Dynamic Scheduling Method for Digital Twin Workshops Considering Learning and Forgetting Effects

Abstract

This invention belongs to the field of flexible job shop scheduling and discloses a dynamic scheduling method for digital twin job shops that considers learning and forgetting effects. The method includes collecting initial state data from the physical job shop and sending it to the virtual job shop. The virtual job shop generates an initial scheduling plan with the goal of minimizing the maximum completion time and total production cost, and the physical job shop executes the initial scheduling plan. The state data includes the states of machines, jobs, and workers. Real-time state data from the physical job shop is continuously collected, and random events are captured. If a random event is captured, the real-time state data and the random event are transmitted to the virtual job shop, and a rescheduling plan returned by the virtual job shop is executed; otherwise, the current scheduling plan is maintained. Random events include random new job arrivals, random worker absences, and random machine malfunctions. This invention achieves a better balance between the solution quality and optimization efficiency of the scheduling plan.

Description

Technical Field

[0001] This invention belongs to the field of flexible workshop scheduling, specifically involving a dynamic scheduling method for digital twin workshops that takes into account the learning and forgetting effects. Background Technology

[0002] The Flexible Job Shop Scheduling Problem (FJSSP), a typical nondeterministic polynomial-time (NP) difficult combinatorial optimization problem characterizing the optimal allocation of limited resources, has become a research focus in recent years. However, traditional FJSSP research is mostly based on static deterministic assumptions, making it difficult to directly apply to the uncertainties of modern workshops.

[0003] Specifically, traditional research on FJSSP (Functional, Execution, and Spatial) is largely limited to static production environments or machine-driven resource allocation. Such findings are no longer adequate for the dynamic, event-driven scenarios of modern manufacturing. Workers are not only a core production resource but also a crucial constraint in scheduling decisions. Nevertheless, existing research primarily focuses on order- and machine-driven dynamic events (such as new order insertions and machine malfunctions), paying relatively little attention to worker-related dynamic events (such as worker absenteeism). However, worker-related disturbances can also interfere with initial scheduling plans, and worker-related factors (such as learning and forgetting effects) can also impact production efficiency.

[0004] From constructing a theoretical scheduling model to achieving dynamic control in a real workshop, two core challenges are faced. Firstly, existing scheduling systems lack effective technical means to perceive and accurately model dynamic changes in the workshop and worker operating status in real time, resulting in difficulty in providing reliable data support. Digital Twin (DT) technology can provide an effective system framework for this. Secondly, facing frequent disturbances in a real workshop, the scheduling system must not only ensure production efficiency but also consider the stability of the rescheduling process. However, most existing methods are limited by static solution mechanisms or single optimization rules, making it difficult to achieve an effective balance between efficiency and stability when facing high-dimensional, dynamic disturbance environments. To achieve coordinated optimization of production efficiency and rescheduling stability in complex dynamic environments, the scheduling system must focus on three key questions: when to trigger rescheduling, what strategy to use to adjust the current plan, and what algorithm to use for efficient solution. Establishing an agile dynamic response mechanism can simultaneously address the needs at both the timing and strategy selection levels of rescheduling.

[0005] Metaheuristic algorithms are an effective method for solving NP-hard combinatorial optimization problems. For example, existing techniques have proposed adaptive hybrid optimization algorithms to handle remanufacturing scheduling problems under uncertain environments. However, metaheuristic algorithms still have limitations when facing extremely complex solution spaces. For instance, these algorithms are prone to getting trapped in local optima in large-scale scheduling scenarios, and they often lack effective adaptive optimization capabilities when faced with high-frequency dynamic disturbances.

[0006] In recent years, artificial intelligence methods have demonstrated significant advantages in solving NP-hard combinatorial optimization problems, especially in the field of dynamic scheduling. Among these, Q-learning, as a classic model-free, value-based reinforcement learning algorithm, has been widely applied to solving various complex scheduling problems. Combining Q-learning with hyperheuristic algorithms has enabled efficient solutions to the multi-objective energy-saving distributed flow shop scheduling problem considering congestion constraints. Utilizing a Q-learning-guided variable neighborhood search mechanism has effectively improved the optimization performance of the Non-dominated Sorting Genetic Algorithm II (NSGA-II). By integrating multi-objective meme algorithms, particle swarm optimization (PSO) algorithms, and Q-learning-based local search strategies, the distributed hybrid flow shop scheduling problem has been solved efficiently. Furthermore, an improved differential evolution algorithm based on Q-learning has been proposed, providing a new approach to addressing the scheduling challenges of dynamic distributed flexible work shops. These studies demonstrate that the dynamic state awareness and reward / penalty feedback mechanism of Q-learning can effectively compensate for the shortcomings of traditional heuristic algorithms in parameter adaptation and strategy selection. However, although Q-learning has shown significant potential in enhancing the optimization performance of metaheuristic algorithms, it still cannot be well applied or achieve ideal results when used to solve complex scheduling problems that simultaneously consider dynamic perturbations, worker constraints, and learning and forgetting effects. Summary of the Invention

[0007] The purpose of this invention is to provide a dynamic scheduling method for digital twin workshops that takes into account the learning and forgetting effects, so as to achieve a better balance between the solution quality and optimization efficiency of the scheduling scheme.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A dynamic scheduling method for digital twin workshops that considers learning and forgetting effects, constructing a virtual workshop that is mapped in real time to the physical workshop using digital twin technology, comprising:

[0010] The initial state data of the physical workshop is collected and sent to the virtual workshop. The virtual workshop generates an initial scheduling plan with the goal of minimizing the maximum completion time and total production cost. The physical workshop executes the initial scheduling plan. The state data includes the status of machines, jobs and workers.

[0011] The system continuously collects real-time status data from the physical workshop and captures random events. If a random event is captured, the real-time status data and the random event are transmitted to the virtual workshop, and the rescheduling scheme returned by the virtual workshop is executed; otherwise, the current scheduling scheme is maintained. The random events include the arrival of random new workpieces, random worker absences, and random machine malfunctions.

[0012] The virtual workshop performs the rescheduling process as follows: assess the feasibility of the partial insertion strategy. If the partial insertion strategy is feasible, then the partial insertion strategy and the full rescheduling strategy are adopted in parallel to minimize the maximum completion time, total production cost, and rescheduling deviation, generating two candidate solutions, and selecting the optimal candidate solution as the rescheduling solution; otherwise, the full rescheduling strategy is adopted to minimize the maximum completion time, total production cost, and rescheduling deviation, generating a rescheduling solution.

[0013] Several alternative methods are provided below, but they are not intended as additional limitations on the overall solution above. They are merely further additions or optimizations. Provided there are no technical or logical contradictions, each alternative method can be combined individually with respect to the overall solution above, or multiple alternative methods can be combined with each other.

[0014] Preferably, the candidate solutions use a weighted relative performance ratio as the evaluation index, and the weighted relative performance ratio is calculated as follows:

[0015] For each of the three objectives—minimizing the maximum completion time, minimizing the total production cost, and minimizing the rescheduling deviation—the ratio of the objective function value corresponding to the candidate scheme to the objective function value corresponding to the initial scheduling scheme is taken as the single-objective performance ratio.

[0016] Based on the weights of each objective, the performance ratios of the three single objectives are summed in weights to obtain the weighted relative performance of the candidate schemes. The candidate scheme with the smallest weighted relative performance value among the two candidate schemes is selected as the optimal candidate scheme.

[0017] As a preferred embodiment, the learning and forgetting effect model for the worker is as follows:

[0018]

[0019] in, For workpiece No. Each process is handled by workers. In the machine Up processing, and in the first The actual processing time for each processing position; This refers to the position of the process in the processing sequence; For processing workpieces No. Each process is handled by workers. In the machine Basic processing time; For workpiece The total number of processes; For workers In the machine Up-processing to workpiece The The cumulative basic processing time in the unit order; For workers In the machine upper processing workpiece The coefficient of induced learning effect, ; For workers In the machine upper processing workpiece The active learning effect coefficient, ; For worker z in the machine upper processing workpiece The forgetting effect coefficient, ; For workpiece The Each process is carried out by workers on the machine. Up processing, and located in the first The idle time before the start of work in the unit order.

[0020] Preferably, the initial scheduling scheme and the rescheduling scheme are obtained by solving the tuna swarm optimization algorithm, and the solution of the tuna swarm optimization algorithm is expressed as follows:

[0021] In the algorithm solution space, the individual position of the tuna swarm optimization algorithm is encoded by a random key vector containing three sub-segments. The position vector of each individual is defined as a continuous random key value with a total dimension of three times the total number of processes. Each random key value is constrained within the search space boundary. The position vector is equally divided into three sub-segments corresponding to machine selection, process ordering and worker selection.

[0022] In the solution space of the problem, the position vector is converted into a discrete scheduling scheme through decoding rules. In the discrete scheduling scheme, the value of the machine selection segment represents the machine number assigned to the corresponding process, the value of the process ordering segment represents the ordering position of each process in the scheduling sequence, and the value of the worker selection segment represents the specific worker number assigned to each process.

[0023] Preferably, the decoding rules include:

[0024] For machine selection and worker selection, take the random key value at the corresponding position in the position vector. ,pass Convert to the corresponding machine number or worker number, where This is the rounding function. For the search space boundary parameters, The number of candidate machines or candidate workers for a process;

[0025] For process sorting, each random key value of the position vector corresponds to a process. First, all random key values ​​corresponding to all processes are sorted in ascending order. Then, a unique rank value is assigned to the corresponding process according to the rank in the sorting list. Finally, the processing order of all processes is determined according to the ascending order of the rank values.

[0026] Preferably, the initial scheduling scheme and the rescheduling scheme are obtained by solving the tuna swarm optimization algorithm. The tuna swarm optimization algorithm includes optimizing the initial population based on a competitive learning strategy, and the execution process is as follows:

[0027] Take all individuals from the initial population and randomly pair them up to form a competitive group;

[0028] For each pair of competing individuals, the fitness values ​​of the two individuals are calculated. The individual with the better fitness value is directly retained to the next generation, while the other individual updates its position vector by learning from the individual with the better fitness value. Then it moves on to the next generation, in which For individuals with better fitness values, For individuals with worse fitness values, The learning rate;

[0029] The fitness value is either the representative Pareto optimal solution that minimizes the maximum completion time and total production cost, or the representative Pareto optimal solution that minimizes the maximum completion time, total production cost, and rescheduling deviation.

[0030] Preferably, the initial scheduling scheme and the rescheduling scheme are obtained by solving the tuna swarm optimization algorithm, which uses the Q-learning algorithm to dynamically assign the most suitable iterative strategy to each individual.

[0031] The action space of the Q-learning algorithm is defined as spiral foraging and parabolic foraging, and an ε-greedy strategy is used to select actions.

[0032] The state space of the Q-learning algorithm is characterized by the improvement of three metrics: maximum completion time, total production cost, and rescheduling deviation between two consecutive generations. For each metric, if the current value is smaller than the value of the previous generation, the corresponding improvement is assigned a value of 1; otherwise, the corresponding improvement is assigned a value of 0. Therefore, the state space contains a total of eight discrete states with two assignments under the three metrics.

[0033] The reward value of the Q-learning algorithm is defined as the weighted sum of the normalized improvements of each metric.

[0034] Preferably, in the Q-learning algorithm, all individuals in the population synchronously update the same global Q-table.

[0035] This invention provides a dynamic scheduling method for digital twin workshops that considers learning and forgetting effects. It constructs a multi-objective mathematical model that takes into account dynamic events, worker constraints, and learning and forgetting effects, aiming to minimize the maximum completion time and total production cost while maximizing rescheduling stability. To enable the model to be effectively applied to real-world production environments and to achieve real-time monitoring, physical modeling, dynamic decision-making, and worker training support, this invention designs a unified DT framework. Based on this, a hybrid rescheduling strategy is further developed, enabling the scheduling system to respond promptly and accurately to various random disturbances. At the algorithm solution level, to efficiently generate high-quality scheduling schemes, this invention proposes an improved tuna swarm optimization (QLTSO) algorithm based on Q-learning enhancement. This algorithm integrates an Iterative Chaotic Map with Infinite Collapses (ICMIC), an extended encoding and decoding mechanism, a pairwise competition mechanism, and a Q-learning-based strategy selection mechanism. To verify the superiority of the proposed algorithm, comparative experiments were conducted on 17 benchmark examples in both static and dynamic scenarios. The results show that the QLTSO algorithm consistently outperforms the three mainstream comparison algorithms in all key performance indicators. Finally, the effectiveness and engineering applicability of the proposed model and algorithm in real-world production environments are further verified by combining them with actual industrial cases. Attached Figure Description

[0036] Figure 1 This is a DT framework diagram of the present invention;

[0037] Figure 2 This is a schematic diagram of the dynamic scheduling process in the DT of this invention;

[0038] Figure 3 A flowchart illustrating the dynamic scheduling method for digital twin workshops that takes into account the learning and forgetting effects of this invention.

[0039] Figure 4This is a diagram of the QLTSO algorithm framework of the present invention;

[0040] Figure 5 This is a schematic diagram illustrating the mapping relationship between the algorithm solution of this invention and the problem solution space;

[0041] Figure 6 This is a graph showing the effect of different parameter levels on fitness values ​​in the experiments of this invention;

[0042] Figure 7 This is the average performance convergence curve of example I_33_183_23_19 in the experiment of this invention;

[0043] Figure 8 This is a performance comparison chart of instance I_15_78_10_8 based on RPD in the experiment of this invention;

[0044] Figure 9 This is a schematic diagram of the Pareto front of the initial scheduling scheme in the experiment of this invention;

[0045] Figure 10 This is a diagram showing the distribution of Pareto optimal solutions during the rescheduling process in the experiment of this invention.

[0046] Figure 11 This is a schematic diagram of a scheduling scheme that considers random machine failures in the experiments of this invention.

[0047] Figure 12 This is a schematic diagram of a scheduling scheme that considers random worker absences in the experiment of this invention. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] Unless otherwise defined, 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. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to limit the invention.

[0050] To address the shortcomings of existing research, this embodiment focuses on the Dynamic Flexible Job Shop Scheduling Problem (DFJSSP) considering worker constraints. It not only considers worker learning and forgetting effects but also introduces three types of dynamic events: random arrival of new jobs, machine malfunctions, and worker absences. Furthermore, this embodiment deeply integrates data visualization (DT) technology with intelligent optimization algorithms. On one hand, DT technology enables virtual-real mapping and state perception of the production process, providing reliable underlying data support for the dynamic decision-making of the shop floor scheduling system. On the other hand, the adaptive search mechanism of the proposed optimization algorithm achieves efficient and stable solutions to complex scheduling problems.

[0051] First, this embodiment establishes the learning and forgetting effects.

[0052] Existing technologies propose a comprehensive learning effect model for single-machine scheduling problems. This model simultaneously considers the position of the workpiece in the processing sequence, the active and induced learning effects of the worker, and the worker heterogeneity, as shown in Equation (1).

[0053] (1)

[0054] in, For workpiece In the first The actual processing time for each processing position; This refers to the position of the workpiece in the processing sequence; For workpiece Basic processing time; and workers The coefficients of induced learning effect and active learning effect.

[0055] The existing technology introduces the forgetting effect caused by idle time during workpiece processing and worker interruption into the flow shop scheduling problem, and constructs a model that integrates workpiece processing sequence, worker experience, worker active learning effect and forgetting effect, as shown in formula (2).

[0056] (2)

[0057] in, For workers' experience factors; For the front The cumulative basic processing time of the workpiece at each processing position; This is the sum of the basic machining times for all workpieces; The summation index for the processing order; This represents the total number of workpieces. This is the forgetting effect coefficient; This represents the active learning effect coefficient. This is a truncation parameter used to limit the minimum processing time under the influence of the learning effect.

[0058] To more realistically reflect the impact of learning and forgetting effects on production efficiency in DFJSSP, this embodiment proposes a novel learning and forgetting effect model by combining formulas (1) and (2). This model replaces the original workpiece processing sequence with the process processing sequence and simultaneously considers the heterogeneity of machines and workers, as shown in formula (3).

[0059] (3)

[0060] in, For workpiece No. Each process is handled by workers. In the machine Up processing, and in the first The actual processing time for each processing position; This refers to the position of the process in the processing sequence; For processing workpieces No. Each process is handled by workers. In the machine Basic processing time; For workpiece The total number of processes; For workers In the machine Up-processing to workpiece The The cumulative basic processing time in the unit order; For workers In the machine upper processing workpiece The coefficient of induced learning effect; For workers In the machine upper processing workpiece The active learning effect coefficient; For worker z in the machine upper processing workpiece The forgetting effect coefficient; For workpiece The Each process (by worker z on the machine) Up processing, and located in the first (Individual digit sequence) The free time before the start of work.

[0061] Secondly, this embodiment establishes random events.

[0062] This embodiment treats the arrival of a new workpiece as a random event and models random machine failures and random worker absences as follows:

[0063] (1) Random machine failure:

[0064] Assuming that the higher the machine's usage intensity, the greater the probability of failure, and that the timing and duration of failure both depend on the machine's cumulative busy time, then the machine... The failure probability can be approximated by formula (4):

[0065] (4)

[0066] in, For machines The probability of failure, For machines The running time, This represents the total cumulative running time of all machines. The timing of the failures follows a uniform distribution as shown in formula (5), and the cumulative maintenance time after the failures follows a uniform distribution as shown in formula (6).

[0067] (5)

[0068] (6)

[0069] in, For machines The moment the fault occurred; The cumulative repair time following the malfunction; , , and This represents the corresponding interval scaling factor.

[0070] (2) Random worker absences:

[0071] According to the definition in the prior art, the random worker absenteeism rate is defined as shown in formula (7):

[0072] (7)

[0073] in, This refers to the average daily attendance rate. The on-the-job rate (i.e., the ratio of the number of on-the-job workers to the total number of workers). It is a discrete random variable that follows a specific distribution and is used to represent the duration of absence; This represents the expected duration of absence. When the total number of workers is... At that time, it is estimated that there will be 100,000 people per day. One worker was absent.

[0074] Therefore, based on the aforementioned learning and forgetting effects and random events, this embodiment proposes a dynamic scheduling method for digital twin workshops that considers learning and forgetting effects, specifically designed to study the impact of various dynamic events on DFJSSP, such as the arrival of random new workpieces, random machine failures, and random worker absences. The scheduling process includes two stages: initial scheduling and rescheduling. First, it is assumed that all resources are available at the initial moment, and an initial scheduling scheme is generated under a static deterministic environment. Subsequently, during production execution, once the aforementioned dynamic disturbance occurs and the rescheduling trigger condition is met, the system will adaptively reschedule the current scheduling scheme.

[0075] In this embodiment, all workpieces, machines, and workers are available at time 0; at any given time, a machine can only process one operation; at any given time, a worker can only operate one machine; at any given time, each operation can only be processed on one machine; during processing, the operation can be temporarily interrupted; when a machine experiences a random malfunction, the processing operation currently in progress on the machine will be interrupted, and the affected operation must be re-processed after the malfunction is repaired; for a newly arrived workpiece, if there is an operation being processed on an available machine, that operation cannot be preempted.

[0076] Based on the existing five-dimensional DT model, this embodiment addresses the scheduling optimization needs in complex production environments and designs a unified DT framework, such as... Figure 1 As shown, the framework covers five core dimensions: physical workshop, virtual workshop, twin data, visualization, and data flow. It further integrates three functional modules at the virtual workshop layer: worker status detection, scheduling optimization, and worker training support.

[0077] Based on this framework, this embodiment further constructs a unified DT (Data Technology) system. In this system, the data management module establishes a crucial "sensing-control" closed loop, promoting high-frequency dynamic interaction and integration between the physical and virtual workshops. Specifically, the physical workshop, leveraging technologies such as sensors, the Industrial Internet, and 5G communication, continuously collects and synchronizes multi-source data, including production process data, task execution information, equipment operating status, and real-time worker status, during the execution of optimized scheduling schemes. Subsequently, this data, after digital processing, is fed into the central data management module as a data stream. This module uniformly manages and integrates real-time, historical, and simulation data, and completes data cleaning, storage, and visualization, providing data support for virtual workshop modeling, scheduling optimization, and status monitoring.

[0078] The virtual workshop receives data transmitted from the data management module and uses it as a high-fidelity digital mapping of the physical workshop, providing a real-time data environment for subsequent dynamic event monitoring, mathematical modeling, rescheduling strategy formulation, and scheduling scheme generation. The intelligent scheduling module, after making decisions in the virtual workshop, sends the newly generated scheduling scheme to the physical workshop for execution. Furthermore, to realistically depict worker constraints in the scheduling model, the virtual workshop integrates a worker status monitoring module to track worker attendance, skill level, work status, and fatigue levels in real time. To improve worker efficiency and meet the adaptive requirements of dynamic scheduling, the framework integrates a simulation training module at the virtual layer. This module provides workers with skill enhancement methods by constructing multi-dimensional interactive scenarios covering theoretical understanding and virtual practice, thereby enhancing their induced learning effect and providing dynamically updated skill parameters for the underlying scheduling model.

[0079] The dynamic scheduling process in the DT system is as follows: Figure 2 As shown in the diagram, firstly, the physical workshop collects and synchronizes production data in real time while executing the current scheduling plan. Then, the data management module receives this data and completes data processing and transmission. Next, the virtual workshop uses the processed data as input to perform dynamic event detection and analysis. For specific disturbance events identified, the virtual workshop determines the corresponding rescheduling strategy and updates the scheduling plan. Finally, the virtual workshop outputs a new scheduling plan and performs simulation verification. After successful verification, the plan is sent to the physical workshop for execution, thus forming a complete dynamic scheduling closed loop.

[0080] Therefore, as Figure 3 As shown in the figure, the proposed method for dynamic scheduling of digital twin workshops considering the learning and forgetting effects includes the following steps:

[0081] Step 1: Collect the initial status data of the physical workshop and send it to the virtual workshop. The virtual workshop generates an initial scheduling plan with the goal of minimizing the maximum completion time and total production cost. The physical workshop executes the initial scheduling plan. The status data includes the status of machines, jobs and workers.

[0082] In this embodiment, the scheduling objective is to minimize the maximum completion time and total production cost, and to maximize rescheduling stability. Maximizing rescheduling stability only takes effect during the rescheduling process. To this end, the objective function is defined by formulas (8)-(13).

[0083] (1) Minimize the maximum completion time:

[0084] (8)

[0085] (2) Minimize total production cost:

[0086] In this embodiment, the total production cost (as defined by formula (9)) includes the total processing cost (as defined by formula (10)) and the total learning cost (as defined by formula (11)).

[0087] (9)

[0088] (10)

[0089] (11)

[0090] (3) Maximize rescheduling stability:

[0091] Maximizing rescheduling stability is achieved by minimizing the total deviation, as shown in equations (12) and (13). The total deviation is used to quantify the degree of deviation of the start time of each process in the rescheduling scheme from the initial scheme.

[0092] (12)

[0093] (13)

[0094] The above formulas must satisfy the constraints shown in formulas (14)-(33):

[0095] (14)

[0096] (15)

[0097] (16)

[0098] (17)

[0099] (18)

[0100] (19)

[0101] (20)

[0102] (twenty one)

[0103] (twenty two)

[0104] (twenty three)

[0105] (twenty four)

[0106] (25)

[0107] (26)

[0108] (27)

[0109] (28)

[0110] (29)

[0111] (30)

[0112] (31)

[0113] (32)

[0114] (33)

[0115] Formulas (14) to (15) define the process. The completion time is set, and it is constrained not to exceed the maximum completion time. Formula (16) is a timing constraint, which constrains the process. Must be in the process Complete before starting. Formulas (17) and (18) stipulate that if there is a priority relationship between processes, then the process... and It must be assigned to the corresponding machine Formula (19) is used to constrain that any two operations on the same machine must have a clear sequential order. Formulas (20) to (23) are used to further define the timing and sequence constraints related to worker assignment, and the logic is consistent with formulas (16) to (19). Formulas (24) to (25) are used to constrain the start time order of adjacent operations within the same workpiece in the initial scheduling and rescheduling schemes. Formulas (26) to (29) are used to constrain that each operation is assigned to only one machine and one worker. Formulas (30) to (33) indicate that the decision variables are 0-1 binary variables.

[0116] in, For a collection of workpieces, For workpiece The set of processes, For machine collection, Gathering the workers For workpiece subscript, , For process indexing, , For machine indexing, , Bidding for workers , For the first One workpiece, For workpiece The j-th process, For the k-th machine, For the z-th worker, To maximize the completion time, For workpiece The completion time, For process The completion time, Total production cost The total processing cost, For the total learning cost, For process Processing costs on machines, , For workers The learning cost , This represents the total deviation of the start time of each process in the rescheduling scheme from the initial schedule. For the rescheduling scheme of processes Compared to the maximum deviation at the initial scheduling, This represents the initial total number of processes. Weighting coefficients , For the initial scheduling of processes The actual start time of construction For the rescheduling scheme of processes The actual start time of construction For workers In the machine Previous execution process The actual processing time is calculated in the same way as shown in formula (3). That is, in this embodiment and equal, It is a sufficiently large positive number; For 0-1 variables: if the process Assigned to machine If processing is required, set the value to 1; otherwise, set the value to 0. For 0-1 variables: if the process Assigned to workers If processing is required, set the value to 1; otherwise, set the value to 0. 0-1 variables: in the machine Previous process exist If it was previously processed, take 1; otherwise, take 0. 0-1 variables: by workers If the process is during operation exist If it was processed previously, take 1; otherwise, take 0.

[0117] Step 2: Continuously collect real-time status data of the physical workshop and capture random events. If a random event is captured, transmit the real-time status data and random event to the virtual workshop and execute the rescheduling scheme returned by the virtual workshop; otherwise, maintain the current scheduling scheme. Random events include random new workpiece arrivals, random worker absences, and random machine failures.

[0118] The virtual workshop rescheduling process involves: evaluating the feasibility of the local insertion strategy; if the local insertion strategy is feasible, then the local insertion strategy and the full rescheduling strategy are adopted in parallel to minimize the maximum completion time, total production cost, and rescheduling deviation, generating two candidate schemes, and selecting the optimal candidate scheme as the rescheduling scheme; otherwise, the full rescheduling strategy is adopted to minimize the maximum completion time, total production cost, and rescheduling deviation, generating a rescheduling scheme.

[0119] In actual production, random dynamic events can disrupt the feasibility of the initial scheduling scheme. To mitigate the adverse effects of such disturbances, effective rescheduling strategies are needed to dynamically modify the current scheme. Currently, widely used rescheduling strategies mainly include four methods: insertion rescheduling (corresponding to the arrival of random new workpieces), right-shift rescheduling (corresponding to random machine failures), worker replacement (corresponding to random worker absences), and full rescheduling. From a response mechanism perspective, insertion rescheduling utilizes machine idle time windows to insert new processes, primarily addressing the random arrival of new workpieces; right-shift rescheduling and worker replacement address random machine failures and random worker absences by extending process processing time and reallocating workers, respectively. These three response strategies aim to locally adjust the scheduling scheme while maintaining the original process processing order and resource allocation as much as possible, minimizing the adverse effects of random disturbances and improving the stability of the rescheduling scheme. In contrast, full rescheduling globally reallocates all currently unprocessed processes. This strategy can more flexibly respond to complex emergencies and achieve a better balance among multiple performance indicators, but it usually comes at the cost of sacrificing rescheduling stability.

[0120] Therefore, in the face of a complex and ever-changing manufacturing environment, it is difficult to effectively balance operational efficiency and system stability using only one of the above-mentioned rescheduling strategies. In order to give full play to the complementary advantages of various rescheduling methods, this embodiment proposes a hybrid rescheduling strategy that integrates four types of methods to deal with dynamic disturbances in the production process. Once a dynamic event occurs, the system will use the weighted relative performance ratio ( ) defined by formula (34) to determine the rescheduling strategy. It adaptively selects the optimal rescheduling method to cope with specific events.

[0121] (34)

[0122] in, For the first The weights of each objective. Since this paper considers three optimization objectives, therefore... , and These are the objective function values ​​for the new scheme and the initial scheme, respectively. It should be noted that, due to the third objective (total deviation)... This only occurs during the rescheduling phase, to ensure... To ensure computational uniformity, this paper will discuss the initial scheme. (Right now The corresponding denominator baseline value is set to 1. In the model of this paper, the maximum completion time, total production cost, and total deviation are all minimized objectives, therefore... The smaller the value, the better the overall performance of the rescheduling method. Based on With dynamic quantitative feedback of indicators, the hybrid rescheduling strategy proposed in this paper can adaptively select a single optimal rescheduling method, thereby realizing intelligent optimization of DFJSSP.

[0123] Taking the arrival of a random new workpiece as an example, the system first calls an existing scheduling algorithm to generate an initial scheduling scheme and obtains a representative Pareto optimal solution aimed at minimizing the maximum completion time and total production cost. During the entire scheduling cycle, when the system detects the arrival of a new workpiece, it first evaluates the feasibility of a local insertion strategy, i.e., whether all operations of the new workpiece can be inserted into the current idle time slot of the required machine without conflict. If the evaluation result is feasible, the system will generate two candidate schemes in parallel: Scheme 1 adopts a local insertion strategy (adopting the corresponding rescheduling strategy based on the corresponding random event, such as insertion rescheduling, right shift rescheduling, or worker replacement); Scheme 2 adopts a full rescheduling strategy and introduces a rescheduling deviation on the basis of the original objective to achieve synergistic optimization of the maximum completion time and total production cost. Subsequently, the system calculates and compares the two schemes. The system will evaluate the data and select the best option for the final scheduling. Conversely, if the machine's idle time slot cannot meet the insertion conditions, the system will abandon the local adjustment and directly trigger a full rescheduling strategy (Scheme 3). If no disturbance occurs in the current time period, the original scheduling scheme will remain unchanged.

[0124] The Tuna Swarm Optimization (TSO) algorithm is a novel metaheuristic algorithm inspired by the cooperative foraging behavior of tuna swarms. This algorithm employs two core strategies—spiral foraging and parabolic foraging—to achieve global search. However, the basic TSO algorithm is prone to getting trapped in local optima and has a slow convergence speed when solving complex discrete high-dimensional scheduling problems. To overcome these limitations and further improve the algorithm's optimization performance and solution efficiency, this embodiment proposes the QLTSO algorithm. The core improvement mechanisms of this algorithm are as follows: an ICMIC mapping mechanism is introduced to enhance the diversity of the initial population; a novel solution representation and decoding mechanism is designed to achieve an effective mapping between the continuous QLTSO search space and the discrete DFJSSP solution space; a pairwise competition mechanism is introduced as a population optimization strategy to eliminate inferior individuals generated in the initialization phase, ensuring the quality of the population in the early stages of evolution; and a Q-learning-based strategy selection mechanism is proposed to achieve an adaptive balance between global exploration and local exploitation.

[0125] In this embodiment, the QLTSO algorithm is used to solve both the initial scheduling phase and the rescheduling phase. The fitness value of the initial scheduling phase is the representative Pareto optimal solution that minimizes the maximum completion time and total production cost. The fitness value of the rescheduling phase is the representative Pareto optimal solution that minimizes the maximum completion time, total production cost, and rescheduling deviation.

[0126] The overall framework of the QLTSO algorithm is as follows: Figure 4 As shown, the process includes the following:

[0127] (1) Population initialization based on ICMIC mapping mechanism.

[0128] The population initialization mechanism has a significant impact on the final performance of metaheuristic algorithms. The basic TSO algorithm usually adopts a standard random initialization strategy, but this strategy is difficult to guarantee population diversity and is prone to premature convergence. Since the ICMIC mapping mechanism has good chaos and ergodicity, this embodiment introduces this mechanism to enhance the diversity of the initial population and provide a more uniform solution space coverage for subsequent optimization. The specific mathematical expression of ICMIC is shown in formula (35).

[0129] (35)

[0130] in, The normalized chaotic state variable for the current iteration; The normalized chaotic state variables for the next iteration are obtained by ICMIC calculation; The parameters are used to control the intensity of chaos. During the initialization process, the initial seed is obtained through initialization, and the remaining seeds are obtained through iterative calculation according to formula (35).

[0131] Given that the basic TSO algorithm is primarily designed for continuous optimization problems, this embodiment constructs a corresponding spatial mapping mechanism to effectively apply it to the DFJSSP, which exhibits significant discrete characteristics. Building upon existing single-resource scheduling methods, this embodiment designs a novel encoding-decoding mechanism to adapt to scheduling scenarios involving both machine and worker resources. This mechanism constructs a "continuous-discrete" two-layer mapping architecture: in the algorithm search space, continuous real-valued vectors represent the positions of individual QLTSOs; in the problem solution space, specific decoding rules transform them into discrete scheduling schemes that include process ordering, machine allocation, and worker assignment.

[0132] In the algorithm's search space, the individual positions of QLTSOs are encoded using random key vectors containing three subdomains. The position vector for each individual is defined as: ,in Let v be the v-th consecutive random key value, and D be the total dimension of the vector. This vector is divided into three equal segments, corresponding to Machine Selection (MS), Operation Ordering (OS), and Worker Selection (WS), respectively. (in This represents the total number of processes. To normalize the search space, each component in the vector... All are constrained within the interval Within, where Δ is a preset parameter used for normalization and defining the boundary of the search space.

[0133] In the solution space, the actual scheduling scheme is also represented as a discrete vector consisting of three sub-segments: MS, OS, and WS. Specifically, the value of the MS segment represents the machine number assigned to the corresponding process; the value of the OS segment represents the order position of each process in the scheduling sequence; and the value of the WS segment represents the specific worker number assigned to that process.

[0134] Figure 5 The code presents an example encoding and decoding process involving 2 workpieces (6 processes in total), 3 machines, and 3 workers. Each process corresponds to a varying number of candidate machines and candidate workers. As shown in the light-colored area at the top of the figure, the individual positions in the algorithm layer are composed of three consecutive random key vectors (MS, OS, WS), each of length 6, forming a combined position vector of dimension 18; and all element values ​​are constrained to the range... Inside. The dark area at the bottom of the diagram shows the discrete scheduling scheme for the problem layer after the decoding rules have been transformed.

[0135] Based on the aforementioned two-layer encoding structure, this embodiment employs a specific transformation strategy to map the continuous algorithm search solution space to a discrete problem solution space through decoding operations. This decoding process is performed separately on the three sub-vectors MS, OS, and WS:

[0136] MS: For each process See formula (36), which converts the numerical value at the corresponding position in the algorithm solution vector into the machine number in the candidate machine set for that process.

[0137] (36)

[0138] in, The machine number selected for a specific process; This represents the corresponding positional value in the algorithm's solution vector; This represents the number of candidate machines for this process.

[0139] OS: The order of operations is determined using the Ranked Value (ROV) method. Specifically, each element of the continuous position vector corresponds to a specific operation. First, the algorithm position values ​​corresponding to all operations are sorted in ascending order. Then, a unique ROV is assigned to each operation based on its rank in the sorted list. Finally, the processing order of all operations is determined according to the ascending order of the ROVs.

[0140] WS: The processing method in the WS stage is the same as that in the MS stage.

[0141] (2) Calculate individual fitness values ​​based on competitive learning strategies.

[0142] While the ICMIC mechanism effectively improves the diversity of the initial population, its inherent randomness may introduce some low-quality individuals, thus affecting the optimization efficiency in the early stages of the algorithm. To further improve the quality of the initial population, this embodiment introduces a pairwise competition mechanism into the proposed QLTSO algorithm to perform a secondary screening of the initial population. This mechanism provides a high-quality initial population for the main evolutionary cycle by eliminating inferior individuals.

[0143] In the QLTSO algorithm, after initialization via ICMIC, a structure containing... Population of individuals Each individual has a position vector. It means that among them The index of an individual (n=1,2,…,N). The index of the vector dimension (v=1,2,…,D). For the first The individual in the first The positional value on the dimension.

[0144] During population optimization, each individual is randomly paired up to compete. For each pair of individuals, the one with better fitness (i.e., the "winner") is directly retained to the next generation; conversely, the one with poorer fitness (i.e., the "loser") updates its position vector by learning from the winner. The update formula is shown in formula (37):

[0145] (37)

[0146] in, and These represent the position vectors of the winner and loser in each pair of individuals; To ensure the learning rate follows a uniform distribution, the range of values ​​is [value range missing]. Once all paired individuals have completed their competition, the optimized population enters the main evolutionary cycle phase.

[0147] (3) Set up the state and action space, and initialize the Q table and initial state.

[0148] The basic TSO algorithm includes two strategies: spiral foraging and parabolic foraging, and the switching between them usually relies on a random selection mechanism. To overcome the blindness of this mechanism, this embodiment introduces Q-learning to construct an adaptive strategy selection mechanism. Specifically, the algorithm queries a shared knowledge base generated by the population evolution process in real time to select an optimal individual (…). Dynamically allocate the most suitable iteration strategy to achieve an adaptive balance between global exploration and local development.

[0149] In the Q-learning model, the agent's action space is defined by two core strategies: spiral foraging and parabolic foraging. The state space is characterized by the improvement of three key objective metrics between two consecutive generations, denoted as […]. , and The improvements in these three dimensions reflect the evolution of the algorithm during the search process. Specifically, the improvement is defined as the difference between the objective function value of the previous generation and the current generation (e.g., ...). To simplify model computation, this paper employs a binary state encoding method: for each objective function, if its current value is improved compared to the previous generation, it is assigned a value of 1; otherwise, it is assigned a value of 0. This encoding mechanism effectively maps the continuous search process to a finite set of states. According to the above definition, the state space of this Q-learning model contains a total of A discrete state.

[0150] In the In the middle of the generation, when the first The next iteration executes the action. Then, calculate the reward value. To evaluate the effectiveness of the strategy, the reward value is used to account for differences in numerical magnitude and units among the various objective functions. Defined as the weighted sum of the normalized improvements of each objective function, its expression is shown in formula (38):

[0151] (38)

[0152] in, Representing the current individual exist , ,and Fitness values ​​for the three objectives; the subscripts `old` and `new` are used to distinguish the fitness values ​​before and after policy implementation, respectively. Weight coefficients. For the parameters related to the problem, satisfying (This is used to reflect decision-making preferences; in this paper, equal weighting is used). For a very small constant (e.g.) This is used to avoid calculation errors when the denominator approaches zero. Because , ,and Both are minimization objectives, therefore, when the overall reward value When the value is 1, it indicates that the current strategy has effectively improved the objective function value.

[0153] (4) Select action A from the Q table based on the current state.

[0154] Subsequently, the agent employs an ε-greedy strategy to select actions, balancing the algorithm's exploration and development capabilities. The corresponding Q-value update rule is shown in formula (39):

[0155] (39)

[0156] in, For the next state Candidate actions in; and These represent the learning rate and the discount factor, respectively. To accelerate algorithm convergence, this embodiment employs an experience-sharing mechanism, whereby all individuals within the population synchronously update the same global Q-table during each generation of evolution.

[0157] (5) Calculate the fitness value of action A and update the position of the fish swarm.

[0158] (6) Obtain the reward function and the new state, and update the Q table.

[0159] (7) Determine whether the iteration condition is met. If yes, obtain the optimal solution and end; otherwise, return to step (1) to continue iterating.

[0160] This embodiment proposes a dynamic scheduling method for digital twin workshops that considers learning and forgetting effects. It constructs a multi-objective mathematical model that considers worker constraints and learning and forgetting effects, aiming to minimize the maximum completion time and total production cost while maximizing rescheduling stability. A DT framework for dynamic scheduling is proposed, providing reliable technical support for worker state perception and agile response to disturbance events through virtual-real mapping and state awareness of production factors. An adaptive hybrid rescheduling strategy based on the DT framework is proposed, integrating four methods: insertion rescheduling, right-shift rescheduling, worker replacement, and full rescheduling, to effectively cope with dynamic disturbance events such as random new job arrivals, random machine failures, and random worker absences. The QLTSO algorithm is proposed, which utilizes ICMIC and pairwise competition mechanisms to enhance population initialization quality, designs a novel encoding / decoding mechanism to adapt to the discrete problem space, and introduces a Q-learning-based strategy selection mechanism to achieve a dynamic balance between global exploration and local development.

[0161] Experimental Analysis:

[0162] This embodiment evaluates the performance of the QLTSO algorithm through experiments such as parameter calibration, key module verification, benchmark comparison, and statistical significance testing, and verifies its application effect through a practical case. All experiments were run in a Windows 11 64-bit operating system environment configured with an Intel Core processor (2.30 GHz) and 16 GB of memory.

[0163] (1) Test examples and performance evaluation indicators.

[0164] This experiment uses 17 publicly available examples for evaluation. These examples range in size from 9 to 38 workpieces, 48 ​​to 213 processes, 6 to 27 machines, and 4 to 22 workers. Each example is named according to the rule "Number of Workpieces_Number of Processes_Number of Machines_Number of Workers" (e.g., I_9_48_4_3). Furthermore, each example triggers dynamic events during execution, such as random new workpiece arrivals, random machine malfunctions, and random worker absences. The specific parameter settings and data sources for these dynamic events are described below.

[0165] The arrival times of new workpieces in each example are detailed in Table 1. The correlation coefficients used to simulate random machine failures are set as follows: The baseline data on worker availability is derived from official reports.

[0166] Table 1 Examples and Arrival Time of Random New Workpieces

[0167]

[0168] This experiment uses two classic metrics, hypervolume (HV) and inverted generational distance (IGD), to comprehensively evaluate the performance of the QLTSO algorithm and various benchmark algorithms in terms of convergence and diversity. To eliminate the influence of dimensions, all evaluation metrics were normalized beforehand. In addition, relative percentage deviation (RPD) was used to quantify the stability and quality finding of the algorithm, and its specific calculation formula is shown in (40):

[0169] (40)

[0170] in, The index value obtained by the current algorithm. RPD represents the optimal performance index observed among all algorithms (i.e., HV at its maximum and IGD at its minimum). When RPD = 0, it indicates that the algorithm has achieved optimal performance; when RPD < 0, it indicates that there is a percentage difference between the algorithm and the optimal algorithm.

[0171] (2) Parameter design.

[0172] The QLTSO algorithm includes three key parameters: population size N, assimilation coefficient, and so on. and search parameters To evaluate the impact of the above parameters on algorithm performance, this experiment used the Taguchi method for parameter tuning. Each parameter was set to three levels, and the specific values ​​are shown in Table 2. Based on this, the following methods were used: Nine parameter combinations were constructed using an orthogonal array. For each parameter combination, the QLTSO algorithm was run independently 10 times on four test cases (I_9_48_6_4, I_15_78_10_8, I_21_105_15_12, I_26_131_18_15).

[0173] Table 2 Parameter Level Settings

[0174]

[0175] Figure 6 The impact of the three key parameters mentioned above on the algorithm's fitness value is demonstrated in different test cases. Figure 6 It can be seen that when the parameter is set to At this point, the QLTSO algorithm exhibits the best overall optimization performance. Therefore, all subsequent numerical experiments used this parameter combination.

[0176] (3) Ablation experiment.

[0177] To further verify the contributions of the pairwise competition mechanism and the Q-learning module to the overall performance of the algorithm, an ablation experiment was conducted. Specifically, two algorithm variants were designed: QLTSO_1 (removing the pairwise competition mechanism) and QLTSO_2 (removing the Q-learning module). Each algorithm was run independently 20 times, with a maximum number of iterations uniformly set to 500. Figure 7 The average performance convergence curves of the three algorithms on test case I_33_183_23_19 are presented.

[0178] Depend on Figure 7 As can be seen, compared with QLTSO_1 and QLTSO_2, the complete QLTSO algorithm achieves a better fitness value at the convergence point, indicating its stronger global optimization ability in searching for high-quality solutions. Furthermore, the statistical results in Table 3 further show that the QLTSO algorithm achieves the lowest average fitness value in the vast majority of instances, with a smaller overall standard deviation, demonstrating higher optimization accuracy and robustness. In contrast, QLTSO_1 and QLTSO_2 have higher fitness values, indicating that they are more prone to getting trapped in local optima. These ablation results verify the effectiveness of the pairwise competition mechanism and the Q-learning module.

[0179] Table 3 Comparison data from ablation experiments

[0180]

[0181] (4) Comparison with benchmark algorithms.

[0182] To fully verify the effectiveness of the proposed algorithm, this experiment compares QLTSO with three classic intelligent optimization algorithms: Non-Dominated Sorting Genetic Algorithm II (NSGA-II), Basic Tuna Swarm Optimization (TSO), and Improved Gray Wolf Optimization (IGWO). These three benchmark algorithms were chosen primarily because they have demonstrated good performance in solving similar complex multi-objective scheduling problems. The specific parameter settings for each algorithm are shown in Table 4.

[0183] Table 4 Parameter Settings

[0184]

[0185] Each algorithm was run independently 20 times on each test case. To comprehensively evaluate the performance advantages of the QLTSO algorithm, the RPD results calculated based on the HV and IGD metrics are shown in Tables 5 and 6, respectively.

[0186] Table 5 HV in the initial scheduling RPD and IGD RPD

[0187]

[0188] Table 6 HV in Rescheduling RPD and IGD RPD

[0189]

[0190] Table 5 shows that the QLTSO algorithm achieved the best initial scheduling performance in over 82% of the test cases. Table 6 shows that in rescheduling scenarios caused by random machine failures, the QLTSO algorithm outperformed other benchmark algorithms in almost all cases.

[0191] To visually demonstrate the performance advantages of the QLTSO algorithm, Figure 8 The RPD distribution of example I_15_78_10_8 under different scheduling stages is given. The horizontal lines in the figure intuitively reflect the performance differences between the algorithms, with the rightmost value (0) representing the best performance in that group. Figure 8 As shown in (a) of the figure, during the initial scheduling phase, although the TSO algorithm shows some competitiveness in the IGD metric, the QLTSO algorithm consistently maintains the optimal value of 0 in all evaluation metrics. Figure 8 As shown in (b), during the rescheduling phase, the performance of each benchmark algorithm degrades to varying degrees. For example, the TSO algorithm shows a significant decline in the IGD metric, while the QLTSO algorithm remains stable at the optimal level. These results further verify that the QLTSO algorithm has a stronger competitive advantage in dealing with dynamic disturbance events.

[0192] (5) Statistical analysis.

[0193] This experiment demonstrates the statistical significance of the above experimental results by conducting nonparametric statistical tests.

[0194] Table 7 lists the p-values ​​calculated using the Wilcoxon signed-rank test at a significance level of 0.05, used to statistically verify the performance advantage of the QLTSO algorithm compared to its ablation variants (i.e., QLTSO_1 and QLTSO_2). As shown in Table 7, the p-values ​​are less than 0.05 in the vast majority of test cases, indicating a statistically significant difference between the QLTSO algorithm and its ablation variants, thus validating the effectiveness of the proposed improvement strategy. Although the algorithmic difference did not reach a significant level (p>0.05) in a few individual cases (such as I_23_112_14_13), the overall statistical results still indicate that the core mechanism of the QLTSO algorithm is effective.

[0195] Table 7. Wilcoxon signed-rank test p-values ​​for ablation experiments

[0196]

[0197] (6) Practical industrial case applications.

[0198] To evaluate the engineering applicability of the QLTSO algorithm in a real-world production environment, this experiment collected actual production data from a large tunnel boring machine manufacturer. The experiment uses the manufacturing process of the company's engine exhaust system as a background, abstracting its component assembly relationships, process sequences, selectable machine sets, and worker assignment relationships into a discrete DFJSSP. This manufacturing process encompasses a specific process sequence and integrates a highly flexible machine allocation and worker assignment mechanism. The engine exhaust system structure includes components such as a heat insulation sleeve, muffler, muffler clamp, flat washer, first Dacrust (bolt), exhaust pipe, bellows, flat washer, spring washer, first heat insulation sleeve, second Dacrust (bolt), second heat insulation sleeve, large flange bolt, nut (Dacrust), diesel engine, exhaust pipe, gasket, and spring washer.

[0199] Figure 9 The Pareto fronts generated by each algorithm in the initial scheduling phase are shown. The comparative results show that the QLTSO algorithm outperforms other benchmark algorithms in both convergence and distribution of its non-dominated solution set, and can obtain a high-quality scheduling scheme with a shorter maximum completion time and lower total production cost.

[0200] Figure 10 This further demonstrates the Pareto fronts of each algorithm during the rescheduling phase. Figure 10 It can be seen that the solution set of the QLTSO algorithm is highly concentrated in the low-value region of each objective function, exhibiting strong rescheduling stability and robustness. In contrast, the Pareto fronts of other benchmark algorithms generally deviate from the low-value region and show more obvious discrete fluctuations after perturbations. The above comparison of front distributions further demonstrates that the QLTSO algorithm has superior competitive performance in dealing with dynamic perturbation events.

[0201] Figure 11 and Figure 12 Using two typical disturbance events—random machine failure and random worker absence—as examples, a Gantt chart is used to visually illustrate the differences in process arrangement between the initial scheduling scheme and the rescheduling scheme. The vertical dashed lines in the chart mark key time nodes, including the occurrence time of the dynamic event, the time when affected resources become available again, and the final completion time of each scheme. As shown, after a dynamic disturbance occurs, the QLTSO algorithm can quickly respond and generate an effective rescheduling scheme; compared to the initial scheme, this rescheduling scheme, while ensuring feasibility, only causes a slight extension of the maximum completion time, demonstrating strong scheduling flexibility.

[0202] In summary, the analysis and verification of the above practical engineering cases demonstrate the engineering applicability of the QLTSO algorithm in real manufacturing environments. This algorithm not only reliably obtains higher-quality Pareto front solutions, but also exhibits strong responsiveness and rescheduling stability in the face of various random dynamic disturbances, thus achieving an effective balance between production efficiency and system robustness.

[0203] This embodiment studies the worker-constrained, techno-driven (DT) dynamic flexible job shop scheduling problem. To effectively characterize this problem, this embodiment constructs a multi-objective dynamic flexible job shop scheduling model that considers worker constraints and learning and forgetting effects to collaboratively optimize maximum completion time, total production cost, and rescheduling stability. To achieve rapid response to production disturbances, this embodiment designs a DT framework integrating real-time monitoring and worker training support modules. Based on this, a hybrid rescheduling strategy incorporating four methods—insertion rescheduling, right-shift rescheduling, worker replacement, and full rescheduling—is further developed to effectively address random dynamic events such as the arrival of new jobs, random machine failures, and random worker absences.

[0204] To obtain a high-quality and efficient scheduling scheme, this embodiment proposes the QLTSO algorithm. This algorithm organically integrates the ICMIC mapping mechanism, a novel encoding and decoding mechanism, a pairwise competition mechanism, and a Q-learning-based adaptive policy selection mechanism. Finally, through benchmark comparison experiments, nonparametric statistical tests, and application analysis of real-world industrial cases, the effectiveness of the QLTSO algorithm in solving complex dynamic flexible job shop scheduling problems and its engineering applicability to practical industrial production scheduling are verified.

[0205] In another embodiment, the present invention also provides a computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the steps of a dynamic scheduling method for digital twin workshops that takes into account learning and forgetting effects.

[0206] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory.

[0207] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this invention.

[0208] The above embodiments merely illustrate several implementation methods of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims

1. A dynamic scheduling method for digital twin workshops considering learning and forgetting effects, characterized by constructing a virtual workshop that is mapped in real time to the physical workshop using digital twin technology. The dynamic scheduling method for digital twin workshops that considers learning and forgetting effects includes: The initial state data of the physical workshop is collected and sent to the virtual workshop. The virtual workshop generates an initial scheduling plan with the goal of minimizing the maximum completion time and total production cost. The physical workshop executes the initial scheduling plan. The state data includes the status of machines, jobs and workers. The system continuously collects real-time status data from the physical workshop and captures random events. If a random event is captured, the real-time status data and the random event are transmitted to the virtual workshop, and the rescheduling scheme returned by the virtual workshop is executed; otherwise, the current scheduling scheme is maintained. The random events include the arrival of random new workpieces, random worker absences, and random machine malfunctions. The virtual workshop performs the rescheduling process as follows: assess the feasibility of the partial insertion strategy. If the partial insertion strategy is feasible, then the partial insertion strategy and the full rescheduling strategy are adopted in parallel to minimize the maximum completion time, total production cost, and rescheduling deviation, generating two candidate solutions, and selecting the optimal candidate solution as the rescheduling solution; otherwise, the full rescheduling strategy is adopted to minimize the maximum completion time, total production cost, and rescheduling deviation, generating a rescheduling solution.

2. The dynamic scheduling method for digital twin workshops considering learning and forgetting effects according to claim 1, characterized in that, The candidate solutions are evaluated using a weighted relative performance ratio, which is calculated as follows: For each of the three objectives—minimizing the maximum completion time, minimizing the total production cost, and minimizing the rescheduling deviation—the ratio of the objective function value corresponding to the candidate scheme to the objective function value corresponding to the initial scheduling scheme is taken as the single-objective performance ratio. Based on the weights of each objective, the performance ratios of the three single objectives are summed in weights to obtain the weighted relative performance of the candidate schemes. The candidate scheme with the smallest weighted relative performance value among the two candidate schemes is selected as the optimal candidate scheme.

3. The dynamic scheduling method for digital twin workshops considering learning and forgetting effects according to claim 1, characterized in that, The learning and forgetting effect model for the workers is as follows: in, For workpiece No. Each process is handled by workers. In the machine Up processing, and in the first The actual processing time for each processing position; This refers to the position of the process in the processing sequence; For processing workpieces No. Each process is handled by workers. In the machine Basic processing time; For workpiece The total number of processes; For workers In the machine Up-processing to workpiece The The cumulative basic processing time in the unit order; For workers In the machine upper processing workpiece The coefficient of induced learning effect, ; For workers In the machine upper processing workpiece The active learning effect coefficient, ; For worker z in the machine upper processing workpiece The forgetting effect coefficient, ; For workpiece The Each process is carried out by workers on the machine. Up processing, and located in the first The idle time before the start of work in the unit order.

4. The dynamic scheduling method for digital twin workshops considering learning and forgetting effects according to claim 1, characterized in that, The initial scheduling scheme and the rescheduling scheme are obtained by solving the tuna swarm optimization algorithm, and the solution of the tuna swarm optimization algorithm is represented as follows: In the algorithm solution space, the individual position of the tuna swarm optimization algorithm is encoded by a random key vector containing three sub-segments. The position vector of each individual is defined as a continuous random key value with a total dimension of three times the total number of processes. Each random key value is constrained within the search space boundary. The position vector is equally divided into three sub-segments corresponding to machine selection, process ordering and worker selection. In the solution space of the problem, the position vector is converted into a discrete scheduling scheme through decoding rules. In the discrete scheduling scheme, the value of the machine selection segment represents the machine number assigned to the corresponding process, the value of the process ordering segment represents the ordering position of each process in the scheduling sequence, and the value of the worker selection segment represents the specific worker number assigned to each process.

5. The dynamic scheduling method for digital twin workshops considering learning and forgetting effects according to claim 4, characterized in that, The decoding rules include: For both machine selection and worker selection, a random key value is taken from the corresponding position in the position vector. ,pass Convert to the corresponding machine number or worker number, where This is the rounding function. For the search space boundary parameters, The number of candidate machines or candidate workers for a process; For process sorting, each random key value of the position vector corresponds to a process. First, all random key values ​​corresponding to all processes are sorted in ascending order. Then, a unique rank value is assigned to the corresponding process according to the rank in the sorting list. Finally, the processing order of all processes is determined according to the ascending order of the rank values.

6. The dynamic scheduling method for digital twin workshops considering learning and forgetting effects according to claim 1, characterized in that, The initial scheduling scheme and rescheduling scheme are obtained by solving the tuna swarm optimization algorithm. The tuna swarm optimization algorithm includes optimizing the initial population based on a competitive learning strategy, and the execution process is as follows: Take all individuals from the initial population and randomly pair them up to form a competitive group; For each pair of competing individuals, the fitness values ​​of the two individuals are calculated. The individual with the better fitness value is directly retained to the next generation, while the other individual updates its position vector by learning from the individual with the better fitness value. Then it moves on to the next generation, in which For individuals with better fitness values, For individuals with worse fitness values, The learning rate; The fitness value is either the representative Pareto optimal solution that minimizes the maximum completion time and total production cost, or the representative Pareto optimal solution that minimizes the maximum completion time, total production cost, and rescheduling deviation.

7. The dynamic scheduling method for digital twin workshops considering learning and forgetting effects according to claim 1, characterized in that, The initial scheduling scheme and the rescheduling scheme are obtained by solving the tuna swarm optimization algorithm. The tuna swarm optimization algorithm uses the Q-learning algorithm to dynamically assign the most suitable iterative strategy to each individual. The action space of the Q-learning algorithm is defined as spiral foraging and parabolic foraging, and an ε-greedy strategy is used to select actions. The state space of the Q-learning algorithm is characterized by the improvement of three metrics: maximum completion time, total production cost, and rescheduling deviation between two consecutive generations. For each metric, if the current value is smaller than the value of the previous generation, the corresponding improvement is assigned a value of 1; otherwise, the corresponding improvement is assigned a value of 0. Therefore, the state space contains a total of eight discrete states with two assignments under the three metrics. The reward value of the Q-learning algorithm is defined as the weighted sum of the normalized improvements of each metric.

8. The dynamic scheduling method for digital twin workshops considering learning and forgetting effects according to claim 7, characterized in that, In the Q-learning algorithm, all individuals in the population synchronously update the same global Q-table.

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