Distributed flow shop scheduling method based on large model assisted multi-objective optimization algorithm

Abstract

The invention discloses a distributed flow shop scheduling method based on a large model aided multi-objective optimization algorithm, and particularly aims to solve the problems of insufficient sequence correlation setting time, insufficient wait-free constraint processing and low multi-objective optimization efficiency in existing distributed heterogeneous factory scheduling. And proposing a non-dominated sorting genetic algorithm based on large language model assistance. The method comprises the following steps: constructing a dual-objective optimization model, adopting a one-dimensional integer array coding solution structure and separating a factory operation sequence through '-1'; in combination with a greedy algorithm idea, selecting a greedy initialization algorithm based on maximum completion time or a greedy initialization algorithm based on sequence-dependent setting time to initialize a population; designing a large model cue word including problem definition, solution example, evolution instruction and legality verification, and executing parent selection, crossover and mutation operation by a large language model; and updating the population through non-dominated sorting, and finally outputting a Pareto frontier solution.

Description

Technical Field

[0001] This invention relates to the field of optimization algorithm technology, specifically to a multi-objective evolutionary algorithm based on a large language model and its application method in the distributed heterogeneous no-wait flow shop scheduling problem considering sequence dependency setting time. Background Technology

[0002] With the global trend of digital transformation in manufacturing, driven by the demand for resilience, flexibility, and sustainability, production models are shifting from single-factory production to distributed heterogeneous factory networks. In this model, production tasks need to be allocated to geographically dispersed factories with varying production capabilities, which brings great complexity to production synchronization and resource optimization.

[0003] Traditional factory scheduling models focus on single-factory, single-objective optimization, primarily using mathematical programming and heuristic algorithms to solve production scheduling problems in flow shops and job shops. Since Johnson et al. first proposed the optimal scheduling method for two-stage flow shops, this field has gradually formed a research paradigm with minimizing the maximum completion time as the main objective. However, traditional FSPs are limited to idealized scenarios and cannot cope with the challenges of distributed heterogeneous environments, which need to consider the differences in production levels and machine efficiencies among different factories. Traditional scheduling models have the following shortcomings: First, although heterogeneous factory configurations and machine-related processing parameters are common in industrial scenarios, many existing models either assume homogeneous machine capabilities or do not fully consider the variability of setup times between consecutive job sequences. Integrating SDST into the optimization framework will increase computational complexity and affect algorithm efficiency. Second, the requirement of no-wait constraints for jobs to be processed continuously between machines without interruption is crucial in industries such as steel casting and food processing, but it is rarely included in multi-objective distributed scheduling models. Third, most studies take minimizing the maximum completion time as the optimization objective, but actual data shows that machine idleness in distributed systems will cause energy waste in high-throughput manufacturing environments. Focusing only on the maximum completion time index to a certain extent only emphasizes the critical machines in critical factories, while ignoring the utilization rate of non-critical factory machines, which is not conducive to resource conservation.

[0004] In recent years, the rapid development of large language models has had a transformative impact on many research fields, bringing new possibilities for solving optimization problems. With their powerful natural language understanding and generation capabilities, large language models can skillfully handle complex problem descriptions and constraints, demonstrating enormous potential in the field of optimization.

[0005] In view of this, the present invention is proposed. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-objective optimization method based on a large model to solve the distributed heterogeneous no-wait permutation pipeline scheduling problem that considers sequence dependency setting time. Compared with existing multi-objective optimization algorithms, the multi-objective optimization method based on a large model proposed in this invention effectively solves the current multi-objective optimization problem by combining greedy initialization, large language model-assisted evolution, and external archiving of non-dominated solutions.

[0007] In the population initialization phase, unlike traditional random initialization methods, this invention specifically designs two greedy initialization strategies to target the two optimization objectives: minimizing the maximum completion time (Cmax) and minimizing the machine's non-working time (Ttot). These strategies are randomly selected with a probability of 0.5. This dual-strategy random selection initialization method ensures that the individuals in the initial population are closer to the optimization objectives, significantly improving the quality of the initial population and thus accelerating the algorithm's convergence efficiency.

[0008] In the process of population evolution, this invention introduces a large language model-assisted mechanism. By constructing a prompt word system comprising four parts—problem definition, solution examples, evolution instructions, and validity verification—the selection, crossover, and mutation operations in population evolution are delegated to the large language model. Based on its powerful natural language understanding and reasoning capabilities, the large language model can select high-quality parents from the current population according to the prompt word requirements, and generate new solutions with higher quality and diversity by executing the CrO1-CrO3 crossover operator and the M1-M3 mutation operator. Compared with the traditional fixed-operator evolution method, this greatly enhances the algorithm's adaptability and search capability for complex problems.

[0009] Furthermore, this invention employs an external archive to store non-dominated solutions during the evolutionary process. After each generation of evolution, the algorithm updates the archive, promptly removing individuals dominated by new solutions and incorporating new solutions that form non-dominated relationships with existing archived solutions. Strategies such as crowding ranking are used to maintain the reasonable size of the archive. This non-dominated solution archiving mechanism fully preserves excellent solutions that emerge during the evolutionary process, ensuring the acquisition of high-quality Pareto front solutions and preventing the loss of high-quality solutions due to the randomness of the evolutionary process.

[0010] 1. This invention achieves the above objective through the following technical solution: a distributed workflow scheduling method based on a large model-assisted multi-objective optimization algorithm, characterized by comprising the following steps:

[0011] S1. Define the problem size and optimization objective: Determine the relevant parameters of the distributed heterogeneous flow shop scheduling problem (DHNPFSP-SDST) that needs to be solved, considering the time of sequence dependency setting, including the total number of jobs n, the total number of factories f, the number of machines in each factory m, the processing time pl,i,j of each job on each machine in different factories, and the machine changeover time sdstl,i,j,v required to process the job, with the optimization objective being to minimize the maximum completion time (Cmax) and minimize the machine non-working time (Ttot).

[0012] S2, Population Initialization: Set the chromosome encoding length according to the problem parameters, and randomly select one method for greedy initialization, including greedy initialization based on Cmax and greedy initialization based on sdst. Initialize and generate Npop individuals.

[0013] S3, Population Evolution: Utilizing a large language model to construct prompt words to assist in performing selection, crossover, and mutation operations in population evolution; the prompt words mainly consist of four parts:

[0014] a) Problem definition module: Describes the DHNPFSP-SDST parameters, decoding format, and optimization objectives Cmax and Ttot;

[0015] b) Solution Example Module: Provides the integer array encoding of the current population solution, the Pareto level of the solution, the completion time of each factory corresponding to the solution, and the total machine conversion time of each factory;

[0016] c) Evolutionary instruction module: executes the parent selection strategy, CrO1-CrO3 crossover operator, and M1-M3 mutation operator;

[0017] d) Legality verification module: requires that the generated solution has no duplicate jobs, conforms to the encoding format and constraints.

[0018] S4, fitness evaluation, and non-dominated sorting of the evolved population. That is, after each operation in step 3, the algorithm evaluates the fitness of the newly generated individuals, and then sorts them based on non-dominated relationships and crowding. The child individuals compete directly with the parent individuals, and the better solution between the two is selected to enter the next generation.

[0019] S5, Archiving of Non-Dominated Solutions: After each generation of evolution, i.e., after each step 3 operation, the algorithm updates the external archive storing non-dominated solutions. Solutions in the archive that are dominated by new solutions are discarded directly, while solutions that form a non-dominated relationship with solutions in the archive are added to the archive.

[0020] S6. Determine if the termination condition is met. If not, proceed to step 3 and continue performing evolutionary operations on the current population. If the condition is met, select a solution from the current external archive and output its corresponding scheduling scheme.

[0021] 2. The distributed flow shop scheduling method based on a large model-assisted multi-objective optimization algorithm according to claim 1, characterized in that, the determination of the problem scale and optimization objective in step S1 specifically follows the following steps:

[0022] S1.1, Define the problem parameters.

[0023] Define the total number of jobs n and the total set of jobs J = {J1, J2, ..., Jn}, the total number of factories f and the total set of factories F = {F1, F2, ..., Ff}, each factory contains m machines with different processing capacities, the machine set is represented as M = {M1, M2, ..., Mm} and the processing flow is fixed as M1 → M2 → ... Mm; the processing time matrix p l,i,j (representing the processing time of job i on machine j in factory l) and the sequence dependency setting time matrix sdst l,I,j,v (This represents the changeover time required between processing job Jv and processing job Jj on machine Mi in the factory.)

[0024] S1.2, Set constraints.

[0025] Job continuity constraint: Each job must complete all processing within the same factory and cannot be transferred across factories; Machine exclusivity constraint: Each machine can process at most one job at a time, and each job can be processed by at most one machine; No waiting constraint: Jobs must be processed continuously between machines within the factory, with no intermediate waiting time; Initial setup time constraint: The setup time for the first job in each factory on the first machine is zero.

[0026] S1.3, Construct optimization objectives.

[0027] Maximum completion time Cmax = maxC l end C l end Let Ttot be the completion time of the last operation in factory Fl. Total machine downtime Ttot = Σ l=1 f Σ i=1 m T l.i idle T l.i idle This refers to the total idle time of machine Mi in all operation processes of factory Fl, including setup time and waiting time.

[0028] 3. The distributed flow shop scheduling method based on a large model-assisted multi-objective optimization algorithm according to claim 1, characterized in that, in step S2, the specific operation of population initialization is as follows:

[0029] S2.1, the chromosome encoding of an individual is a one-dimensional integer array X=[x1, -1, x2, -1, ..., xf], where xl represents the job processing sequence of factory Fl, and each job Jj is represented by a unique integer identifier, with "-1" used only as an identifier separator;

[0030] S2.2, generate a random number Prand between (0,1). If Prand>0.5, the individual is initialized using a greedy algorithm based on Cmax; if Prand<0.5, the individual is initialized using a greedy algorithm based on Ttot.

[0031] S2.3, Initialize the population using a greedy strategy;

[0032] a) The greedy initialization based on Cmax has the following operations: randomly shuffle all job sequences to generate Xshuffled; initialize the current completion time C of each factory. l current =0, for each job Jj in Xshuffled, find the one that satisfies l * =arg min l C l current Factory l inserts job Jj into the job processing sequence of factory l;

[0033] b) The greedy initialization based on Ttot has the following operation form: randomly shuffle all job sequences to generate Xshuffled; for each job Jj in Xshuffled, find the factory l with the minimum SDST time required to process job Jj, and insert job Jj into the job processing sequence of factory l;

[0034] 4. The distributed workflow scheduling method based on a large model-assisted multi-objective optimization algorithm according to claim 1, characterized in that, in step S3, for population evolution, that is, the population performs crossover and mutation operations, it is mainly achieved by using prompt words with the help of a large model;

[0035] First, the information such as the task allocation, task sequence, and corresponding objective function value of individual solutions in the population is encoded into a natural language format suitable for large language model processing;

[0036] Then, construct a prompt word that includes the following four parts:

[0037] a) Problem definition and solution representation: The DHNPFSP-SDST problem is described in detail, the number of factories and the number of jobs are specified, the solution is defined as a one-dimensional integer array encoding, "-1" is used as the factory job sequence separator, and the optimization objectives of minimizing the maximum completion time (Cmax) and minimizing machine downtime (Ttot) are clearly defined.

[0038] b) Input Solution Example Section: Select several solutions from the current population, encode them in integer array form, and provide the Pareto level, completion time of each factory, total machine turnaround time of each factory and other attribute values ​​of each solution to the large model as context learning material to help the large model understand the relationship between solution structure and optimization objective;

[0039] c) Evolutionary Operation Instructions: This section provides explicit instructions to the large model, guiding it to perform parent selection, crossover, and mutation operations. Parent selection requires the large model to randomly select diverse parent solutions from the current population. Crossover instructions require the large model to choose one of three crossover operators: CrO1, CrO2, and CrO3. CrO1 retrieves the completion time list of each factory in the two parent solutions, finds the factory index corresponding to the maximum value, and swaps the job sequences of that factory in the two parent solutions. CrO2 retrieves the total SDST list of each factory in the two parent solutions, finds the factory index corresponding to the maximum value, and swaps the job sequences of that factory in the two parent solutions. CrO3 performs multi-point crossover on the encoding of the two parent solutions, i.e., randomly selects multiple crossover points and swaps the encoding fragments between the crossover points to generate new offspring encodings. The mutation operation instruction requires the large model to select one of three mutation operators, M1, M2, and M3, to execute. M1 randomly selects two elements in the code and swaps their positions; M2 selects any interval in the code and reverses the order of the elements in that interval; M3 selects any two factory operation sequences in the code and swaps them.

[0040] d) Output validity verification: The large model is required to verify the generated new solutions, ensuring that the new solutions conform to the specified encoding format, do not involve duplicate work, and satisfy all constraints of the DHNPFSP-SDST problem. If any new solutions do not meet the requirements, they are modified until they do. Simultaneously, a pre-defined number of valid solutions are returned in integer array format for direct integration into the next generation population of the NSGAII algorithm.

[0041] Finally, the constructed prompt words are input into the large model. Based on its own pre-trained knowledge and inference algorithm, the large model performs crossover and mutation operations according to the prompt word requirements to generate new individual solutions.

[0042] 5. A multi-objective optimization method with large language model assistance for solving a distributed heterogeneous flow shop scheduling problem considering sequence dependency setting time, as described in claim 1, is characterized in that, in step S5, the archive of non-dominated solutions is updated, that is, after each evolution, it is necessary to check whether the newly generated solutions update the archive, and the following three criteria must be met:

[0043] a) If the newly generated solution completely dominates a solution in the archive, then delete the dominated solution from the archive and add the newly generated solution to the archive;

[0044] b) If the newly generated solution forms a non-dominant relationship with all solutions in the archive, then add the newly generated solution to the archive;

[0045] c) If the newly generated solution is dominated by a solution in the archive, then no update is performed.

[0046] The technical effects and advantages of this invention are as follows: This invention addresses the multi-objective scheduling problem of DHNPFSP-SDST by designing a large-model-assisted multi-objective optimization method. First, based on a greedy strategy, a greedy initialization method is designed to minimize both the maximum completion time and the machine downtime, providing a high-quality initial population for subsequent evolution. Then, a large language model-assisted evolution approach is employed, leveraging its powerful natural language understanding and reasoning capabilities to drive selection, crossover, and mutation operations in the population. Combined with an external archiving mechanism for storing non-dominated solutions, this effectively solves the multi-objective optimization problem.

[0047] This invention designs an evolutionary operation mode based on a large model. By constructing a prompt word system that includes problem definition, solution examples, evolution instructions, and validity verification, the large language model participates in the population evolution process, enabling the algorithm to explore the solution space more intelligently, generate high-quality and diverse new solutions, and enhance its adaptability to complex scheduling scenarios.

[0048] This invention associates population initialization with dual optimization objectives and randomly selects two greedy strategies to improve the quality of the initial population from the source, thereby accelerating the convergence efficiency of the algorithm. At the same time, the non-dominated solution archiving mechanism fully preserves excellent solutions in the evolution process, providing a guarantee for obtaining high-quality Pareto front solutions, making the multi-objective optimization process more efficient and the solutions of higher quality.

[0049] This invention has good versatility and can be effectively applied in various distributed heterogeneous no-wait replacement flow workshop scenarios, facing different numbers of operations, factory sizes and time constraints for sequence dependencies. It provides strong technical support for production scheduling optimization for relevant manufacturing enterprises and helps improve production efficiency and resource utilization. Attached Figure Description

[0050] Figure 1This is a flowchart of the overall algorithm of the present invention;

[0051] Figure 2 The distribution of non-dominated solution sets obtained by running the present invention on the 01_DHNPFSP-SDST_20_5_2 instance. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] Please see Figure 1 As shown, a distributed flow shop scheduling method based on a large model-assisted multi-objective optimization algorithm includes the following steps:

[0054] 1) Define the problem scale and optimization objective: Determine the relevant parameters of DHNPFSP-SDST. Taking the 01DHNPFSP-SDST_20_5_2 example, these include the total number of jobs (20), the total number of factories (2), the number of machines in each factory (5), the processing time pl,i,j for each job on each machine in different factories, and the machine changeover time sdstl,i,j,v required to process the job. The optimization objective is to minimize the maximum completion time (Cmax) and minimize the machine's non-working time (Ttot).

[0055] 2) Population Initialization: The chromosome encoding length is set based on the total number of jobs n=20. The chromosome encoding for each individual uses a one-dimensional integer array X=[x1, -1, x2], where x1 represents the job processing sequence of factory F1, x2 represents the job processing sequence of factory F2, and each job Jj is represented by a unique integer identifier. "-1" is used only as a separator. A greedy initialization method is randomly selected with a probability of 0.5, including greedy initialization based on Cmax and greedy initialization based on sdst. 50 individuals are generated during initialization.

[0056] 3) Population Evolution: Using a large language model to construct cue words to assist in the selection, crossover, and mutation operations during population evolution; the cue words mainly consist of four parts, details of which can be found in [link to documentation]. Figure 1 :

[0057] a) Problem definition module: Describes the DHNPFSP-SDST parameters, decoding format, and optimization objectives Cmax and Ttot;

[0058] b) Solution Example Module: Provides the integer array encoding of the solution for the current population, the Pareto level of the solution, the completion time of each factory corresponding to the solution, and the total machine conversion time of each factory;

[0059] c) Evolutionary instruction module: executes the parent selection strategy, CrO1-CrO3 crossover operator, and M1-M3 mutation operator;

[0060] d) Validity verification module: This module requires generated solutions to be free of duplicates and conform to the encoding format and constraints. If a new solution does not meet the requirements, it should be modified until the requirements are met. Simultaneously, it returns a pre-defined number of valid solutions in integer array format for direct integration into the next generation of the NSGAII algorithm population.

[0061] 4) Fitness assessment and non-dominated sorting of the evolved population. That is, after each operation in step 3, the algorithm will assess the fitness of the newly generated individuals, and then sort them based on non-dominated relationships and crowding. The child individuals directly compete with the parent individuals, and the better solution between the two is selected to enter the next generation.

[0062] 5) Archiving of Non-Dominant Solutions: After each generation of evolution, i.e., after each operation in step 3, the algorithm updates the external archive storing non-dominant solutions. If a newly generated solution completely dominates a solution in the archive, the dominated solution in the archive is deleted, and the newly generated solution is added to the archive; if the newly generated solution forms a non-dominant relationship with all solutions in the archive, the newly generated solution is added to the archive; if the newly generated solution is dominated by a solution in the archive, no update is performed.

[0063] 6) Determine if the termination condition is met, i.e., the number of generations does not exceed 50. If not, proceed to step 3 and continue performing evolutionary operations on the current population; if so, select a solution from the current external archive and output its corresponding scheduling scheme. The output results on 01DHNPFSP-SDST_20_5_2 can be seen... Figure 2 .

[0064] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0065] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A distributed workflow scheduling method based on a large model-assisted multi-objective optimization algorithm, characterized in that, Includes the following steps: S1. Define the problem size and optimization objective: Determine the relevant parameters of the distributed heterogeneous flow shop scheduling problem (DHNPFSP-SDST) that needs to be solved, considering the sequence dependency setting time, including the total number of jobs n, the total number of factories f, the number of machines in each factory m, the processing time pl,i,j of each job on each machine in different factories, and the machine changeover time sdstl,i,j,v required to process the job, with the optimization objective being to minimize the maximum completion time (Cmax) and minimize the machine non-working time (Ttot); S2, Population Initialization: Based on the problem parameters, set the chromosome encoding length and randomly select a greedy initialization method, including both Cmax-based and sdst-based greedy initialization. Initialize and generate Npop individuals; S3, Population Evolution: Utilizing a large language model to construct prompt words to assist in performing selection, crossover, and mutation operations in population evolution; the prompt words mainly consist of four parts: a) Problem definition module: Describes the DHNPFSP-SDST parameters, decoding format, and optimization objectives Cmax and Ttot; b) Solution Example Module: Provides the integer array encoding of the current population solution, the Pareto level of the solution, the completion time of each factory corresponding to the solution, and the total machine conversion time of each factory; c) Evolutionary instruction module: executes the parent selection strategy, CrO1-CrO3 crossover operator, and M1-M3 mutation operator; d) Legality verification module: requires that the generated solution has no duplicate jobs, conforms to the encoding format and constraints; S4, fitness evaluation, and non-dominated sorting of the evolved population. That is, after each operation in step 3, the algorithm will evaluate the fitness of the newly generated individuals, and then sort them based on non-dominated relationships and crowding. The child individuals directly compete with the parent individuals, and the better solution between the two is selected to enter the next generation. S5, Archiving of Non-Dominant Solutions: After each generation of evolution, i.e., after each step 3 operation, the algorithm updates the external archive storing non-dominant solutions. Solutions in the archive that are dominated by new solutions are discarded directly, while solutions that form a non-dominant relationship with solutions in the archive are added to the archive. S6. Determine if the termination condition is met. If not, proceed to step 3 and continue performing evolutionary operations on the current population. If the condition is met, select a solution from the current external archive and output its corresponding scheduling scheme.

2. The distributed workflow scheduling method based on a large model-assisted multi-objective optimization algorithm according to claim 1, characterized in that, Step S1, which defines the problem size and optimization objective, specifically follows these steps: S1.1, Define the problem parameters; Define the total number of jobs n and the total set of jobs J = {J1, J2, ..., Jn}, the total number of factories f and the total set of factories F = {F1, F2, ..., Ff}, each factory contains m machines with different processing capacities, the machine set is represented as M = {M1, M2, ..., Mm} and the processing flow is fixed as M1 → M2 → ... Mm; the processing time matrix p l,i,j (Represents the processing time of job i on machine j in factory l) and the sequence dependency setting time matrix sdst l,I,j,v (This represents the changeover time required between processing job Jv and processing job Jj on machine Mi in the factory.) S1.2, Set constraints; Job continuity constraint: Each job must be completed entirely within the same factory and cannot be transferred across factories; Machine exclusivity constraint: Each machine can process at most one job at a time, and each job can be processed by at most one machine; No waiting constraint: Jobs must be processed continuously between machines in the factory, with no intermediate waiting time; Initial setup time constraint: The setup time for the first job in each factory on the first machine is zero. S1.3, Construct optimization objectives; Maximum completion time Cmax = maxC l end C l end Let Ttot be the completion time of the last operation in factory Fl. Total machine downtime Ttot = Σ l=1 f Σ i=1 m T l.i idle T l.i idle This refers to the total idle time of machine Mi in all operation processes of factory Fl, including setup time and waiting time.

3. The distributed workflow scheduling method based on a large model-assisted multi-objective optimization algorithm according to claim 1, characterized in that, In step S2, the specific operations for population initialization are as follows: S2.1, the chromosome encoding of an individual is a one-dimensional integer array X=[x1, -1, x2, -1, ..., xf], where xl represents the job processing sequence of factory Fl, and each job Jj is represented by a unique integer identifier, with "-1" used only as an identifier separator; S2.2, generate a random number Prand between (0,1). If Prand>0.5, the individual is initialized using a greedy algorithm based on Cmax; if Prand<0.5, the individual is initialized using a greedy algorithm based on Ttot. S2.3, Initialize the population using a greedy strategy; a) The greedy initialization based on Cmax has the following operations: randomly shuffle all job sequences to generate Xshuffled; initialize the current completion time C of each factory. l current =0, for each job Jj in Xshuffled, find the one that satisfies l * =arg min l C l current Factory l inserts job Jj into the job processing sequence of factory l; b) The greedy initialization based on Ttot has the following operation form: randomly shuffle all job sequences to generate Xshuffled; for each job Jj in Xshuffled, find the factory l with the minimum SDST time required to process job Jj, and insert job Jj into the job processing sequence of factory l.

4. The distributed workflow scheduling method based on a large model-assisted multi-objective optimization algorithm according to claim 1, characterized in that, In step S3, population evolution, that is, the crossover and mutation operations of the population, is mainly achieved by using prompt words with the help of a large model; First, the information such as the task allocation, task sequence, and corresponding objective function value of individual solutions in the population is encoded into a natural language format suitable for large language model processing; Then, construct a prompt word that includes the following four parts: a) Problem definition and solution representation: The DHNPFSP-SDST problem is described in detail, the parameters such as the number of factories and the number of jobs are clarified, the solution is specified to be encoded using a one-dimensional integer array, with "-1" as the factory job sequence separator, and the optimization objectives of minimizing the maximum completion time (Cmax) and minimizing machine downtime (Ttot) are clearly defined. b) Input Solution Example Section: Select several solutions from the current population, encode them in integer array form, and provide the Pareto level, completion time of each factory, total machine turnaround time of each factory and other attribute values ​​of each solution to the large model as context learning material to help the large model understand the relationship between solution structure and optimization objective; c) Evolutionary Operation Instructions: This section provides explicit instructions to the large model, guiding it to perform parent selection, crossover, and mutation operations. Parent selection requires the large model to randomly select diverse parent solutions from the current population. Crossover instructions require the large model to choose one of three crossover operators: CrO1, CrO2, and CrO3. CrO1 retrieves the completion time list of each factory in the two parent solutions, finds the factory index corresponding to the maximum value, and swaps the job sequences of that factory in the two parent solutions. CrO2 retrieves the total SDST list of each factory in the two parent solutions, finds the factory index corresponding to the maximum value, and swaps the job sequences of that factory in the two parent solutions. CrO3 performs multi-point crossover on the encoding of the two parent solutions, i.e., randomly selects multiple crossover points and swaps the encoding fragments between the crossover points to generate new offspring encodings. The mutation operation instruction requires the large model to select one of three mutation operators, M1, M2, and M3, to execute. M1 randomly selects two elements in the code and swaps their positions; M2 selects any interval in the code and reverses the order of the elements in that interval; M3 selects any two factory operation sequences in the code and swaps them. d) Output validity verification: The large model is required to verify the generated new solutions, ensuring that the new solutions conform to the specified encoding format, do not involve duplicate work, and satisfy all constraints of the DHNPFSP-SDST problem. If any new solutions do not meet the requirements, they are modified until they do. Simultaneously, a pre-defined number of valid solutions are returned in integer array format for direct integration into the next generation population of the NSGAII algorithm. Finally, the constructed prompt words are input into the large model. Based on its own pre-trained knowledge and inference algorithm, the large model performs crossover and mutation operations according to the prompt word requirements to generate new individual solutions.

5. A multi-objective optimization method with large language model assistance for solving the distributed heterogeneous flow shop scheduling problem considering sequence dependency setting time, as described in claim 1, is characterized in that... In step S5, the archive of non-dominated solutions is updated. That is, after each evolution, it is necessary to check whether the newly generated solutions update the archive, and the following three criteria must be met: a) If the newly generated solution completely dominates a solution in the archive, then delete the dominated solution from the archive and add the newly generated solution to the archive; b) If the newly generated solution forms a non-dominant relationship with all solutions in the archive, then add the newly generated solution to the archive; c) If the newly generated solution is dominated by a solution in the archive, then no update is performed.

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