A flexible job-shop scheduling method considering worker behavior factors

Abstract

This invention belongs to the field of intelligent scheduling technology for workshop production, and particularly relates to a flexible workshop scheduling method that considers worker behavior factors. The method includes: S1, acquiring workshop production information required to construct a scheduling model; S2, establishing a flexible workshop scheduling model based on the workshop production information to generate a scheduling scheme that includes processing machines, operators, start times, and rework arrangements for critical processes; S3, solving the scheduling model using an improved non-dominated sorting genetic algorithm III to obtain a Pareto optimal scheduling scheme set; and S4, comprehensively evaluating the Pareto optimal scheduling scheme set based on the analytic hierarchy process (AHP) and entropy weight method to determine the final scheduling scheme. This method can effectively integrate the impact of worker behavior factors on processing time and quality in flexible workshop scheduling, synergistically optimizing the maximum completion time, total workshop energy consumption, and total worker cost, thereby generating an efficient, energy-saving, economical, and executable scheduling scheme.

Description

Technical Field

[0001] This invention belongs to the field of intelligent scheduling technology for workshop production, and particularly relates to a flexible workshop scheduling method that takes into account worker behavior factors. Background Technology

[0002] To adapt to the increasingly diversified and personalized market demands, highly flexible multi-variety, small-batch production models have become the mainstream choice for global manufacturing enterprises. Against this backdrop, the Flexible Job Shop Scheduling Problem (FJSP) has attracted widespread attention due to its ability to flexibly allocate processes to multiple available machines. However, in actual production environments, especially in precision manufacturing and customized assembly scenarios, despite continuous improvements in automation levels, many critical processes still heavily rely on manual operation. Workers not only participate in equipment operation but also play an irreplaceable role in process adjustment, anomaly handling, and quality control. Therefore, FJSP that only considers machine resources is insufficient to meet real-world needs, and the Dual-Resource Constrained FJSP (DRCFJSP)—which simultaneously considers the collaborative constraints of machines and operators—has gradually become a research hotspot. Due to the introduction of workers as a dynamic, heterogeneous resource with behavioral uncertainty, the solution space of DRCFJSP is significantly expanded, and its complexity far exceeds that of traditional FJSP, classifying it as a typical NP-hard problem.

[0003] Currently, manufacturing enterprises face three core demands: improving processing efficiency to shorten delivery cycles, ensuring product quality to enhance market competitiveness, and controlling operating costs to respond to the trend of green and low-carbon development. To this end, scheduling optimization objectives are gradually shifting from solely pursuing the minimization of maximum completion time (makespan) to multi-objective collaborative optimization that considers energy consumption, labor costs, and quality stability. It is particularly noteworthy that workers, as the core active element in the production system, directly influence processing time, energy consumption, and even product quality through their skill level, fatigue level, and operating habits. For example, experienced workers may achieve shorter processing times and higher pass rates on the same equipment, while fatigue or emotional fluctuations may lead to decreased efficiency or even rework.

[0004] However, most existing DRCFJSP studies simplify workers into static, homogeneous "resource units," considering only their availability or skill level, and fail to effectively model the actual impact of their dynamic behavior on the processing. At the same time, quality feedback mechanisms for key processes (such as rework strategies for non-conforming products) are often ignored or simplified, causing scheduling schemes to deviate from expectations in actual implementation.

[0005] Therefore, how to effectively integrate the impact of worker behavior factors on processing time and quality in flexible workshop scheduling, and collaboratively optimize the maximum completion time, total workshop energy consumption, and total worker cost to generate an efficient, energy-saving, economical, and executable scheduling scheme has become an urgent problem to be solved. Summary of the Invention

[0006] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a flexible job shop scheduling method that considers worker behavior factors. This method effectively integrates the impact of worker behavior factors on processing time and quality in flexible job shop scheduling, and collaboratively optimizes the maximum completion time, total workshop energy consumption, and total worker costs, thereby generating an efficient, energy-saving, economical, and executable scheduling scheme.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] A flexible job shop scheduling method that considers worker behavior factors includes the following steps:

[0009] S1. Obtain the shop floor production information required to build the scheduling model, including:

[0010] Information on the available processing machines for each process and the available operators for each machine;

[0011] Parameters used to quantify the impact of worker behavior on processing time;

[0012] Energy consumption parameters used to calculate total energy consumption in the workshop and wage parameters used to calculate total worker costs;

[0013] Key process identifiers, corresponding quality acceptance thresholds, and quality assessment parameters used to evaluate the processing quality of key processes;

[0014] S2. Based on the workshop production information obtained in S1, establish a scheduling model for the flexible operation workshop to generate a scheduling scheme that includes processing machines, operators, start times, and rework arrangements for key processes for each process.

[0015] The scheduling model aims to minimize the maximum completion time, total workshop energy consumption, and total worker cost simultaneously. It integrates workpiece AGV transportation time constraints, machine and worker exclusivity constraints, and a rework mechanism that allows the same machine and worker originally assigned to perform secondary processing for critical processes that fail to meet quality standards.

[0016] S3. The improved non-dominated sorting genetic algorithm III is used to solve the scheduling model established in S2 to obtain the Pareto optimal scheduling scheme set.

[0017] The improvements include: using a hybrid initialization strategy to generate the initial population, introducing a multi-rule-based global redistribution strategy during the evolution process, performing local search with an embedded simulated annealing mechanism on elite individuals, and using an elite retention strategy based on a reference point association mechanism with dynamic external archives and PBI distance.

[0018] S4. Based on the analytic hierarchy process and the entropy weight method, a comprehensive evaluation is performed on the Pareto optimal scheduling scheme set obtained in S3 to determine the final scheduling scheme.

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] 1. More realistically reflects the actual production process. Unlike existing methods that typically treat workers as static, homogeneous resources, this solution introduces parameters that quantify the impact of worker behavior on processing time. Combined with a quality assessment mechanism for key processes, this enables the scheduling model to dynamically reflect the actual impact of operator skills, status, and other behavioral factors on efficiency and quality, significantly improving the model's real-world fit and the feasibility of the scheduling scheme.

[0021] 2. Achieve multi-objective collaborative optimization. Traditional scheduling methods often focus on minimizing the maximum completion time, while this solution simultaneously optimizes three major objectives: maximum completion time, total workshop energy consumption, and total labor cost. It ensures production efficiency while taking into account green manufacturing and labor cost control, breaking through the limitations of single-objective or dual-objective optimization and better meeting the needs of modern manufacturing enterprises to maximize comprehensive benefits.

[0022] 3. Effectively ensures the quality of key processes. By embedding a quality closed-loop mechanism for rework performed by the original machines and workers, this solution avoids secondary errors or learning costs caused by arbitrarily changing resources. Compared with existing methods that ignore rework or adopt general rework strategies, it can more reliably maintain the processing consistency and pass rate of key processes.

[0023] 4. Improve the performance and robustness of the solution algorithm. The improved non-dominated sorting genetic algorithm III integrates hybrid initialization, multi-rule global redistribution, simulated annealing local search, and dynamic reference point elite retention mechanism. While maintaining population diversity, it accelerates convergence. Compared with the standard multi-objective evolutionary algorithm, it can explore the high-dimensional and strongly constrained solution space more efficiently and obtain a uniformly distributed Pareto optimal solution set that approximates the real solution.

[0024] 5. Enhance the scientific rigor and objectivity of the final decision. In the scheme selection stage, the analytic hierarchy process (AHP) and entropy weight method are combined to achieve a comprehensive evaluation that integrates subjective and objective weights. This overcomes the one-sidedness of a single weighting method and makes the final selected scheduling scheme more adaptable and reliable.

[0025] In summary, this method can effectively integrate the impact of worker behavior factors on processing time and quality in flexible workshop scheduling, and collaboratively optimize the maximum completion time, total workshop energy consumption, and total worker cost, thereby generating an efficient, energy-saving, economical, and executable scheduling scheme.

[0026] Preferably, in S1, the parameters used to quantify the impact of worker behavior on processing time include: the skill level coefficient of the worker operating each machine, the worker's initial processing capability for different workpieces, learning ability, and capability ceiling.

[0027] This setup, by introducing parameters such as the skill level coefficient of workers operating each machine, the initial processing capacity for different workpieces, learning ability, and capacity limit, can dynamically reflect the actual processing efficiency of workers in different task situations. It avoids the scheduling deviation caused by the traditional method of simplifying workers into homogeneous resources, and makes the processing time prediction closer to actual production.

[0028] 2. By considering the learning ability and upper limit of workers, the model can not only reflect the current state, but also predict the efficiency improvement trend in repetitive or similar tasks. This allows for the rational use of the learning effect in task allocation and optimization of long-term work arrangements. This is especially crucial in multi-variety, small-batch production and is significantly better than static scheduling methods that ignore dynamic changes in human factors.

[0029] Preferably, in S1, the quality assessment parameters used to evaluate the processing quality of key processes include: the processing accuracy of each machine and the stability coefficient of the worker operating each machine.

[0030] This setup, which models both the inherent precision of the machine and the stability of worker operation, can more accurately predict the processing quality level of key processes. This proactively avoids the risk of assigning high-precision processes to low-stability human-machine combinations during the scheduling phase. Compared to traditional methods that rely solely on equipment parameters or ignore human factors, it significantly improves quality assurance capabilities.

[0031] Preferably, in S3, the improved non-dominated sorting genetic algorithm III solves the scheduling model, including the following steps:

[0032] S3.1: A four-layer coding structure is used to encode individuals in the population. The four layers are the process sorting layer, the machine selection layer, the worker selection layer, and the process rework layer. An initial population is generated based on a hybrid initialization strategy.

[0033] S3.2: Calculate the objective function values ​​of the three optimization objectives for each scheduling scheme in the current population;

[0034] S3.3: During the evolution process, a global redistribution strategy based on multiple rules is introduced to dynamically adjust the resource allocation between machines and workers;

[0035] S3.4: Select elite individuals from the current population and perform a local search on them using an embedded simulated annealing mechanism;

[0036] S3.5: An elite retention strategy based on a reference point association mechanism using dynamic external archives and PBI distance is adopted to generate the next generation population;

[0037] S3.6: Iteratively execute the evolutionary operations from S3.2 to S3.5 until the preset termination condition is met, and output the Pareto optimal scheduling scheme set.

[0038] This setup effectively supports the collaborative optimization of complex scheduling elements. Employing a four-layer coding structure encompassing process sequencing, machine selection, worker selection, and rework arrangement, it can completely and conflict-free express multi-dimensional coupled decision-making information related to people, machines, tasks, quality, and rework in flexible work workshops. Combined with a hybrid initialization strategy, it significantly improves the diversity and feasibility of initial solutions, overcoming the limitations of traditional coding methods that struggle to simultaneously handle dual resource constraints and rework logic.

[0039] 2. Balancing global exploration and local refinement capabilities. The algorithm enhances the global search capability of the population in high-dimensional solution spaces through multi-rule global redistribution, while simultaneously performing local deep optimization of the elite individual embedding simulated annealing mechanism. This effectively balances the algorithm's exploration and development, avoiding premature convergence. Furthermore, the reference point association mechanism based on dynamic external archives and PBI distance further ensures the convergence and uniformity of the Pareto front, outperforming standard algorithms such as NSGA-III on complex DRCFJSP problems.

[0040] Preferably, in S3.3, the multi-rule-based global redistribution strategy includes the following four redistribution operators:

[0041] Machine load balancing operator: Reassign any operation on the machine with the largest sum of actual processing times of currently assigned operations to the machine with the smallest sum of actual processing times of currently assigned operations, and assign the machine with the highest skill level available worker.

[0042] Worker load balancing operator: Reassign any process handled by the worker with the largest sum of actual processing time of currently assigned processes to the worker whose corresponding machine is available and whose sum of actual processing time of currently assigned processes is the smallest.

[0043] Operator that triggers the learning effect: Assigns the last process of a certain workpiece to the worker who has processed the workpiece the most times in the current scheduling scheme;

[0044] Avoiding rework in critical processes: During the scheduling scheme generation phase, if the expected processing quality of a critical process is lower than its corresponding quality qualification threshold, the process will be reassigned to the available machine-worker combination with the highest expected processing quality to avoid triggering the rework mechanism.

[0045] This setup offers several advantages: 1. It improves the balance and efficiency of the scheduling scheme. Machine load balancing and worker load balancing effectively alleviate the problem of uneven workload caused by uneven resource allocation in traditional scheduling, preventing individual machines or workers from becoming bottlenecks. This improves the overall process smoothness without increasing additional costs, and is more system-coordinated than existing methods that rely solely on random or greedy allocation.

[0046] 2. Proactively integrate human factors and dynamic characteristics to enhance solution quality and economy. By stimulating learning effects in operations and making reasonable use of workers' repeated processing experience on specific workpieces, the time for subsequent processes is shortened. At the same time, rework operations in critical processes are avoided by optimizing human-machine combinations in advance based on quality prediction, reducing the probability of rework from the source. These two strategies explicitly integrate human learning ability and quality stability into scheduling decisions, which not only reduces total cost and energy consumption but also improves delivery reliability, breaking through the limitations of traditional methods that passively respond to quality problems.

[0047] This multi-rule global redistribution mechanism organically combines load balancing, human factor learning, and quality prevention. During the evolutionary process, it continuously guides the population to evolve towards more efficient, robust, and economical solutions, significantly enhancing the algorithm's adaptability and practical value in complex human-machine collaborative environments.

[0048] Preferably, in S3.4, in the local search of the embedded simulated annealing mechanism, a new solution is generated using a neighborhood structure corresponding to the optimization objective.

[0049] This setup enables refined local optimization guided by multiple objectives, significantly improving the quality of elite individuals while maintaining solution diversity, and providing key support for obtaining a Pareto optimal solution set with high convergence and high distribution.

[0050] Preferably, the neighborhood structure includes the following three types:

[0051] Neighborhood structure oriented towards maximum completion time: Adjust the machine-worker allocation of operations on the critical path that directly affects completion time, or swap the order of operations within subsequences of operations that are processed consecutively on the same machine in the sequence;

[0052] Neighborhood structure oriented towards total workshop energy consumption: reallocate the processes on the machine with the highest energy consumption per unit time to the machine with lower energy consumption per unit time that is available for the process, or adjust the processes involving machine changes to be processed on the same machine as the previous process to reduce AGV transportation.

[0053] Neighborhood structure oriented towards total worker cost: the process performed by the worker with the highest total cost per unit time is reassigned to the available worker with the lower total cost per unit time on the same machine.

[0054] This setup, by constructing dedicated neighborhood operations for maximum completion time, total shop floor energy consumption, and total labor cost, allows local searches to directly impact key decision variables affecting the corresponding objectives. For example, it can compress the project duration by adjusting the sequence of processes or resource allocation on the critical path, reduce energy consumption by reallocating tasks on energy-intensive machines or reducing AGV transportation, and control labor costs by replacing high-cost workers. This goal-oriented perturbation mechanism avoids the blind search problem of traditional general neighborhood operations, significantly improving optimization efficiency.

[0055] Preferably, in the scheduling model, the actual processing time of the process is dynamically calculated based on the parameters used to quantify the impact of worker behavior on processing time, so that the efficiency of the same worker in subsequent processing of the same workpiece is improved due to the learning effect, and the efficiency improvement is constrained by its initial processing capacity and capacity limit.

[0056] Unlike existing methods that typically assume fixed processing time or rely solely on static skill levels, this approach allows the same worker to shorten processing time due to the learning effect when repeatedly processing the same or similar workpieces. Simultaneously, it reasonably constrains learning gains through initial processing capacity and capacity limits, avoiding overly optimistic estimations. This enables scheduling to proactively leverage the efficiency benefits of accumulated experience, optimizing task allocation order and resource matching, making it particularly suitable for scenarios with repetitive tasks in small batches of diverse products.

[0057] Preferably, for critical processes that fail to meet quality standards, the secondary processing time is recalculated based on the actual time of the initial processing and a preset rework coefficient.

[0058] This setup, by dynamically calculating the secondary processing time of key processes based on the initial actual processing time and a preset rework coefficient, makes the time estimation for the rework process more closely match the actual production situation. It takes into account the potential efficiency improvement of the original operators due to experience accumulation during repeated processing, and reasonably reflects the additional time costs of debugging, testing, or careful operation that usually occur in rework operations through the rework coefficient, avoiding the crude assumption of simply equating the rework time with the initial processing time or a fixed value.

[0059] Preferably, the scheduling model also integrates the following constraints:

[0060] Priority constraints between workpiece processes: the subsequent process can only begin after the preceding process is completed and the AGV transportation time is taken into account.

[0061] The exclusive constraint of machines and workers means that at any given time, a machine can only process one operation and a worker can only operate one machine.

[0062] Rework constraints for critical processes: rework must be performed by the same machine and the same worker originally assigned, and subsequent processes can only begin after the rework is completed.

[0063] This setup clearly defines the sequential logic between workpiece processes and AGV transport delays, ensuring process compliance; it strictly adheres to the exclusivity of machines and workers to avoid resource conflicts; and it stipulates that rework of critical processes must be completed by the original human-machine combination, ensuring processing consistency and preventing secondary quality issues caused by arbitrary resource changes. Compared to simplified models that ignore transport time and allow multiple machines to share resources or arbitrarily allocate rework, this solution is closer to actual workshop operating rules, significantly reducing the risk that a scheduling plan may be theoretically feasible but difficult to implement on-site. Attached Figure Description

[0064] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0065] Figure 1 This is a flowchart of the method;

[0066] Figure 2 This is a flowchart of the flexible workshop scheduling method that considers worker behavior factors in Example 1;

[0067] Figure 3 This is a schematic diagram of the encoding in Example 1;

[0068] Figure 4 This is a schematic diagram of the crossover operator in MS and WS in Example 1;

[0069] Figure 5 This is a schematic diagram of the mutation operators in MS and WS in Example 1;

[0070] Figure 6 This is a flowchart of the local search in Example 1;

[0071] Figure 7 This is a schematic diagram of the transformation of the neighborhood structure 4 in Example 1;

[0072] Figure 8 Box plots of IGD for different algorithms in Example 2;

[0073] Figure 9 HV box plots for different algorithms in Example 2;

[0074] Figure 10 This is an example of a scheduling Gantt chart under the non-dominated sorting genetic algorithm III proposed in this invention, as shown in Example 2. Detailed Implementation

[0075] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0076] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 a part of the embodiments of the present invention, not all of them. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0077] It should be noted that similar reference numerals and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the figures, or the orientation or positional relationship commonly used when the product is in use. They are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance. In addition, the terms "horizontal," "vertical," etc., do not indicate that the component is required to be absolutely horizontal or suspended, but can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; 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; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0078] Example 1

[0079] like Figure 1 As shown, this invention provides a flexible workshop scheduling method that considers worker behavior factors, comprising the following steps:

[0080] S1. Obtain the shop floor production information required to build the scheduling model, including:

[0081] Information on the available processing machines for each process and the available operators for each machine;

[0082] Parameters used to quantify the impact of worker behavior on processing time;

[0083] Energy consumption parameters used to calculate total energy consumption in the workshop and wage parameters used to calculate total worker costs;

[0084] Key process identifiers, corresponding quality acceptance thresholds, and quality assessment parameters used to evaluate the processing quality of key processes.

[0085] In practical implementation, the parameters used to quantify the impact of worker behavior on processing time include: the skill level coefficient of the worker operating each machine, the worker's initial processing capacity for different workpieces, learning ability, and capacity ceiling. By introducing parameters such as the worker's skill level coefficient for each machine, initial processing capacity for different workpieces, learning ability, and capacity ceiling, the actual processing efficiency of workers under different task scenarios can be dynamically reflected. This avoids the scheduling bias caused by the traditional method of simplifying workers as homogeneous resources, making the processing time prediction closer to actual production. Furthermore, considering the worker's learning ability and capacity ceiling allows the model to not only reflect the current state but also predict its efficiency improvement trend in repetitive or similar tasks. This enables the rational use of learning effects in task allocation and optimization of long-term job arrangements, which is particularly crucial in multi-variety, small-batch production and significantly outperforms static scheduling methods that ignore dynamic changes in human factors.

[0086] In specific implementation, in S1, the quality assessment parameters used to evaluate the processing quality of key processes include: the processing accuracy of each machine and the stability coefficient of the worker operating each machine. The processing accuracy is the error range of a machine processing a specific workpiece, and the stability coefficient is the stability index of a worker operating a specific machine. Jointly modeling the inherent accuracy of the machines and the stability of worker operation allows for a more accurate prediction of the processing quality level of key processes. This proactively avoids the risk of assigning high-precision processes to low-stability human-machine combinations during the scheduling phase, significantly improving quality assurance capabilities compared to traditional methods that rely solely on equipment parameters or ignore human-caused fluctuations.

[0087] S2. Based on the workshop production information obtained in S1, establish a scheduling model for the flexible operation workshop to generate a scheduling scheme that includes processing machines, operators, start times, and rework arrangements for key processes for each process.

[0088] The scheduling model aims to minimize the maximum completion time, total workshop energy consumption, and total worker cost simultaneously. It integrates workpiece AGV transportation time constraints, machine and worker exclusivity constraints, and a rework mechanism that allows critical processes with unqualified quality to be reprocessed by the same machine and worker originally assigned.

[0089] In practical implementation, the actual processing time of a process in the scheduling model is dynamically calculated based on the parameters used to quantify the impact of worker behavior on processing time. This allows the efficiency of subsequent processing of the same workpiece by the same worker to improve due to the learning effect, and the efficiency improvement is constrained by the worker's initial processing capacity and capacity limit. The dynamic calculation is based on the worker's skill level coefficient for operating the machine, the worker's learning ability for different workpieces, and the capacity limit. Thus, unlike existing methods that typically assume fixed processing time or rely solely on static skill levels, this scheme allows the same worker to shorten processing time due to the learning effect when repeatedly processing the same or similar workpieces. Simultaneously, it reasonably constrains the learning gains through initial processing capacity and capacity limit, avoiding overly optimistic estimations. This enables the scheduling arrangement to proactively utilize the efficiency benefits brought by accumulated experience, optimizing task allocation order and resource matching, and is particularly suitable for scenarios with repetitive operations in multi-variety, small-batch production.

[0090] For critical processes that fail to meet quality standards, the secondary processing time is recalculated based on the actual time of the initial processing and a preset rework coefficient. This rework coefficient is a preset empirical value used to adjust the secondary processing time. By dynamically calculating the secondary processing time of critical processes based on the initial actual processing time and the preset rework coefficient, the time estimation for the rework process more closely reflects the actual production situation. This approach considers the potential efficiency improvement of the original operators due to accumulated experience during rework, and also reasonably reflects the additional time costs typically associated with rework operations, such as debugging, testing, or careful operation, through the rework coefficient. It avoids the crude assumption of simply equating the rework time with the initial processing time or a fixed value.

[0091] In practice, the scheduling model also integrates the following constraints:

[0092] Priority constraints between workpiece processes: the subsequent process can only begin after the preceding process is completed and the AGV transportation time is taken into account.

[0093] The exclusive constraint of machines and workers means that at any given time, a machine can only process one operation and a worker can only operate one machine.

[0094] Rework constraints for critical processes: rework must be performed by the same machine and the same worker originally assigned, and subsequent processes can only begin after the rework is completed.

[0095] This approach clearly defines the sequential logic between workpiece processes and AGV transport delays, ensuring process compliance; strictly adheres to the exclusivity of machines and workers to avoid resource conflicts; and stipulates that rework of critical processes must be completed by the original human-machine combination, ensuring processing consistency and preventing secondary quality issues caused by arbitrary resource changes. Compared to simplified models that ignore transport time and allow multiple machines to share resources or arbitrarily allocate rework, this solution is closer to actual workshop operating rules, significantly reducing the risk that a scheduling plan may be theoretically feasible but difficult to implement on-site.

[0096] To facilitate a better understanding of the scheduling model in this method by those skilled in the art, the following explanation is provided.

[0097] Table 1. Parameter Description in the Scheduling Model

[0098]

[0099]

[0100] The mathematical model constructed based on the mixed integer programming method is as follows:

[0101] Taking into account differences in worker skill levels, learning effects, and rework mechanisms, the actual processing time for each process is:

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] The objective function of the scheduling model is:

[0108]

[0109]

[0110]

[0111] The constraints of the scheduling model include:

[0112]

[0113]

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] Equation (9) means that the end processing time of any workpiece shall not exceed the maximum completion time; Equation (10) means that any process can only be processed by one worker and one machine; Equation (11) means that any process, especially the current worker controlling the current machine processing is continuous without interruption ; Equation (12) means that there is a priority constraint relationship between different processes of the same workpiece; Equation (13) means that at the same time, a machine can only process one process at most; Equation (14) means that at the same time, a worker can only process one process; Equation (15) represents the process The processing quality calculation process; Equation (16) indicates that the machines and workers for the secondary processing of the process are the same as those for the first process; Equation (17) indicates that if the process is the same If the quality is unqualified, it will be reworked immediately for secondary processing; equation (18) means that the rework process meets the sequence constraints of the process.

[0123] S3. Use the improved non-dominated sorting genetic algorithm III (INSGA-III) to solve the scheduling model established in S2 and obtain the Pareto optimal scheduling scheme set;

[0124] The improvements include: using a hybrid initialization strategy to generate the initial population, introducing a multi-rule-based global redistribution strategy during the evolutionary process, performing local search with an embedded simulated annealing mechanism on elite individuals, and employing an elite retention strategy based on a reference point association mechanism with dynamic external archives and PBI distance.

[0125] In practice, the improved non-dominated sorting genetic algorithm III solves the scheduling model, including the following steps:

[0126] S3.1: A four-layer coding structure is used to encode individuals in the population. The four layers are the process sequencing layer, machine selection layer, worker selection layer, and process rework layer. An initial population is generated based on a hybrid initialization strategy. In specific implementation, the hybrid initialization strategy includes the following rules: the machine selection layer and the worker selection layer include the minimum processing time resource allocation rule, the global search rule for machine load, the global search rule for worker load, and a random rule; the process sequencing layer includes the shortest process processing time rule, the longest remaining workpiece processing time rule, and a random rule; the process rework layer is initialized based on the machine selection layer and the worker selection layer.

[0127] S3.2: Calculate the objective function values ​​of the three optimization objectives for each scheduling scheme in the current population;

[0128] S3.3: During the evolution process, a global redistribution strategy based on multiple rules is introduced to dynamically adjust the resource allocation between machines and workers;

[0129] S3.4: Select elite individuals from the current population and perform a local search on them using an embedded simulated annealing mechanism; wherein, 20% of the individuals are selected as elite individuals from the non-dominant frontier of the current population. In specific implementation, those skilled in the art can set other proportions according to actual needs, which will not be elaborated here.

[0130] S3.5: An elite retention strategy based on a reference point association mechanism using dynamic external archiving and PBI distance is adopted to generate the next generation population. In specific implementation, an improved elite retention strategy is adopted to generate the next generation population, which is as follows: a dynamically updated external library is established to archive the associated individuals with the minimum vertical distance for each reference point, and these individuals are directly retained to the next generation; for the remaining required individuals, a reference point association mechanism based on PBI distance is introduced, and the individuals with the largest PBI distance are eliminated from the non-dominated layer until the preset population size is reached, thereby balancing the diversity and convergence of the population.

[0131] S3.6: Iteratively execute the evolutionary operations from S3.2 to S3.5 until the preset termination condition is met, and output the Pareto optimal scheduling scheme set.

[0132] Employing a four-layer coding structure encompassing process sequencing, machine selection, worker selection, and rework arrangement, this approach can comprehensively and conflict-free express multi-dimensional coupled decision-making information related to human-machine-task-quality rework in flexible workshops. Combined with a hybrid initialization strategy, it significantly enhances the diversity and feasibility of initial solutions, overcoming the limitations of traditional coding methods that struggle to simultaneously handle dual resource constraints and rework logic. Furthermore, a multi-rule global redistribution strategy enhances the population's global search capability in high-dimensional solution spaces, while local deep optimization of the elite individual embedding simulated annealing mechanism effectively balances algorithm exploration and development, preventing premature convergence. Coupled with a reference point association mechanism based on dynamic external archives and PBI distance, it further ensures the convergence and uniformity of the Pareto front, outperforming standard algorithms such as NSGA-III on complex DRCFJSP problems.

[0133] In specific implementation, in S3.1: each individual in the population uses a four-layer coding method, with the length of each layer equal to the total number of processes. Process ordering layer: each number represents the workpiece number, and the frequency of each number represents the process number. The machine selection layer, worker selection layer, and process rework layer all arrange the workpiece processes sequentially from left to right: in the machine selection layer, each number is the sequential index of the machine selected for the corresponding process from the available machine set; the worker selection layer is determined based on the machine selected in the machine selection layer, and its number represents the sequential index of the selected worker from the available worker set for that machine; the process rework layer consists of 0 and 1, where 0 indicates the process does not require rework, and 1 indicates rework is required. During population initialization, the machine selection layer and worker selection layer use a multi-rule initialization method based on the minimum processing time priority rule, the global search rule for machine load, the global search rule for worker load, and random rules; the process ordering layer uses a multi-rule initialization method based on the shortest process processing time rule, the longest remaining workpiece processing time rule, and random rules. The process rework layer is determined based on the machine selection layer and worker selection layer.

[0134] In specific implementation, the multi-rule-based global redistribution strategy in S3.3 includes the following four redistribution operators:

[0135] Machine load balancing operator: Reassign any operation on the machine with the largest sum of actual processing times of currently assigned operations to the machine with the smallest sum of actual processing times of currently assigned operations, and assign the machine with the highest skill level available worker.

[0136] Worker load balancing operator: Reassign any process handled by the worker with the largest sum of actual processing time of currently assigned processes to the worker whose corresponding machine is available and whose sum of actual processing time of currently assigned processes is the smallest.

[0137] Operator that triggers the learning effect: Assigns the last process of a certain workpiece to the worker who has processed the workpiece the most times in the current scheduling scheme;

[0138] Avoiding rework in critical processes: During the scheduling scheme generation phase, if the expected processing quality of a critical process is lower than its corresponding quality qualification threshold, the process will be reassigned to the available machine-worker combination with the highest expected processing quality to avoid triggering the rework mechanism.

[0139] Machine load balancing and worker load balancing effectively alleviate the uneven workload caused by unequal resource allocation in traditional scheduling, preventing individual machines or workers from becoming bottlenecks. This improves overall process smoothness without increasing additional costs, demonstrating greater system coordination compared to existing methods that rely solely on random or greedy allocation. Furthermore, by stimulating learning effects, the system leverages workers' repeated processing experience on specific workpieces to shorten subsequent process times. Simultaneously, it avoids rework in critical processes by optimizing human-machine combinations in advance based on quality prediction, reducing the probability of rework from the outset. These two strategies explicitly integrate human learning ability and quality stability into scheduling decisions, reducing total costs and energy consumption while improving delivery reliability, overcoming the limitations of traditional methods that passively respond to quality issues. This multi-rule-based global redistribution strategy organically combines load balancing, human learning, and quality prevention, continuously guiding the population towards more efficient, robust, and economical solutions during the evolutionary process, significantly enhancing the algorithm's adaptability and practical value in complex human-machine collaborative environments.

[0140] In specific implementation, in S3.4, the local search using the embedded simulated annealing mechanism generates a new solution by employing a neighborhood structure corresponding to the optimization objective. The main steps of the local search include:

[0141] 1) Generate neighborhood solutions: Generate new solutions from the current solution based on various neighborhood structures.

[0142] 2) Evaluation and acceptance of new solutions: If the new solution is better, it is accepted directly; otherwise, the Metropolis criterion is used to determine whether to accept the inferior solution.

[0143] 3) Temperature update: After each state transition, the temperature is reduced according to the cooling coefficient to gradually reduce the probability of accepting a poor solution.

[0144] 4) If the current temperature is higher than the threshold and the Markov chain length has not reached the upper limit, continue the loop; otherwise, terminate the process.

[0145] In this way, multi-objective-oriented refined local optimization is achieved, which significantly improves the quality of elite individuals while maintaining the diversity of solutions, and provides key support for obtaining a Pareto optimal solution set with high convergence and high distribution.

[0146] The neighborhood structure includes the following three types:

[0147] Neighborhood structure oriented towards maximum completion time: Adjusting the machine-worker allocation of operations on the critical path that directly affects the completion time, or swapping the order of operations within a subsequence of operations that are processed consecutively on the same machine in the sequence; In this invention, the 'critical path' refers to the longest chain of operations that determines the maximum completion time in the current scheduling scheme, and its path length is equal to the makespan of the scheduling scheme.

[0148] Neighborhood structure oriented towards total workshop energy consumption: reallocate the processes on the machine with the highest energy consumption per unit time to the machine with lower energy consumption per unit time that is available for the process, or adjust the processes involving machine changes to be processed on the same machine as the previous process to reduce AGV transportation.

[0149] Neighborhood structure oriented towards total worker cost: the process performed by the worker with the highest total cost per unit time is reassigned to the available worker with the lower total cost per unit time on the same machine.

[0150] In this way, dedicated neighborhood operations are constructed for maximum completion time, total shop floor energy consumption, and total labor cost, allowing local searches to directly affect key decision variables influencing the corresponding objectives. For example, the project duration can be shortened by adjusting the sequence of processes or resource allocation on the critical path, energy consumption can be reduced by reallocating tasks on high-energy-consuming machines or reducing AGV transportation, and labor costs can be controlled by replacing high-cost workers. This goal-oriented perturbation mechanism avoids the problem of blind searching in traditional general neighborhood operations, significantly improving optimization efficiency.

[0151] like Figure 2 As shown, in order to facilitate those skilled in the art to better understand the detailed solution process of S3 in this method, the following explanation is provided.

[0152] • Encode the individuals in the population and generate the initial population based on a hybrid initialization strategy.

[0153] Each individual in the population uses a four-layer coding system, with each layer's length equal to the total number of processes. The Process Ordering Layer (OS) uses numbers representing workpiece numbers, and the frequency of each number represents the process number. The Machine Selection Layer (MS), Worker Selection Layer (WS), and Process Rework Layer (PR) arrange the workpiece's processes sequentially from left to right: in the Machine Selection Layer, each number is the sequential index of the machine selected for the corresponding process from the available machine set; the Worker Selection Layer is determined based on the machine selected in the Machine Selection Layer, and its numbers represent the sequential index of the selected worker from the available worker set for that machine; the Process Rework Layer consists of 0s and 1s, where 0 indicates the process does not require rework, and 1 indicates rework is required.

[0154] To facilitate understanding, a simple example will be used to illustrate the coding. This example includes 3 workpieces, 4 machines, and 3 workers, with each workpiece having 3, 2, or 3 processes respectively. Figure 3 This is a coding diagram for this example. For instance, the "3" appearing for the third time in the OS represents the workpiece. The third process In MS, the last digit "2" indicates a process. Choose the second machine from the available machine selection for processing, i.e., machine In WS, the last digit "2" indicates... The second worker is selected from the pool of available workers to perform the operation, i.e., the worker... (Changed to) In PR, the last "1" indicates a process. It needs to be reworked.

[0155] • During population initialization, the MS layer and WS layer adopt the following four rules in proportion:

[0156] Minimum processing time resource allocation rule: Based on a randomly generated sequence of processes, select the machine-worker combination with the shortest actual processing time for each process. Global search rule for machine load: Based on a randomly generated sequence of processes, select the machine-worker combination with the minimum cumulative machine load for each process. Global search rule for worker load: Based on a randomly generated sequence of processes, select the machine-worker combination with the minimum cumulative worker load for each process. Random rule: For each process, randomly select one machine from its candidate machine set and randomly select one worker from the candidate worker set corresponding to that machine.

[0157] During population initialization, the OS layer adopts the following three rules proportionally:

[0158] Randomization rule: Generate the process sequence by random arrangement. Shortest process processing time rule: Based on the initialization of WS and MS, arrange the processes in ascending order of processing time, prioritizing the process with the shortest processing time. Longest remaining processing time rule: Based on the initialization of WS and MS, dynamically calculate the remaining processing time for each workpiece, prioritizing the first process to be processed for the workpiece with the longest remaining time.

[0159] The PR layer is determined by the WS layer and the MS layer.

[0160] • Each individual is decoded using an insertion-based greedy decoding method that takes into account transportation time.

[0161] • Perform priority-based crossover and two-point exchange mutation operations on the process sequencing layer; for the machine selection and worker selection layers, use methods such as... Figure 4 The single-segment crossover operation shown and as follows Figure 5The multipoint mutation operation is shown.

[0162] By employing a global redistribution strategy based on multiple rules, worker and machine resources are adjusted and optimized.

[0163] In specific implementation, the multi-rule-based global redistribution strategy includes the following redistribution operators:

[0164] Machine load balancing operator: Select the machine with the highest load, randomly select a process on it, and reassign it to another optional machine with a lower load, and assign the machine with the highest skill level worker.

[0165] Worker load balancing operator: Select the worker with the highest load, randomly select a process on their work, and reassign them to another available worker with a lower load.

[0166] The learning effect operator: randomly select a workpiece and assign its last process to the worker with the most experience in processing that workpiece, so as to maximize the use of the worker's learning effect and improve processing efficiency.

[0167] Key process rework avoidance operator: For processes that require rework, they are reassigned to higher-quality machine and worker combinations to improve processing quality and thus avoid rework.

[0168] • Select 20% of the individuals from the non-dominant frontier of the current population as elite individuals, and perform a local search with an embedded simulated annealing mechanism by calling the neighborhood structure corresponding to different optimization objectives.

[0169] In specific implementation, such as Figure 6 The main steps of the local search include:

[0170] Generate neighborhood solutions: Generate new solutions from the current solution based on various neighborhood structures.

[0171] Evaluation and acceptance of new solutions: If the new solution is better, it is accepted directly; otherwise, the Metropolis criterion is used to determine whether to accept the inferior solution.

[0172] Temperature update: After each state transition, the temperature is reduced by the cooling coefficient to gradually reduce the probability of accepting a poor solution.

[0173] If the current temperature is above the threshold and the Markov chain length has not reached the upper limit, the loop continues; otherwise, the process terminates.

[0174] In specific implementation, the neighborhood structure includes neighborhood structures 1 and 2 oriented towards completion time, neighborhood structures 3 and 4 oriented towards energy consumption, and neighborhood structure 5 oriented towards labor cost. Neighborhood structure 1 involves randomly selecting two processes on the critical path and adjusting their machine-labor processing combinations; neighborhood structure 2 involves exchanging processes within different types of critical blocks on the critical path; neighborhood structure 3 involves reallocating any process from the highest energy-consuming machine to a low-energy-consuming machine; neighborhood structure 4 involves reallocating any process involving machine switching on the workpiece with the highest transport energy consumption to the machine of the preceding process to reduce AGV transport energy consumption, such as... Figure 7 middle Example, will The processing machines were adjusted to be compatible with Same. Neighborhood structure 5 involves randomly selecting a process from the workers with the highest cost and replacing it with a lower-cost available worker on the same machine.

[0175] • The next generation of population is generated by using a dynamically updated external library and integrating a reference point association and elimination mechanism based on PBI distance.

[0176] In practice, a dynamically updated external library is established to archive associated individuals with the minimum vertical distance for each reference point, and these individuals are directly retained to the next generation. For the remaining required individuals, a reference point association mechanism based on PBI distance is introduced, which differs from the traditional niche selection mechanism that selects individuals from the last non-dominated layer. Instead of selecting high-quality individuals, an elimination operation is used to... arrive Individuals with the largest PBI distance are removed from the dominance layer until the preset population size is reached, thereby balancing the diversity and convergence of the population.

[0177] • Determine if the iteration termination condition is met; if so, determine the final scheduling scheme from the Pareto optimal solution set based on the analytic hierarchy process and the entropy weight method; otherwise, return to continue the iteration.

[0178] S4. Based on the analytic hierarchy process and the entropy weight method, a comprehensive evaluation is performed on the Pareto optimal scheduling scheme set obtained in S3 to determine the final scheduling scheme.

[0179] This invention incorporates worker behavior factors directly affecting processing efficiency—namely, differences in worker skill levels with machines and the learning effect on workpiece processing—into the scheduling model. It also considers AGV transportation constraints between machines and designs a secondary processing stage for critical processes, requiring rework if the process quality is substandard, thus ensuring processing quality and constructing a dual-resource-constraint scheduling model that more closely reflects actual production. Furthermore, to respond to enterprises' core needs for efficiency, energy saving, and cost control, the model sets the optimization objective as minimizing the maximum completion time, total workshop energy consumption, and total worker costs. In addition, this invention employs a four-layer encoding method with a clear structure, where each layer independently corresponds to process sequencing, machine selection, worker allocation, and rework decisions. This structure facilitates the design of operations such as crossover, mutation, reallocation, and neighborhood search. Each operation can be performed independently at its corresponding encoding layer, always satisfying process and resource constraints. This allows for efficient search of the solution space while maintaining solution feasibility, significantly improving the overall performance of the algorithm.

[0180] Furthermore, population mixing initialization significantly improves the quality and diversity of initial solutions, laying a solid foundation for global search; multi-rule-based global redistribution dynamically optimizes the allocation of machine and worker resources during evolution, effectively helping the algorithm escape local optima; local search embedded with simulated annealing enhances the ability to find elite individuals by invoking neighborhood structures oriented towards different optimization objectives, improving convergence accuracy and speed; and the improved elite retention strategy effectively balances the convergence and diversity of the population. These improved strategies collectively ensure that the algorithm has better convergence efficiency and stronger robustness when solving complex scheduling models.

[0181] This method can effectively integrate the impact of worker behavior factors on processing time and quality in flexible workshop scheduling, and collaboratively optimize the maximum completion time, total workshop energy consumption, and total worker cost, thereby generating an efficient, energy-saving, economical, and executable scheduling scheme.

[0182] Example 2

[0183] To better illustrate the effectiveness of this method, the following experiment was conducted.

[0184] Based on the Brandimarte standard test set MK01-MK10, 10 extended test cases were constructed, named DMK01-DMK10. Based on these constructed cases, the feasibility of the scheduling mathematical model proposed in this invention was verified, and the performance of the proposed improved non-dominated sorting genetic algorithm III (INSGA-III) was tested.

[0185] The INSGA-III algorithm used in this invention is compared with the MOEA_D, MA, NSGA-II, and TLBO algorithms.

[0186] Each algorithm was run independently 10 times on each test case, and its performance was evaluated using three metrics: Inverse Generation Distance (IGD), Hypervolume (HV), and Non-Dominant Ratio (NR). NR and HV values ​​were positively correlated with algorithm performance, while IGD values ​​were negatively correlated. To ensure fairness, the population size and number of iterations for all comparison algorithms were consistent with the algorithm of this invention. The parameters for the INSGA-III algorithm were: population size popsize = 150, number of iterations = 300, crossover probability cr = 0.8, mutation probability cm = 0.05, initial temperature t = 3, termination temperature T = 0.1, temperature decrease rate CR = 0.9, and Markov chain length Itr = 10.

[0187] This experiment utilizes an improved non-dominated sorting genetic algorithm III (INSGA-III) to solve the flexible job shop scheduling problem that considers worker behavior factors. Based on the shop production information, a mathematical model of the flexible job shop scheduling problem considering worker behavior factors is established. Then, the improved non-dominated sorting genetic algorithm III (INSGA-III) is used to obtain the scheduling solution.

[0188] Table 2 Comparison of INSGA-III and other algorithms (optimal values ​​are bolded)

[0189]

[0190] Based on the experimental results in Table 2, the model successfully generated feasible scheduling schemes that met all constraints in all 10 test cases, and achieved coordinated optimization of the three objectives of maximum completion time, total workshop energy consumption, and total worker cost, verifying the feasibility of the scheduling mathematical model proposed in this invention. Furthermore, from the perspective of algorithm performance comparison, the INSGA-III algorithm only slightly lagged behind the TLBO algorithm in the DMK08 case, while its HV index was on par. In all other cases, the algorithm achieved the best performance in terms of IGD, HV, and NR. This confirms that the non-dominated solution set obtained by the algorithm of this invention has superior overall performance in terms of convergence, diversity, and non-dominated relationships. To more intuitively demonstrate the comparison results, this invention plotted the IGD and HV data in Table 2 as a box plot, as shown below. Figure 8 and Figure 9 As shown, INSGA-III has the highest HV median and the lowest IGD median, indicating that its solution set quality is the best. Furthermore, both of its metrics have the smallest box ranges, suggesting that INSGA-III has better stability compared to the other four algorithms.

[0191] Taking the MK06 example, the weight coefficients of both the analytic hierarchy process (AHP) and the entropy weight method are set to 0.5. The Gantt chart of the resulting scheduling scheme is as follows: Figure 10As shown. To make the Gantt chart concise and clear, for processes requiring secondary processing, the initial and secondary processing stages are combined and not separately drawn. At the same time, the AGV transport time of the workpiece is not directly drawn in the chart.

[0192] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A flexible workshop scheduling method considering worker behavior factors, characterized in that, Includes the following steps: S1. Obtain the shop floor production information required to build the scheduling model, including: Information on the available processing machines for each process and the available operators for each machine; Parameters used to quantify the impact of worker behavior on processing time; Energy consumption parameters used to calculate total energy consumption in the workshop and wage parameters used to calculate total worker costs; Key process identifiers, corresponding quality acceptance thresholds, and quality assessment parameters used to evaluate the processing quality of key processes; S2. Based on the workshop production information obtained in S1, establish a scheduling model for the flexible operation workshop to generate a scheduling scheme that includes processing machines, operators, start times, and rework arrangements for key processes for each process. The scheduling model aims to minimize the maximum completion time, total workshop energy consumption, and total worker cost simultaneously. It integrates workpiece AGV transportation time constraints, machine and worker exclusivity constraints, and a rework mechanism that allows the same machine and worker originally assigned to perform secondary processing for critical processes that fail to meet quality standards. S3. The improved non-dominated sorting genetic algorithm III is used to solve the scheduling model established in S2 to obtain the Pareto optimal scheduling scheme set. The improvements include: using a hybrid initialization strategy to generate the initial population, introducing a multi-rule-based global redistribution strategy during the evolution process, performing local search with an embedded simulated annealing mechanism on elite individuals, and using an elite retention strategy based on a reference point association mechanism with dynamic external archives and PBI distance. S4. Based on the analytic hierarchy process and the entropy weight method, a comprehensive evaluation is performed on the Pareto optimal scheduling scheme set obtained in S3 to determine the final scheduling scheme.

2. The flexible workshop scheduling method considering worker behavior factors according to claim 1, characterized in that, In S1, the parameters used to quantify the impact of worker behavior on processing time include: the skill level coefficient of the worker operating each machine, the worker's initial processing capability for different workpieces, learning ability, and capability ceiling.

3. The flexible workshop scheduling method considering worker behavior factors according to claim 1, characterized in that, In S1, the quality assessment parameters used to evaluate the processing quality of key processes include: the processing accuracy of each machine and the stability coefficient of the worker operating each machine.

4. The flexible workshop scheduling method considering worker behavior factors according to claim 1, characterized in that, In S3, the improved non-dominated sorting genetic algorithm III solves the scheduling model, including the following steps: S3.1: A four-layer coding structure is used to encode individuals in the population. The four layers are the process sorting layer, the machine selection layer, the worker selection layer, and the process rework layer. An initial population is generated based on a hybrid initialization strategy. S3.2: Calculate the objective function values ​​of the three optimization objectives for each scheduling scheme in the current population; S3.3: In the process of evolution, introduce a global redistribution based on multiple rules to dynamically adjust the resource allocation between machines and workers; S3.4: Select elite individuals from the current population and perform a local search on them using an embedded simulated annealing mechanism; S3.5: An elite retention strategy based on a reference point association mechanism using dynamic external archives and PBI distance is adopted to generate the next generation population; S3.6: Iteratively execute the evolutionary operations from S3.2 to S3.5 until the preset termination condition is met, and output the Pareto optimal scheduling scheme set.

5. The flexible workshop scheduling method considering worker behavior factors according to claim 4, characterized in that, In S3.3, the multi-rule-based global redistribution strategy includes the following four redistribution operators: Machine load balancing operator: Reassign any operation on the machine with the largest sum of actual processing times of currently assigned operations to the machine with the smallest sum of actual processing times of currently assigned operations, and assign the machine with the highest skill level available worker. Worker load balancing operator: Reassign any process handled by the worker with the largest sum of actual processing time of currently assigned processes to the worker whose corresponding machine is available and whose sum of actual processing time of currently assigned processes is the smallest. Operator that triggers the learning effect: Assigns the last process of a certain workpiece to the worker who has processed the workpiece the most times in the current scheduling scheme; Avoiding rework in critical processes: During the scheduling scheme generation phase, if the expected processing quality of a critical process is lower than its corresponding quality qualification threshold, the process will be reassigned to the available machine-worker combination with the highest expected processing quality to avoid triggering the rework mechanism.

6. The flexible workshop scheduling method considering worker behavior factors according to claim 4, characterized in that, In S3.4, during the local search of the embedded simulated annealing mechanism, a new solution is generated using a neighborhood structure corresponding to the optimization objective.

7. The flexible workshop scheduling method considering worker behavior factors according to claim 6, characterized in that, The neighborhood structure includes the following three types: Neighborhood structure oriented towards maximum completion time: Adjust the machine-worker allocation of operations on the critical path that directly affects completion time, or swap the order of operations within subsequences of operations that are processed consecutively on the same machine in the sequence; Neighborhood structure oriented towards total workshop energy consumption: reallocate the processes on the machine with the highest energy consumption per unit time to the machine with lower energy consumption per unit time that is available for the process, or adjust the processes involving machine changes to be processed on the same machine as the previous process to reduce AGV transportation. Neighborhood structure oriented towards total worker cost: the process performed by the worker with the highest total cost per unit time is reassigned to the available worker with the lower total cost per unit time on the same machine.

8. The flexible workshop scheduling method considering worker behavior factors according to claim 1, characterized in that, In the scheduling model, the actual processing time of a process is dynamically calculated based on the parameters used to quantify the impact of worker behavior on processing time, so that the efficiency of the same worker in subsequent processing of the same workpiece is improved due to the learning effect, and the efficiency improvement is constrained by its initial processing capacity and capacity limit.

9. The flexible workshop scheduling method considering worker behavior factors according to claim 8, characterized in that, For critical processes that fail to meet quality standards, the secondary processing time is recalculated based on the actual time of the initial processing and the preset rework coefficient.

10. The flexible workshop scheduling method considering worker behavior factors according to claim 1, characterized in that, The scheduling model also integrates the following constraints: Priority constraints between workpiece processes: the subsequent process can only begin after the preceding process is completed and the AGV transportation time is taken into account. The exclusive constraint of machines and workers means that at any given time, a machine can only process one operation and a worker can only operate one machine. Rework constraints for critical processes: rework must be performed by the same machine and the same worker originally assigned, and subsequent processes can only begin after the rework is completed.

Images