Digital twin driven dynamic optimization method for flexible job shop scheduling

Abstract

The application belongs to the field of workshop scheduling, and discloses a flexible job shop scheduling dynamic optimization method driven by digital twinning, which comprises the following steps: generating an initial scheduling scheme of all operations in outsourcing waiting windows and main waiting windows with the double targets of minimizing the maximum completion time and minimizing the total carbon emission; if no abnormal event occurs, processing all operations according to the initial scheduling scheme; if an abnormal event occurs, generating a rescheduling scheme of all operations in the execution window and the outsourcing waiting window, and updating the execution mapping window; at the same time, generating a rescheduling scheme of all operations in the outsourcing waiting window and the main waiting window, and updating the unexecuted mapping window; and processing all operations of all jobs according to the rescheduling scheme. The application improves the efficiency and reliability of flexible job shop scheduling, obtains a high-quality scheduling scheme, and can efficiently optimize the rescheduling scheme in a real-time dynamic environment.

Description

Technical Field

[0001] This invention belongs to the field of workshop scheduling, specifically relating to a dynamic optimization method for flexible workshop scheduling driven by digital twins. Background Technology

[0002] Currently, flexible job shop scheduling, which focuses on addressing the diverse, small-batch order production needs, has become a research hotspot in the field of manufacturing system optimization. The core objective of flexible job shop scheduling is to rationally determine the processing sequence and allocate available machines for a given set of jobs, in order to minimize production cycles and reduce energy consumption. As a critical decision-making link in the production system, flexible job shop scheduling has a significant impact on production cost control and efficiency improvement.

[0003] However, previous studies have largely relied on the assumption that all processing operations are completed within a single job shop. With increasing product complexity and business specialization, outsourcing some operations to external job shops has gradually become a common practice for companies. This model demonstrates significant advantages in alleviating capacity bottlenecks and reducing operating costs. Against this backdrop, scholars have successively proposed and studied the flexible job shop scheduling problem that considers outsourced operations.

[0004] Meanwhile, in actual production processes, unpredictable anomalies such as machine malfunctions and product insertions frequently occur, often rendering pre-defined initial scheduling plans ineffective or even infeasible. This makes dynamic job shop scheduling a key research focus. However, existing research combining operation outsourcing and dynamic job shop scheduling remains limited. Therefore, it is necessary to conduct in-depth research on dynamic flexible job shop scheduling problems that simultaneously involve anomalies and outsourced operations to ensure the stability and efficiency of shop shop production.

[0005] Currently, although some researchers have studied the dynamic job shop scheduling problem, most studies rely primarily on physical space data for modeling and optimization due to technological limitations, neglecting the real-time interaction between the physical and virtual spaces. This leads to a lag in response to abnormal events. In contrast, digital twin technology, by integrating physical models, operational data, and maintenance information, achieves a two-way mapping between the physical and virtual spaces. This provides new technical support for real-time intelligent control and process optimization of complex production systems in dynamic job shops, thereby helping to reduce the risk of production interruptions.

[0006] Digital twin technology has been widely applied in the field of flexible job shop scheduling. For example, existing technologies propose a dynamic scheduling method based on digital twins and edge computing to address scheduling deviations caused by abnormal events. Another example is the development of a scheduling model that considers worker learning and forgetting processes, with manufacturing costs, production cycles, total carbon emissions, and product quality stability as optimization objectives. Yet another scholar has proposed a scheduling framework integrating cloud-edge computing and digital twin technologies to address the scheduling problem of flexible job shops with limited transportation resources. However, all of these existing methods provide valuable insights into the interaction mechanism between the digital twin system and the actual operating state in a single job shop, but none address operational outsourcing. In actual production, the technological and cost limitations of a single workshop often prevent it from independently completing all production tasks, prompting operational outsourcing to become a widely adopted strategy. Therefore, research on collaborative scheduling between the master workshop and outsourced workshops using digital twin technology is of great significance. Summary of the Invention

[0007] The purpose of this invention is to provide a dynamic optimization method for flexible job shop scheduling driven by digital twins, which improves the scheduling efficiency and reliability of flexible job shops under the premise of considering outsourcing, obtains high-quality scheduling schemes, and can efficiently optimize rescheduling schemes in a real-time dynamic environment.

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

[0009] A digital twin-driven dynamic optimization method for flexible job shop scheduling, which constructs a virtual workshop that is mapped in real time to the physical workshop using digital twin technology, includes:

[0010] The scheduling process of the physical workshop is divided into executed windows, execution windows, outsourcing waiting windows, and main waiting windows based on the rolling classification window mechanism. At the same time, the scheduling process of the virtual workshop is divided into executed mapping windows, execution mapping windows, and unexecuted mapping windows. The executed mapping windows are mappings of the executed windows, the execution mapping windows are mappings of the execution windows, and the unexecuted mapping windows are mappings of the outsourcing waiting windows and the main waiting windows.

[0011] With the dual objectives of minimizing the maximum completion time and minimizing the total carbon emissions, a multi-objective multi-microgroup parallel optimization algorithm is used to generate the initial scheduling scheme for all operations in the outsourcing waiting window and the main waiting window.

[0012] If no abnormal event occurs, the processing of all jobs and all operations in the outsourced waiting window and the main waiting window will be completed according to the initial scheduling plan;

[0013] If an abnormal event occurs, a multi-objective multi-microgroup parallel optimization algorithm is used to generate a rescheduling scheme for all operations in the execution window and the outsourced waiting window, and the execution mapping window is updated; at the same time, a multi-objective multi-microgroup parallel optimization algorithm is used to generate a rescheduling scheme for all operations in the outsourced waiting window and the main waiting window, and the unexecuted mapping window is updated; all jobs and all operations are processed according to the rescheduling scheme.

[0014] 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.

[0015] Preferably, if no abnormal event occurs, the scheduling process is as follows:

[0016] Update the operations in the unexecuted mapping window according to the initial scheduling scheme in the outsourced waiting window and the main waiting window;

[0017] Move the first pending operation in the unexecuted mapping window to the executed mapping window, and update the operations in the executed window, the outsourced waiting window, and the main waiting window;

[0018] Perform the operations in the execution mapping window, move the executed operations from the execution mapping window to the executed mapping window, and update the operations in the executed window and the execution window;

[0019] Repeatedly move the first pending operation in the unexecuted mapping window to the executed mapping window until all operations are completed.

[0020] As a preferred approach, before generating a rescheduling scheme for all operations in the execution window and the outsourced waiting window using a multi-objective multi-microgroup parallel optimization algorithm, the operations that have been completed in the execution mapping window are moved to the executed mapping window, and the operations in the executed window and the execution window are updated.

[0021] Preferably, the solution encoding method of the multi-objective multi-microgroup parallel optimization algorithm is as follows:

[0022] The solution is represented by a two-dimensional matrix. The first row of the two-dimensional matrix represents the processing order of each operation. Each element value in the first row represents the job index. The number of times the job index appears indicates the operation of the corresponding index in the job.

[0023] The second row of the two-dimensional matrix represents the machine allocation for each operation, and each element value in the second row represents the machine index.

[0024] Preferably, the multi-objective multi-microgroup parallel optimization algorithm includes inversion operators, replacement operators, and delay operators as local search operators;

[0025] The reversal operator is: randomly select two operations and swap their processing order;

[0026] The replacement operator is: randomly select an operation and replace the machine corresponding to the selected operation with another machine;

[0027] The delay operator is as follows: randomly select an outsourced operation, delay the processing time of the selected outsourced operation, and randomly select an operation after the selected outsourced operation and insert it before the selected outsourced operation.

[0028] Preferably, the method of selecting a local search operator to generate a new solution is adopted; a corresponding score is assigned according to the quality of the new solution; and the score is weighted and fused with the operator weight of the previous iteration using the response factor to obtain the updated operator weight of the current iteration.

[0029] Preferably, the global search operator of the multi-objective multi-microgroup parallel optimization algorithm is:

[0030] For two original individuals, randomly select a first segment containing multiple elements from the first original individual, and find the elements in the second original individual that have the same operation as the first segment and arrange them in order to form the second segment;

[0031] If the objective function values ​​of the two offspring individuals obtained after swapping the first and second segments are both better than those of the corresponding original individuals, then swap the first and second segments to obtain two offspring individuals; otherwise, do not swap.

[0032] Preferably, the multi-objective multi-microgroup parallel optimization algorithm includes a microgroup propagation strategy comprising a shuffling strategy, a jumping strategy, and a replacement strategy.

[0033] The shuffling strategy is as follows: when the current optimal solution in the entire population has not been updated for q1 consecutive generations, all micro-populations are randomly reorganized.

[0034] The skipping strategy is as follows: when the current best solution in the microgroup has not been updated for q2 consecutive generations, the best solution in other microgroups is randomly introduced to replace the worst solution in the current microgroup.

[0035] The replacement strategy is as follows: calculate the exchange probability of each solution in the microgroup and generate a random number. For solutions with exchange probabilities greater than the random number, randomly replace the current solution with solutions from other microgroups.

[0036] Preferably, the exchange probability is calculated as follows:

[0037] If the first in the microgroup The number of times the objective function value of each solution is not improved This is equal to the maximum number of times the objective function value of all solutions in the entire population has not been improved. Then set the first in the microgroup The probability of swapping solutions is 1;

[0038] If the first in the microgroup The number of times the objective function value of each solution is not improved This is equal to the minimum number of times the objective function value of all solutions in the entire population is not improved. Then set the first in the microgroup The probability of swapping solutions is 0;

[0039] Otherwise, set the number of microgroups. The probability of exchanging solutions is .

[0040] This invention provides a dynamic optimization method for flexible job shop scheduling driven by digital twins, proposing a dynamic scheduling problem for flexible job shops considering outsourced operations (DFJSP-O). In this problem, the master job shop and the outsourced job shops can achieve collaborative operation, dynamically respond to anomalies occurring during processing, and optimize the scheduling scheme in real time. Compared with existing technologies, the method of this invention has the following advantages:

[0041] (1) The operation outsourcing was introduced into the dynamic optimization framework of the flexible workshop, and a DFJSP-O bi-objective model considering the available time constraint of outsourced operations was constructed to minimize the maximum completion time and total carbon emissions.

[0042] (2) A dynamic scheduling architecture based on digital twins is proposed to solve DFJSP-O, which divides the overall system into physical space and virtual space to realize real-time interaction and collaborative optimization between the main operation workshop and the outsourced operation workshop.

[0043] (3) A digital twin-driven real-time rescheduling strategy based on a rolling classification window mechanism is proposed, which divides the scheduling process into multiple continuous classification optimization windows, thereby effectively responding to dynamic disturbances and realizing collaborative dynamic scheduling between the main operation workshop and the outsourced operation workshop.

[0044] (4) An improved multi-objective multi-microgroup parallel optimization algorithm (IMMPO) is proposed, which adopts a matrix-based representation scheme, local and global search operators, adaptive search strategy and new microgroup propagation strategy, which effectively improves the search efficiency and solution quality of the algorithm. Attached Figure Description

[0045] Figure 1 This is a diagram of the dynamic scheduling architecture based on digital twins of the present invention;

[0046] Figure 2This is a virtual reality interaction diagram based on digital twins, as presented in this invention.

[0047] Figure 3 This is a schematic diagram illustrating the impact of abnormal events in this invention;

[0048] Figure 4 This is a flowchart of the dynamic optimization method for flexible job shop scheduling driven by digital twins according to the present invention;

[0049] Figure 5 This is a flowchart of the IMMPO algorithm of the present invention;

[0050] Figure 6 Here are three example diagrams of the local search operator of this invention;

[0051] Figure 7 This is an example diagram of the global search operator of the present invention;

[0052] Figure 8 The figure shows the experimental results of the Pareto solution sets obtained by the three algorithms in examples J15_M12_O4 and J30_M18_O6 in the experiment of this invention.

[0053] Figure 9 This is a schematic diagram of the initial scheduling scheme in the experiment of this invention;

[0054] Figure 10 This is a schematic diagram of the rescheduling scheme under test scenario 1 in the experiment of this invention;

[0055] Figure 11 This is a schematic diagram of the rescheduling scheme under test scenario 2 in the experiment of this invention;

[0056] Figure 12 This is a schematic diagram of the rescheduling scheme under test scenario 3 in the experiment of this invention;

[0057] Figure 13 This is a schematic diagram of the rescheduling scheme under test scenario 4 in the experiment of this invention. Detailed Implementation

[0058] 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.

[0059] 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.

[0060] Currently, due to the limitations of single-workshops in handling highly complex products and meeting the demands of highly specialized business needs, the flexible job shop scheduling problem considering operations outsourcing has gradually become a research hotspot. Furthermore, abnormal events during the production process can cause deviations between the initial scheduling plan and the actual operating state. Digital twin technology, by integrating physical and virtual spaces, provides a solution for dynamically optimizing job shop production in the real world. Therefore, this embodiment proposes a digital twin-driven dynamic scheduling problem for flexible job shops and constructs a corresponding bi-objective optimization model considering operations outsourcing. For the collaborative dynamic scheduling requirements between the master job shop and outsourced job shops, a digital twin-driven real-time rescheduling strategy based on a rolling classification window mechanism is proposed. Further, an improved multi-objective multi-microgroup parallel optimization algorithm is proposed, which combines matrix-based encoding representation, local and global search operators, adaptive search strategies, and a novel microgroup propagation strategy to efficiently solve the proposed scheduling model.

[0061] The DFJSP-O problem involves two job shops: the master job shop and the subcontracted job shop. The master job shop includes... Each job consists of a series of sequential operations. Different jobs may involve different product types, requiring different combinations of operations, and the operations within each job must be performed in a predetermined order. The main job shop provides multiple optional processing machines for each operation, and the processing time for each operation may vary depending on the machine. Furthermore, due to technical or cost limitations, some operations need to be completed in outsourced job shops. These outsourced job shops also provide multiple optional machines for each operation, with varying processing times on different machines.

[0062] In actual production, random anomalies may cause deviations between the actual state in the physical space and the initial scheduling scheme in the virtual space. To solve this problem, DFJSP-O uses digital twin technology to compare the production status in the physical and virtual spaces in real time and dynamically adjust the production plan accordingly.

[0063] To address the DFJSP-O problem, this embodiment employs a dynamic scheduling architecture based on digital twins, such as... Figure 1As shown, the architecture consists of a physical space and a virtual space, corresponding to the actual work workshop and its digital mapping, respectively. The two parts interact via Cyber-Physical Systems (CPS). The virtual space continuously collects and processes real-time data from the physical space, including production data, machine status, task information, and outsourcing-related data. Based on this data, dynamic scheduling strategies and optimization algorithms are used to optimize and simulate the scheduling scheme, and the optimized scheme is then transmitted back to the physical space for execution.

[0064] The interaction process between physical and virtual spaces in a dynamic scheduling architecture based on digital twins is as follows: Figure 2 As shown, firstly, data acquisition devices such as smart sensors dynamically monitor potential abnormal events in the main workshop and outsourced workshops, such as product changes and machine malfunctions. Secondly, processing data from the physical space is synchronized to the virtual space via a data transmission protocol, and relevant data is also transmitted in real time when abnormal events occur to maintain consistency between the two spaces. Finally, in the virtual space, the actual states of the main workshop and outsourced workshops are modeled and simulated based on the received information, and the scheduling scheme is dynamically optimized using the proposed scheduling strategy and optimization algorithm. This interactive mechanism can dynamically adjust and execute the scheduling scheme according to abnormal events, thereby improving the overall operating efficiency of the production system.

[0065] In the DFJSP-O problem, consider three types of randomly occurring anomalous events: product anomalies, machine anomalies, and machine availability anomalies in outsourced workshops. Their definitions and effects are as follows.

[0066] (1) Product anomaly: A product anomaly occurs when the number of unfinished jobs in the physical space and the virtual space are inconsistent. For example, the urgent insertion of a new job will cause the processing order of existing jobs to be delayed, while a sudden reduction in job demand may accelerate the production schedule.

[0067] (2) Machine malfunction: If a machine malfunctions during operation, it must be stopped immediately until the malfunction is repaired. Such malfunctions will cause delays in related operations and disrupt the original processing sequence. Machine malfunctions are among the most serious malfunctions, directly affecting the continuity of production.

[0068] (3) Abnormal available time: Each machine in the outsourced workshop is originally allocated a fixed available time for handling outsourced operations. However, factors such as fluctuations in equipment status or adjustments to plans during the production process may cause changes in the actual available time of the machines, which in turn cause changes in processing time and adjustments to the selection of machines for outsourced operations, thereby affecting overall efficiency and workflow.

[0069] like Figure 3The diagram illustrates examples of various abnormal events. Different colored rectangles represent operations within different jobs; dashed lines represent planned operations, solid lines represent actual operations, and shaded areas represent the available time range for outsourced operations. Information about the abnormal events is also labeled. This example includes a main job shop and an outsourced job shop. The main job shop has three machines, and the outsourced job shop has one machine. There are three jobs in total, containing 2, 3, and 2 operations respectively. The third operation (operation 3-2) of job 2 is an outsourced operation. (See diagram for details.) Figure 3 As shown in (a), after inserting operations 1-4 and 2-4, the initial scheduling scheme shown by the dashed line is not feasible. After adjustment, operation 2-3 on the main workshop machine M1 is delayed, and operation 1-4 is inserted before it; operation 2-4 is then assigned to the idle time slot of M3. The final rescheduling result is shown by the solid line. Figure 3 As shown in (b), machine M1 malfunctioned during the period indicated by the red dashed line, causing a delay in operation 2-2. Subsequently, operation 2-3 was rescheduled to machine M2 for execution. Figure 3 As shown in (c), the processing of outsourced operation 3-2 is delayed accordingly after the available start time is postponed.

[0070] Specifically, this embodiment of a digital twin-driven dynamic optimization method for flexible job shop scheduling includes the following steps:

[0071] Step 1: Divide the scheduling process into multiple consecutive classification optimization windows according to the rolling classification window mechanism.

[0072] When an abnormal event occurs in the dynamic scheduling architecture, this embodiment extends the basic rolling window mechanism and proposes a real-time rescheduling strategy driven by a digital twin based on a rolling classification window.

[0073] The basic rolling window mechanism divides the scheduling process into multiple consecutive windows based on the processing order of operations, aiming to solve simple dynamic scheduling problems. However, since it does not consider the available time constraints of outsourced operations, this mechanism cannot directly solve the proposed DFJSP-O problem. Therefore, this embodiment extends it to a rolling classification window mechanism, dividing the scheduling process into multiple consecutive classification optimization windows to distinguish between operations executed in the master job shop or outsourced job shops, thereby effectively solving the collaborative dynamic scheduling problem between the master job shop and outsourced job shops.

[0074] The scrolling classification window mechanism comprises two types of windows: physical windows and virtual windows. The physical window includes four sub-windows: the executed window S1, the executing window S2, the outsourced waiting window S3, and the main waiting window S4. The virtual window includes three sub-windows: the executed mapping window S5, the executing mapping window S6, and the unexecuted mapping window S7. Each window contains the following operations:

[0075] S1 contains all operations executed in all job shops in the physical space. S2 contains all operations currently being executed in all job shops in the physical space. S3 contains operations awaiting execution in outsourced job shops in the physical space. S4 contains operations awaiting execution in the main job shop in the physical space. S5 contains all operations executed in all job shops in the virtual space; it is a numerical mapping of S1. S6 contains all operations currently being executed in all job shops in the virtual space; it is a numerical mapping of S2. S7 contains all operations awaiting execution in all job shops in the virtual space; it is a numerical mapping of S3 and S4.

[0076] Step 2: With the dual objectives of minimizing the maximum completion time and minimizing the total carbon emissions, a multi-objective multi-microgroup parallel optimization algorithm is used to generate the initial scheduling scheme for all operations in the outsourced waiting window and the main waiting window.

[0077] The DFJSP-O problem constructed in this embodiment has two optimization objectives: first, to minimize the maximum completion time, which is the maximum value of the final completion time of all operations; and second, to minimize the total carbon emissions, which encompass the sum of carbon emissions generated by all machines in both running and idle states. The following constraints are set: any operation can only be processed on one machine at a time, and a machine can only process one operation at a time. The processing time of operations on different machines is a predetermined value, and the operation process cannot be interrupted once it begins. All machines are available at time zero. Machines do not generate carbon emissions during maintenance. The maintenance time required for a machine is known, and it can be immediately restored to use after maintenance. Random abnormal events may occur at any time during the scheduling process.

[0078] To minimize the maximum completion time and total carbon emissions, this embodiment proposes a bi-objective optimization model for the DFJSP-O problem, as shown below:

[0079] (1)

[0080] (2)

[0081] The model constraints are shown in equations (3) to (10):

[0082] (3)

[0083] (4)

[0084] (5)

[0085] (6)

[0086] (7)

[0087] (8)

[0088] (9)

[0089] (10)

[0090] Formulas (1) and (2) represent two objective functions: minimizing the maximum completion time and minimizing total carbon emissions. Formula (3) stipulates that any operation cannot be interrupted once processing begins. Formula (4) states that each operation can only be executed by one available machine. Formula (5) limits a machine to processing at most one operation at a time, where Q is an infinitely large positive number. Formula (6) requires that operations within the same job must be executed sequentially according to their preset order. Formulas (7) and (8) stipulate that the start and end times of each operation are positive numbers. Formulas (9) and (10) stipulate that the processing time of outsourced operations must fall within the processing time window of the corresponding machine in the outsourced workshop. Indicates the total number of jobs; Indicates the total number of machines; Indicates work The total number of operations; Indicates the index of the job. , ; Indicates the index of the operation. , ; Indicates the machine index. ; Indicates work The One operation; Indicates operation In the machine The processing start time; Indicates operation In the machine The processing end time; Indicates operation In the machine Processing time; Indicates outsourcing operations In the machine Available start time; Indicates outsourcing operations In the machine Available end time; Indicates machine deal with Carbon emissions during operation; Indicates machine Carbon emissions during idle periods; If it is a binary variable, In the machine If the above processing is performed, the value is 1; otherwise, it is 0. If it is a binary variable, and All If the processing is done on the machine and the former occurs before the latter, the value is 1; otherwise, the value is 0. Indicates the maximum completion time; This indicates the total amount of carbon emissions.

[0091] Step 3: If no abnormal event occurs, process all jobs and all operations in the outsourcing waiting window and the main waiting window according to the initial scheduling scheme. If an abnormal event occurs, use a multi-objective multi-microgroup parallel optimization algorithm to generate a rescheduling scheme for all operations in the execution window and the outsourcing waiting window, and update the execution mapping window. At the same time, use a multi-objective multi-microgroup parallel optimization algorithm to generate a rescheduling scheme for all operations in the outsourcing waiting window and the main waiting window, and update the unexecuted mapping window. Process all jobs and all operations according to the rescheduling scheme.

[0092] In this embodiment, the operations contained in each window are dynamically updated as production progresses and abnormal events occur. For example... Figure 4 As shown, the specific rolling process of the proposed digital twin-driven real-time rescheduling strategy based on the rolling classification window mechanism is as follows.

[0093] (1) Use the improved multi-objective multi-microgroup parallel optimization algorithm (IMMPO) to schedule all operations in the outer waiting window S3 and the main waiting window S4.

[0094] (2) Update the operations in the unexecuted mapping window S7 according to the initial scheduling scheme in the outsourced waiting window S3 and the main waiting window S4.

[0095] (3) Move the first operation to be executed in the unexecuted mapping window S7 to the execution mapping window S6, and update the operations in the execution window S2, the outsourced waiting window S3 and the main waiting window S4.

[0096] (4) If no abnormal event occurs, the production process is normal and step (9) is executed; if an abnormal event occurs, the rescheduling process is started and steps (5), (6), (7) and (8) are executed in sequence.

[0097] (5) Move the completed operations in the execution mapping window S6 to the executed mapping window S5, and update the operations in the executed window S1 and the execution window S2.

[0098] (6) Use the IMMPO algorithm to reschedule all operations in execution window S2 and outsourced waiting window S3. At the same time, update the operations in execution mapping window S6 according to the rescheduling scheme in execution window S2.

[0099] (7) Reschedule all operations in the outsourced waiting window S3 and the main waiting window S4 using the IMMPO algorithm. At the same time, update the operations in the unexecuted mapping window S7 according to the rescheduling scheme in the outsourced waiting window S3 and the main waiting window S4.

[0100] (8) Execute the operation in the execution mapping window S6, move the executed operation from the execution mapping window S6 to the executed mapping window S5, and update the operation in the executed window S1 and the execution window S2.

[0101] (9) Repeat steps (3)-(8) until all operations are completed.

[0102] Based on a scrolling categorized window mechanism, operations in child windows are updated in real time when an abnormal event occurs. Furthermore, during periods without abnormal events, operations in both physical and virtual windows are periodically updated according to a set scrolling frequency. The scrolling frequency of the physical window... The virtual window's scrolling frequency is set to 1 to 2 times the median processing time of all operations, as shown in formulas (11) and (12). The scrolling frequency of the virtual window is set to the maximum completion time of the current scheduling scheme.

[0103] (11)

[0104] (12)

[0105] In the formula, This represents the median of the maximum completion time for the current scheduling scheme.

[0106] This embodiment employs an improved multi-objective multi-microgroup parallel optimization algorithm in both the initial scheduling and rescheduling processes. The basic multi-objective multi-microgroup parallel optimization (MMPO) algorithm in existing technologies uses a multi-microgroup parallel search structure, dividing the population into four microgroups of equal size for separate searches. This structure helps expand the search range of the solution space and shows good performance in solving simple continuous optimization problems. However, since the DFJSP-O problem proposed in this embodiment is a complex discrete optimization problem, it cannot be directly solved using the basic MMPO algorithm, and the algorithm has certain limitations in optimization efficiency. Therefore, this embodiment extends the basic MMPO algorithm to the IMMPO algorithm in the following three aspects: 1) It proposes a matrix-based encoding representation to more efficiently and intuitively describe the solution to the DFJSP-O problem; 2) It designs local and global search operators and introduces an adaptive search strategy to improve the algorithm's convergence speed; 3) It designs a new microgroup propagation strategy to promote the sharing of information about high-quality solutions among microgroups. The overall process of the IMMPO algorithm is as follows: Figure 5 As shown.

[0107] (1) Initialize the population, as well as the scores and weights of the local search operators.

[0108] Considering that the DFJSP-O problem includes two types of information: process sequence and machine allocation, this embodiment adopts a matrix-based encoding method to efficiently and intuitively represent this two-dimensional optimization problem.

[0109] For example, a two-dimensional matrix This represents a solution containing eight operations. The first line indicates the processing order of each operation, and the second line indicates the machine allocation for each operation. The numbers in the first line represent the job index, and the job index is... The first occurrence represents the first job. One operation. The numbers in the second row represent the machine index. For example, the first column... This indicates that the first operation of task 1 is assigned to machine 3, the second column... This indicates that the first operation of task 2 is assigned to machine 4, in the third column. This indicates that the second operation of job 1 is assigned to machine 1, and so on until all operations are assigned.

[0110] (2) The population is randomly divided into four microgroups of equal size.

[0111] (3) Use an adaptive search strategy to select a local search operator to update the solution in each microgroup, and update the score and weight of the selected local search operator.

[0112] To improve the search efficiency of the IMMPO algorithm, this embodiment designs three local search operators: the inversion operator, the replacement operator, and the delay operator, such as... Figure 6 As shown.

[0113] Reversal operator: Randomly selects two operations and swaps their processing order. For example... Figure 6 As shown in (a) in the solution, the third column and the fifth column are swapped.

[0114] Replacement operator: Randomly selects an operation and replaces its machine assignment with another available machine. For example... Figure 6 As shown in (b), the machine 2 originally assigned to the first operation of job 3 in the fifth column is randomly replaced with machine 3.

[0115] Delay operator: Randomly selects an outsourced operation, delays its processing time, and inserts a feasible operation before it. For example... Figure 6 As shown in (c), the original sixth column is delayed in processing time, and the original eighth column after the original sixth column is inserted before the original sixth column to become the new sixth column. The original sixth column is delayed to become the seventh column, and the original seventh column is delayed to become the eighth column.

[0116] To further improve the search efficiency of each microgroup, this embodiment introduces an adaptive search strategy. This strategy dynamically adjusts the selection weights of each operator based on their performance during the search process. In each iteration, the adaptive search strategy selects a local search operator to improve the current solution. At initialization, all operator weights are equal; in each iteration, the weights are adjusted according to the response factor. and score Iterative update iteration Middle Operator weight In this embodiment, the response factor is set to 0.9, and the scores for different operators are... The acquisition rules are shown in Table 1.

[0117] Table 1 Scores of the corresponding operators

[0118]

[0119] The weight update formula is shown in formula (13). Finally, the selected operator is determined by the roulette wheel selection method based on the operator weight.

[0120] (13)

[0121] in, For the first Sub-iteration operator The weight.

[0122] (4) Execute the global search operator to update the solutions in each microgroup.

[0123] This embodiment designs a global search operator to improve the global convergence of the algorithm. The global search operator is as follows: For two original individuals, a first segment containing multiple elements is randomly selected from the first original individual, and the elements at the corresponding positions in the second original individual that contain the same operation as the first segment are found and arranged in order to form a second segment; if the objective function values ​​of the two offspring individuals obtained after swapping the first and second segments are both better than the corresponding original individuals, then the first and second segments are swapped to obtain two offspring individuals; otherwise, no swapping is performed.

[0124] like Figure 7 As shown, the operator randomly selects segment 1 (columns 3 to 5) from individual 1, and finds corresponding positions in individual 2 that contain the same operation as segment 1 to form segment 2 (columns 2, 4, and 6). Two offspring are generated by swapping the two segments. If the objective function value of the offspring is better than that of the original individual, then the offspring is replaced.

[0125] (5) Update all microgroups using microgroup propagation strategy.

[0126] During the search process of the basic MMPO algorithm, information isolation between microgroups can easily cause the algorithm to get stuck in local optima and reduce population diversity. To address this, this embodiment proposes the following three microgroup propagation strategies to promote the sharing of high-quality solutions among microgroups.

[0127] Shuffling strategy: When the current best solution in the entire population has not been updated for q1 (e.g. 5) consecutive generations, all microgroups are reorganized (re-randomly initialized into 4 new microgroups).

[0128] Skip strategy: When the current best solution in a microgroup has not been updated for q2 (e.g. 3) consecutive generations, introduce the best solution from other microgroups to replace the worst solution in the current microgroup.

[0129] Replacement strategy: Allow solutions to be replaced between different microgroups with a certain probability: Calculate the exchange probability of each solution in the microgroup and generate a random number. For solutions whose exchange probability is greater than the random number, randomly replace the current solution with a solution from another microgroup. As shown in formula (14), in this embodiment, the first... The probability of commutation of solutions The objective function value of the solution increases linearly with the degree of improvement.

[0130] (14)

[0131] in, It is the first The number of iterations in which the objective function value of a solution is not improved; and It represents the maximum and minimum number of times the objective function value of all solutions in the entire population has not been improved.

[0132] (6) Determine whether the termination condition is met. If so, merge all microgroups and output the global optimal solution in the population as the best scheduling scheme; otherwise, return to step (3) to continue iterative execution.

[0133] experiment:

[0134] To verify the performance of the method of this invention, experiments were conducted in both static and dynamic environments. The experiments were performed using Python 3.7 on a personal computer equipped with a Windows 10 operating system, an Intel(R) Core processor with a clock speed of 1.60 GHz, and 8 GB of memory.

[0135] (1) Experimental setup

[0136] The experimental data comes from a real-world case study of a physical enterprise. However, since actual production data is difficult to support complex experimental analysis, this experiment simulates the production conditions of a flexible workshop by generating multiple sets of instances. The number of jobs is set to {4, 8, 10, 12, 15, 20, 25, 30, 40, 50}, and the number of machines in the main workshop and outsourced workshop are set to {4, 6, 8, 10, 12, 14, 16, 18, 22, 26} and {2, 3, 4, 5, 6, 8, 10}, respectively. A total of 10 instances are generated based on different combinations of job and machine numbers. Each instance is named according to the number of jobs and machines. For example, "J4_M4_O2" represents an instance containing 4 jobs, 6 machines in the main workshop, and 2 machines in the outsourced workshop.

[0137] To verify the effectiveness of the IMMPO algorithm, this experiment compared it with two benchmark algorithms: the MMPO algorithm and the ALNS (Adaptive Large Neighborhood Search) algorithm. After trial operation, the population size for all algorithms was set to 40, and the number of iterations was set to 200. The parameters used in the experiment are detailed in Table 2.

[0138] Table 2 Parameters used in the experiment

[0139]

[0140] In order to comprehensively evaluate the performance of the algorithm in terms of problem-solving ability and running efficiency, this experiment uses relative percentage deviation (RPD) as an additional evaluation index, and its calculation formula is shown in formula (15).

[0141] (15)

[0142] in, and These are the maximum completion time obtained by this algorithm and the minimum maximum completion time obtained by all algorithms, respectively. and These represent the total carbon emissions obtained by this algorithm and the minimum total carbon emissions obtained by all algorithms, respectively. The smaller the RPD value, the higher the uniformity of the Pareto solution set generated by the algorithm, and the better its performance.

[0143] (2) Analysis of experimental results

[0144] (2.1) Effectiveness in a static environment

[0145] To demonstrate the effectiveness of the proposed method in a static environment, this experiment independently ran the IMMPO, MMPO, and ALNS algorithms 10 times each on 10 sets of instances. The average objective function, computation time, and average RPD (ARPD) of the three algorithms are shown in Tables 3-5. The experiments show that IMMPO performs slightly better than the comparison algorithms when dealing with small-scale DFJSP-O problems, while IMMPO performs even better when solving medium- and large-scale problems. Although IMMPO's computation time increases due to the integration of adaptive search and micro-group propagation strategies, it still obtains better solutions within an acceptable time in most cases. Furthermore, the average ARPD of IMMPO on all instances is lower than that of other baseline algorithms, indicating that the Pareto solution set generated by IMMPO has higher uniformity.

[0146] Table 3 Solution performance of IMMPO on different instance sizes

[0147]

[0148] Table 4. Solution performance of MMPO on instances of different sizes

[0149]

[0150] Table 5. Solution performance of ALNS on instances of different sizes

[0151]

[0152] Note: The optimal results in Tables 3-5 are marked in bold, and "↓" indicates that the smaller the value, the better.

[0153] Figure 8The Pareto solution set distributions of the three algorithms are shown on instances J15_M12_O4 and J30_M18_O6. The solution set obtained by the IMMPO algorithm has a wider distribution and better convergence in the target space compared to the other two algorithms. This indicates that its solution set more comprehensively approximates the true Pareto front, thus verifying that the IMMPO algorithm possesses superior search and optimization capabilities.

[0154] (2.2) Effectiveness in dynamic environments

[0155] To verify the effectiveness of the proposed method in solving the DFJSP-O problem under dynamic conditions, this experiment constructed test scenarios containing different abnormal events and compared them with the traditional right-shift rescheduling method. In each scenario, the two methods were run independently 10 times, and the optimal solutions were selected for analysis. The results are presented using Gantt charts. Test scenario 1 considers product abnormalities, i.e., operations 1-9 and 2-9 are inserted at time 60. Test scenario 2 considers machine abnormalities, i.e., machine 1 fails between time 85 and 95. Test scenario 3 considers availability time abnormalities, i.e., the available start time of outsourced operation 3-3 on machine 8 is delayed to time 50. Test scenario 4 considers all abnormal events in test scenarios 1, 2, and 3 simultaneously.

[0156] The static scheduling results of instance J8_M6_O2 obtained by IMMPO in the previous section for each scenario ( Figure 9 This serves as the initial scheduling scheme. Different colored rectangles represent operations on different jobs. T and C represent the maximum completion time and total carbon emissions of the scheduling scheme, respectively.

[0157] Figure 10 , Figure 11 , Figure 12 and Figure 13 The performance comparison of the rescheduling schemes generated by the method of this invention and the right-shift rescheduling method is shown in four test scenarios. Thin dashed lines represent planned operations before the occurrence of an abnormal event. Solid lines represent the actual operations generated by the method of this invention after the occurrence of an abnormal event. When the actual operations generated by the right-shift rescheduling method differ from those generated by the method of this invention, the actual operations generated by the right-shift rescheduling method will be represented by thick dashed lines. For example... Figure 10 As shown, after insertion operations 1-9 and 2-9, the objective function values ​​obtained by the method of this invention are T=95 and C=8027, while the objective function values ​​of the right-shift rescheduling method are T=97 and C=8037. Table 6 shows a performance comparison of the two methods for rescheduling schemes in four test scenarios.

[0158] Table 6. Performance comparison of the rescheduling solutions of the present invention method and the right-shift rescheduling method in four test scenarios.

[0159]

[0160] Note: The optimal result is marked in bold, and "↓" indicates that the smaller the value, the better.

[0161] As shown in Table 6, the results obtained by the method of this invention are superior to the right-shift rescheduling method in all four test scenarios. Furthermore, although the method of this invention sometimes requires longer execution time, it effectively optimizes the scheduling target value, and the computation time remains within an acceptable range. Therefore, in the event of abnormal events, the method of this invention outperforms the right-shift rescheduling method.

[0162] (2.3) Case Studies

[0163] By selecting a professional tunnel boring machine manufacturer as a case study, this experiment verifies the effectiveness of the DFJSP-O problem proposed in this invention, and realizes dynamic scheduling optimization of production in the real-world workshop through the integration of physical and virtual spaces.

[0164] This case study focuses on the manufacturing process of the auxiliary water tank assembly. Each component in the assembly, such as the cover plate, air filter, and spring washer, requires processing according to a specific operational sequence. For example, the manufacturing of the cover plate involves processes such as cleaning, laser processing, universal milling, drilling, and powder coating. Multiple cleaning machines and grinding machines can be used during production, providing flexible scheduling for the manufacturing plan. Table 7 compares the solution results of the IMMPO algorithm with two baseline algorithms in this practical case. Experimental results show that, with similar computation time, IMMPO outperforms the comparative algorithms in terms of maximum completion time, total carbon emissions, and ARPD index, indicating that this method has better performance in practical applications.

[0165] Table 7 Comparison of solution performance of IMMPO, MMPO and ALNS algorithms in case studies

[0166]

[0167] Note: The optimal result is marked in bold, and "↓" indicates that the smaller the value, the better.

[0168] Digital twins provide a feasible approach to information interaction between physical and virtual spaces. This invention addresses the DFJSP-O problem by constructing a dynamic scheduling architecture based on digital twins. Building upon the rolling classification window mechanism, a novel digital twin-driven real-time rescheduling strategy is proposed to solve the collaborative dynamic scheduling problem between the master job shop and outsourced job shops. Simultaneously, the IMMPO algorithm is designed, employing matrix encoding representation and combining local and global search operators, an adaptive search strategy, and a novel micro-group propagation strategy to improve solution performance.

[0169] To verify the effectiveness of the method of this invention in solving the DFJSP-O problem, experiments were conducted in both static and dynamic environments. Experimental results show that the method can not only find high-quality solutions in static environments but also efficiently optimize rescheduling schemes in real-time dynamic environments. Furthermore, applications in real-world enterprise cases further illustrate the positive role of this method in improving production scheduling efficiency.

[0170] In another embodiment, the present invention also provides a computer-readable storage medium having a computer program stored thereon, the computer program, when executed by a processor, implementing the steps of a digital twin-driven dynamic optimization method for flexible job shop scheduling.

[0171] 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 above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0172] 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 specification.

[0173] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are 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 modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A dynamic optimization method for flexible job shop scheduling driven by digital twins, characterized in that, The method for dynamic optimization of flexible workshop scheduling driven by digital twin technology, which constructs a virtual workshop that is mapped in real time to the physical workshop, includes: The scheduling process of the physical workshop is divided into executed windows, execution windows, outsourcing waiting windows, and main waiting windows based on the rolling classification window mechanism. At the same time, the scheduling process of the virtual workshop is divided into executed mapping windows, execution mapping windows, and unexecuted mapping windows. The executed mapping windows are mappings of the executed windows, the execution mapping windows are mappings of the execution windows, and the unexecuted mapping windows are mappings of the outsourcing waiting windows and the main waiting windows. With the dual objectives of minimizing the maximum completion time and minimizing the total carbon emissions, a multi-objective multi-microgroup parallel optimization algorithm is used to generate the initial scheduling scheme for all operations in the outsourcing waiting window and the main waiting window. If no abnormal event occurs, the processing of all jobs and all operations in the outsourced waiting window and the main waiting window will be completed according to the initial scheduling plan; If an abnormal event occurs, a multi-objective multi-microgroup parallel optimization algorithm is used to generate a rescheduling scheme for all operations in the execution window and the outsourced waiting window, and the execution mapping window is updated; at the same time, a multi-objective multi-microgroup parallel optimization algorithm is used to generate a rescheduling scheme for all operations in the outsourced waiting window and the main waiting window, and the unexecuted mapping window is updated; all jobs and all operations are processed according to the rescheduling scheme.

2. The method for dynamic optimization of flexible job shop scheduling driven by digital twins according to claim 1, characterized in that, If no abnormal event occurs, the scheduling process is as follows: Update the operations in the unexecuted mapping window according to the initial scheduling scheme in the outsourced waiting window and the main waiting window; Move the first pending operation in the unexecuted mapping window to the executed mapping window, and update the operations in the executed window, the outsourced waiting window, and the main waiting window; Perform the operations in the execution mapping window, move the executed operations from the execution mapping window to the executed mapping window, and update the operations in the executed window and the execution window; Repeatedly move the first pending operation in the unexecuted mapping window to the executed mapping window until all operations are completed.

3. The method for dynamic optimization of flexible job shop scheduling driven by digital twins according to claim 1, characterized in that, Before generating a rescheduling scheme for all operations in the execution window and the outsourced waiting window using a multi-objective multi-microgroup parallel optimization algorithm, the operations that have been completed in the execution mapping window are moved to the executed mapping window, and the operations in the executed window and the execution window are updated.

4. The method for dynamic optimization of flexible job shop scheduling driven by digital twins according to claim 1, characterized in that, The solution encoding method of the multi-objective multi-microgroup parallel optimization algorithm is as follows: The solution is represented by a two-dimensional matrix. The first row of the two-dimensional matrix represents the processing order of each operation. Each element value in the first row represents the job index. The number of times the job index appears indicates the operation of the corresponding index in the job. The second row of the two-dimensional matrix represents the machine allocation for each operation, and each element value in the second row represents the machine index.

5. The method for dynamic optimization of flexible job shop scheduling driven by digital twins according to claim 1, characterized in that, The multi-objective multi-microgroup parallel optimization algorithm includes inversion operators, replacement operators, and delay operators as local search operators; The reversal operator is: randomly select two operations and swap their processing order; The replacement operator is: randomly select an operation and replace the machine corresponding to the selected operation with another machine; The delay operator is as follows: randomly select an outsourced operation, delay the processing time of the selected outsourced operation, and randomly select an operation after the selected outsourced operation and insert it before the selected outsourced operation.

6. The method for dynamic optimization of flexible job shop scheduling driven by digital twins according to claim 5, characterized in that, The method employs a roulette wheel selection to select a local search operator to generate a new solution; assigns a corresponding score based on the quality of the new solution; and uses a response factor to weight and fuse the score with the operator weights from the previous iteration to obtain the updated operator weights for this iteration.

7. The method for dynamic optimization of flexible job shop scheduling driven by digital twins according to claim 1, characterized in that, The global search operator for the multi-objective, multi-microgroup parallel optimization algorithm is: For two original individuals, randomly select a first segment containing multiple elements from the first original individual, and find the elements in the second original individual that have the same operation as the first segment and arrange them in order to form the second segment; If the objective function values ​​of the two offspring individuals obtained after swapping the first and second segments are both better than those of the corresponding original individuals, then swap the first and second segments to obtain two offspring individuals; otherwise, do not swap.

8. The method for dynamic optimization of flexible job shop scheduling driven by digital twins according to claim 1, characterized in that, The multi-objective, multi-microgroup parallel optimization algorithm includes a microgroup propagation strategy comprising a shuffling strategy, a jumping strategy, and a replacement strategy. The shuffling strategy is as follows: when the current optimal solution in the entire population has not been updated for q1 consecutive generations, all micro-populations are randomly reorganized. The skipping strategy is as follows: when the current best solution in the microgroup has not been updated for q2 consecutive generations, the best solution in other microgroups is randomly introduced to replace the worst solution in the current microgroup. The replacement strategy is as follows: calculate the exchange probability of each solution in the microgroup and generate a random number. For solutions with exchange probabilities greater than the random number, randomly replace the current solution with solutions from other microgroups.

9. The method for dynamic optimization of flexible job shop scheduling driven by digital twins according to claim 8, characterized in that, The exchange probability is calculated as follows: If the first in the microgroup The number of times the objective function value of each solution is not improved This is equal to the maximum number of times the objective function value of all solutions in the entire population has not been improved. Then set the first in the microgroup The probability of swapping solutions is 1. If the first in the microgroup The number of times the objective function value of each solution is not improved This is equal to the minimum number of times the objective function value of all solutions in the entire population is not improved. Then set the first in the microgroup The probability of swapping solutions is 0; Otherwise, set the number of microgroups. The probability of exchanging solutions is .

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