembly sequence meet the assembly requirements, the assembly begins; otherwise, the task needs to continue waiting; finally, the maximum value of the assembly completion time of all segments is used as the fitness value of the chromosome.

[0048] Furthermore, in the termination judgment of the algorithm optimization described in S2.4, the algorithm adopts the combined effect of stopping strategy 1 and stopping strategy 2. The stopping strategy 1 is that the maximum number of algorithm iterations is 100 times; the stopping strategy 2 is that if no new optimal solution appears after more than 50 consecutive iterations, the algorithm converges; as long as one of the two stopping strategies is met, the algorithm stops calculating.

[0049] The beneficial effects of the present invention are:

[0050] 1. The present invention constructs a model for the personnel reallocation problem in a ship block assembly workshop, takes minimizing the completion time as the optimization goal, and transforms personnel attribute constraints and task priority constraints in the processing and assembly stages into mathematical model constraints.

[0051] 2. Based on the characteristics of the personnel redistribution scheduling model in the ship block assembly workshop, the present invention designs a variety of improvement strategies based on the Grey Wolf Algorithm to enhance the Grey Wolf Algorithm's ability to solve the multi-stage collaborative personnel redistribution problem, effectively solve the personnel redistribution problem in the ship block assembly workshop, and has high solution accuracy and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of the personnel redistribution method of the ship block assembly workshop of the present invention;

[0053] Figure 2 Schematic diagram of the comparison results between the present invention and other allocation methods. DETAILED DESCRIPTION

[0054] Specific implementation method 1: Combination Figure 1 and Figure 2 This embodiment is described as follows. Figure 1 As shown, the personnel reallocation method for a ship block assembly workshop described in this embodiment is implemented by the following steps:

[0055] S1: Construct a model for the personnel reallocation problem in a ship block assembly workshop; the ship block assembly workshop adopts a hybrid model of segmented parallel production. The production process includes two stages: processing and assembly. The task transfer between stages is not restricted by a fixed beat, but is flexibly adjusted according to the process flow and actual production progress. In addition, a major feature of this workshop is that multiple workers collaborate to complete tasks. In the process of personnel reallocation, it is necessary to consider the multi-skill characteristics of workers and the differences in skill levels at the same time, which makes the formulation of a reasonable personnel reallocation plan more complex and challenging. The goal of this study is to develop an optimal worker-task reallocation strategy to minimize the completion time of the ship block assembly workshop.

[0056] The ship block assembly workshop personnel redistribution problem model consists of two parts: objective function and constraint conditions, and is implemented through the following steps:

[0057] S1.1: Construct an optimization objective for redistributing personnel in the assembly workshop to minimize completion time. The optimization objective (objective function) is specifically:

[0058]

[0059] In formula (1), f is the optimization target, P is the segment set, p is the segment index value, and B p It represents the completion time of the segment corresponding to p, min represents minimization, and max represents maximization.

[0060] S1.2: Convert personnel attribute constraints into mathematical model constraints; Converting personnel attribute constraints into mathematical model constraints (constraints) specifically includes:

[0061]

[0062] z wa ≤c wa ,w∈W,a∈T a (5)

[0063]

[0064] In formulas (2) and (3), it is constrained that in the processing and assembly stages, each operator has multiple operating skills and their operating efficiency varies when working on different processing machines or assembly workstations. Where M is the processing machine set, m is the machine index value, and T r is the set of workers assigned to the processing stage, r is the index value of the processing worker, W is the set of assembly workstations, w is the workstation index value, T a is the set of workers assigned to the assembly stage, a is the index value of the assembly worker, χ mr is the skill level of the processing operator corresponding to r when processing machine m, χ wa is the skill level of the assembly operator corresponding to a at assembly workstation w. When the skill level is 0, it means that the operator does not master the operation skills of the corresponding equipment or workstation;

[0065] In formula (4) and formula (5), it is constrained that during the processing and assembly stages, workers can only be assigned to machines or workstations with corresponding operating capabilities. p is the segmented processing parts set corresponding to p, c is the processing parts index value, O cp For the processing parts set C p Where c corresponds to the process set of the part, o is the process index value, z mr represents the state variable. When the processing worker corresponding to r is assigned to the processing machine m, then z mr is 1, otherwise 0, c mr Represents the state variable. When the processing operator corresponding to r has the ability to operate the processing machine m, then c mr is 1, otherwise 0, z wa represents the state variable. When the assembly worker corresponding to a is assigned to workstation w, then z wais 1, otherwise 0, c wa represents the state variable. When the assembly worker corresponding to a has the ability to operate workstation w, then c wa is 1, otherwise 0;

[0066] In formula (6) and formula (7), it is constrained that during the processing stage, the processing workers can only perform one task at a time. r is the set of tasks executed by the processing personnel corresponding to r, and k is the set of tasks executed K r The location of the event; H r Is the maximum index value of the event position in the execution task set. ocprk Represents the state variable. When the operation corresponding to the processing part o corresponding to the segment c corresponding to p is the kth event in the task set executed by the processing personnel corresponding to r, then X ocprk is 1, otherwise it is 0, X ocpr,k+1 Represents the state variable. When the operation corresponding to the processing part o corresponding to the segment c corresponding to p is the k+1th event in the task set executed by the processing personnel corresponding to r, then X ocpr,k+1 is 1, otherwise 0;

[0067] In formula (8) and formula (9), it is constrained that during the assembly phase, the assembly workers can only perform one task at a time. a is the set of tasks performed by the assembly personnel corresponding to a, H a is the set of tasks K a The maximum index value of the event position in X pak Represents the state variable. When the segment corresponding to p is the kth event in the set of tasks performed by the assembly personnel corresponding to a, then X pak is 1, otherwise it is 0, X pa,k+1 represents the state variable. When the segment corresponding to p is the k+1th event in the set of tasks performed by the assembly personnel corresponding to a, then X pa,k+1 is 1 if the value is set, otherwise it is 0.

[0068] S1.3: Converting the priority constraints of the tasks in the processing and assembly phases into mathematical model constraints; converting the priority constraints of the tasks in the processing and assembly phases into mathematical model constraints (constraint conditions) specifically includes:

[0069]

[0070] In formula (10), the premise that the assembly workstation can carry out assembly work is that the required parts have been processed. cp | is the process set O cp The last process index value in the assembly process, T is the assembly segment sequence set, t is the assembly segment sequence set index value, bcpw Represents the state variable, when the processing parts set C p When the part corresponding to c is assembled on the workstation corresponding to w, then b cpw =1, otherwise b cpw =0, is the process set O cp The process completion time corresponding to o, It indicates the time when the segment corresponding to t starts to be assembled on the workstation corresponding to w;

[0071] In formula (11), the premise for the segment to start the assembly operation at a workstation is that the segment has completed the assembly operation at the previous workstation and no segment has stopped at the workstation. In formula (12), the premise for the segment to transfer between workstations is that the segment has completed the assembly operation at the current workstation and no segment has stopped at the next workstation. Where N is the maximum index value of the assembly workstation set W, I is the maximum index value of the assembly segment sequence set T, represents the end time of the assembly segment corresponding to t at the workstation corresponding to w, represents the end time of the assembly segment corresponding to t at the workstation corresponding to w-1; represents the departure time of the assembly segment corresponding to t at the workstation corresponding to w, represents the departure time of the assembly segment corresponding to t-1 at the workstation corresponding to w, It represents the departure time of the assembly segment corresponding to t-1 at the workstation corresponding to w+1.

[0072] At this point, a unified mathematical model description of personnel attribute constraints and task priority constraints in the processing and assembly stages has been developed, and the construction of a model for the personnel reallocation problem in the ship block assembly workshop has been realized.

[0073] S2: Solve the model constructed in S1 based on the improved grey wolf algorithm to obtain the optimal allocation method.

[0074] Solving the personnel redistribution problem in the ship block assembly workshop based on the improved grey wolf algorithm includes the following steps:

[0075] S2.1: Population initialization. In the population initialization stage, there are three operations, namely chromosome coding design, decision parameter setting, and initial population construction. The chromosome coding design constructs a double-layer chromosome coding structure suitable for the personnel redistribution problem in the ship segment assembly workshop, which is used to optimize the allocation of workers in the processing and assembly stages. The decision parameter setting is used to improve the solving ability. The initial population is constructed as a hybrid initial population generation method that combines the population initialization strategy of the critical chain progressive mechanism with random initialization.

[0076] S2.1.1: Chromosome Coding Design. This paper designs a two-layer chromosome coding structure for optimizing worker allocation in the processing and assembly stages. The first layer of coding is used to represent the allocation of workers in the processing stage. The coding length is consistent with the number of processing tasks. Each unit is a set, and the set status includes the following three: If the status is "None", it means that the task is completed or in progress and no more workers can be assigned; if it is an empty set, it means that the task has not yet been assigned a worker; if the set contains elements, it means that the elements in the set are specific workers assigned to the task. The second-level code is used to represent the allocation of workers in the assembly stage. The code length is consistent with the number of assembly tasks. Each unit is a set, and the set status is consistent with the first-level code: if the status is "None", it means that the task has been completed or is in progress, and workers cannot be assigned anymore; if it is an empty set, it means that workers have not yet been assigned to the task; if the set contains elements, it means that the elements in the set are specific workers assigned to the task; based on the above coding ideas, the present invention constructs a double-layer chromosome coding structure suitable for the problem of personnel reallocation in ship section assembly workshops; for example: the present invention implements chromosome coding construction based on the design rules of the double-layer coding structure, such as the workers in the processing stage are coded as {(None), (), (r1, r3)...}, and the workers in the assembly stage are coded as {(a2, a3, a4), (), (a1, a3)...}.

[0077] S2.1.2: Decision parameter settings. This invention designs multiple decision parameters to enhance the algorithm's solution-solving capabilities. Specific parameters include: population size, maximum number of algorithm iterations, maximum number of consecutive iterations without optimal solution changes, population initialization ratio of the critical chain progressive mechanism, high-amplitude evolution ratio of processing code, low-amplitude evolution ratio of processing code, high-amplitude evolution ratio of assembly code, and low-amplitude evolution ratio of assembly code. Specifically, the population size is 100, the maximum number of algorithm iterations is 100, the maximum number of consecutive iterations without optimal solution changes is 50, the population initialization ratio of the critical chain progressive mechanism is 0.5, the high-amplitude evolution ratio of processing code is 0.1, the low-amplitude evolution ratio of processing code is 0.05, the high-amplitude evolution ratio of assembly code is 0.2, and the low-amplitude evolution ratio of assembly code is 0.1.

[0078] S2.1.3: Construction of initial population; Since randomness will affect the quality of the randomly initialized population solution, a hybrid initial population generation method combining the population initialization strategy of the critical chain progressive mechanism and random initialization is adopted. The population initialization strategy of the critical chain progressive mechanism includes the following steps: First, based on the chromosome encoding (initially empty units) assigned to the workers, combined with the topological sorting of the tasks in the processing and assembly stages, the critical path task nodes of the processing and assembly stages are identified. Secondly, for each task node in the critical path, workers are randomly assigned, or suitable workers are selected from the predecessor tasks and transferred to the critical path nodes. Then, a conflict resolution mechanism is applied to eliminate personnel task conflicts to ensure that the generated chromosome encoding is a feasible solution. Finally, the above steps are repeated until there are no assignable workers in the worker pool. The random initialization strategy quickly generates feasible individuals by randomly selecting available workers from the resource pool and combining it with a conflict resolution algorithm.

[0079] S2.2: Population evolution; in the population evolution stage, the population evolution includes global search and local search, and the decision parameters of the global search include the high-amplitude evolution ratio of processing coding, the low-amplitude evolution ratio of processing coding, the high-amplitude evolution ratio of assembly coding and the low-amplitude evolution ratio of assembly coding; the local search is a resource reallocation strategy based on the critical path control mechanism.

[0080] S2.2.1: Global Search Operation: During the global search phase, four decision parameters are set: the proportion of high-magnitude evolution of the processing code, the proportion of low-magnitude evolution of the processing code, the proportion of high-magnitude evolution of the assembly code, and the proportion of low-magnitude evolution of the assembly code. These parameters determine the number of genetic loci to be evolved within the individual. The target wolf for the global search is represented by P1, the gray wolf individual to be evolved is represented by P2, and the evolved gray wolf individual is represented by O1. First, genetic loci to be evolved are randomly selected from the processing code and assembly code. Second, the genetic loci to be evolved from P1 are copied to P2. Finally, through the combination of a conflict resolution algorithm, the offspring individual O1 is generated, completing the evolution process.

[0081] S2.2.2: Local Search Operation. The local search phase introduces a resource reallocation strategy based on the critical path control mechanism. In each iteration, we first identify individual task nodes on the critical path and prioritize assigning idle workers from the resource pool to these critical task nodes. At the same time, workers assigned to non-critical paths can be reallocated to critical tasks through resource adjustments.

[0082] S2.3: Fitness value calculation; the fitness value calculation is based on the decoding strategy, and the fitness value of each chromosome in the population is calculated.

[0083] A semi-active decoding strategy is used to calculate the fitness of each chromosome. This strategy consists of two phases: the first phase involves encoding and decoding the workers during the processing phase. During this phase, the completion times of all parts are calculated sequentially based on the workers assigned to each process. The second phase involves encoding and decoding the workers during the assembly phase. During this phase, assembly begins when the parts supply, assembly workstations, and assembly sequence meet the assembly requirements according to the assembly sequence of each segment. Otherwise, the task continues to wait. Ultimately, the maximum of all segment assembly completion times is used as the fitness value of the chromosome.

[0084] S2.4: Termination judgment of the algorithm optimization; the termination judgment of the algorithm optimization determines whether the number of iterations has been reached. If so, the optimal solution set is output; otherwise, jump to S2.2.

[0085] The algorithm uses the following two stopping strategies to work together. As long as one of the stopping strategies is met, the algorithm stops calculating;

[0086] Stopping strategy 1: The maximum number of algorithm iterations is 100;

[0087] Stopping strategy 2: If no new optimal solution appears after more than 50 consecutive iterations, the algorithm converges.

[0088] The examples of this invention were constructed based on a random generation strategy. Two scales were designed for each stage: 15 and 20 workers for the processing stage, and 10 and 15 workers for the assembly stage. To evaluate operational efficiency, two levels were set, with random integers ranging from [0, 3] and [0, 5], respectively. A skill level of 0 indicates that a worker lacks the necessary skills to perform the task. By combining different numbers of workers and efficiency levels in the processing and assembly stages, 16 examples of different scales were generated.

[0089] At this point, the entire process of the personnel redistribution method for a ship block assembly workshop of the present invention is completed.

[0090] Based on the business characteristics of the personnel reallocation problem in ship block assembly workshops, this paper constructs a model for this problem. With minimizing completion time as the optimization objective, it transforms personnel attribute constraints and task priority constraints in the processing and assembly stages into mathematical model constraints. Secondly, the paper solves the scheduling problem for ship block assembly workshops based on an improved Grey Wolf Algorithm. This algorithm uses a two-layer coding structure to represent the complex relationship between personnel reallocation in the processing and assembly stages, establishes multiple decision variables to enhance the algorithm's solution capabilities, and employs a mixed population initialization strategy to improve the quality and diversity of the initial population. Furthermore, by combining a global search with a local search mechanism, the algorithm's solution efficiency and global optimization capabilities are effectively improved, thereby ensuring the generation of high-quality personnel reallocation solutions.

[0091] In order to verify the beneficial effects of the method of the present invention, the method of the present invention and other methods were compared and verified on 16 examples of different scales, and the solution curves were compared. Figure 2 As shown, the A-axis represents the instance number in the comparative verification, and the B-axis represents the job completion time, in minutes. The lower the B-axis value, the higher the job efficiency. Figure 2 The circular node curve refers to the basic grey wolf optimization algorithm, the triangular node curve refers to the genetic algorithm, the quadrilateral node curve refers to the simulated annealing algorithm, the pentagonal node curve refers to the elephant herd optimization algorithm, and the star node curve refers to the algorithm of the present invention.

[0092] The personnel redistribution method for ship block assembly workshops of the present invention is more in line with the actual personnel redistribution operation background of ship block assembly workshops, and the improved grey wolf algorithm proposed in the present invention has strong applicability. It can be seen that the method proposed in the present invention is of great significance for guiding the personnel redistribution of ship block assembly workshops.

[0093] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present invention, within the spirit and principles of the present invention, without departing from the content of the technical solution of the present invention, shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for redistributing personnel in a ship block assembly workshop, characterized by: The method for redistributing personnel in the ship block assembly workshop is achieved by the following steps: S1: Construct a model for personnel redistribution in ship block assembly workshops; S2: Solve the model constructed in S1 based on the improved grey wolf algorithm to obtain the optimal allocation method.

2. A method for redistributing personnel in a ship block assembly workshop according to claim 1, characterized in that: The model for constructing the personnel redistribution problem in the ship block assembly workshop described in S1 includes the following steps: S1.1: Construct an optimization objective for redistributing personnel in the assembly workshop to minimize completion time; S1.2: Convert personnel attribute constraints into mathematical model constraints; S1.3: Convert the task priority constraints of the processing and assembly stages into mathematical model constraints.

3. A method for redistributing personnel in a ship block assembly workshop according to claim 2, characterized in that: The optimization objectives described in S1.1 are specifically: In formula (1), f is the optimization target, P is the segment set, p is the segment index value, and B p It represents the completion time of the segment corresponding to p, min represents minimization, and max represents maximization.

4. The method for redistributing personnel in a ship block assembly workshop according to claim 2, characterized in that: The conversion of personnel attribute constraints into mathematical model constraints as described in S1.2 specifically includes: With wa ≤c wa ,w∈W,a∈T a (5) In formulas (2) and (3), it is constrained that during the processing and assembly stages, each operator has multiple operating skills and their operating efficiency varies when working on different processing machines or assembly workstations. Here, M is the set of processing machines, m is the machine index value, and T r is the set of workers assigned to the processing stage, r is the index value of the processing worker, W is the set of assembly workstations, w is the workstation index value, T a is the set of workers assigned to the assembly stage, a is the index value of the assembly worker, χ mr is the skill level of the processing operator corresponding to r when processing machine m, χ wa is the skill level of the assembly operator corresponding to a at assembly workstation w. When the skill level is 0, it means that the operator does not master the operation skills of the corresponding equipment or workstation; In formula (4) and formula (5), it is constrained that during the processing and assembly stages, workers can only be assigned to machines or workstations with corresponding operating capabilities, where C p is the segmented processing parts set corresponding to p, c is the processing parts index value, O cp For the processing parts set C p Where c corresponds to the process set of the part, o is the process index value, z mr represents the state variable. When the processing worker corresponding to r is assigned to the processing machine m, then z mr is 1, otherwise 0, c mr Represents the state variable. When the processing operator corresponding to r has the ability to operate the processing machine m, then c mr is 1, otherwise 0, z wa represents the state variable. When the assembly worker corresponding to a is assigned to workstation w, then z wa is 1, otherwise 0, c wa represents the state variable. When the assembly worker corresponding to a has the ability to operate workstation w, then c wa is 1, otherwise 0; In formula (6) and formula (7), it is constrained that during the processing stage, the processing workers can only perform one task at a time, where K r is the set of tasks executed by the processing personnel corresponding to r, and k is the set of tasks executed K r The location of the event; r Is the maximum index value of the event position in the execution task set. ocprk Represents the state variable. When the operation corresponding to the processing part o corresponding to the segment c corresponding to p is the kth event in the task set executed by the processing personnel corresponding to r, then X ocprk is 1, otherwise it is 0, X ocpr,k+1 Represents the state variable. When the operation corresponding to the processing part o corresponding to the segment c corresponding to p is the k+1th event in the task set executed by the processing personnel corresponding to r, then X ocpr,k+1 is 1, otherwise 0; In formula (8) and formula (9), it is constrained that during the assembly phase, the assembly workers can only perform one task at a time, where K a is the set of tasks performed by the assembly personnel corresponding to a, H a is the set of tasks K a The maximum index value of the event position in X pak Represents the state variable. When the segment corresponding to p is the kth event in the set of tasks performed by the assembly personnel corresponding to a, then X pak is 1, otherwise it is 0, X pa,k+1 represents the state variable. When the segment corresponding to p is the k+1th event in the set of tasks performed by the assembly personnel corresponding to a, then X pa,k+1 is 1 if the value is set, otherwise it is 0.

5. The method for redistributing personnel in a ship block assembly workshop according to claim 2, characterized in that: The conversion of the task priority constraints of the processing and assembly stages into mathematical model constraints as described in S1.3 specifically includes: In formula (10), the premise that the assembly workstation can carry out assembly work is that the required parts have been processed. cp | is the process set O cp The last process index value in the assembly process, T is the assembly segment sequence set, t is the assembly segment sequence set index value, b cpw Represents the state variable, when the processing parts set C p When the part corresponding to c is assembled on the workstation corresponding to w, then b cpw =1, otherwise b cpw =0, is the process set O cp The process completion time corresponding to o, represents the time when the segment corresponding to t starts to be assembled on the workstation corresponding to w; In formula (11), the premise for the segment to start the assembly operation at a workstation is that the segment has completed the assembly operation at the previous workstation and no segment has stopped at the workstation. In formula (12), the premise for the segment to transfer between workstations is that the segment has completed the assembly operation at the current workstation and no segment has stopped at the next workstation. N is the maximum index value of the assembly workstation set W, and I is the maximum index value of the assembly segment sequence set T. represents the end time of the assembly segment corresponding to t at the workstation corresponding to w, represents the end time of the assembly segment corresponding to t at the workstation corresponding to w-1; represents the departure time of the assembly segment corresponding to t at the workstation corresponding to w, represents the departure time of the assembly segment corresponding to t-1 at the workstation corresponding to w, It represents the departure time of the assembly segment corresponding to t-1 at the workstation corresponding to w+1.

6. The method for redistributing personnel in a ship block assembly workshop according to claim 1, characterized in that: Solving the constructed model based on the improved grey wolf algorithm described in S2 includes the following steps: S2.1: Population initialization; the population initialization includes chromosome coding design, decision parameter setting and initial population construction; the chromosome coding design constructs a double-layer chromosome coding structure suitable for the personnel redistribution problem in the ship segment assembly workshop, which is used to optimize the allocation of workers in the processing stage and the assembly stage; the decision parameter setting is used to improve the solving ability; the initial population is constructed as a hybrid initial population generation method that combines the population initialization strategy of the critical chain progressive mechanism with random initialization. S2.2: Population evolution; the population evolution includes global search and local search, and the decision parameters of the global search include the high-amplitude evolution ratio of processing coding, the low-amplitude evolution ratio of processing coding, the high-amplitude evolution ratio of assembly coding and the low-amplitude evolution ratio of assembly coding; the local search is a resource reallocation strategy based on the critical path control mechanism. S2.3: Fitness value calculation; the fitness value calculation is based on the decoding strategy, and the fitness value of each chromosome in the population is calculated; S2.4: Termination judgment of the algorithm optimization; the termination judgment of the algorithm optimization determines whether the number of iterations has been reached. If so, the optimal solution set is output; otherwise, jump to S2.

2.

7. The method for redistributing personnel in a ship block assembly workshop according to claim 6, characterized in that: The hybrid initial population generation method combining the population initialization strategy of the critical chain progressive mechanism for initial population construction described in S2.1 with the random initialization strategy specifically includes: Population initialization strategy of critical chain progressive mechanism: a. Based on the chromosome codes assigned to operators and combined with the topological sorting of tasks in the processing and assembly stages, identify the critical path task nodes in the processing and assembly stages; b. For each task node in the critical path, randomly assign operators or select suitable operators from the previous tasks and transfer them to the critical path node; c. Apply conflict resolution mechanisms to eliminate conflicts between personnel and tasks and ensure that the generated chromosomes are encoded as feasible solutions; d. Repeat the above steps until there are no more workers to assign to the worker pool; Random initialization strategy: By randomly selecting available workers from the resource pool and combining it with a conflict resolution algorithm, feasible individuals are quickly generated. The population initialization strategy of the critical chain progressive mechanism and the random initialization strategy constitute a mixed initial population.

8. The method for redistributing personnel in a ship block assembly workshop according to claim 6, characterized in that: The specific process of the global search for population evolution described in S2.2 is as follows: The target wolf of the global search is represented as P1, the gray wolf individual to be evolved is represented as P2, and the evolved gray wolf individual is represented as O1. First, the gene sites to be evolved are randomly selected in the processing code and assembly code; secondly, the gene sites to be evolved in P1 are copied to P2; finally, by combining the conflict resolution algorithm, the offspring O1 individual is generated, thus completing the evolution process.

9. The method for redistributing personnel in a ship block assembly workshop according to claim 6, characterized in that: The specific calculation process of the fitness value described in S2.3 is as follows: A semi-active decoding strategy is used to calculate the fitness value of each chromosome, which includes two stages: the first stage is the encoding and decoding of the operators in the processing stage. During this process, the completion time of all parts is calculated in sequence based on the processing personnel assigned to each process; the second stage is the encoding and decoding of the operators in the assembly stage. In this stage, according to the assembly sequence of each segment, when the parts supply, assembly workstation and assembly sequence meet the assembly requirements, the assembly begins; otherwise, the task needs to continue waiting; finally, the maximum value of the assembly completion time of all segments is used as the fitness value of the chromosome.

10. The method for redistributing personnel in a ship block assembly workshop according to claim 6, characterized in that: In the termination judgment of the algorithm optimization described in S2.4, the algorithm adopts the combined effect of stopping strategy 1 and stopping strategy 2. The stopping strategy 1 sets the maximum number of algorithm iterations to 100 times; the stopping strategy 2 sets the algorithm to converge if no new optimal solution appears after more than 50 consecutive iterations; as long as one of the two stopping strategies is met, the algorithm stops calculating.

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