A multi-objective flexible job-shop large model adaptive optimization scheduling method

Abstract

The present application relates to the field of flexible job shop scheduling, and particularly relates to a multi-objective flexible job shop large model adaptive optimization scheduling method, comprising the following steps: S1: constructing a double-objective optimization model; S2: using a large language model to generate an initial candidate heuristic rule population of the double-objective optimization model; S3: performing population evaluation on the heuristic rules in the initial candidate heuristic rule population; S4: performing performance gap evaluation and rule cluster division on the parent heuristic rule population; S5: performing hierarchical reflection guidance and a double-path evolution mechanism on the parent heuristic rule population after the population performance gap evaluation and rule cluster division; S6: repeating the iteration of steps S3-S5 and outputting a final rule population; the multi-objective flexible job shop scheduling solution set quality, optimization stability and industrial scene adaptation ability are improved.

Description

Technical Field

[0001] This invention relates to the field of flexible shop scheduling, and specifically to an adaptive optimization scheduling method for a large-scale multi-objective flexible shop model. Background Technology

[0002] Flexible workshop scheduling is a typical combinatorial optimization problem in the field of intelligent manufacturing. In a flexible workshop, the same process can be processed by multiple machines, and scheduling requires the simultaneous determination of the process sequence and machine allocation plan. With the scaling up of manufacturing systems, the heterogeneity of resources, and the increasing demands of orders, scheduling has evolved from optimizing a single completion time to a multi-objective collaborative optimization problem that includes minimizing the maximum completion time and the total delay time.

[0003] Existing scheduling solutions mainly include exact optimization methods, intelligent optimization algorithms, deep learning methods, reinforcement learning (RL) methods, and rule-based scheduling methods. Exact optimization methods model and solve using integer programming and constrained programming, primarily suitable for small-scale scenarios. However, as the problem size increases, the solution time is long and resource consumption is high, making it difficult to meet real-time scheduling requirements. Intelligent optimization algorithms include single-objective algorithms (genetic algorithms, particle swarm optimization, etc.) and multi-objective optimization algorithms (NSGA II, SPEA2, etc.), optimizing scheduling schemes through iterative search and possessing multi-objective balancing capabilities. However, they rely on manually designed codes and operators, are prone to premature convergence, have insufficient population diversity, and only optimize scheduling schemes, making it difficult to generate reusable scheduling rules. Deep learning methods (such as neural networks) rely on neural networks to extract scheduling features, requiring massive samples and long training periods. Adaptation costs are high after scenario changes, and decision interpretability is weak. Reinforcement learning learns scheduling strategies through trial and error with the environment, requiring manual design of states, actions, and reward functions. Modeling costs are high, the output is an implicit policy, and the decision logic is difficult to trace.

[0004] Rule-based scheduling methods have been widely researched and applied in the field of flexible workshop scheduling due to their simple structure, high efficiency, and strong interpretability. Early manual pre-setting of scheduling rules required workers to design each rule individually, resulting in low automation, poor adaptability, and difficulty in meeting multi-objective optimization needs. Subsequently, with technological advancements, automatic generation methods such as scheduling rule combination optimization, genetic programming (GP), and hyperheuristic rules emerged. However, rule combination optimization relies on manual assembly and has poor optimization targeting; genetic programming is constrained by fixed expression structures and predefined function sets, resulting in limited rule expression space and strong blind crossover mutation; and hyperheuristic rules are mostly limited to dynamically selecting existing rules, making it difficult to independently innovate rule structures. All of these methods are insufficient to fully adapt to the actual needs of multi-objective flexible scheduling.

[0005] In recent years, Large Language Models (LLMs) have provided a novel technical approach for optimizing scheduling rules due to their pre-trained language understanding, code generation, and logical reasoning capabilities. Compared to traditional rule generation methods, they can directly generate and rewrite executable scheduling rule code without complex modeling and long-term training. The rules are flexible, interpretable, and easily transferable, offering significant advantages in automatic rule generation and policy optimization. While existing large model scheduling methods have achieved applications such as rule generation and algorithm assistance, they still have significant shortcomings in multi-objective flexible workshop scheduling: the integration of multi-objective optimization is not deep enough, rule distribution and quality lack quantitative control, evolutionary operations lack targeted improvement strategies, and it is difficult to balance convergence, diversity, and evolutionary efficiency. Summary of the Invention

[0006] The purpose of this invention is to provide an adaptive optimization scheduling method for a large-scale, flexible multi-objective workshop model that combines multi-objective optimization to achieve rule-based balanced screening.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: An adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model includes the following steps executed sequentially: S1: Using maximum completion time and total delay time as optimization objectives, define the maximum completion time and total delay time, and construct a dual-objective optimization model based on these defined times. Then, apply machine selectability constraints, process timing constraints, and machine exclusiveness constraints to this dual-objective optimization model. It is expressed by the following formula: ; in, To maximize the completion time, Total delay time; S2: Preset workshop state, based on which the process is adjusted. Distributed to machine The priority is evaluated to obtain the priority evaluation result. The optimal scheduling decision is selected based on the priority evaluation result. The optimal scheduling decision is used to update the status of the workshop, and the target value vector corresponding to the heuristic rule is generated. The initial candidate heuristic rule population of the bi-objective optimization model is generated using a large language model. S3: Perform population evaluation on the heuristic rules in the initial candidate heuristic rule population, that is, batch evaluate all heuristic rules in the population on multiple standard flexible workshop instances, calculate the maximum completion time and total delay time of each heuristic rule on each instance, and normalize the target value vector in each instance to obtain a normalized dual-objective vector. Then, calculate the cross-instance average normalized target value for each heuristic rule to form a rule-level dual-objective aggregation vector. Use a screening mechanism of non-dominated solution sorting priority and adaptive dynamic grid truncation assistance to retain a preset number of rules from multiple legal candidates as the parent heuristic rule population. S4: Evaluate the performance gap and divide the rule clusters of the parent heuristic rule population: Based on the normalized bi-objective vector, extract the set of non-dominated rules from all heuristic rules in the parent heuristic rule population, and select the heuristic rule with the smallest weighted normalized objective value from the set of non-dominated rules as the first... The reference rules for the nth instance are used to obtain the nth... The reference normalized target vector corresponding to the nth instance is defined as the Euclidean distance between the normalized target vector and the reference normalized target vector. The performance gap of the heuristic rules in each instance is used to calculate the average performance gap of the heuristic rules. The heuristic rules are then divided according to a preset performance gap threshold to obtain a low-performance gap rule cluster and a high-performance gap rule cluster. S5: After assessing the population performance gap and dividing the rule clusters according to the above method, the parent heuristic rule population is subjected to hierarchical reflection guidance and dual-path evolution mechanism: local reflection inputs are constructed for the low-performance gap rule cluster and the high-performance gap rule cluster respectively, and the large language model is called to generate the low-performance gap reflection results and the high-performance gap reflection results. Furthermore, the global evolution reflection results are generated, and the low-performance gap rule cluster is subjected to reflective crossover and recombination, and the high-performance gap rule cluster is subjected to reflective repair mutation to obtain the offspring heuristic rules; S6: Offspring Evaluation and Population Update: The offspring heuristic rule population generated in each generation is merged with the current parent heuristic rule population to form a new candidate heuristic rule population. The new candidate heuristic rule population repeats steps S3 to S5. After each complete iteration, the number of iterations is accumulated. When the number of iterations reaches the preset maximum value, the loop terminates and the current parent heuristic rule population is output as the final rule set. Each rule in the rule set is applied to the current scheduling instance.

[0008] Preferably, step S1 specifically includes the following steps: S1-1: Let the set of workpieces be... n represents the number of workpiece types, and the number of workpieces... The included processes are defined as follows The machine set is , m is the total number of machines, for workpieces The jth process The set of available machines is denoted as And satisfy The optimization objectives are maximum completion time and total delay time. Maximum completion time is defined as: ; in, Indicates workpiece Completion time, Indicates the workpiece number. Indicates the total number of workpieces to be scheduled; Total delay time is defined as: ; in, Indicates workpiece Delivery time; S1-2: To ensure the executability of the generated scheduling scheme, the following constraints are applied to this bi-objective optimization model: Machine optional constraint: This machine optional constraint ensures that each process Just in its set of optional machines Processing is performed on one of the machines, and the machine selection constraints are expressed by the following formula: ; in, Indicates the type of workpiece The This process is done on the machine. 0-1 decision variables for the allocation of processing time on the surface; Process timing constraints: This process timing constraint ensures that the process... In the process Once completed, the sequential relationship is ensured. The timing constraint for this process is expressed by the following formula: ; in, Indicates the type of workpiece The This process is done on the machine. The start time of the project Indicates the type of workpiece The This process is done on the machine. The start time of the project Indicates the type of workpiece The This process is done on the machine. Processing time on Assign 0-1 decision variables to the machines corresponding to the preceding processes; Machine exclusivity constraint: A machine can only process one operation at a time. This constraint ensures that on the same machine, any two operations can be performed simultaneously. and They will not execute simultaneously; the machine exclusive constraint is expressed by the following formula: ; in, Indicates the type of workpiece The This process is done on the machine. Processing time on Indicates the type of workpiece The This process is done on the machine. The start time of the project Indicates the type of workpiece The This process is done on the machine. The processing time.

[0009] Preferably, the specific steps of step S2 are as follows: S2-1: Let the current heuristic rule population be... N represents the current size of the rule-based population. Indicates the first A heuristic rule; S2-2: At scheduling time t, the workshop state is denoted as... ; in, This indicates the current status of an incomplete set of workpieces. Indicates the current machine operating status. This represents the set of currently schedulable operations; S2-3: Regarding the current workshop status , set up process The optional set of machines is heuristic rules Evaluate candidate processes and machine combinations; processes Distributed to machine The priority evaluation value at that time is expressed by the following formula: ; The optimal scheduling decision is selected based on the priority evaluation results of all candidate processes and machine combinations: ; in, This represents the set of selected processes. This represents the set of machines to be allocated. S2-4: Adjust the workshop state based on this optimal scheduling decision. Update to obtain the new workshop status. Repeat steps S2-2 and S2-3 until all workpieces are processed, thus generating the heuristic rule. The corresponding complete scheduling scheme is evaluated to obtain the heuristic rule. The corresponding target value vector: ; in, For corresponding heuristic rules Maximum completion time For corresponding heuristic rules Total delay time; S2-5: Let the initial population size of the candidate heuristic rules be... The parent-generation heuristic rule population retention size is ,in, The population diversity of the initial candidate heuristic rules is increased by expanding the candidate sample base. Then, a fixed number of parent heuristic rules are retained through a multi-objective screening mechanism. The initial candidate heuristic rule population is represented as follows: ; Generate initial heuristic rules using a large language model to obtain 10 valid heuristic rules are used to form the initial candidate heuristic rule population. .

[0010] Preferably, the specific steps for heuristic rule population evaluation in step S3 are as follows: S3-1: Let the set of training instances be... For heuristic rules In the The first test instance The target value is denoted as ,in, hour, Representing heuristic rules In the Maximum completion time on a single instance; hour, Representing heuristic rules In the Total delay time on each instance; Since different instances and different targets have different units and numerical ranges, normalization is first performed within each instance, let's say the first instance... In the first instance The minimum and maximum values ​​of the targets are as follows: ; ; Heuristic rules In the The first instance Normalized target value Defined as: ; in, To prevent extremely small constants with a denominator of zero, the range of values ​​is 10. -12 ≤ ≤10 12 ; After the above processing, the heuristic rules In the example The normalized biobjective vector on can be expressed as: ; S3-2: Rule Set Performance Analysis: Since each heuristic rule needs to be comprehensively evaluated on multiple test instances, the performance of the heuristic rules... The normalized objective values ​​across all instances are averaged to obtain a rule-based bi-objective aggregation vector: ; in, , , This is the number of test instances. Representing heuristic rules The average normalized maximum completion time across all test instances. Representing heuristic rules Average normalized total latency across all test instances; The aggregation objective value of this heuristic rule is then: ; Used to characterize heuristic rules The comprehensive dual-objective performance is used as the basis for subsequent non-dominated sorting and parent selection; S3-3: Non-dominated solution sorting of rule set: Calculate the bi-objective aggregation vector of all heuristic rules, perform non-dominated sorting on the heuristic rule set, and obtain the frontier level of each heuristic rule; S3-4: Dynamic grid truncation based on the hierarchical division of the frontier level: This dynamic grid truncation is not uniformly applied to all heuristic rules, but only during the non-dominated sorting process. When the number of rules in a certain frontier level exceeds the remaining retention quota, the frontier level is taken as the frontier boundary layer, and grid truncation is performed on the rules of the frontier boundary layer. If the number of rules in a certain frontier level can be fully incorporated into the current parent population, all rules in that frontier level are retained, and no further grid truncation is performed. For boundary layer rules that need to be truncated, a bi-objective aggregation vector is aggregated based on its heuristic rule level. The position in the two-dimensional target space is normalized and mapped, and then divided accordingly. There are 1 grid cells, where K is the grid division dimension, and each rule falls into the corresponding grid cell according to its aggregated normalization target value; During the grid truncation process, each non-empty grid cell retains at most one representative heuristic rule. If multiple heuristic rules exist within the same grid cell, the rule with the better aggregation target value is retained first, so that only the more representative rule is retained in the same local area. If the number of rules represented by the grid is still insufficient under the preset maximum grid division dimension, then the remaining required number of heuristic rules are selected from the boundary layer rules to complete the truncation based on the principle that the aggregation target value is better. The candidate heuristic rule population is truncated by a dynamic grid, and the heuristic rule population that is retained is used as the parent heuristic rule population.

[0011] Preferably, the specific steps of step S4 are as follows: S4-1: For the first In one instance, the parent heuristic rule population is based on a normalized bi-objective vector. and Extract the set of non-dominated rules from all heuristic rules. From this set of non-dominated rules, select the heuristic rule with the smallest weighted normalization objective value as the first heuristic rule. Reference rules for each instance: ; in, This is the dual-objective balance coefficient, with a value range of [value range missing]. ; No. The reference normalized target vector corresponding to each instance is: ; in, Refers to the first Reference rules for each instance Refer to the rules In the The first normalized target value on each instance, Refer to the rules In the The second normalized target value on each instance; S4-2: For the first Heuristics in a Specific Example Its performance gap Defined as the Euclidean distance between the normalized biobjective vector and the reference normalized objective vector: ; in Heuristic rules In the example Normalized biobjective vector on, Refer to the rules In the example Normalized biobjective vector on; The smaller the performance gap, the stronger the heuristic rule. In the example The closer the heuristic is to the reference good region, the larger the performance gap, indicating a stronger heuristic rule. In the example The farther away from the optimal region, the lower-performance gap rules prioritize retaining their existing structure and participating in crossover recombination, while the high-performance gap rules prioritize entering the repair mutation process. S4-3: Average Performance Gap of Heuristic Rules: To characterize heuristic rules The overall optimization potential across all test instances can be defined as the average performance gap as: ; in, Representing heuristic rules The average performance gap across all instances is used to guide the selection of differentiated evolutionary paths for heuristic rules and to control subsequent crossover recombination, repair mutation, and boundary layer preservation processes. S4-4: High and Low Performance Gap Rules: For the first Let there be an instance where the average performance gap of all heuristic rules is [value]. The standard deviation is The performance gap threshold for this instance is defined as follows: ; in, This threshold adjustment coefficient controls the tightness of the separation between high and low notches; based on this threshold adjustment coefficient... No. In this instance, heuristic rules can be used... Classified as: like heuristic rules In the example The above belongs to the high-performance gap rule cluster; like heuristic rules In the example The above belongs to the low-performance gap rule cluster; Statistical heuristics The number of times a rule is classified into a high-performance gap region and a low-performance gap region in all instances is used to classify rules belonging to high-performance gaps in more instances into high-performance gap rule clusters, and rules belonging to low-performance gaps in more instances into low-performance gap rule clusters. Subsequently, the evolution mode of different rules is controlled based on the rule performance gap, where high-performance gap rules preferentially trigger the repair mutation process, and low-performance gap rules preferentially trigger the crossover recombination process.

[0012] Preferably, the specific steps of step S5 are as follows: S5-1: Local rule reflection generation: For each rule in the parent population, it is statistically analyzed whether it belongs to the high gap or low gap region in each instance. Combined with its cross-instance average normalized target value, average performance gap and other indicators, a rule-level aggregation feature is formed. Based on this information, a low performance gap rule cluster and a high performance gap rule cluster are constructed. Then, local reflection inputs are constructed for the low performance gap rule cluster and the high performance gap rule cluster respectively, and the large language model is called to generate the corresponding reflection results. The reflection results include the low performance gap reflection results and the high performance gap reflection results. S5-2: Global Evolutionary Reflection Generation: Input the overall information of the current generation's parent population, the reflection result of the low gap, and the reflection result of the high gap into the large language model to generate the global evolutionary reflection result; S5-3: Reflective cross-recombination of the low-performance gap rule cluster: For the low-performance gap rule cluster, select two low-gap parent rules as cross-inputs; input the two low-gap parent rules, the low-performance gap reflection results, the global evolution reflection results, and the scheduling rule interface specifications into the large language model to generate low-performance offspring heuristic rules. S5-4: Reflective and restorative mutation of the high-performance gap rule cluster: For the high-performance gap rule cluster, a restorative mutation method of high-gap parent and elite reference parent is adopted. That is, a high-gap parent heuristic rule is selected as the object to be repaired and a low-gap or elite parent heuristic rule with better overall performance is selected as the structural reference object. These two parent heuristic rules, the high-performance gap reflection results, the global evolution reflection results and the scheduling rule interface specification are input into the large language model to generate high-performance offspring heuristic rules. The low-performance offspring heuristic rule and the high-performance offspring heuristic rule are sequentially subjected to syntax validation, interface validation, runtime validation, and constraint validation. If they fail, the error reason is sent back to the large language model for repair until the offspring heuristic rule is obtained or the retry limit is reached.

[0013] Preferably, in steps S2-5, the prompt template for generating initial candidate heuristic rules by the large language model consists of the following parts: Role instructions: used to guide the model to generate diverse rules based on different algorithm design styles; Task: Specify that the large model needs to complete the design heuristic rule code; Problem Description: Define the dual-objective optimization task of the flexible workshop as minimizing the maximum completion time and the total delay time, and provide a complete constraint description, including machine exclusive constraints, process sequence constraints, and machine selectability constraints; Input / output interface description: The function to generate rule code named "heuristic" is required. The rule input is defined as instance data of shop floor scheduling, and the output is a specific scheduling scheme. The input problem must include at least the number of workpieces, the number of machines, and the available machines and processing times for each workpiece's process. The output is a complete scheduling dictionary organized by workpiece, with each process recording the process number, assigned machine, start time, end time, and processing time. Restriction: Specifies the generation form of heuristic rules; Seed heuristics: used to provide examples of basic code format and output structure; Output instructions: The output should return a standard Python code block and its corresponding functional documentation. Perform the following validations on each heuristic rule generated by the large language model in sequence: Syntax validation checks whether the code can be parsed and loaded successfully. Interface validation checks whether a heuristic function is defined. Run the verification process by placing the rules into the scheduling environment for small-scale instance testing. Output structure validation: Check if a complete scheduling dictionary is returned. Constraint verification checks whether the scheduling results satisfy constraints such as machine exclusivity, process sequence, and machine selectability. If any step fails, the error message, the previous prompt, and the failure code are fed back to the large language model, which is required to generate a repair version based on the cause of the error, until the candidate heuristic rule passes the verification or reaches the preset maximum number of verifications.

[0014] Preferably, in step S5, the Prompt construction method for the large language model reflection guidance process is as follows: In S5-1, local reflection input contexts are constructed for the low-performance gap rule cluster and the high-performance gap rule cluster, respectively. The content includes: Role setting: Multi-objective flexible shop floor scheduling heuristic design expert; Task description: Analyze the parent heuristic rules of the low-performance gap or high-performance gap and extract effective design patterns; Problem description: Explain that the current reflection targets the low-performance or high-performance gap parent rules in all selected training instances and performs a comprehensive comparison across the entire selected parent group; Input context: Global context information of the low-performance or high-performance gap rule cluster, including the parent heuristic rule name, the complete code of the parent heuristic rule, and the corresponding average normalized target value and average performance gap index; Output requirements: Extract common advantages and disadvantages, summarize effective patterns, and identify key decision factors; Output specifications: Output length not exceeding 80 characters, strictly limited to 3 lines of plain text, returned in a fixed format, and without additional explanations. In S5-2, the Global Evolutionary Reflection Prompt consists of the following parts: Role Setting: used to clarify the identity and professional perspective of the large language model in global rule evolution analysis; Task Description: used to specify the core objectives that the current global reflection needs to achieve; Problem Description: used to explain the analytical background, overall comparison objects, and next-generation rule generation requirements of the current global reflection; Input Context: including parent population summary information, low-performance gap reflection results, and high-performance gap reflection results. The parent population summary information is used to reflect the overall performance of the currently selected parent rules on multiple instances. This parent population summary information includes the average normalized target value and average performance gap of the parents; the low-performance gap reflection results are used to provide common advantages and inheritable structural information of excellent rules; the high-performance gap reflection results are used to provide information on the main defects and repairable problems of weak rules; Output Requirements: used to limit the analytical focus that the global reflection results need to cover; Output Specification: used to constrain the length, structure, and expression form of the global reflection results, facilitating direct use in subsequent crossover and mutation generation.

[0015] Preferably, during the cross-input process in step S5-3, the large language model input includes: Role definition: Used to clarify the task of cross-generation of heuristic rules for offspring currently undertaken by the large language model; Task Description: This task specifies the heuristic rules for generating new multi-objective flexible shop floor scheduling offspring. Problem Description: This description illustrates that the current optimization problem is a flexible job shop bi-objective scheduling problem, including minimizing the maximum completion time and the total delay time, along with some constraint descriptions. Rule code input / output interface description: Function interface, input data structure, and output scheduling scheme format used to uniformly generate rules; Cross generation description: This is used to clarify that the current offspring is generated by the cross generation of heuristic rules from two low-performance gap parents, and specifies the form of the output heuristic rule; Parent: Enter the name and code of the parent rule to be used for crossover; Reflection Results: Provides reflection results on low-performance gaps and global evolutionary reflection results respectively: used to provide common advantages of good rules, effective laws and design points suitable for inheritance, as well as provide overall evolutionary guidance information across instance levels; Generation requirements: The crossover process should integrate effective scheduling ideas from both parent generations, retain structures that are conducive to optimizing both maximum completion time and total delay time, and avoid directly copying either parent generation; at the same time, the output rules should include necessary comments, brief descriptions, and child generation identification information to improve the interpretability of the rules.

[0016] Preferably, in step S5-4, the inputs for the large language model to perform reflective repair mutations include: Role definition: Used to clarify the current task of repairing and mutating high-performance gap rules that the large model is responsible for; Task Description: This task specifies the heuristic rules for generating new mutated offspring. Problem Description: This section describes the current optimization problem, the bi-objective requirements, and the background of mutation generation. Rule code input / output interface description: Used to unify the format of function interfaces, input data structures, and output scheduling schemes; Mutation generation instructions: This is used to ensure that the generation rules meet the requirements of complete scheduling feasibility, and to clarify that the current offspring completes the repair mutation generation by combining the high-performance gap parent generation with the elite parent generation; Parent generation: Describes the high-performance gap parent generation rules and the elite reference parent generation rules, which are used to provide the complete structure and scheduling logic of the rules to be repaired and the good design ideas that can be learned from. Reflection Results: Provides high-performance gap reflection results and global evolutionary reflection results to provide local repair directions and key failure information, as well as overall evolutionary guidance across instance levels; Generation requirements: to constrain the direction of improvement, innovation and structural form of mutation generation; at the same time, the output rules are required to include necessary comments, brief descriptions and offspring identification information to improve the interpretability of the rules; Based on this, the large model retains the basic feasible framework of the high-gap parent generation, draws on the robust structure of the elite parent generation, performs targeted repairs on its local scheduling logic, and generates a new complete scheduling heuristic function. At the same time, the mutated offspring generation also needs to pass syntax, runtime and constraint verification. If it fails, it enters the error feedback and repair process.

[0017] By adopting the aforementioned design scheme, the beneficial effects of this invention are as follows: It introduces a heuristic rule adaptive evolution mechanism based on performance gap hierarchical guidance, enabling automatic generation and low-overhead iterative optimization of scheduling rules. Through a large language model combined with scheduling objectives, process constraints, parent rules from the iteration process, performance evaluation data, and reflection conclusions, candidate rules are automatically generated, rewritten, fused, and repaired, reducing reliance on manual rule design. Simultaneously, it avoids the problems of complex modeling, long-term training, and reliance on large amounts of sample data in traditional deep learning and reinforcement learning methods. While preserving rule interpretability and manual modifiability, it improves rule generation efficiency, rule expression flexibility, and rapid adaptation capabilities under different flexible workshop scenarios. By combining a dynamic grid truncation screening strategy, the balanced distribution optimization of the rule population is achieved. By using the dynamic grid truncation mechanism to divide and sort the positions of candidate rules in the target space, the diversity of the rule population is maintained while retaining excellent rules. This effectively alleviates the problem of high-performance rules being concentrated in local areas, thereby improving the coverage, distribution balance and overall optimization quality of the Pareto solution set. Establish a performance gap quantitative evaluation mechanism to analyze rule quality and optimization potential. By establishing a performance gap index of the Euclidean distance between the normalized target vector of heuristic rules and reference rules, the merits and demerits of rules and potential optimization directions can be quantitatively characterized, providing a basis for rule selection, ranking and subsequent rule optimization, and improving the pertinence, interpretability and traceability of the rule optimization process. By combining local and global reflection mechanisms, adaptive control of the rule evolution direction can be achieved. By analyzing the performance status of candidate rules, population distribution characteristics, and current evolution results, corresponding rule optimization directions and evolutionary suggestions are generated to guide subsequent rule crossover, mutation, and repair processes, thereby improving the directional optimization capability and iterative effectiveness in the rule evolution process. The reflective and restorative mutation of this high-performance gap rule cluster achieves targeted optimization based on the rule performance state. Different crossover, mutation and repair strategies are adopted for rules with different performance states. For excellent rules, the focus is on the inheritance and recombination of advantages, and for low-performance rules, the focus is on defect repair and targeted optimization. This reduces the blindness brought about by unified random evolution and improves the rule evolution efficiency and optimization stability. In summary, this application combines the rule generation capabilities of a large language model with a multi-objective adaptive optimization mechanism to form a complete collaborative optimization process of rule generation, rule selection, rule evaluation, rule guidance, and rule evolution. While maintaining the interpretability of rules, it improves the solution quality, optimization stability, and industrial scenario adaptability of multi-objective flexible job shop scheduling. Attached Figure Description

[0018] Figure 1 This is a flowchart of the adaptive optimization scheduling method of the present invention; Figure 2 This is a schematic diagram illustrating the initial rule population generation prompt of the present invention; Figure 3 This is a schematic diagram of the dynamic mesh truncation of the present invention; Figure 4 This is a schematic diagram of the low-performance gap reflection prompt of the present invention; Figure 5 A schematic diagram of the high-performance gap reflection prompt of the present invention. Figure 6 This is a schematic diagram of the global evolutionary reflection Prompt of the present invention; Figure 7 This is a schematic diagram of the cross-prompt of the present invention; Figure 8 This is a schematic diagram of a variant Prompt of the present invention; Figure 9 This is a flowchart illustrating the evolutionary process of the large language model of the present invention. Figure 10 This is a scatter plot comparing the scheduling method of the present invention with the manual rules in the Mk01 instance; Figure 11 This is a heuristic rule code representation of the present invention; Figure 12 This is a schematic diagram illustrating the representative solution of the present invention and GP; Figure 13 This is a schematic diagram comparing HV and IGD in this invention. Detailed Implementation

[0019] 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. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0020] The terms "first," "second," "third," etc., used in the specification, claims, and accompanying drawings of this invention are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0021] This invention is applied to flexible manufacturing workshop environments and is suitable for flexible workshop scheduling scenarios with multiple devices, multiple processes, and multiple objectives requiring collaborative optimization, such as textile and apparel manufacturing, machining, electronic assembly, and discrete manufacturing. The following explanation uses a flexible textile manufacturing workshop as an example, but the invention is not limited to this specific application scenario.

[0022] This invention addresses the multi-objective flexible job shop scheduling problem. In a flexible job shop environment, each workpiece typically consists of several processes with sequential constraints. Each process can be processed by multiple different machines, each with a different processing time. Therefore, the scheduling process requires simultaneously determining the process execution order and the machine allocation scheme. This invention uses maximum completion time and total delay time as optimization objectives, and generates an executable scheduling scheme while satisfying process sequence constraints, machine resource constraints, and machine selectability constraints.

[0023] To facilitate the establishment of a unified scheduling model, this invention makes the following assumptions: (1) All workpieces had arrived at the workshop when the scheduling began.

[0024] (2) Each workpiece is processed sequentially according to the predetermined process sequence.

[0025] (3) Only one corresponding machine is selected to complete the processing for each process.

[0026] (4) At any given time, a machine can process at most one process.

[0027] (5) No interruption is allowed during the process.

[0028] (6) The processing time of each process, the machine selection relationship, and the workpiece delivery time are all known.

[0029] (7) The impact of equipment failure, emergency order insertion and extra transportation time is not considered.

[0030] An adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model, such as Figure 1 As shown, the steps are executed sequentially as follows: S1: Using maximum completion time and total delay time as optimization objectives, define the maximum completion time and total delay time, and construct a dual-objective optimization model based on these defined maximum completion time and total delay time. Then, apply machine selectability constraints, process timing constraints, and machine exclusive constraints to the dual-objective optimization model. The specific steps include the following: S1-1: Let the set of workpieces be... n represents the number of workpiece types, and the number of workpieces... The included processes are defined as follows: The machine set is , m is the total number of machines, for workpieces The jth process The set of available machines is denoted as And satisfy The optimization objectives are maximum completion time and total delay time. Maximum completion time refers to the time required to complete the last process in all orders. The shorter the time, the faster the order delivery time, indicating a better scheduling plan. Maximum completion time is defined as: ; in, Indicates workpiece Completion time, Indicates the workpiece number. Indicates the total number of workpieces to be scheduled; This target is used to measure the overall production cycle; the smaller the target value, the higher the scheduling efficiency.

[0031] Total delay time refers to the sum of the actual completion time of all workpieces exceeding their corresponding delivery dates. Only the portion of the order being delayed is counted; workpieces completed ahead of schedule are not included in the delay time. The total delay time is defined as follows: ; in, Indicates workpiece Delivery time; This target measures the cumulative delay of all workpieces beyond their delivery date; a smaller target value indicates better delivery performance.

[0032] S1-2: Bi-objective optimization model It is expressed by the following formula: ; The optimization objective of this invention is to minimize both the maximum completion time and the total delay time while satisfying relevant scheduling constraints, i.e., to solve... .

[0033] S1-3: To ensure the executability of the generated scheduling scheme, the following constraints are applied to the bi-objective optimization model: Machine selectability constraint: Ensures that each operation is performed on exactly one machine. This machine selectability constraint ensures that each operation... Just in its set of optional machines Processing is performed on one of the machines, and the machine selection constraints are expressed by the following formula: ; in, Indicates the type of workpiece The This process is done on the machine. The 0-1 decision variable for the allocation of processing time.

[0034] Process sequence constraint: Processes on the same workpiece must be processed sequentially according to the technological order, ensuring the continuity of processes and the non-overlapping of machines. This process sequence constraint ensures the continuity of processes. In the process Once completed, the sequential relationship is ensured. The timing constraint for this process is expressed by the following formula: ; in, Indicates the type of workpiece The This process is done on the machine. The start time of the project Indicates the type of workpiece The This process is done on the machine. The start time of the project Indicates the type of workpiece The This process is done on the machine. Processing time on Assign 0-1 decision variables to the machines corresponding to the preceding processes.

[0035] Machine exclusivity constraint: A machine can only process one operation at a time. This constraint ensures that on the same machine, any two operations can be performed simultaneously. and They will not execute simultaneously; the machine exclusive constraint is expressed by the following formula: ; in, Indicates the type of workpiece The This process is done on the machine. Processing time on Indicates the type of workpiece The This process is done on the machine. The start time of the project Indicates the type of workpiece The This process is done on the machine. Processing time; The above constraints together ensure that the generated scheduling scheme meets the basic processing requirements and resource constraints of the flexible workshop.

[0036] This application does not directly search and optimize scheduling schemes, but uses heuristic rules that can generate scheduling schemes as optimization objects. By generating, filtering, evaluating and evolving heuristic rules, the scheduling strategy is continuously optimized.

[0037] Specifically, each heuristic rule, given a workshop instance, can dynamically select processes and allocate machines based on the current workshop state, and gradually construct a complete scheduling scheme; then, the rule performance is evaluated based on the objective function value corresponding to the scheduling scheme. Subsequent processes such as large language model rule generation, dynamic grid filtering, performance gap analysis, differentiated rule evolution, and two-layer reflection guidance all revolve around heuristic rules.

[0038] S2: Preset workshop state, based on which the process is adjusted. Distributed to machine The priorities are evaluated to obtain the priority evaluation results. Based on the priority evaluation results, the optimal scheduling decision is selected, and the workshop state is updated with the optimal scheduling decision. The target value vector corresponding to the heuristic rule is generated. The initial candidate heuristic rule population for the bi-objective optimization model is generated using a large language model. The specific steps are as follows: S2-1: Let the current heuristic rule population be... N represents the current size of the rule-based population. Indicates the first This invention employs heuristic rules, which are essentially scheduling decision functions. Their function is to evaluate schedulable processes and their corresponding machines based on the current workshop state during the scheduling process, and output corresponding priority results to guide process selection and machine allocation. Unlike traditional fixed dispatch rules such as SPT (Shortest Processing Time) and EDD (Earliest Due Date), the heuristic rules in this invention do not rely on manually pre-designed fixed decision logic. Instead, they are automatically generated by a large language model and continuously optimized during the evolution process. The rules can simultaneously integrate multiple scheduling characteristics such as processing time, machine load, remaining workload, workpiece delivery date, number of remaining processes, and delay risk. Through different combinations of features and decision logic, new scheduling strategies are formed, thereby improving the rule's expressive power and scenario adaptability.

[0039] S2-2: At scheduling time t, the workshop state is denoted as... ; in, This indicates the current status of an incomplete set of workpieces. Indicates the current machine operating status. This represents the set of currently schedulable operations.

[0040] The workshop status can be further included in scheduling features such as process processing time, machine load, remaining workload, number of remaining processes, workpiece delivery time, equipment utilization rate, and process completion progress.

[0041] S2-3: Regarding the current workshop status Set up the process The optional set of machines is heuristic rules Evaluate candidate processes and machine combinations; processes Distributed to machine The priority evaluation value at that time is expressed by the following formula: ; The optimal scheduling decision is selected based on the priority evaluation results of all candidate processes and machine combinations: ; in, This represents the set of selected processes. This represents the set of machines to be assigned.

[0042] S2-4: Adjust the workshop state based on this optimal scheduling decision. Update to obtain the new workshop status. Repeat steps S2-2 and S2-3 until all workpieces are processed, generating heuristic rules. The corresponding complete scheduling scheme is evaluated to obtain the heuristic rule. The corresponding target value vector: ; in, For corresponding heuristic rules Maximum completion time For corresponding heuristic rules Total delay time.

[0043] Subsequent rule selection, dynamic grid sorting, performance gap analysis, and rule evolution processes are all based on the aforementioned target values.

[0044] S2-5: Let the initial population size of the candidate heuristic rules be... The parent-inspired population retention size is ,in, The population diversity of the initial heuristic rules is increased by expanding the candidate sample size, and then a fixed number of high-quality parent rules are retained through a multi-objective selection mechanism. The initial population is represented as: ; like Figure 2 As shown, a large language model is used to generate initial heuristic rules. The prompt template for generating heuristic rules consists of the following parts: (1) Role instructions: used to guide the model to generate diverse rules from different algorithm design styles.

[0045] (2) Task: The large model needs to complete the design heuristic rule code.

[0046] (3) Problem description: The dual objective optimization task of the flexible workshop is to minimize the maximum completion time and the total delay time, and the complete constraint description includes machine exclusive constraint, process sequence constraint and machine selectability constraint.

[0047] (4) Input / output interface description: The rule code with the function name heuristic(problem) is required to be generated. The rule input is defined as instance data of shop floor scheduling, and the output is a specific scheduling scheme. Among them, the input problem includes at least the number of workpieces, the number of machines, and the optional machines and processing time corresponding to each workpiece process; the output is a complete scheduling dictionary organized by workpiece, and each process records the process number, allocated machine, start time, end time and processing time.

[0048] (5) Restriction: Specify the generation form of the heuristic rules.

[0049] (6) Seed heuristic rules: used to provide examples of basic code format and output structure.

[0050] (7) Output description: The output should return the standard Python code block and the corresponding functional documentation.

[0051] Perform the following validations on each heuristic rule generated by the large language model in sequence: (1) Syntax check: Check whether the code can be parsed and loaded successfully.

[0052] (2) Interface verification: Check whether the heuristic(problem) function is defined.

[0053] (3) Run the verification: put the rules into the scheduling environment for small-scale instance testing.

[0054] (4) Output structure verification: check whether a complete scheduling dictionary is returned.

[0055] (5) Constraint verification: Check whether the scheduling result satisfies the constraints of machine exclusivity, process sequence and machine selectability.

[0056] If any step fails, the error message, the previous prompt, and the failure code are fed back to the large language model, which is required to generate a repair version based on the cause of the error, until the candidate heuristic rule passes the verification or reaches the preset maximum number of verifications.

[0057] S3: Perform population evaluation on the heuristic rules in the initial candidate heuristic rule population. This involves batch evaluating all heuristic rules on multiple standard flexible workshop instances, calculating the maximum completion time and total delay time for each rule on each instance, and normalizing the target values ​​within each instance to obtain a normalized dual-objective vector. Next, calculate the cross-instance average normalized target value for each heuristic rule, forming a rule-level dual-objective aggregation vector. Finally, a non-dominated sorting priority and adaptive grid truncation-assisted selection mechanism is used to select the best rule from the... Reservation of legal candidates The rule is used as the initial parent population. To preserve heuristic rules with superior overall performance while ensuring diversity, this application employs a population selection mechanism based on multi-instance normalized performance evaluation, rule-level aggregation, and dynamic grid truncation. This mechanism uses heuristic rules as the basic object, normalizes the target values ​​of each rule across different instances, constructs a rule-level aggregated target vector, and finally combines non-dominated sorting and dynamic grid partitioning to complete parent generation selection. The specific steps of the heuristic rule population evaluation are as follows: S3-1: Let the set of training instances be... For heuristic rules In the The first test instance The target value is denoted as ,in, hour, Representing heuristic rules In the Total delay time per instance.

[0058] Because different instances and different objectives have different units and numerical ranges, normalization needs to be performed within each instance first. Let the first instance be... In the 1st instance, the 1st The minimum and maximum values ​​of the targets are respectively: ; ; Heuristic rules In the The first instance Normalized target value Defined as: ; in, To prevent extremely small constants with a denominator of zero, the range of values ​​is 10. -12 ≤ ≤10 12 .

[0059] After the above processing, the heuristic rules In the example The normalized biobjective vector on can be expressed as: S3-2: Rule Set Performance Analysis: Since each rule needs to be comprehensively evaluated on multiple test instances, the performance of heuristic rules... The normalized objective values ​​across all instances are averaged to obtain a rule-based bi-objective aggregation vector: ; in, , , This is the number of test instances. Representing heuristic rules The average normalized maximum completion time across all test instances. Representing heuristic rules Average normalized total latency across all test instances Used to characterize heuristic rules The comprehensive dual-objective performance is used as the basis for subsequent non-dominated sorting and parent selection.

[0060] S3-3: Non-dominated solution sorting of rule sets: Bi-objective aggregation vector based on all heuristic rules Perform a non-dominated sort on the rule set to obtain the frontier ranking of each heuristic rule. If the heuristic rules... It is no worse than heuristics in both objectives. And at least one objective is strictly superior to heuristic rules. Then it is considered a heuristic rule Dominant Heuristic Rules A higher frontier level indicates better overall dual-objective performance of the heuristic rules. During the selection process, heuristic rules with higher frontier levels are prioritized; a dynamic grid truncation mechanism is only employed when the number of heuristic rules at a certain boundary layer exceeds the remaining number to be retained.

[0061] S3-4: Dynamic Grid Truncation Based on Frontier Level Division: The dynamic grid truncation in this application is not applied uniformly to all heuristic rules. Instead, it is applied only during the non-dominated sorting process. When the number of rules in a certain frontier level exceeds the remaining retention quota, that frontier level is designated as the frontier boundary layer, and grid truncation is performed on the rules of that boundary layer. If the number of rules in a certain frontier level can be fully incorporated into the current parent population, all rules in that frontier level are retained without further grid truncation.

[0062] For boundary layer rules that need to be truncated, first aggregate the bi-objective aggregation vector according to its rule level. The position in the two-dimensional target space is normalized and mapped, and then divided accordingly. There are K grid cells, where K is the grid division dimension. Each rule falls into the corresponding grid cell based on its aggregated normalized target value.

[0063] During the grid truncation process, each non-empty grid cell retains at most one representative heuristic rule, i.e., the parent heuristic rule that is retained. If multiple heuristic rules exist within the same grid cell, the rule with the better aggregate objective value is retained first, thus ensuring that only the more representative rule is retained within the same local region.

[0064] In this application, the grid partitioning dimension K is not fixed but adaptively adjusted within a preset range. Specifically, it starts with a smaller grid partitioning dimension. If, at the current K value, the number of representative rules generated by each non-empty grid cell is less than the remaining retention quota, it indicates that the current grid partitioning is too coarse, with multiple heuristic rules concentrated in the same grid cell, making it difficult to provide a sufficient number of spatial representative rules. At this point, the K value is increased to perform a finer-grained partitioning of the target space, distributing the heuristic rules originally concentrated in the same grid cell as much as possible to different grid cells, thereby increasing the number of selectable representative rules. This process continues until at least the number of grid representative rules is obtained that is not less than the remaining retention quota, or the preset maximum grid partitioning dimension is reached. When the number of grid representative rules obtained at a certain K value is not less than the remaining retention quota, there is no need to continue adjusting the K value. Even if the number of representative rules is greater than the remaining retention quota, it is not required that they be exactly equal to the remaining retention quota. Instead, the representative rule set is further sorted according to the principle of smaller average performance gap and better aggregation target value, and the number of rules corresponding to the remaining retention quota is selected as the final retention result.

[0065] If the number of rules represented by the grid is still insufficient under the preset maximum grid division dimension, then the remaining required number of rules are selected from the boundary layer rules to complete the truncation based on the principle of better aggregation target value.

[0066] Through the aforementioned dynamic grid truncation mechanism, this application can, under the constraint of a fixed parent population size, distribute the retained parent heuristic rules as widely as possible across different target space regions. This improves the distribution balance and diversity of the parent population in the dual-target space while ensuring the overall performance of the parent heuristic rules. A specific dynamic grid truncation diagram is shown below. Figure 3 As shown.

[0067] The candidate heuristic rule population is used to obtain the corresponding parent heuristic rule population based on the above heuristic rule population evaluation process, which is then used for the subsequent division of performance gaps and rule clusters.

[0068] S4: Performance Gap Assessment and Rule Cluster Division. To differentiate the optimization differences of parent heuristic rules and control the subsequent evolutionary behavior of different parent heuristic rules based on these differences, this application introduces a performance gap mechanism. The performance gap is defined at the single-instance level and is used to quantify heuristic rules. Distance relative to the reference rule.

[0069] The performance gap of the parent heuristic rule population is evaluated and rule clusters are divided: Based on the normalized bi-objective vector, the set of non-dominated rules from all heuristic rules in the parent heuristic rule population is extracted, and the heuristic rule with the smallest weighted normalized objective value is selected from the set of non-dominated rules as the first heuristic rule. The reference rules for the nth instance are used to obtain the nth... The reference normalized target vector corresponding to the nth instance is defined as the Euclidean distance between the normalized target vector and the reference normalized target vector. The performance gap of heuristic rules in each instance is analyzed. Based on this performance gap, the average performance gap of the heuristic rules is calculated. Then, the heuristic rules are divided according to a preset performance gap threshold to obtain a low-performance gap rule cluster and a high-performance gap rule cluster. The specific steps are as follows: S4-1: For the first One example, based on normalized dual-objective vectors and Extract the set of non-dominated rules from all heuristic rules. From this set of non-dominated rules, select the heuristic rule with the smallest weighted normalization objective value as the first heuristic rule. Reference rules for each instance: ; in, This is the dual-objective balance coefficient, with a value range of [value range missing]. By adjusting the dual-objective balance coefficient The value of controls the relative importance of the two optimization objectives during the selection of the reference rule. When, it means that the maximum completion time and the total delay time have the same weight; when When the maximum completion time target takes precedence, the selection process for reference rules tends to prioritize reducing the overall production cycle; when When the total delay time target accounts for a larger proportion, the reference rule selection process tends to reduce the risk of workpiece delay.

[0070] No. The reference normalized target vector corresponding to each instance is: ; in, Refers to the first Reference rules for each instance Refer to the rules In the The first normalized target value on each instance, Refer to the rules In the The second normalized target value on each instance.

[0071] S4-2: For the first Arbitrary heuristic rule in an instance Its performance gap Defined as the Euclidean distance between the normalized target vector and the reference normalized target vector. ; in Heuristic rules In the example Normalized biobjective vector on, Refer to the rules In the example Normalized biobjective vector on; The smaller the performance gap, the stronger the heuristic rule. In the example The closer the heuristic is to the reference good region, the larger the performance gap, indicating a stronger heuristic rule. In the example The further away from the optimal region, the greater the potential for optimization and repair. Low-performance gap rules prioritize retaining their existing structure and participating in crossover recombination, while high-performance gap rules prioritize entering the repair mutation process.

[0072] S4-3: Rule-level average performance gap: for characterizing heuristic rules The overall optimization potential across all test instances can be further defined as follows: ; in, Representing heuristic rules The average performance gap across all instances is used to guide the selection of differentiated evolutionary paths for heuristic rules and to control subsequent crossover recombination, repair mutation, and boundary layer preservation processes.

[0073] S4-4: High and Low Performance Gap Rule Division: To avoid imbalance in the division across different instances due to the use of a fixed threshold, this invention adaptively calculates the threshold based on the performance gap distribution within each instance. For the first... Let there be an instance where the average performance gap of all heuristic rules is [value]. The standard deviation is The performance gap threshold for this instance is defined as follows: ; in, This is the threshold adjustment coefficient, used to control the tightness of the division between high and low notches. This avoids over-classifying rules with normal fluctuations into the high-gap set; compared to using larger coefficients, this setting retains enough defect rules for subsequent corrective mutations. Therefore, A compromise was reached between exploring the flaws in the rules and maintaining population stability. Accordingly, the first... In this instance, heuristic rules can be used... Classified as: like heuristic rules In the example The above belongs to the high-performance gap rule; like heuristic rules In the example The above belongs to the low-performance gap rule.

[0074] Furthermore, statistical heuristics The number of times each instance is classified into the high-performance gap region and the low-performance gap region is determined. Rules belonging to the high-performance gap in more instances are grouped into high-performance gap rule clusters, and rules belonging to the low-performance gap in more instances are grouped into low-performance gap rule clusters. After the performance gap of the parent heuristic rules is evaluated and the rule clusters are divided, the evolution mode of different parent heuristic rules is subsequently controlled based on the performance gap of the parent heuristic rules. Among them, parent heuristic rules with high-performance gaps preferentially trigger the repair mutation process, while parent heuristic rules with low-performance gaps preferentially trigger the crossover recombination process.

[0075] S5: After assessing the population performance gap and dividing the rule clusters according to the above method, the parent heuristic rule population is subjected to hierarchical reflection guidance and dual-path evolution mechanism: local reflection inputs are constructed for the low-performance gap rule cluster and the high-performance gap rule cluster respectively, and the large language model is called to generate the low-performance gap reflection results and the high-performance gap reflection results. Furthermore, the global evolution reflection results are generated, and the low-performance gap rule cluster is subjected to reflective crossover and recombination, and the high-performance gap rule cluster is subjected to reflective repair mutation to obtain the offspring heuristic rules; After each generation of parent population is formed and the rules are clustered based on performance gaps, this application uses a large language model to generate low-gap reflections, high-gap reflections, and global reflections to guide the generation of rules for the next generation of offspring. The specific steps are as follows: S5-1: Local Rule Reflection Generation: For each rule in the parent population, its position in high-gap or low-gap regions across instances is statistically analyzed. This data, combined with cross-instance average normalized target value and average performance gap, forms rule-level aggregated features. Based on this information, low-performance gap rule clusters and high-performance gap rule clusters are constructed. Then, local reflection inputs are built for each cluster, and the large language model is invoked to generate corresponding reflection results, including low-performance gap reflection results and high-performance gap reflection results. Large model input contexts are constructed for each cluster. The input content includes: (1) Role setting: Heuristic design expert for multi-objective flexible workshop scheduling.

[0076] (2) Task description: Analyze low performance gaps or parent heuristic rules and extract effective design patterns.

[0077] (3) Problem description: Explain the current reflection on the low or high performance gap parent rules in all selected training instances, and make a comprehensive comparison for the entire selected parent group.

[0078] (4) Input context: Global context information of low or high performance gap rule clusters, including the parent heuristic rule name, the complete code of the parent heuristic rule and the corresponding average normalized target value, average performance gap and other indicators.

[0079] (5) Output requirements: Extract common advantages and disadvantages, summarize effective rules and point out key decision factors.

[0080] (6) Output Specifications: The output length shall not exceed 80 characters, strictly limited to 3 lines of plain text, returned in a fixed format, and without any additional instructions. See the specific Prompt for details. Figure 4 and Figure 5 As shown.

[0081] S5-2: Global Evolutionary Reflection Generation: After obtaining the reflection results of low-performance gaps and high-performance gaps, the overall summary information of the current generation's parent population, the low-gap reflections, and the high-gap reflections are further input into the large language model to generate global evolutionary reflections.

[0082] The Global Evolutionary Reflection Prompt mainly consists of the following parts: (1) Role setting: used to clarify the identity and professional perspective of the large language model in the global rule evolution analysis.

[0083] (2) Task description: This is used to define the core objectives that need to be achieved in the current overall reflection.

[0084] (3) Problem description: used to explain the analytical background of the current global reflection, the overall comparison objects, and the requirements for generating the next generation of rules.

[0085] (4) Input context: including ① Parent population summary information: used to reflect the overall performance of the currently selected parent rule on multiple instances; ② Low performance gap reflection results: used to provide information on the common advantages and inheritable structure of good rules; ③ High performance gap reflection results: used to provide information on the main defects and repairable problems of weak rules.

[0086] (5) Output requirements: Used to limit the analytical focus that the global reflection results need to cover.

[0087] (6) Output Specification: Used to constrain the length, structure, and expression of the global reflection results, facilitating direct calls for subsequent crossover and mutation generation. Specific Prompt examples are as follows: Figure 6 As shown.

[0088] S5-3: As Figure 7 As shown, the reflexive cross-recombination of low-performance gap rule clusters involves selecting two low-gap parent rules as cross-inputs for each cluster. The large language model inputs include: (1) Role setting: used to clarify the task of cross-generation of heuristic rules for offspring currently undertaken by the large language model; (2) Task Description: Used to specify the heuristic rules for generating new multi-objective flexible shop scheduling offspring; (3) Problem description: This section describes the current optimization problem as a flexible job shop bi-objective scheduling problem, including minimizing the maximum completion time and the total delay time, as well as some constraint descriptions.

[0089] (4) Description of rule code input and output interface: Function interface, input data structure and output scheduling scheme format used to uniformly generate rules; (5) Cross-generation description: This is used to clarify that the current offspring is generated by the cross-generation of two low-performance gap parent heuristic rules. It specifies the form of the output heuristic rule.

[0090] (6) Parent: Enter the name and code of the parent rule used for crossover.

[0091] (7) Reflection results: Provide reflection results on low performance gaps and global evolutionary reflection results respectively: to provide common advantages of good rules, effective laws and design points suitable for inheritance, and to provide overall evolutionary guidance information across instance levels; (8) Generation requirements: The generation process should integrate the effective scheduling ideas of the two parent generations, retain the structure that is conducive to the optimization of maximum completion time and total delay time, and avoid directly copying either parent generation; at the same time, the output rules should include necessary comments, brief descriptions and child generation identification information to improve the interpretability of the rules. After the offspring are generated, they undergo syntax validation, interface validation, runtime validation, and constraint validation in sequence. If they fail, the error reason is sent back to the large language model for repair until a valid offspring is obtained or the retry limit is reached.

[0092] S5-4: As Figure 8 As shown, the reflective and restorative mutation of high-performance gap rule clusters: For high-performance gap rule clusters, this invention adopts a restorative mutation method using a high-gap parent and an elite reference parent. Specifically, a high-gap parent is used as the object to be repaired, and a low-gap or high-performance elite parent is used as the structural reference object. The large language model input includes: (1) Role setting: used to clarify the current task of repairing and mutating high-performance gap rules that the large model is responsible for.

[0093] (2) Task description: Used to specify the heuristic rules for generating new mutant offspring.

[0094] (3) Problem description: used to explain the current optimization problem, the dual objective requirements and the background of mutation generation.

[0095] (4) Rule code input / output interface description: used to unify the function interface, input data structure and output scheduling scheme format; (5) Mutation generation description: This is used to ensure that the generation rules meet the requirements of complete scheduling feasibility and to clarify that the current offspring completes the repair mutation generation by combining the high-performance gap parent generation with the elite parent generation.

[0096] (6) Parent generation: Describe the high-performance gap parent generation rules and elite reference parent generation rules, which are used to provide the complete structure and scheduling logic of the rules to be repaired and the good design ideas that can be learned from; (7) Reflection results: Provide high-performance gap reflection results and global evolution reflection results to provide local repair directions and major failure information as well as overall evolution guidance across instance levels; (8) Generation requirements: Used to constrain the direction of improvement, innovation and structural form of mutation generation; at the same time, the output rules are required to include necessary comments, brief descriptions and offspring identification information to improve the interpretability of the rules; Based on this, the large model retains the basic feasible framework of the high-gap parent generation, draws on the robust structure of the elite parent generation, and performs targeted repairs on its local scheduling logic to generate a new complete scheduling heuristic function. At the same time, the mutated offspring generation also needs to pass syntax, runtime, and constraint verification; if it fails, it enters the error feedback and repair process.

[0097] S6: As Figure 9 As shown, offspring evaluation and population update: The offspring heuristic rule population generated in each generation is merged with the current parent heuristic rule population to form a new candidate heuristic rule population. The new candidate heuristic rule population repeats steps S3 to S5. After each complete iteration (i.e., completing the screening of the current parent rule population, performance gap division, hierarchical reflection guidance, and dual-path evolution to generate the offspring rule population), the number of iterations is accumulated. When the number of iterations reaches the preset maximum value, the loop terminates, and the current parent heuristic rule population is output as the final rule set. Each rule in the rule set is applied to the current scheduling instance, and a complete scheduling scheme and corresponding dual-objective performance values ​​are generated according to the method of step S2, namely, the maximum completion time and the total delay time, forming a scheduling scheme set. According to the actual production task's preference for the two objectives, i.e., focusing on completion time, focusing on delay time, or a balance between the two, the optimal scheduling scheme is selected from the scheduling scheme set. In this embodiment, the preset maximum number of iterations is 10.

[0098] To better illustrate the technical effectiveness of the scheduling method in this application, the following technical effectiveness verification and test configurations are performed.

[0099] This application uses the Brandimarte and Dauzere flexible job shop standard datasets for experimental verification. In the experiments, the heuristic rules generated by the large language model are uniformly placed in the same scheduling solution environment for evaluation, and the maximum completion time and total delay time are calculated on multiple Brandimarte instances to verify the effectiveness and stability of the proposed method in multi-objective scheduling scenarios.

[0100] Traditional manual rule comparison experiment To verify the effectiveness of the heuristic rules generated in this application, the Mk01 instance was selected, and a dual-objective comparison was performed between the best-performing rule in the final rule set of this application and six typical manually generated rules (Table 1). The comparison metrics included maximum completion time and total delay time, and were presented as a scatter plot (e.g., ...). Figure 10 The distribution of each method in the dual-objective space is shown in the form shown, so as to intuitively reflect the optimization bias and comprehensive performance of different rules.

[0101] Table 1. Explanation of Traditional Manual Scheduling Rules:

[0102] Comparative experiments with traditional manual rules show that traditional manual rules are usually constructed around a single scheduling principle, such as prioritizing short processing time, delivery date, or remaining workload. Therefore, in multi-objective flexible job shop scheduling scenarios, optimization biases are prone to occur, making it difficult to simultaneously consider both maximum completion time and total delay time. This application, through large language model generation, performance gap partitioning, local reflection, and global evolutionary reflection to guide cross-mutation, can automatically discover and integrate more effective scheduling structures. Experimental results show that the optimal rule obtained in this application (proposed) outperforms the baseline of manual rules in terms of bi-objective performance on the Mk01 instance, verifying the effectiveness of this method in rule quality and bi-objective balanced optimization.

[0103] To verify the effectiveness of this invention in automatic rule generation and multi-objective optimization, Generalized Principles (GP) were further selected as a comparison method. The GP method also optimizes scheduling rules and can automatically evolve rule expressions, thus it is highly comparable to this invention in terms of rule generation. The GP algorithm iteratively generates scheduling rules based on the terminal set and function set in Table 2.

[0104] Table 2 GP Terminal Sets and Function Sets:

[0105] The GP method can automatically obtain better scheduling rules through evolution of rule expressions, such as the formula: Sorting rules: determine which process is processed first. ; Routing rules: determine which machine to use for each process. ; Clearly, the GP method primarily relies on a fixed set of terminals and an arithmetic expression tree structure for searching. Its rule generation and rewriting processes are largely constrained by random combinations at the syntactic level, lacking explicit analysis and targeted guidance regarding the merits and demerits of rules. In contrast, this application only requires constructing a Prompt and reflecting on performance gaps to achieve targeted reflection, while simultaneously outputting the complete code representation of the heuristic rules along with relevant explanations, such as... Figure 11 As shown, the scheduling logic is clear and easy for humans to understand, modify and reuse.

[0106] Furthermore, this application demonstrates strong competitiveness in terms of optimal solutions and balanced solutions for maximum completion time and total delay time, and achieves superior results in several instances. The representative solution distribution for instance Mk01 is as follows: Figure 12As shown, this application achieves better total delay time and balanced solutions while maintaining the maximum completion time optimization capability. This indicates that the application can generate high-quality rules with different optimization biases and improve the coverage and distribution diversity of the non-dominated solution set in the target space. Therefore, this application not only improves scheduling optimization performance but also has good engineering application value and practical deployment potential.

[0107] To comprehensively verify the effectiveness and practicality of this application in the multi-objective flexible job shop scheduling problem, this embodiment selects four representative reinforcement learning scheduling methods for comparative analysis. These methods include scheduling models based on graph neural networks or dual attention networks. Each comparative method uses its own predetermined training settings and testing environment, and the evaluation metric is the maximum completion time.

[0108] The experimental results are shown in Table 3. On 10 standard instances from Mk01 to Mk10, the proposed method achieved maximum completion times comparable to or even better than existing advanced reinforcement learning (RL) methods on most instances. For example, on instance Mk06, the proposed method achieved a completion time of 68, which is better than the best result among all contrastive RL methods (72); on instance Mk10, the proposed method achieved a maximum completion time of 219, which is better than the best result among the four contrastive reinforcement learning methods (221). These results verify the superior performance and stable competitiveness of the proposed method in multi-objective flexible shop floor scheduling tasks.

[0109] Although the completion time of this application is slightly longer than that of some RL methods in certain instances (such as Mk04 and Mk09), the overall performance remains in the superior range, and the difference is within an acceptable range. More importantly, compared with RL methods, this application has more prominent features in the following aspects: (1) The modeling cost is low. There is no need to define Markov decision process, design state space, action space or reward function, nor is it necessary to build graph neural network or train complex policy network such as PPO.

[0110] (2) High training efficiency, no need for a large number of interactive sampling and long-term iterative training, significantly reducing the consumption of computing resources; (3) High interpretability: The generated scheduling rules are presented in the form of explicit code, which makes it easy for engineers to understand, modify and reuse.

[0111] (4) High adaptability: When the problem constraints, optimization goals or production environment change, there is no need to retrain. Only the Prompt or rule structure needs to be adjusted to adapt quickly.

[0112] In summary, this application significantly reduces model building and training costs while maintaining scheduling performance similar to advanced RL methods, and improves the interpretability and engineering feasibility of scheduling rules. Therefore, it has stronger practical value and deployment potential in actual flexible workshop scheduling scenarios.

[0113] Table 3. Comparison of maximum completion time between the present invention and reinforcement learning methods:

[0114] The ablation experiment of this application: To verify the effectiveness of the performance gap-guided reflection mechanism and its differentiated evolution strategy in this application, three comparative methods were designed: the full method (including performance gap hierarchies and local reflections), the global_only method (retaining only global reflections and not employing a performance gap hierarchies mechanism), and the none method (not employing any reflections and not employing a performance gap hierarchies mechanism). The full method includes local reflections of low-performance gap rule clusters, local reflections of high-performance gap rule clusters, global reflections, and differentiated crossover and mutation based on performance gap hierarchies. The global_only method retains only cross-instance global reflections, no longer constructing low-gap and high-gap local reflections, and no longer dividing parent rule clusters based on performance gaps. The none method further removes global reflections, directly generating rules only in a unified parent pool. All three methods use the same initial rule population, the same Dauzere training instance set, the same number of generations, the same crossover and mutation scale, and the same selection mechanism to ensure fairness in the comparison. The evaluation metrics used are the hypervolume (HV) metric and the inverted generational distance (IGD). HV measures the coverage of the reference frontier by the current rule population in the target space. A higher value indicates better overall coverage of the obtained non-dominated rule set on both the maximum completion time and total delay time objectives. IGD measures the average distance between the current rule population and the reference frontier. A lower value indicates that the rule population is closer to the reference frontier, and the quality of the frontier approximation is higher. To ensure comparability between different methods and generations, this embodiment uses a joint reference frontier and a fixed normalization method to uniformly calculate the two indicators.

[0115] Because all three methods use the same initial rule population, their indices are completely identical in generation 0. For example... Figure 13As shown, the evolutionary trajectories of the three methods gradually diverged starting from the first generation. The full method exhibited the most stable and significant continuous improvement trend, with its HV steadily increasing from 0.3268 in the first generation to 0.4856 in the tenth generation; simultaneously, its average normalized IGD decreased from 0.2925 in the first generation to 0.0964 in the tenth generation. This indicates that the method of this invention can continuously improve the approximation ability of the rule population to the reference front throughout the evolutionary process and maintain a strong target space coverage ability, demonstrating good evolutionary stability and search balance. In contrast, although global_only also showed significant optimization effects, with its HV and IGD continuously improving, it indicates that relying solely on long-term global reflection can also help large language models identify the overall strength and weakness trends of parent rules, thereby improving the quality of subsequent rule generation. However, global_only experienced a stage performance decline in the fourth generation, indicating that when relying solely on global reflection, the rule population is more prone to regional concentration during the evolutionary process, temporarily reducing the current population's coverage ability to the reference front. In contrast, the performance gap-driven local reflection in the complete method can more stably maintain the search balance of different target regions, thereby reducing such fluctuations. Although the none method also achieves some improvement with the increase of evolutionary generations, the overall improvement is significantly weaker than the first two methods. A comprehensive analysis of the entire evolutionary process shows that, in most generations, the three methods generally exhibit a relationship where full is superior to global_only, and global_only is superior to none. This indicates that the performance gap-driven local reflection and global reflection synergistic mechanism proposed in this invention can more effectively improve the quality of rule evolution and outperforms comparative methods that only use global reflection or do not use reflection at all in terms of frontier approximation ability, coverage ability, and evolutionary stability.

[0116] The results above demonstrate that the effectiveness of this invention does not solely stem from general reflection and feedback, but primarily from the synergistic effect of the performance gap layering mechanism and the local reflection mechanism. Performance gap layering distinguishes between well-suited rule structures suitable for inheritance and weak rule structures requiring repair; local reflection further refines targeted design points for cross-inheritance and mutation repair; and global reflection provides supplementary guidance for the overall evolutionary direction. The combined effect of these three mechanisms enables the complete method to achieve superior frontier approximation capability, stronger target space coverage, and better evolutionary stability in the heuristic rule evolution process of multi-objective flexible workshop scheduling.

[0117] Generalization experiment of this application: To verify the adaptability of the heuristic rules generated in this application under different flexible job shop instances, this application adopts a method of separating the training instance set and the independent test instance set for rule generalization verification. Specifically, in the rule evolution stage, the Dauzere standard flexible job shop dataset is used as the training instance set to perform multi-objective evolutionary optimization on the heuristic rules. In the rule generalization testing stage, the Brandimarte standard flexible job shop dataset, which did not participate in the rule evolution process, is used as the independent test instance set to directly schedule the evolved heuristic rules. Both the Dauzere and Brandimarte datasets belong to the standard test sets of classic flexible job shop scheduling problems. They share the same basic constraints of flexible job shops, including process sequence constraints, machine selectability constraints, and machine resource exclusivity constraints, but differ in terms of job size, machine size, number of processes, and flexibility. Therefore, this testing method can verify the cross-instance generalization ability of the rules generated in this application under the same scheduling constraints for instances of different sizes and structures.

[0118] During the generalization test, the heuristic rules, after evolution, are not retrained, re-evolved, or have their parameters adjusted. Instead, they are directly applied to Brandimarte test instances to generate corresponding scheduling schemes, in order to verify the rules' transferability and scene adaptation capabilities in unseen instances. The experimental results, as shown in Table 4, indicate that the heuristic rules generated in this application can still maintain good multi-objective optimization performance on new instances that have not participated in the evolution. This demonstrates that the rule evolution mechanism in this application can not only adapt to training instances but also possesses good rule stability, cross-instance transferability, and generalization capability for similar flexible workshop scenarios.

[0119] Table 4 Generalization experiments of this application on Brandimarte instances:

[0120] Furthermore, compared with traditional manual rules and comparison methods, the method in this application still maintains strong bi-objective optimization capabilities on test instances that have not participated in training. This indicates that its advantages are not only reflected in the rule evolution effect during the training phase, but also in the stable generalization performance under cross-dataset conditions. This further verifies the practical application value of the method in flexible job shop scheduling scenarios.

[0121] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model, characterized in that: The steps are as follows, performed sequentially: S1: Using maximum completion time and total delay time as optimization objectives, define the maximum completion time and total delay time, and construct a dual-objective optimization model based on these defined times. Then, apply machine selectability constraints, process timing constraints, and machine exclusiveness constraints to this dual-objective optimization model. It is expressed by the following formula: ； in, To maximize the completion time, Total delay time; S2: Preset workshop state, based on which the process is adjusted. Distributed to machine The priority is evaluated to obtain the priority evaluation result. The optimal scheduling decision is selected based on the priority evaluation result. The optimal scheduling decision is used to update the status of the workshop, and the target value vector corresponding to the heuristic rule is generated. The initial candidate heuristic rule population of the bi-objective optimization model is generated using a large language model. S3: Perform population evaluation on the heuristic rules in the initial candidate heuristic rule population, that is, batch evaluate all heuristic rules in the population on multiple standard flexible workshop instances, calculate the maximum completion time and total delay time of each heuristic rule on each instance, and normalize the target value vector in each instance to obtain a normalized dual-objective vector. Then, calculate the cross-instance average normalized target value for each heuristic rule to form a rule-level dual-objective aggregation vector. Use a screening mechanism of non-dominated solution sorting priority and adaptive dynamic grid truncation assistance to retain a preset number of rules from multiple legal candidates as the parent heuristic rule population. S4: Evaluate the performance gap and divide the rule clusters of the parent heuristic rule population: Based on the normalized bi-objective vector, extract the set of non-dominated rules from all heuristic rules in the parent heuristic rule population, and select the heuristic rule with the smallest weighted normalized objective value from the set of non-dominated rules as the first... The reference rules for the nth instance are used to obtain the nth... The reference normalized target vector corresponding to the nth instance is defined as the Euclidean distance between the normalized target vector and the reference normalized target vector. The performance gap of the heuristic rules in each instance is used to calculate the average performance gap of the heuristic rules. The heuristic rules are then divided according to a preset performance gap threshold to obtain a low-performance gap rule cluster and a high-performance gap rule cluster. S5: After assessing the population performance gap and dividing the rule clusters according to the above method, the parent heuristic rule population is subjected to hierarchical reflection guidance and dual-path evolution mechanism: local reflection inputs are constructed for the low-performance gap rule cluster and the high-performance gap rule cluster respectively, and the large language model is called to generate the low-performance gap reflection results and the high-performance gap reflection results. Furthermore, the global evolution reflection results are generated, and the low-performance gap rule cluster is subjected to reflective crossover and recombination, and the high-performance gap rule cluster is subjected to reflective repair mutation to obtain the offspring heuristic rules; S6: Offspring Evaluation and Population Update: The offspring heuristic rule population generated in each generation is merged with the current parent heuristic rule population to form a new candidate heuristic rule population. The new candidate heuristic rule population repeats steps S3 to S5. After each complete iteration, the number of iterations is accumulated. When the number of iterations reaches the preset maximum value, the loop terminates and the current parent heuristic rule population is output as the final rule set. Each rule in the rule set is applied to the current scheduling instance.

2. The adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model as described in claim 1, characterized in that: Step S1 specifically includes the following steps: S1-1: Let the set of workpieces be... n represents the number of workpiece types, and the number of workpieces... The included processes are defined as follows The machine set is m is the total number of machines, for workpieces The jth process The set of available machines is denoted as And satisfy The optimization objectives are maximum completion time and total delay time. Maximum completion time is defined as: ； in, Indicates workpiece Completion time, Indicates the workpiece number. Indicates the total number of workpieces to be scheduled; Total delay time is defined as: ； in, Indicates workpiece Delivery time; S1-2: To ensure the executability of the generated scheduling scheme, the following constraints are applied to this bi-objective optimization model: Machine optional constraint: This machine optional constraint ensures that each process Just in its set of optional machines Processing is performed on one of the machines, and the machine selection constraints are expressed by the following formula: ； in, Indicates the type of workpiece The This process is done on the machine. 0-1 decision variables for the allocation of processing time on the surface; Process timing constraints: This process timing constraint ensures that the process... In the process Once completed, the sequential relationship is ensured. The timing constraint for this process is expressed by the following formula: ； in, Indicates the type of workpiece The This process is done on the machine. The start time of the project Indicates the type of workpiece The This process is done on the machine. The start time of the project Indicates the type of workpiece The This process is done on the machine. Processing time on Assign 0-1 decision variables to the machines corresponding to the preceding processes; Machine exclusivity constraint: A machine can only process one operation at a time. This constraint ensures that on the same machine, any two operations can be performed simultaneously. and They will not execute simultaneously; the machine exclusive constraint is expressed by the following formula: ； in, Indicates the type of workpiece The This process is done on the machine. Processing time on Indicates the type of workpiece The This process is done on the machine. The start time of the project Indicates the type of workpiece The This process is done on the machine. The processing time.

3. The adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model as described in claim 2, characterized in that: The specific steps of step S2 are as follows: S2-1: Let the current heuristic rule population be... N represents the current size of the rule-based population. Indicates the first A heuristic rule; S2-2: At scheduling time t, the workshop state is denoted as... ; in, This indicates the current status of an incomplete set of workpieces. Indicates the current machine operating status. This represents the set of currently schedulable operations; S2-3: Regarding the current workshop status , set up process The optional set of machines is heuristic rules Evaluate candidate processes and machine combinations; processes Distributed to machine The priority evaluation value at that time is expressed by the following formula: ； The optimal scheduling decision is selected based on the priority evaluation results of all candidate processes and machine combinations: ； in, This represents the set of selected processes. This represents the set of machines to be allocated. S2-4: Adjust the workshop state based on this optimal scheduling decision. Update to obtain the new workshop status. Repeat steps S2-2 and S2-3 until all workpieces are processed, thus generating the heuristic rule. The corresponding complete scheduling scheme is evaluated to obtain the heuristic rule. The corresponding target value vector: ； in, For corresponding heuristic rules Maximum completion time For corresponding heuristic rules Total delay time; S2-5: Let the initial population size of the candidate heuristic rules be... The parent-generation heuristic rule population retention size is ,in, The population diversity of the initial candidate heuristic rules is increased by expanding the candidate sample base. Then, a fixed number of parent heuristic rules are retained through a multi-objective screening mechanism. The initial candidate heuristic rule population is represented as follows: ； Generate initial heuristic rules using a large language model to obtain 10 valid heuristic rules are used to form the initial candidate heuristic rule population. .

4. The adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model as described in claim 3, characterized in that: The specific steps for heuristic rule-based population evaluation in step S3 are as follows: S3-1: Let the set of training instances be... For heuristic rules In the The first test instance The target value is denoted as ,in, hour, Representing heuristic rules In the Maximum completion time on a single instance; hour, Representing heuristic rules In the Total delay time on each instance; Since different instances and different targets have different units and numerical ranges, normalization is first performed within each instance, let's say the first instance... In the first instance The minimum and maximum values ​​of the targets are as follows: ； ； Heuristic rules In the The first instance Normalized target value Defined as: ； in, To prevent extremely small constants with a denominator of zero, the range of values ​​is 10. -12 ≤ ≤10 12 ; After the above processing, the heuristic rules In the example The normalized biobjective vector on can be expressed as: ； S3-2: Rule Set Performance Analysis: Since each heuristic rule needs to be comprehensively evaluated on multiple test instances, the performance of the heuristic rules... The normalized objective values ​​across all instances are averaged to obtain a rule-based bi-objective aggregation vector: ； in, , , This is the number of test instances. Representing heuristic rules The average normalized maximum completion time across all test instances. Representing heuristic rules Average normalized total latency across all test instances; The aggregation objective value of this heuristic rule is then: ； Used to characterize heuristic rules The comprehensive dual-objective performance is used as the basis for subsequent non-dominated sorting and parent selection; S3-3: Non-dominated solution sorting of rule set: Calculate the bi-objective aggregation vector of all heuristic rules, perform non-dominated sorting on the heuristic rule set, and obtain the frontier level of each heuristic rule; S3-4: Dynamic grid truncation based on the hierarchical division of the frontier level: This dynamic grid truncation is not uniformly applied to all heuristic rules, but only during the non-dominated sorting process. When the number of rules in a certain frontier level exceeds the remaining retention quota, the frontier level is taken as the frontier boundary layer, and grid truncation is performed on the rules of the frontier boundary layer. If the number of rules in a certain frontier level can be fully incorporated into the current parent population, all rules in that frontier level are retained, and no further grid truncation is performed. For boundary layer rules that need to be truncated, a bi-objective aggregation vector is aggregated based on its heuristic rule level. The position in the two-dimensional target space is normalized and mapped, and then divided accordingly. There are 1 grid cells, where K is the grid division dimension, and each rule falls into the corresponding grid cell according to its aggregated normalization target value; During the grid truncation process, each non-empty grid cell retains at most one representative heuristic rule. If multiple heuristic rules exist within the same grid cell, the rule with the better aggregation target value is retained first, so that only the more representative rule is retained in the same local area. If the number of rules represented by the grid is still insufficient under the preset maximum grid division dimension, then the remaining required number of heuristic rules are selected from the boundary layer rules to complete the truncation based on the principle that the aggregation target value is better. The candidate heuristic rule population is truncated by a dynamic grid, and the heuristic rule population that is retained is used as the parent heuristic rule population.

5. The adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model as described in claim 4, characterized in that: The specific steps of step S4 are as follows: S4-1: For the first In one instance, the parent heuristic rule population is based on a normalized bi-objective vector. and Extract the set of non-dominated rules from all heuristic rules. From this set of non-dominated rules, select the heuristic rule with the smallest weighted normalization objective value as the first heuristic rule. Reference rules for each instance: ； in, This is the dual-objective balance coefficient, with a value range of [value range missing]. ; No. The reference normalized target vector corresponding to each instance is: ； in, Refers to the first Reference rules for each instance Refer to the rules In the The first normalized target value on each instance, Refer to the rules In the The second normalized target value on each instance; S4-2: For the first Heuristics in a Specific Example Its performance gap Defined as the Euclidean distance between the normalized biobjective vector and the reference normalized objective vector: ； in Heuristic rules In the example Normalized biobjective vector on, Refer to the rules In the example Normalized biobjective vector on; The smaller the performance gap, the stronger the heuristic rule. In the example The closer the heuristic is to the reference good region, the larger the performance gap, indicating a stronger heuristic rule. In the example The farther away from the optimal region, the lower-performance gap rules prioritize retaining their existing structure and participating in crossover recombination, while the high-performance gap rules prioritize entering the repair mutation process. S4-3: Average Performance Gap of Heuristic Rules: To characterize heuristic rules The overall optimization potential across all test instances can be defined as the average performance gap as: ； in, Representing heuristic rules The average performance gap across all instances is used to guide the selection of differentiated evolutionary paths for heuristic rules and to control subsequent crossover recombination, repair mutation, and boundary layer preservation processes. S4-4: High and Low Performance Gap Rules: For the first Let there be an instance where the average performance gap of all heuristic rules is [value]. The standard deviation is The performance gap threshold for this instance is defined as follows: ； in, This threshold adjustment coefficient controls the tightness of the separation between high and low notches; based on this threshold adjustment coefficient... No. In this instance, heuristic rules can be used... Classified as: like heuristic rules In the example The above belongs to the high-performance gap rule cluster; like heuristic rules In the example The above belongs to the low-performance gap rule cluster; Statistical heuristics The number of times a rule is classified into a high-performance gap region and a low-performance gap region in all instances is used to classify rules belonging to high-performance gaps in more instances into high-performance gap rule clusters, and rules belonging to low-performance gaps in more instances into low-performance gap rule clusters. Subsequently, the evolution mode of different rules is controlled based on the rule performance gap, where high-performance gap rules preferentially trigger the repair mutation process, and low-performance gap rules preferentially trigger the crossover recombination process.

6. The adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model as described in claim 5, characterized in that: The specific steps of step S5 are as follows: S5-1: Local rule reflection generation: For each rule in the parent population, it is statistically analyzed whether it belongs to the high gap or low gap region in each instance. Combined with its cross-instance average normalized target value, average performance gap and other indicators, a rule-level aggregation feature is formed. Based on this information, a low performance gap rule cluster and a high performance gap rule cluster are constructed. Then, local reflection inputs are constructed for the low performance gap rule cluster and the high performance gap rule cluster respectively, and the large language model is called to generate the corresponding reflection results. The reflection results include the low performance gap reflection results and the high performance gap reflection results. S5-2: Global Evolutionary Reflection Generation: Input the overall information of the current generation's parent population, the reflection result of the low gap, and the reflection result of the high gap into the large language model to generate the global evolutionary reflection result; S5-3: Reflective cross-recombination of the low-performance gap rule cluster: For the low-performance gap rule cluster, select two low-gap parent rules as cross-inputs; input the two low-gap parent rules, the low-performance gap reflection results, the global evolution reflection results, and the scheduling rule interface specifications into the large language model to generate low-performance offspring heuristic rules. S5-4: Reflective and restorative mutation of the high-performance gap rule cluster: For the high-performance gap rule cluster, a restorative mutation method of high-gap parent and elite reference parent is adopted. That is, a high-gap parent heuristic rule is selected as the object to be repaired and a low-gap or elite parent heuristic rule with better overall performance is selected as the structural reference object. These two parent heuristic rules, the high-performance gap reflection results, the global evolution reflection results and the scheduling rule interface specification are input into the large language model to generate high-performance offspring heuristic rules. The low-performance offspring heuristic rule and the high-performance offspring heuristic rule are sequentially subjected to syntax validation, interface validation, runtime validation, and constraint validation. If it fails, the error reason is sent back to the large language model for repair until the offspring heuristic rule is obtained or the retry limit is reached.

7. The adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model as described in claim 6, characterized in that: In steps S2-5, the prompt template for generating initial candidate heuristic rules by the large language model consists of the following parts: Role instructions: used to guide the model to generate diverse rules based on different algorithm design styles; Task: Specify that the large model needs to complete the design heuristic rule code; Problem Description: Define the dual-objective optimization task of the flexible workshop as minimizing the maximum completion time and the total delay time, and provide a complete constraint description, including machine exclusive constraints, process sequence constraints, and machine selectability constraints; Input / output interface description: The function to generate rule code named "heuristic" is required. The rule input is defined as instance data of shop floor scheduling, and the output is a specific scheduling scheme. The input problem must include at least the number of workpieces, the number of machines, and the available machines and processing times for each workpiece's process. The output is a complete scheduling dictionary organized by workpiece, with each process recording the process number, assigned machine, start time, end time, and processing time. Restriction: Specifies the generation form of heuristic rules; Seed heuristics: used to provide examples of basic code format and output structure; Output instructions: The output should return a standard Python code block and its corresponding functional documentation. Perform the following validations on each heuristic rule generated by the large language model in sequence: Syntax validation checks whether the code can be parsed and loaded successfully. Interface validation checks whether a heuristic function is defined. Run the verification process by placing the rules into the scheduling environment for small-scale instance testing. Output structure validation: Check if a complete scheduling dictionary is returned. Constraint verification checks whether the scheduling results satisfy constraints such as machine exclusivity, process sequence, and machine selectability. If any step fails, the error message, the previous prompt, and the failure code are fed back to the large language model, which is required to generate a repair version based on the cause of the error, until the candidate heuristic rule passes the verification or reaches the preset maximum number of verifications.

8. The adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model as described in claim 7, characterized in that: In step S5, the Prompt construction method for the large language model reflection guidance process is as follows: In S5-1, local reflection input contexts are constructed for the low-performance gap rule cluster and the high-performance gap rule cluster, respectively. The content includes: Role setting: Multi-objective flexible shop floor scheduling heuristic design expert; Task description: Analyze the parent heuristic rules of the low-performance gap or high-performance gap and extract effective design patterns; Problem description: Explain that the current reflection targets the low-performance or high-performance gap parent rules in all selected training instances and performs a comprehensive comparison across the entire selected parent group; Input context: Global context information of the low-performance or high-performance gap rule cluster, including the parent heuristic rule name, the complete code of the parent heuristic rule, and the corresponding average normalized target value and average performance gap index; Output requirements: Extract common advantages and disadvantages, summarize effective patterns, and identify key decision factors; Output specifications: Output length not exceeding 80 characters, strictly limited to 3 lines of plain text, returned in a fixed format, and without additional explanations. In S5-2, the Global Evolutionary Reflection Prompt consists of the following parts: Role Setting: used to clarify the identity and professional perspective of the large language model in global rule evolution analysis; Task Description: used to specify the core objectives that the current global reflection needs to achieve; Problem Description: used to explain the analytical background, overall comparison objects, and next-generation rule generation requirements of the current global reflection; Input Context: including parent population summary information, low-performance gap reflection results, and high-performance gap reflection results. The parent population summary information is used to reflect the overall performance of the currently selected parent rules on multiple instances. This parent population summary information includes the average normalized target value and average performance gap of the parents; the low-performance gap reflection results are used to provide common advantages and inheritable structural information of excellent rules; the high-performance gap reflection results are used to provide information on the main defects and repairable problems of weak rules; Output Requirements: used to limit the analytical focus that the global reflection results need to cover; Output Specification: used to constrain the length, structure, and expression form of the global reflection results, facilitating direct use in subsequent crossover and mutation generation.

9. The adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model as described in claim 8, characterized in that: When performing cross-input in step S5-3, the large language model input includes: Role definition: Used to clarify the task of cross-generation of heuristic rules for offspring currently undertaken by the large language model; Task Description: This task specifies the heuristic rules for generating new multi-objective flexible shop floor scheduling offspring. Problem Description: This description illustrates that the current optimization problem is a flexible job shop bi-objective scheduling problem, including minimizing the maximum completion time and the total delay time, along with some constraint descriptions. Rule code input / output interface description: Function interface, input data structure, and output scheduling scheme format used to uniformly generate rules; Cross generation description: This is used to clarify that the current offspring is generated by the cross generation of heuristic rules from two low-performance gap parents, and specifies the form of the output heuristic rule; Parent: Enter the name and code of the parent rule to be used for crossover; Reflection Results: Provides reflection results on low-performance gaps and global evolutionary reflection results respectively: used to provide common advantages of good rules, effective laws and design points suitable for inheritance, as well as provide overall evolutionary guidance information across instance levels; Generation requirements: The crossover process should integrate effective scheduling ideas from both parent generations, retain structures that are conducive to optimizing both maximum completion time and total delay time, and avoid directly copying either parent generation; at the same time, the output rules should include necessary comments, brief descriptions, and child generation identification information to improve the interpretability of the rules.

10. The adaptive optimization scheduling method for a large-scale multi-objective flexible workshop model as described in claim 9, characterized in that: In step S5-4, the inputs for the large language model to perform reflective repair mutations include: Role definition: Used to clarify the current task of repairing and mutating high-performance gap rules that the large model is responsible for; Task Description: This task specifies the heuristic rules for generating new mutated offspring. Problem Description: This section describes the current optimization problem, the bi-objective requirements, and the background of mutation generation. Rule code input / output interface description: Used to unify the format of function interfaces, input data structures, and output scheduling schemes; Mutation generation instructions: This is used to ensure that the generation rules meet the requirements of complete scheduling feasibility, and to clarify that the current offspring completes the repair mutation generation by combining the high-performance gap parent generation with the elite parent generation; Parent generation: Describes the high-performance gap parent generation rules and the elite reference parent generation rules, which are used to provide the complete structure and scheduling logic of the rules to be repaired and the good design ideas that can be learned from. Reflection Results: Provides high-performance gap reflection results and global evolutionary reflection results to provide local repair directions and key failure information, as well as overall evolutionary guidance across instance levels; Generation requirements: to constrain the direction of improvement, innovation and structural form of mutation generation; at the same time, the output rules are required to include necessary comments, brief descriptions and offspring identification information to improve the interpretability of the rules; Based on this, the large model retains the basic feasible framework of the high-gap parent generation, draws on the robust structure of the elite parent generation, performs targeted repairs on its local scheduling logic, and generates a new complete scheduling heuristic function. At the same time, the mutated offspring generation also needs to pass syntax, runtime and constraint verification. If it fails, it enters the error feedback and repair process.

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