Methods and equipment for batch-flow hybrid production line scheduling in the manufacture of nanometer time-grating displacement sensors

Abstract

This invention belongs to the technical field of workshop scheduling, and discloses a batch flow hybrid production line scheduling method and equipment for the manufacturing of nanometer time-grating displacement sensors. It employs a local search optimization approach based on critical paths to address two sub-problems: machine selection and process sequencing. The first sub-problem is based on inserting critical processes on the same machine: for the sequencing sub-problem, the critical path of the workpiece with the maximum weighted delay is shortened by optimizing the processing sequence on a single machine. The second sub-problem is based on inserting critical processes on different machines: this strategy simultaneously addresses both the sequencing and machine selection sub-problems, searching for insertable positions of critical processes on other available machines, and shortening the critical path of the workpiece with the maximum weighted delay by balancing machine load and utilizing idle machine resources. Both strategies fully explore the solution space, effectively improving the quality and efficiency of the scheduling solution. Furthermore, a mathematical heuristic method combining the LP relaxation model and the MILP exact model is used to achieve efficient and rapid solutions to the batch sub-problems.

Description

Technical Field

[0001] This invention belongs to the technical field of workshop scheduling, and more specifically, relates to a batch flow hybrid production line scheduling method and equipment for the manufacturing of nanometer time-grating displacement sensors. Background Technology

[0002] The manufacturing industry is accelerating its transformation towards intelligent and digital transformation. As a crucial foundational component for high-end equipment manufacturing, the manufacturing efficiency and scheduling level of nano-timegratings directly impact the production quality and delivery capabilities of related products. With the continued growth in market demand, enterprises urgently need to improve production efficiency through flexible production models that offer diverse varieties and small batches to adapt to the demands of industrial upgrading.

[0003] The nanometer time-grating sensor manufacturing line has the following characteristics: multi-variety, high-volume, assembly-line production; only different products within the same major category are allowed to be produced on the same line; batch production is only allowed to start after minimum batch size constraints are met; in some processing stages, such as potting and functional testing, different products require specific machines. The complex constraints of the nanometer time-grating production line bring the following challenges: In the mixed-line production mode, when changing between different product models, the corresponding changeover time needs to be considered, placing extremely high demands on the quality of the batching scheme. Excessively large batch sizes can easily lead to overloading of individual machines and increased workshop production cycles, while excessively small batch sizes will increase machine changeover time and production management difficulty; the batching sub-problem is strongly coupled with the process sequencing and machine selection sub-problems, and the actual number of non-zero sub-batches directly determines the number of processes to be sequenced in the sub-batches, resulting in a large and complex solution space; there are machine resource limitations during processing, with some machines only usable for a specific process of a specific product, leading to unrelated parallel machine problems and posing significant challenges to scheduling.

[0004] Currently, the production scheduling of nano-time grating sensors mainly relies on manual experience, which cannot meet the ever-increasing production demands. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a batch flow hybrid production line scheduling method and equipment for the manufacturing of nano-time grating displacement sensors, which aims to solve the problems of low efficiency and difficulty in batch optimization of the existing production scheduling methods for nano-time grating sensors.

[0006] To achieve the above objectives, according to one aspect of the present invention, a batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors is provided, comprising the following steps: (1) Based on the total weighted delay value of the initial scheduling scheme corresponding to the scheduling problem of the batch flow mixed flow workshop for the manufacturing of nanometer time-grating displacement sensors, the initial scheduling scheme is selected and directly enters the new population; crossover and mutation operations are performed on the initial scheduling scheme, and the new individuals obtained also enter the new population. (2) The local optimization strategy based on the critical path is adopted to optimize the individuals in the new population; among them, for the process sequencing subproblem, the same machine insertion strategy of the maximum delayed workpiece process based on the critical path is adopted, and the corresponding key process on the critical path of the workpiece with the largest weighted delay is inserted to filter the process sequencing code; for the two subproblems of process sequencing and machine selection, the variable machine insertion strategy of the maximum delayed workpiece process based on the critical path is adopted, so that the key process of the workpiece with the largest weighted delay is inserted on other optional machines to explore, thereby optimizing the process sequencing code and the machine selection code. (3) Under the premise that the process sequencing code and machine selection code remain unchanged, the linear programming model constructed only for non-zero sub-batches is solved and heuristically rounded to obtain the batch partitioning code; at the same time, the sub-batches that do not meet the minimum batch constraint in the batch partitioning code obtained by solving the LP model corresponding to all sub-batches are defined as 0, and then the MILP model is constructed for non-zero sub-batches, and then the MILP model is solved to obtain the batch partitioning code; the two batch partitioning codes obtained form the current latest batch partitioning code, and then the optimal scheduling scheme is obtained.

[0007] Furthermore, the selection operations employ elite selection and tournament selection; at the process level, POX crossover and JBX crossover are used, at the machine level, two-point crossover is used, and at the batch level, uniform crossover is used; the mutation operations include: at the process level, two-point exchange mutation is used, at the machine level, single-point mutation is used, and at the batch level, single-workpiece mutation is used.

[0008] Furthermore, in the local search based on the critical path, the search process based on the insertion of critical processes of variable machines includes the following specific steps: (11) Find the workpiece with the longest weighted delay. The critical path it is on; (12) Try to include the critical path belonging to The process is moved to another feasible location on another machine; (13) Conduct a feasibility assessment, the assessment rules are as follows: Calculation process In the process , Interleaved time windows :

[0009]

[0010] in, , For adjacent processes on other optional machines, For process The preceding process of the process, For process The next process after the process, Indicates the earliest completion time. Indicates the latest start time; When the process Processing time At that time, movement is feasible.

[0011] Furthermore, in the local search based on the critical path, the search process based on the insertion of critical processes on the same machine includes the following sub-steps: (21) Find the workpiece with the longest weighted delay. The critical path it is on; (22) Try to include the critical path belonging to The process is moved to another feasible location on the same machine; (23) Conduct a feasibility assessment, and the assessment rules are as follows: Calculation process In the process , Interleaved time windows :

[0012]

[0013] in, , For adjacent processes on the current machine, for The preceding process of the process, for The next process after the process, Indicates the earliest completion time. Indicates the latest start time; When the process The processing time is less than or equal to At that time, movement is feasible.

[0014] Furthermore, individuals are selected based on their optimized fitness to obtain the optimal scheduling scheme.

[0015] Furthermore, the fitness function representing the individual's merits is:

[0016] in, For workpiece type The final completion time, For workpiece type Delivery date, For workpiece type The delay time, For workpiece type The weight.

[0017] Furthermore, prior to step (1), the scheduling problem of the batch flow hybrid production line for manufacturing nanometer time-grating displacement sensors is divided into three sub-problems: process sequencing, machine selection, and batch partitioning. An initial scheduling scheme is generated for the three sub-problems by combining heuristic rules and random generation. The initial scheduling scheme is represented by a three-layer collaborative coding scheme of process sequencing coding, machine selection coding, and batch partitioning coding. The initial scheduling scheme then forms the initial population.

[0018] Furthermore, after decoding the individuals in the initial population using a semi-active decoding method, the total weighted delay value of the individuals is calculated based on the constraints of the preceding processing stage, machine availability, changeover time, and batch quantity.

[0019] The present invention also provides a batch-flow hybrid flow shop scheduling system for the manufacture of nanometer time-grating displacement sensors. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the batch-flow hybrid flow shop scheduling method for the manufacture of nanometer time-grating displacement sensors as described above.

[0020] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the batch-flow hybrid production line scheduling method for the manufacture of nanometer time-grating displacement sensors as described above.

[0021] In summary, compared with the prior art, the batch flow hybrid production line scheduling method and equipment for manufacturing nanometer time-grating displacement sensors provided by the present invention have the following advantages: 1. This invention employs a local search based on the critical path to further optimize two sub-problems: machine selection and process sequencing. This achieves machine reallocation of critical processes and process exchange of critical blocks. The first strategy is based on inserting critical processes on the same machine. This strategy targets the sequencing sub-problem by optimizing the processing sequence on a single machine to shorten the critical path of the workpiece with the maximum weighted delay. The second strategy is based on inserting critical processes on a different machine. This strategy addresses both the sequencing and machine selection sub-problems simultaneously, searching for insertable positions of critical processes on other available machines. By balancing machine load and utilizing idle machine resources, it shortens the critical path of the workpiece with the maximum weighted delay. Both strategies fully explore the solution space, effectively improving the quality and efficiency of the scheduling solution. Simultaneously, for the batch partitioning sub-problem, a mathematical model is established. A mathematical heuristic method combining the LP relaxation model and the MILP exact model is employed to leverage the high-quality solution of the exact method, fully exploring the optimal batch partitioning information for the current individual components, and achieving efficient and rapid solution to the batch partitioning sub-problem.

[0022] 2. At the process level, a combination of POX and JBX is employed. POX ensures process feasibility while improving population diversity and global search capability. At the machine level, a two-point crossover method is used to effectively inherit the superior characteristics of the parent generation in local machine allocation, while enhancing the ability of offspring individuals to combine and reconstruct equipment selection. At the batching level, a uniform crossover strategy is adopted, which can more flexibly reorganize the parent generation's batching scheme and attempt to discover better batch partitioning codes. Regarding mutation operators: two-point exchange mutation is used at the process level; single-point mutation is used at the machine level; and single-job mutation is used at the batching level. These mutation operators effectively prevent the algorithm from getting trapped in local optima. Simultaneously, tournament selection and elite retention strategies work synergistically to avoid the loss of superior genes, improving convergence speed and global optimization capability.

[0023] 3. The initial solution generation adopts a combination of random and heuristic rule generation methods based on problem characteristics, effectively improving the quality of the initial solutions. This combined strategy avoids the initial population from getting trapped in local optima and introduces a search-oriented approach to solutions in the early stages of iteration, laying a solid foundation for subsequent optimization and balancing the exploratory and developmental aspects of the method.

[0024] 4. This invention combines the advantages of metaheuristic algorithms and mathematical model-based search, achieving reasonable and efficient batch partitioning, efficient optimization in the solution space, balancing solution speed and solution quality, improving equipment utilization, shortening production cycle, increasing order delivery rate, breaking through the limitations of traditional experience-based scheduling, and providing a systematic solution for the efficient production of nanometer time-grating displacement sensors, effectively improving overall production stability. Attached Figure Description

[0025] Figure 1 This is a flowchart of a batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors, provided by an embodiment of the present invention. Figure 2 This is a schematic diagram of chromosome crossover mutation operation according to an embodiment of the present invention; Figure 3 This is a Gantt chart of the solution result of an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0027] This invention provides a batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors. The method embeds mathematical programming into a metaheuristic algorithm framework, utilizing metaheuristics to explore the global solution space and employing mathematical programming to accurately solve sub-problems such as batch partitioning. This method can quickly obtain high-quality scheduling schemes that satisfy multiple complex constraints, providing a systematic solution for the efficient and stable production of nanometer time-grating displacement sensors.

[0028] The proposed method combines a local search strategy tailored to specific problem characteristics to achieve efficient production in a nanometer-scale time-grating displacement sensor workshop, overcoming the technical bottlenecks of low production efficiency, difficulty in batch optimization, and challenges in meeting order delivery rates in existing technologies. Specifically, the method first employs a three-layer encoding structure, constructing initial solutions through random generation and various heuristic methods; then, semi-active decoding is performed on the initial individuals; subsequently, population evolution is achieved through customized genetic operations (crossover, mutation strategies, and a selection mechanism combining tournament and elite retention); finally, based on corresponding sub-problems, corresponding local search operators are used, efficiently utilizing the advantages of metaheuristic methods and mathematical model-based search to explore the optimal solution. This method effectively balances algorithmic optimization with the ability to handle complex constraints, significantly improving the production efficiency of the nanometer-scale time-grating displacement sensor workshop and ultimately achieving efficient and stable production scheduling.

[0029] Please see Figure 1 , Figure 2 and Figure 3 The method mainly includes the following steps: Step 1: The scheduling problem of the batch-flow hybrid production line for manufacturing nanometer time-grating displacement sensors is divided into three sub-problems: process sequencing, machine selection, and batch partitioning. An initial scheduling scheme is generated for the three sub-problems by combining heuristic rules and random generation. The initial scheduling scheme is represented by a three-layer collaborative coding scheme of process sequencing coding, machine selection coding, and batch partitioning coding. The initial scheduling schemes then form the initial population.

[0030] During coding, the three-layer coding adopts a fixed upper limit length code. The length of the process sequence code is the sum of the number of processes in all sub-batches, which sequentially represents the processing order between each workpiece sub-batches in each processing stage. The length of the machine selection code is the same as that of the process sequence code, which represents the processing machine of the corresponding sub-batch process in a fixed order of "processing stage-workpiece type-batch". The length of the batch division code is the sum of the maximum allowed number of batches for each workpiece type, which sequentially represents the batch division information for different workpiece types. Unused sub-batch positions are filled with 0.

[0031] The initial population consists of a random number generation component and a heuristic rule generation component. The random number generation mechanism randomly divides each workpiece into batches according to the maximum batch size constraint and the minimum sub-batch size constraint, randomly arranges the processing order of each workpiece's sub-batch operations, and randomly assigns an available processing machine to each sub-batch operation, thus forming random individuals. In the heuristic rule generation component, at least one priority rule (earliest delivery date priority, weighted earliest delivery date priority, weighted shortest processing time priority) is used to construct the operation sorting code. For machine selection coding, either the fastest machine allocation rule or the minimum load machine allocation rule is used to construct the machine selection code. For batch coding, at least one rule (minimum type change partitioning rule, balanced partitioning rule, or maximum sub-batch splitting rule) is used to construct the batch partitioning code.

[0032] In one implementation, 50% of the individuals in the initial population are generated by randomly dividing the batch, randomly shuffling the process sequence, and randomly assigning machines to ensure the diversity of solutions; the remaining 50% of the individuals are generated through a variety of heuristic rules.

[0033] Step 2: After decoding the individuals in the initial population using a semi-active decoding method, calculate the total weighted delay value of the individuals based on the constraints of the preceding processing stage, machine availability, changeover time, and batch quantity.

[0034] The specific decoding sub-steps are as follows: (1) Process each sub-batch sequentially according to the order of the process sequence within each stage; (2) Determine the target machine of the sub-batch in the current stage based on the machine selection code; (3) Determine the actual start time of the current sub-batch based on the completion time of the same sub-batch in the previous stage and the idle time of the target machine; (4) Calculate the changeover time based on whether the previous workpiece type on the current machine is the same as the current workpiece type. The changeover time of the first processing sub-batch is related to the current unit processing time. The changeover time when different workpiece types are processed continuously is determined by the unit processing time of the previous workpiece and the unit processing time of the current workpiece. (5) Calculate the processing time based on the number of sub-batches and the unit processing time, and update the corresponding sub-batch completion time and machine idle time; (6) An order corresponds to several workpieces of one type; after all stages are decoded, the completion time of the last completed sub-batch of the workpiece type corresponding to each order is compared with the delivery date of the order, and the total weighted delay value is calculated as the objective function value.

[0035] Step 3: Select individuals based on the obtained total weighted delay value. Selected individuals directly enter the new population. Perform crossover and mutation operations on the individuals to obtain new individuals that enter the new population.

[0036] The selection operations employ both elite selection and tournament selection. At the process level, POX and JBX cross-operations are used; at the machine level, two-point cross-operations are used; and at the batch level, uniform cross-operations are used. Mutation operations include: at the process level, two-point exchange mutation; at the machine level, single-point mutation; and at the batch level, single-workpiece mutation.

[0037] In one specific implementation, the selection operator employs a tournament selection strategy for individual selection: individuals participating in genetic operations are selected for crossover and mutation through a tournament selection strategy; simultaneously, an elite preservation strategy is implemented, replicating the most fit individual from each generation and adding it to the new population to ensure the inheritance of superior genes. Regarding the crossover operator: at the process level, a combination of POX and JBX is used. POX and JBX can effectively preserve the process priority relationships and local processing sequences of parent individuals during the crossover process. The combination of the two can improve population diversity and global search capabilities while ensuring process feasibility. At the machine level, a two-point crossover method is used, which can effectively inherit the superior characteristics of the parent in local machine allocation, while enhancing the combinatorial reconstruction capabilities of the offspring in equipment selection. At the batching level, a uniform crossover strategy is adopted. This uniform crossover strategy can more flexibly reorganize the parent's batching scheme, attempting to discover better batch partitioning codes. Regarding mutation operators: at the process level, two-point exchange mutation is used, which randomly selects two positions in an individual and swaps their corresponding processes to change the local processing order. This can introduce new process arrangements without significantly disrupting the original optimal structure, thus effectively preventing the algorithm from getting trapped in local optima. At the machine level, single-point mutation is used, which randomly selects a gene locus and reassigns the processing machine corresponding to that gene locus to another feasible device. This enhances the ability to explore the device allocation space and helps improve machine load balancing. At the batching level, single-workpiece mutation is used, which randomly selects a workpiece and re-batches it, which can break free from the limitations of the original batching structure and explore better solutions.

[0038] Step four involves optimizing individuals in the new population using a local optimization strategy based on the critical path. Specifically, for the process sequencing subproblem, a same-machine insertion strategy for the maximum delayed workpiece's process is adopted. This involves inserting the corresponding critical processes on the critical path of the workpiece with the largest weighted delay to filter the process sequencing codes. For the process sequencing and machine selection subproblems, a variable-machine insertion strategy for the maximum delayed workpiece's process is adopted. This allows the critical processes of the workpiece with the largest weighted delay to be inserted on other available machines for exploration, thus optimizing both the process sequencing code and the machine selection code.

[0039] In a local search based on the critical path, the search process based on the insertion of critical processes on the same machine includes the following sub-steps: (1) Find the workpiece with the longest weighted delay. The critical path it is on; (2) Try to include the critical path belonging to The process is moved to another feasible location on the same machine; (3) A feasibility assessment was conducted, and the assessment was as follows: Calculation process In the process , Interleaved time windows :

[0040]

[0041] in, , For adjacent processes on the current machine, for The preceding process of the process, for The next process after the process, Indicates the earliest completion time. This indicates the latest start time for work.

[0042] When the process The processing time is less than or equal to At that time, movement is feasible.

[0043] In the local search based on the critical path, the search process based on the insertion of critical processes of variable machines includes the following specific steps: (1) Find the workpiece with the longest weighted delay. The critical path it is on; (2) Try to include the critical path belonging to The process is moved to another feasible location on another machine; (3) A feasibility assessment was conducted, and the assessment was as follows: Calculation process In the process , Interleaved time windows :

[0044]

[0045] in, , For adjacent processes on other optional machines, For process The preceding process of the process, For process The next process after the process, Indicates the earliest completion time. This indicates the latest start time for work.

[0046] When the process Processing time At that time, movement is feasible.

[0047] Step 5: For the batch partitioning subproblem, based on the call frequency, solution time, and solution quality, and with the process sorting code and machine selection code remaining unchanged, a linear programming model is constructed only for non-zero sub-batches. After solving the obtained linear programming model, heuristic rounding is performed to obtain the batch partitioning code. At the same time, an LP model is constructed for all sub-batches. Sub-batches that do not meet the minimum batch constraint in the batch partitioning code obtained by solving the current LP model are defined as 0. Then, a MILP model is constructed for the non-zero sub-batches, and the MILP model is solved to obtain the batch partitioning code. The two batch partitioning codes obtained constitute the current latest batch partitioning code.

[0048] The local search based on the LP model optimizes only the batch partitioning code while keeping the process sequencing code and machine selection code unchanged. This strategy uses the set of sub-batches corresponding to non-zero batches in the current individual as the optimization object, establishing a continuous variable linear programming model, where the batch quantity variable is a real number. For each workpiece type, the sum of all batch quantities is constrained to equal the total demand for that workpiece; for the current non-zero sub-batches, the lower bound of the batch size is set to the minimum batch size. After solving the linear programming model, the obtained batch partitioning result is heuristically rounded.

[0049] In the local search based on mathematical models, the local search based on the MILP model is as follows: the exact optimization strategy also fixes the process ordering code and the machine selection code. Considering that the MILP model has the disadvantage of very long solution time in large-scale problems, a two-stage solution is adopted for batch coding.

[0050] Step 5: Based on the fitness of the optimized individuals, the individuals are screened to obtain the current optimal solution. Then, it is determined whether the termination condition is met. If not, the process returns to step 2; otherwise, the current optimal solution is the optimal scheduling scheme.

[0051] The fitness function representing the quality of an individual is:

[0052] in, For workpiece type The final completion time, For workpiece type Delivery date, For workpiece type The delay time, For workpiece type The weight.

[0053] This invention focuses on the workshop scheduling scenario of nanometer time-grating displacement sensors, proposing a batch-flow hybrid flow shop scheduling method for the manufacturing of nanometer time-grating displacement sensors. This method aims to solve problems such as low production efficiency, difficulty in batch optimization, and difficulty in meeting order delivery rates, achieving efficient and stable workshop production as its core objective. It constructs a complete optimization mechanism covering encoding, decoding, genetic operations, and local search. At the encoding and initial solution generation level, a three-layer fixed upper bound length encoding structure is adopted. The initial solution is generated through a hybrid heuristic strategy: 50% is randomly generated to ensure diversity, and 50% is generated according to multiple heuristic rules to improve rationality. At the decoding level, semi-active decoding is used. At the genetic operation level, selection operators are combined with tournament and elite retention strategies. Regarding crossover operators: at the process level, a combination of POX and JBX is used; at the machine level, a two-point crossover method is used; and at the batch level, a uniform crossover strategy is used. Regarding mutation operators: at the process level, two-point exchange mutation is used; at the machine level, single-point mutation is used; and at the batch level, single-workpiece mutation is used. At the local search level, local search operators are designed according to the characteristics of the sub-problems. For the subproblem of process sequencing and machine selection, a critical path-based approach is adopted to insert critical processes on the same or different machines, fully searching the solution space and improving machine utilization. For the subproblem of batch partitioning, a local search based on LP or MILP models is used to balance solution speed and quality. This method, through the synergy of various strategies, effectively improves production efficiency, batch optimization effect, and order delivery rate, providing an effective solution for intelligent scheduling of nanometer time-grating displacement sensors in the workshop.

[0054] The present invention also provides a batch-flow hybrid flow shop scheduling system for the manufacture of nanometer time-grating displacement sensors. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the batch-flow hybrid flow shop scheduling method for the manufacture of nanometer time-grating displacement sensors as described above.

[0055] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the batch-flow hybrid production line scheduling method for the manufacture of nanometer time-grating displacement sensors as described above.

[0056] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A batch flow hybrid flow shop scheduling method for nano-time grid displacement sensor manufacturing, characterized in that, The steps are as follows: (1) Based on the total weighted delay value of the initial scheduling scheme corresponding to the scheduling problem of the batch flow mixed flow workshop for the manufacturing of nanometer time-grating displacement sensors, the initial scheduling scheme is selected and directly enters the new population; crossover and mutation operations are performed on the initial scheduling scheme, and the new individuals obtained also enter the new population. (2) The local optimization strategy based on the critical path is adopted to optimize the individuals in the new population; among them, for the process sequencing subproblem, the same machine insertion strategy of the maximum delayed workpiece process based on the critical path is adopted, and the corresponding key process on the critical path of the workpiece with the largest weighted delay is inserted to filter the process sequencing code; for the two subproblems of process sequencing and machine selection, the variable machine insertion strategy of the maximum delayed workpiece process based on the critical path is adopted, so that the key process of the workpiece with the largest weighted delay is inserted on other optional machines to explore, thereby optimizing the process sequencing code and the machine selection code. (3) Under the premise that the process sequencing code and machine selection code remain unchanged, the linear programming model constructed only for non-zero sub-batches is solved and heuristically rounded to obtain the batch partitioning code; at the same time, the sub-batches that do not meet the minimum batch constraint in the batch partitioning code obtained by solving the LP model corresponding to all sub-batches are defined as 0, and then the MILP model is constructed for non-zero sub-batches, and then the MILP model is solved to obtain the batch partitioning code; the two batch partitioning codes obtained form the current latest batch partitioning code, and then the optimal scheduling scheme is obtained.

2. The batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors as described in claim 1, characterized in that: The selection operations employ elite selection and tournament selection; at the process level, POX crossover and JBX crossover are used, at the machine level, two-point crossover is used, and at the batch level, uniform crossover is used; the mutation operations include: at the process level, two-point exchange mutation is used, at the machine level, single-point mutation is used, and at the batch level, single-workpiece mutation is used.

3. The batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors as described in claim 1, characterized in that: In the local search based on the critical path, the search process based on the insertion of critical processes of variable machines includes the following specific steps: (11) Find the workpiece with the longest weighted delay. The critical path it is on; (12) Try to include the critical path belonging to The process is moved to another feasible location on another machine; (13) Conduct a feasibility assessment, the assessment rules are as follows: Calculation process In the process , Interleaved time windows : in, , For adjacent processes on other optional machines, For process The preceding process of the process, For process The next process after the process, Indicates the earliest completion time. Indicates the latest start time; When the process Processing time At that time, movement is feasible.

4. The batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors as described in claim 1, characterized in that: In a local search based on the critical path, the search process based on the insertion of critical processes on the same machine includes the following sub-steps: (21) Find the workpiece with the longest weighted delay. The critical path it is on; (22) Try to include the critical path belonging to The process is moved to another feasible location on the same machine; (23) Conduct a feasibility assessment, and the assessment rules are as follows: Calculation process In the process , Interleaved time windows : in, , For adjacent processes on the current machine, for The preceding process of the process, for The next process after the process, Indicates the earliest completion time. Indicates the latest start time; When the process The processing time is less than or equal to At that time, movement is feasible.

5. The batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors as described in any one of claims 1-4, characterized in that: Individuals are selected based on their optimized fitness to obtain the optimal scheduling scheme.

6. The batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors as described in claim 5, characterized in that: The fitness function representing the merits of an individual is: in, For workpiece type The final completion time, For workpiece type Delivery date, For workpiece type The delay time, For workpiece type The weight.

7. The batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors as described in any one of claims 1-4, characterized in that: Before step (1), the scheduling problem of the batch flow hybrid production line for the manufacturing of nanometer time-grating displacement sensors is divided into three sub-problems: process sequencing, machine selection, and batch partitioning. An initial scheduling scheme is generated for the three sub-problems by combining heuristic rules and random generation. The initial scheduling scheme is represented by a three-layer collaborative coding scheme of process sequencing coding, machine selection coding, and batch partitioning coding. The initial scheduling scheme then forms the initial population.

8. The batch-flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors as described in claim 7, characterized in that: After decoding individuals in the initial population using a semi-active decoding method, the total weighted delay value of each individual is calculated based on constraints such as preprocessing stage constraints, machine availability constraints, changeover time constraints, and batch quantity constraints.

9. A batch-flow hybrid production line scheduling system for manufacturing nanometer time-grating displacement sensors, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the batch flow hybrid production line scheduling method for manufacturing nanometer time-grating displacement sensors as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions that, when invoked and executed by a processor, cause the processor to implement the batch-flow hybrid flow shop scheduling method for the manufacture of nanometer time-grating displacement sensors as described in any one of claims 1-8.

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