A distributed hybrid flow shop scheduling method and system considering worker fatigue

Abstract

The application belongs to the technical field of workshop production scheduling, and discloses a distributed mixed flow water workshop scheduling method and system considering worker fatigue, which comprises the following steps: defining a problem, and constructing an objective function and constraint conditions; evenly distributing workpieces to each factory, each machine and each worker to obtain a workpiece scheduling sequence, a machine distribution vector and a worker distribution vector; performing a crossover operation on the workpiece scheduling sequence to obtain a first workpiece scheduling sequence, and performing a mutation operation on the machine distribution vector and the worker distribution vector to obtain a first machine distribution vector and a first worker distribution vector; performing an operation on the first workpiece scheduling sequence of a key factory to obtain a second workpiece scheduling sequence, calculating the value of the objective function based on the second workpiece scheduling sequence, and outputting a final workpiece scheduling sequence. The application establishes a mathematical model considering the constraint of worker fatigue, adopts a multi-objective evolutionary algorithm based on Q learning to solve the problem, and can simultaneously minimize the maximum completion time and total energy consumption.

Description

Technical Field

[0001] This invention relates to the field of workshop production scheduling technology, and in particular to a distributed hybrid assembly line workshop scheduling method and system that takes into account worker fatigue. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Scheduling problems are an important research topic, especially in typical industrial production processes such as steel production systems, semiconductor manufacturing systems, and prefabricated component production systems. Many different types of scheduling problems exist in real-world industrial systems, such as the flow shop scheduling problem (FSP), the hybrid flow shop problem (HFS), the job shop problem (JSP), and the flexible job shop problem (FJSP). Most existing literature on scheduling problems considers deterministic factors, assuming that the processing time of all processes is a fixed value. However, in real-world industrial environments, the processing time of workpieces is usually not deterministic.

[0004] With the development of globalization in the world economy, more and more companies are adopting distributed production to improve production efficiency and reduce costs. Therefore, many researchers are focusing on distributed scheduling problems, such as distributed FSP, distributed HFS, distributed JSP, and distributed FJSP. Meanwhile, more and more real-world production processes are also considering issues such as resource shortages and worker fatigue; therefore, to adapt to real-world industrial environments, the processing time for each workpiece should be set to a fuzzy value rather than a deterministic value.

[0005] Furthermore, with the continued demand for low carbon emissions, relevant literature has also conducted research on the energy consumption of machine processing and standby energy consumption during the processing. It is generally assumed here that the faster the processing speed, the greater the energy consumption. Through analysis of existing literature, we found that there are many realistic constraints when solving HFS, and currently there are relatively few studies considering resource constraints, worker fatigue, and distributed constraint HFS (hereinafter referred to as DHFSPW). Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a distributed hybrid assembly line scheduling method and system that considers worker fatigue. By taking into account the constraint of worker fatigue, a mathematical model is established, and a multi-objective evolutionary algorithm based on Q-learning is used to solve the problem, which can simultaneously minimize the maximum completion time and total energy consumption.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a distributed hybrid assembly line workshop scheduling method considering worker fatigue, comprising the following steps:

[0009] Define a distributed hybrid flow shop scheduling problem that considers resource constraints and worker fatigue, and construct the objective function expected in actual production and the constraints that satisfy the problem.

[0010] The workpieces are evenly allocated to each factory, each machine within the factory, and each worker, to obtain the workpiece scheduling sequence, machine allocation vector, and worker allocation vector for each factory.

[0011] Perform a crossover operation on the workpiece scheduling sequence to obtain the first workpiece scheduling sequence, and perform a mutation operation on the machine allocation vector and the worker allocation vector to obtain the first machine allocation vector and the first worker allocation vector.

[0012] The first workpiece scheduling sequence of the key plant is operated on to obtain the second workpiece scheduling sequence. Based on the second workpiece scheduling sequence, the first machine allocation vector, and the first worker allocation vector, the objective function is calculated, and the final workpiece scheduling sequence is output.

[0013] As an alternative implementation, cross-operation of the workpiece scheduling sequence includes BEC cross-operation and MC cross-operation;

[0014] The BEC cross selects one parent from the parent population and another parent from the mating pool. The elements of the scheduling sequences of the two parents are divided according to the factory. If the number of elements in the scheduling sequences of the two parents is the same, the scheduling sequence elements of the parent selected from the mating pool are allocated to the offspring.

[0015] The MC cross selects one parent from the parent population and another parent from the mating pool. The elements of the scheduling sequences of the two parents are divided according to the factories. If the number of elements in the scheduling sequences of the two parents is different, the parent selected from the mating pool is ignored. Two elements are randomly selected from the scheduling sequence of each factory in the parent population and the two elements are mirrored.

[0016] As an alternative implementation, the parent population is the workpiece scheduling sequence obtained by evenly distributing workpieces to each factory, each machine in the factory, and each worker, and the mating pool is the sequence of all workpieces obtained by arranging workpieces in a certain order.

[0017] As an alternative implementation, a mutation operation is performed on the machine allocation vector and the worker allocation vector, specifically as follows:

[0018] Based on the different factories to which they are assigned, all workpieces are divided into multiple parts. The workpieces in each part are sorted in descending order of processing time. The sorted workpieces are then evenly distributed to each worker and machine. For the initially assigned machine and worker, if they match the sorted assignment, they remain unchanged; otherwise, they are assigned to other machines and workers.

[0019] As an alternative implementation, operating the first workpiece scheduling sequence of the critical plant includes:

[0020] In a critical plant, two workpieces are randomly selected, and an exchange operation is performed on the two workpieces.

[0021] In the critical factory, two workpieces are randomly selected, and the first workpiece is inserted after the second workpiece;

[0022] In the critical plant, randomly select two workpieces and perform a mirror operation on the two workpieces;

[0023] In the critical factory, a subsequence of consecutive workpieces is randomly selected. Then, a workpiece is randomly selected outside the subsequence and swapped with the subsequence.

[0024] In the critical plant, a subsequence of consecutive workpieces is randomly selected. Then, a workpiece is randomly selected from outside the subsequence and inserted into the subsequence.

[0025] In a critical factory, two subsequences of consecutive workpieces are randomly selected. A workpiece is randomly selected outside the subsequences, and the two subsequences are mirrored around the selected workpiece.

[0026] As an alternative implementation, the objective function of the distributed hybrid flow shop scheduling problem that considers resource constraints and worker fatigue is to simultaneously minimize the maximum completion time and total energy consumption.

[0027] Secondly, the present invention provides a distributed hybrid assembly line scheduling system that takes into account worker fatigue, comprising:

[0028] The model building module is configured to: define a distributed hybrid flow shop scheduling problem that considers resource constraints and worker fatigue, and construct the objective function expected in the actual production process and the constraints that satisfy the problem;

[0029] The initialization module is configured to: evenly allocate workpieces to each factory, each machine within a factory, and each worker, and obtain the workpiece scheduling sequence, machine allocation vector, and worker allocation vector for each factory;

[0030] The global search module is configured to: perform cross operations on the workpiece scheduling sequence to obtain the first workpiece scheduling sequence, and perform mutation operations on the machine allocation vector and the worker allocation vector to obtain the first machine allocation vector and the first worker allocation vector.

[0031] The local enhancement search module is configured to: operate on the first workpiece scheduling sequence of the key plant to obtain the second workpiece scheduling sequence, calculate the value of the objective function based on the second workpiece scheduling sequence, the first machine allocation vector, and the first worker allocation vector, and output the final workpiece scheduling sequence.

[0032] Thirdly, the present invention provides an electronic device including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in the first aspect.

[0033] Fourthly, the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in the first aspect.

[0034] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the method described in the first aspect.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] This disclosure proposes a distributed hybrid flow shop scheduling method and system considering worker fatigue. Taking into account resource constraints, worker fatigue constraints, and distribution constraints, a mathematical model is established, and a multi-objective evolutionary algorithm based on Q-learning is used to solve the problem. A four-dimensional vector is designed to represent each solution, simultaneously considering factory allocation, scheduling order, worker allocation, and machine allocation to optimize two conflicting objectives simultaneously. An initialization method based on multiple heuristics and random combinations not only improves the population quality and obtains better solutions but also enhances the population's convergence and shortens the algorithm's evolution time. Through crossover and mutation operations, the algorithm can explore different regions of the solution space, avoiding premature convergence to local optima and increasing the chance of finding the global optimum. Enhanced local search based on key factories further improves the search capability. The method of this disclosure can simultaneously minimize the maximum completion time and total energy consumption. Experimental results demonstrate the competitive performance of the algorithm.

[0037] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0038] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0039] Figure 1 A flowchart of a distributed hybrid assembly line scheduling method considering worker fatigue provided in Embodiment 1 of the present invention;

[0040] Figure 2 This is a representation example of a solution in Embodiment 1 of the present invention;

[0041] Figure 3 This is an example of two crossing methods in Embodiment 1 of the present invention;

[0042] Figure 4 This is an example of the mutation method in Embodiment 1 of the present invention;

[0043] Figure 5 This is an example of a local enhancement search representation from Embodiment 1 of the present invention;

[0044] Figure 6 This is an HV level diagram of parameters αβγ in Embodiment 1 of the present invention;

[0045] Figure 7 The following is a comparison chart of the ANOVA performance of the initialization strategy in Embodiment 1 of the present invention, wherein (a) is a comparison chart of the ANOVA performance of the RPI_HV index of the initialization strategy, and (b) is a comparison chart of the ANOVA performance of the RPI_IGD index of the initialization strategy.

[0046] Figure 8 The following is a comparison chart of the ANOVA performance of the cross-validation method in Embodiment 1 of the present invention, wherein (a) is a comparison chart of the ANOVA performance of the RPI_HV index of the cross-validation method, and (b) is a comparison chart of the ANOVA performance of the RPI_IGD index of the cross-validation method.

[0047] Figure 9 The above are ANOVA performance comparison charts of various indicators of the mutation method in Embodiment 1 of the present invention, wherein (a) is an ANOVA performance comparison chart of the RPI_HV indicator of the mutation method, and (b) is an ANOVA performance comparison chart of the RPI_IGD indicator of the mutation method.

[0048] Figure 10 The following is a comparison chart of the ANOVA performance of various indicators of the local reinforcement search strategy in Embodiment 1 of the present invention, wherein (a) is a comparison chart of the ANOVA performance of the RPI_HV indicator of the local reinforcement search strategy, and (b) is a comparison chart of the ANOVA performance of the RPI_IGD indicator of the local reinforcement search strategy.

[0049] Figure 11The following are ANOVA performance comparison results of various indicators of multiple algorithms in Embodiment 1 of the present invention, wherein (a) is the ANOVA performance comparison result of the RPI_HV indicator of multiple algorithms, and (b) is the ANOVA performance comparison result of the RPI_IGD indicator of multiple algorithms.

[0050] Figure 12 The above are EAF diagrams comparing QMOEA with other algorithms in Embodiment 1 of the present invention, wherein (a) is the EAF diagram comparing QMOEA with ARMOEA, (b) is the EAF diagram comparing QMOEA with CMOPSO, (c) is the EAF diagram comparing QMOEA with GrEA, and (d) is the EAF diagram comparing QMOEA with NSGAII.

[0051] Figure 13 The solution set diagrams for two examples of the present invention are shown, wherein (a) is the Pareto solution set diagram for example 20x3x4 and (b) is the Pareto solution set diagram for example 60x4x3.

[0052] Figure 14 This is a 20x2x2 Gantt chart for the present invention. Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0054] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0055] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. Furthermore, it should be understood that the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0056] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0057] Example 1

[0058] like Figure 1 As shown, this embodiment provides a distributed hybrid assembly line scheduling method that considers worker fatigue, including the following steps:

[0059] S1 defines a distributed hybrid flow shop scheduling problem that considers resource constraints and worker fatigue, and constructs the objective function expected in the actual production process and the constraints that satisfy the problem.

[0060] S2 evenly distributes workpieces to each factory, each machine within a factory, and each worker, obtaining the workpiece scheduling sequence, machine allocation vector, and worker allocation vector for each factory.

[0061] S3 performs a crossover operation on the workpiece scheduling sequence to obtain the first workpiece scheduling sequence, and performs a mutation operation on the machine allocation vector and the worker allocation vector to obtain the first machine allocation vector and the first worker allocation vector.

[0062] S4 operates on the first workpiece scheduling sequence of the key plant to obtain the second workpiece scheduling sequence. Based on the second workpiece scheduling sequence, the first machine allocation vector, and the first worker allocation vector, it calculates the value of the objective function and outputs the final workpiece scheduling sequence.

[0063] Consider a typical actual steelmaking production process with multiple distributed plants, each typically consisting of five stages or processes. The first process involves loading molten iron into a device called a torpedo car (TPC). The TPC then undergoes processing through second and third refining stages. The fourth stage is the pouring process, and the final stage is continuous casting.

[0064] Based on the analysis of actual steelmaking processes, we studied a special extension of HFS, which includes the following characteristics: (1) There are f plants, each plant has m machines, and each machine is operated by one worker; there are j jobs, and each job has a certain number of operations to be processed without needing to occupy a designated plant; (2) Each job can select a suitable machine from a set of available machines for processing; (3) Each job can select one worker from idle workers to operate a machine; (4) Each machine can only process one job at a time, and each workpiece can only be processed on one machine tool at a time; (5) Each machine requires one worker to assist in processing; (6) Each machine may encounter worker fatigue or even rest during processing, at which time the worker's efficiency decreases; (7) The objective of this disclosure is to minimize the completion time and machine processing and standby energy consumption.

[0065] Based on this, there are five main tasks for solving this type of problem: (1) how to select a suitable factory for each workpiece; (2) how to select a suitable machine for each workpiece; (3) how to determine the start and finish times for each workpiece; (4) how to determine the scheduling sequence of the workpieces; and (5) how to assign the appropriate workers to each machine.

[0066] The assumptions of the problem include:

[0067] (1) Each workpiece is assigned to a single factory, and all its processes must be carried out in this factory. Changing factories midway is not allowed.

[0068] (2) For each process of each workpiece, a unique available machine tool must be selected from a set of available machine tools;

[0069] (3) Every machine tool is available;

[0070] (4) Seizure is not permitted;

[0071] (5) The worker's fatigue function is known;

[0072] (6) Workers are allowed to rest;

[0073] (7) The number of workers at each stage is limited;

[0074] (8) If the workers required for the workpiece are occupied, then you need to wait until the workpiece is finished before you can continue processing.

[0075] The parameters of the DHFSW problem model include:

[0076] i represents the workpiece, t represents the workpiece processing stage, j represents the machine, f represents the factory, w represents the worker, and o represents the machine operation.

[0077] n represents the number of workpieces, m represents the number of machines, s represents the number of stages, F represents the number of factories, T represents the number of workers, D represents the number of operations, and P... i,t,w PE represents the processing time of workpiece i by worker w at stage t. i,t,w V represents the energy consumption of workpiece i per unit time by worker w at stage t. m,w,t,f D represents the processing speed of machine m by worker w at stage t in factory f. i,o Let S represent the o-th operation of workpiece i, IPE represent the worker's theoretical productivity, APE represent the worker's actual productivity, and S... i,t C represents the start time of workpiece i in stage t. i,t PEC represents the end time of workpiece i at stage t. j,t,w,f SEC represents the processing energy consumption of worker w operating machine j in the t-th stage of factory f. j,t,w,f Let L represent the standby power consumption of machine j in the t-th stage of factory f, and let L represent a maximum number.

[0078] x i,f The variable is 0 / 1, indicating whether workpiece i is assigned to factory f, y i,j,t,w,f are 0 / 1 variables, representing whether worker w is assigned to process workpiece i on machine j at stage t in factory f, and z i,i` ,j,t,w,f are 0 / 1 variables, indicating whether there is a worker to process workpiece i after it has been processed by worker w on machine j at stage t of factory f.

[0079] The objective function of the model is:

[0080] minC max (1)

[0081] minTEC=PE+SE(2)

[0082] The constraints of the model are:

[0083]

[0084]

[0085] Formulas (1)-(2) describe the two objectives of the problem: maximum completion time and total energy consumption. Equation (3) ensures that each workpiece is assigned to only one factory. Equation (4) ensures that machines and workers can only process one workpiece at a time. Constraint (5) ensures that the start time of workpiece processing must be in the first stage and greater than 0. Constraint (6) ensures the processing relationship between two successive workpieces on the same machine, where the start time of the subsequent operation must be later than the completion time of the previous operation. Constraint (7) describes the completion time of each operation. Constraints (8)-(10) indicate that a workpiece can only be processed by one machine and one worker at a time. Constraint (11) indicates that the completion time is the longest completion time for all workpieces. Equation (12) represents the energy consumption of the machine in the processing state. Equation (13) represents the energy consumption of the machine in the standby state. Equation (14) represents the total energy consumption of all machines in all factories. Constraints (15)-(17) represent binary decision variables.

[0086] Based on a multi-objective optimization function, a Q-learning-based multi-objective evolutionary algorithm (QMOEA) is employed to solve the proposed DHFSW problem. First, the main framework of the proposed algorithm is described. Then, heuristic algorithms for encoding, decoding, and specific problems are presented.

[0087] The main framework of the algorithm includes:

[0088] (1) An effective problem-specific initialization heuristic algorithm was developed, which effectively improved the quality and diversity of the initial population;

[0089] (2) In order to ensure the breadth and depth of the search space, two crossover operators and one mutation operator global search strategy were designed;

[0090] (3) A search mechanism based on key factories was designed. The enhanced local search heuristic strategy further improved the search capability of the algorithm.

[0091] The specific implementation process of the algorithm is as follows:

[0092] Each solution to the problem under consideration is represented by a four-dimensional vector, which describes the factory allocation of the workpiece, the scheduling sequence, the machine allocation, and the worker allocation, respectively.

[0093] Figure 2 An example solution representation is given, with 10 jobs. Different colors indicate that the jobs are assigned to different factories: J2, J6, and J9 are processed in the first factory; J1, J5, J7, and J8 are processed in the second factory; and J3, J4, and J9 are processed in the third factory. 10 The workpiece is assigned to the third factory. The code specifies the scheduling order of each job within each factory. For example, for factory 1, J2, J6, and J9 are assigned, resulting in a scheduling sequence of {2, 1, 3}, and the processing order is {J6, J2, J9}. The code also specifies machine and worker assignments. For example, workpiece 1 is processed by the second machine and the first worker in its factory.

[0094] Based on the considered solutions, the following decoding scheme is proposed:

[0095] Two issues need to be addressed: selecting a factory to process the workpiece and selecting a machine tool to process the workpiece.

[0096] To address these issues, a decoding mechanism combining First-Come, First-Served (FCFS) and Earliest Available (EAFS) rules is proposed. First, in the initial phase, tasks are processed in the order they are scheduled until all machines are in a processing state. However, while a machine is waiting, it is considered unavailable. When a machine becomes available, the tasks immediately enter the processing state. Second, in subsequent phases, based on the processing order of the first phase, the earlier a job is processed, the earlier it enters the subsequent phase for processing.

[0097] Initialization of the Q-learning-based multi-objective algorithm:

[0098] Population initialization plays a crucial role in evolutionary algorithms. A good initialization method can not only improve population quality and obtain better solutions, but also improve population convergence and shorten the algorithm's evolution time. Therefore, designing a well-functioning initialization method is essential for the entire algorithm. For four-dimensional encoding methods, factory allocation, scheduling order, worker allocation, and machine allocation must be considered simultaneously to optimize two conflicting objectives. However, directly obtaining the optimal solution is usually very difficult, but it is possible to analyze the problem and design heuristics, which often yield excellent results. However, using a single heuristic algorithm may cause the algorithm to fall into local optima, while using multiple heuristic algorithms reduces overall diversity. Therefore, an initialization method based on multiple heuristics and random combination is designed to overcome this problem. The specific steps are as follows:

[0099] In factory allocation, when a workpiece is assigned to one factory, the next workpiece cannot be assigned to that factory but must be assigned to another factory. This means that workpieces are distributed to each factory as evenly as possible. There are benefits to balancing factory workloads by distributing all workpieces equally among all factories. By distributing all workpieces equally among all factories, factory workloads can be balanced and manufacturing cycle times can be reduced.

[0100] For machine allocation, a workpiece is assigned to one machine, and subsequent workpieces must be assigned to another machine. This ensures that the task is distributed as evenly as possible across all machines. By balancing the workload among machines, the completion time of each stage is reduced, ultimately shortening the overall processing time.

[0101] Regarding worker allocation, considering that workers may become fatigued, each worker cannot work for too long. Distributing the workload evenly among all workers minimizes worker fatigue, thereby reducing rest time. This reduces the completion time of each stage, thus reducing the total completion time.

[0102] Global search strategy:

[0103] Crossover and mutation are crucial in evolutionary algorithms, driving their efficiency and effectiveness in solving complex problems. Through these two operations, the algorithm can explore different regions of the solution space, avoiding premature convergence to local optima and thus increasing the chance of finding the global optimum.

[0104] Based on the encoded scheduling sequence, we propose two novel crossover methods. Figure 3 Detailed examples are provided:

[0105] (1) Encoding-based cross

[0106] Encoding-based crossover consists of the following steps. First, one parent is selected from the parental population, and another parent is selected from the mating pool. Then, the scheduling sequence genes of each factory are color-coded according to the number of factories they produce. If the number of genes in their scheduling sequences is the same, the scheduling sequence genes from the parent selected from the mating pool are assigned to the offspring, such as... Figure 3 The blue part in the image.

[0107] (2) Mirror Cross

[0108] Mirror crossover and coding-based crossover are identical in parent selection but differ in offspring production. If the number of genes in their scheduling sequences differs, the parent selected from the mating pool is ignored. Instead, two points are randomly selected from the scheduling sequences of each factory in the parent population, and the genes between the two points are mirror-crossed, as shown below. Figure 3 The yellow and purple parts.

[0109] The parent population is the workpiece scheduling sequence obtained by evenly distributing workpieces to each factory, each machine in the factory, and each worker. The mating pool is the sequence of all workpieces obtained by arranging workpieces in a certain order.

[0110] Based on encoded machine and worker assignment vectors, we propose a novel mutation method. Figure 4 Detailed examples are provided:

[0111] The mutation operator is primarily executed at the MA and WA layers of the encoding. Although the load on machines and workers is balanced during population initialization, this only considers ensuring that each machine and worker has the same number of jobs, not necessarily the same processing time. Therefore, the purpose of the mutation operation is to balance the processing time of machines and workers, thereby reducing the completion time. The mutation operation is as follows: Figure 4 As shown, the specific steps are as follows.

[0112] Step 1: Divide all artifacts into multiple parts according to the FA layer encoding.

[0113] Step 2: Sort the workpieces in each section in descending order of processing time.

[0114] Step 3: Distribute the sorted workpieces evenly among each worker and machine. For the initially assigned machine and worker, if it matches the sorted assignment, it remains unchanged; otherwise, it is assigned to another machine and worker.

[0115] Local reinforcement search strategy:

[0116] In distributed scheduling problems, the completion time is determined by the critical factory with the longest completion time. Reducing the completion time of the critical factory is an effective method to reduce the overall completion time. Therefore, six subsequence-based operators are designed for the critical factory in the local reinforcement search strategy. Figure 5 Examples of local reinforcement search representations are given, including: key factory-based internal exchange (QLS1), key factory-based insertion (QLS2), key factory-based mirror transformation (QLS3), key factory-based subsequence exchange (QLS4), key factory-based subsequence insertion (QLS5), and key factory-based subsequence mirror transformation (QLS6).

[0117] The six subsequence-based operators for critical plants are as follows:

[0118] QLS1: Randomly select two workpieces in the critical plant and perform an exchange operation on the two workpieces.

[0119] QLS2: Randomly select two workpieces in the critical plant and insert the first workpiece after the second workpiece.

[0120] QLS3: Randomly select two workpieces in the critical plant and perform a mirror operation on the two workpieces.

[0121] QLS4: Randomly select consecutive workpieces in the critical plant to form a subsequence, randomly select a workpiece outside the subsequence, and exchange the selected workpiece with the subsequence.

[0122] QLS5: Randomly select consecutive workpieces in the critical plant to form a subsequence, randomly select a workpiece outside the subsequence, and insert the selected workpiece into the subsequence.

[0123] QLS6: Randomly select consecutive workpieces in the critical plant to form two subsequences. Randomly select a workpiece outside the subsequences and mirror the two subsequences around the selected workpiece.

[0124] In the proposed Q-learning for selecting local search operators, actions represent six local search strategies, including QLS1 to QLS6, and states represent nine scenarios generated by the difference in completion time and energy consumption, which are the original target value minus the current target value. Furthermore, during Q-learning, feedback is received in the form of rewards after taking action. In this work, state changes can reflect the search performance of the action because the state changes according to the reward function. For action selection, an epsilon-greedy strategy is used. This is a key action selection strategy that balances exploration and exploitation through parameters. This strategy allows the algorithm to select the currently known best exploitation operation with probability and to randomly select any operation with probability for exploration. The algorithm can be used to explore the solution space with probability . This helps the algorithm to extensively explore the solution space in the early stages and gradually increase the utilization of effective actions as learning progresses, thus effectively contributing to the efficiency and effectiveness of learning.

[0125] Experimental Results and Analysis:

[0126] To test the performance of the QMOEA algorithm, 27 instances of different sizes were generated based on a real factory. All compared algorithms were used to solve the problem under consideration, including encoding, decoding, initialization, crossover, mutation, and local search processes. For each instance, the stopping condition was set to 1000 iterations.

[0127] To test the algorithm's performance, 30 independent runs were performed, and all non-dominated solutions obtained from the comparison algorithms were collected for performance comparison. Comparisons were made using hypervolume (HV) and inverse generation distance (IGD). Analysis of variance was performed using relative percentage increase (RPI), calculated as follows:

[0128]

[0129] Where v(s,P) represents the volume of the hypercube formed by the diagonal of the line between the solution and the reference point. It is also the space formed by the solutions and the reference point in the non-dominated solution set. A larger HV index value for the non-dominated solution set indicates that the solution set is closer to the true Pareto front in terms of convergence and diversity, and is a better non-dominated solution set. Furthermore, X represents the Pareto solution set, s represents the Pareto optimal solution, and P represents the reference point. In the following experiments, (1,1) is chosen as the reference point for HV.

[0130]

[0131] IGD is used to calculate the average Euclidean distance between all solutions in the true Pareto front and the non-dominant solutions obtained by the proposed algorithm. Here, X represents the solution generated by the algorithm, x* represents the solution on the Pareto front, p* represents the Pareto front, indicating the number of solutions in |p*|. d(x*,X) represents the minimum Euclidean distance from a point on the Pareto front to a solution.

[0132]

[0133] Where f represents the evaluation metric of the current algorithm, and fb represents the maximum value of the evaluation metrics of all current algorithms. The evaluation metric is HV or IGD.

[0134] Experimental parameter settings:

[0135] The proposed QMOEA algorithm consists of three main parameters: learning rate (α), discount factor (β), and exploration probability (γ). To investigate the impact of these parameters on QMOEA performance, the widely used Taguchi Design of Experiments (DOE) method was employed. Each parameter corresponds to four levels. Therefore, an orthogonal array containing 16 different combinations was selected. Based on the orthogonal array, combinations of parameter levels can be obtained. Each combination was run 30 times on an instance, and HV was used as its response value. Figure 6 It can be seen that α=0.2, β=0.6, and γ=0.3.

[0136] Twenty-seven problem instances of varying sizes were randomly generated to solve the distributed hybrid flow shop scheduling problem considering worker constraints, and the effectiveness of the QMOEA algorithm was tested based on actual production data. For example, instance 1 can represent 20 jobs in two stages across two factories, with each stage including two workers. The job indices are {20, 60, 100}, the factory indices are {2, 3, 4}, and the stage indices are {2, 3, 4}. Five algorithms were run independently 30 times each.

[0137] Verify the effectiveness of the initialization strategy:

[0138] To verify the effectiveness of the initialization method discussed, we compared it with random initialization (denoted as QMOEA-NI) and tested the two algorithms for significant differences using analysis of variance. Figure 7 The analysis of variance results clearly show that QMOEA is significantly better than QMOEA-NI in both the HV and IGD indices, verifying the effectiveness of the proposed initialization method.

[0139] Verify the effectiveness of the global search strategy:

[0140] To demonstrate the effectiveness of our proposed global search strategy, we conducted a comparative experiment: the algorithm without crossover is denoted as QMOEA-NC, and the algorithm without mutation is denoted as QMOEA-NM. The algorithms using both methods are denoted as QMOEA. Both comparative algorithms were run 30 times on 27 instances. Figure 8 It can be seen that the RPI_HV value of QMOEA is significantly higher than that of QMOEA-NC, while the RPI_IGD value of QMOEA is significantly lower than that of QMOEA-NC. Therefore, the proposed crossover strategy can be considered an effective method for solving DHFSPW.

[0141] Figure 9 The results show that QMOEA outperforms QMOEA-NM in both RPI_HV and RPI_IGD values, so we can conclude that the proposed mutation strategy is more advantageous when solving DHFSPW.

[0142] Verify the effectiveness of the local search strategy:

[0143] To demonstrate the effectiveness of the aforementioned local search, we conduct a detailed comparison of algorithms employing and not employing strategies, as well as algorithms employing variable neighborhoods. Algorithms without critical factory-based local reinforcement are denoted as QMOEA-NL, while algorithms employing variable neighborhoods are denoted as QMOEA-VNS.

[0144] from Figure 10 As can be seen from (a) and (b), QMOEA has the highest RPI_HV value range (e.g., Figure 10 (a) shows that the RPI_IGD value range is the lowest (as shown in the diagram). Figure 10 (b) shows that QMOEA significantly outperforms QMOEA-NL and QMOEA-VNS. Therefore, for the 27 proposed instances of different sizes, the local reinforcement search strategy based on the critical factory is significantly better than other local search algorithms.

[0145] Verify the effectiveness of the algorithm:

[0146] To further verify the performance of the proposed algorithm compared to other algorithms, the following four algorithms were selected: ARMOEA, CMOPSO, GrEA, and NSGAII. ARMOEA achieves efficient optimization and diversity of the solution set through dynamic resource allocation and diversity maintenance mechanisms. CMOPSO uses an effective constraint handling strategy and the global search capability of PSO to quickly find Pareto optimal solutions that satisfy the constraints. GrEA employs a grid partitioning method to ensure a uniform distribution of solutions, maintain population diversity, and reduce computational complexity. NSGAII provides efficient solution set diversity and accurate Pareto boundary approximation through fast non-dominated sorting and congestion comparison operations. Each algorithm was run independently 30 times on the same computer, testing 27 instances.

[0147] from Figure 11 As can be seen from (a) and (b), compared with other algorithms, QMOEA has a higher RPI_HV and a lower RPI_IGD, resulting in better performance metrics. Therefore, the solution generated by the QMOEA algorithm is closer to the global optimum. QMOEA demonstrates good performance in solving the proposed problem.

[0148] In addition, we tested the five comparison algorithms mentioned above using the Experience Achievement Function (EAF), which is available on GitHub. Figure 12 This shows the EAF differences between QMOEA and ARMOEA, CMOPSO, GrEA, and NSGAII. In the EAF, the color represents the difference in the probability that the algorithm dominates the corresponding solution compared to other algorithms. The larger the difference, the darker the color, indicating that the algorithm's result dominates the solution more probably than other algorithms. In short, the darker the color and the larger the area, the better the algorithm. Figure 12 The following conclusions can be drawn: (1) The shaded portion of QMOEA is larger than that of other comparison algorithms, which proves that QMOEA has better performance. (2) Under different scheduling environments, QMOEA also outperforms the other four comparison algorithms. Therefore, EAF proves that QMOEA has excellent performance.

[0149] like Figure 13 As shown in the figure, the Pareto fronts generated by several different algorithms for instances of different sizes are illustrated. Different colors represent the Pareto fronts generated by different algorithms. From Figure 13 The following conclusions can be drawn: (1) Compared with other algorithms, QMOEA generates solutions that are significantly closer to the Pareto front. (2) Considering diversity and convergence, QMOEA performs better than the other four comparison algorithms for instances of different sizes. Therefore, the proposed QMOEA can obtain better non-dominated solution sets within a finite range and has stability.

[0150] Figure 14 A Gantt chart for a real-world example is provided, where each operation is represented by a rectangle labeled with a job sequence number, and rectangles of different colors represent different jobs.

[0151] Example 2

[0152] This embodiment provides a distributed hybrid assembly line scheduling system that considers worker fatigue, including:

[0153] The model building module is configured to: define a distributed hybrid flow shop scheduling problem that considers resource constraints and worker fatigue, and construct the objective function expected in the actual production process and the constraints that satisfy the problem;

[0154] The initialization module is configured to: evenly allocate workpieces to each factory, each machine within a factory, and each worker, and obtain the workpiece scheduling sequence, machine allocation vector, and worker allocation vector for each factory;

[0155] The global search module is configured to: perform cross operations on the workpiece scheduling sequence to obtain the first workpiece scheduling sequence, and perform mutation operations on the machine allocation vector and the worker allocation vector to obtain the first machine allocation vector and the first worker allocation vector.

[0156] The local enhancement search module is configured to: operate on the first workpiece scheduling sequence of the key plant to obtain the second workpiece scheduling sequence, calculate the value of the objective function based on the second workpiece scheduling sequence, the first machine allocation vector, and the first worker allocation vector, and output the final workpiece scheduling sequence.

[0157] It should be noted that the above modules correspond to the steps described in Embodiment 1, and the examples and application scenarios implemented by the above modules and the corresponding steps are the same, but are not limited to the content disclosed in Embodiment 1. It should also be noted that the above modules, as part of the system, can be executed in a computer system such as a set of computer-executable instructions.

[0158] In further embodiments, the following is also provided:

[0159] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in Embodiment 1. For brevity, further details are omitted here.

[0160] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0161] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.

[0162] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in Embodiment 1.

[0163] The method in Example 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the field, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0164] A computer program product includes a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0165] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer-executable instructions, such as instructions included in program modules, which execute in a device on a target real or virtual processor to perform the processes / methods described above. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc., that perform specific tasks or implement specific abstract data types. In various embodiments, the functionality of program modules can be combined or divided among program modules as needed. The machine-executable instructions for the program modules can execute within a local or distributed device. In a distributed device, the program modules can reside in both local and remote storage media.

[0166] The computer program code used to implement the methods of the present invention may be written in one or more programming languages. This computer program code may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the computer or other programmable data processing device, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a computer, partially on a computer, as a stand-alone software package, partially on a computer and partially on a remote computer, or entirely on a remote computer or server.

[0167] In the context of this invention, computer program code or related data may be carried by any suitable carrier to enable a device, apparatus, or processor to perform the various processes and operations described above. Examples of carriers include signals, computer-readable media, and so on. Examples of signals may include electrical, optical, radio, sound, or other forms of propagation signals, such as carrier waves, infrared signals, etc.

[0168] Those skilled in the art will recognize that the units and algorithm steps described in conjunction with the embodiments herein can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0169] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A distributed hybrid assembly line scheduling method considering worker fatigue, characterized in that, Includes the following steps: Define a distributed hybrid flow shop scheduling problem that considers resource constraints and worker fatigue, and construct the objective function expected in actual production and the constraints that satisfy the problem. The workpieces are evenly allocated to each factory, each machine within the factory, and each worker, to obtain the workpiece scheduling sequence, machine allocation vector, and worker allocation vector for each factory. Perform a crossover operation on the workpiece scheduling sequence to obtain the first workpiece scheduling sequence, and perform a mutation operation on the machine allocation vector and the worker allocation vector to obtain the first machine allocation vector and the first worker allocation vector. The first workpiece scheduling sequence of the key plant is operated on to obtain the second workpiece scheduling sequence. Based on the second workpiece scheduling sequence, the first machine allocation vector, and the first worker allocation vector, the objective function is calculated, and the final workpiece scheduling sequence is output.

2. The distributed hybrid assembly line scheduling method considering worker fatigue as described in claim 1, characterized in that, Crossing operations on the job scheduling sequence include BEC crossover and MC crossover; The BEC cross selects one parent from the parent population and another parent from the mating pool. The elements of the scheduling sequences of the two parents are divided according to the factory. If the number of elements in the scheduling sequences of the two parents is the same, the scheduling sequence elements of the parent selected from the mating pool are allocated to the offspring. The MC cross selects one parent from the parent population and another parent from the mating pool. The elements of the scheduling sequences of the two parents are divided according to the factories. If the number of elements in the scheduling sequences of the two parents is different, the parent selected from the mating pool is ignored. Two elements are randomly selected from the scheduling sequence of each factory in the parent population and the two elements are mirrored.

3. A distributed hybrid assembly line scheduling method considering worker fatigue as described in claim 2, characterized in that, The parent population is the workpiece scheduling sequence obtained by evenly distributing workpieces to each factory, each machine in the factory, and each worker. The mating pool is the sequence of all workpieces obtained by arranging workpieces in a certain order.

4. A distributed hybrid assembly line scheduling method considering worker fatigue as described in claim 1, characterized in that, The mutation operation is performed on the machine assignment vector and the worker assignment vector, specifically as follows: Based on the different factories to which they are assigned, all workpieces are divided into multiple parts. The workpieces in each part are sorted in descending order of processing time. The sorted workpieces are then evenly distributed to each worker and machine. For the initially assigned machine and worker, if they match the sorted assignment, they remain unchanged; otherwise, they are assigned to other machines and workers.

5. A distributed hybrid assembly line scheduling method considering worker fatigue as described in claim 1, characterized in that, Operating the first job scheduling sequence of the critical plant includes: In a critical plant, two workpieces are randomly selected, and an exchange operation is performed on the two workpieces. In the critical factory, two workpieces are randomly selected, and the first workpiece is inserted after the second workpiece; In the critical plant, randomly select two workpieces and perform a mirror operation on the two workpieces; In the critical factory, a subsequence of consecutive workpieces is randomly selected. Then, a workpiece is randomly selected outside the subsequence and swapped with the subsequence. In the critical plant, a subsequence of consecutive workpieces is randomly selected. Then, a workpiece is randomly selected from outside the subsequence and inserted into the subsequence. In a critical factory, two subsequences of consecutive workpieces are randomly selected. A workpiece is randomly selected outside the subsequences, and the two subsequences are mirrored around the selected workpiece.

6. A distributed hybrid assembly line scheduling method considering worker fatigue as described in claim 4, characterized in that, The objective function of the distributed hybrid flow shop scheduling problem, which considers resource constraints and worker fatigue, is to simultaneously minimize the maximum completion time and total energy consumption.

7. A distributed hybrid assembly line scheduling system considering worker fatigue, characterized in that, include: The model building module is configured to: define a distributed hybrid flow shop scheduling problem that considers resource constraints and worker fatigue, and construct the objective function expected in the actual production process and the constraints that satisfy the problem; The initialization module is configured to: evenly allocate workpieces to each factory, each machine within a factory, and each worker, and obtain the workpiece scheduling sequence, machine allocation vector, and worker allocation vector for each factory; The global search module is configured to: perform cross operations on the workpiece scheduling sequence to obtain the first workpiece scheduling sequence, and perform mutation operations on the machine allocation vector and the worker allocation vector to obtain the first machine allocation vector and the first worker allocation vector. The local enhancement search module is configured to: operate on the first workpiece scheduling sequence of the key plant to obtain the second workpiece scheduling sequence, calculate the value of the objective function based on the second workpiece scheduling sequence, the first machine allocation vector, and the first worker allocation vector, and output the final workpiece scheduling sequence.

8. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the method according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, perform the method described in any one of claims 1-6.

10. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, implements the method described in any one of claims 1-6.

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