A human-machine dual-resource collaborative workshop flexible scheduling method based on an industrial knowledge graph

Abstract

The application discloses a kind of based on industrial knowledge graph man-machine dual resource coordination workshop flexible scheduling method.First, the workshop scheduling knowledge graph of fusing workpiece, process, machine, worker entity and its associated relationship is constructed, to provide structured semantic constraint support for decoding process.Further, a kind of dual population collaborative evolution framework is designed, wherein global population focuses on convergence, and local population protects isomeric solution through decision space niche to maintain diversity.In the evolution process, the adaptive knowledge transfer mechanism based on the edge weight change of knowledge graph is introduced, and the information exchange between populations is dynamically adjusted.The output Pareto optimal solution set is fed back to the knowledge graph as scheduling experience, to enhance the weight of high-quality resource path.The application combines physical constraint modeling and scheduling knowledge accumulation, significantly improves the search efficiency and solution quality in huge solution space, and can effectively obtain collaborative optimization scheduling scheme considering maximum completion time, total cost and total carbon emission.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing technology, specifically relating to production scheduling and optimization in industrial engineering, and particularly to a flexible scheduling method for human-machine dual-resource collaborative workshops based on industrial knowledge graphs. Background Technology

[0002] In the context of intelligent manufacturing and Industry 4.0, flexible job shop scheduling is a core element in improving production efficiency and achieving green manufacturing. Currently, with the increasing complexity of manufacturing systems, the scheduling problem has expanded from the traditional single-resource constraint to the dual-resource constraint multi-speed green flexible job shop scheduling problem (DRCFJSP), which simultaneously considers machines, workers, and processing speed. This problem not only requires allocating suitable machines and workers capable of operating them to each process, but also selecting processing speeds and simultaneously optimizing multiple conflicting objectives, such as maximum completion time, total cost, and total carbon emissions. It includes the classic job shop scheduling problem (JSP) as a special case, and the JSP has been proven to be NP-hard. With the addition of flexibility (multiple machine selection), dual resources (human + machine), multiple speeds, and multiple objectives, the solution space explodes exponentially. This type of problem has extremely high combinatorial complexity and is an NP-hard problem. Its decision variables include process sequencing, machine selection, worker selection, and speed selection, resulting in an extremely large solution space. Therefore, it is impossible to find a globally optimal solution within a reasonable time.

[0003] Existing scheduling optimization methods have significant shortcomings when dealing with DRCFJSP, mainly in the following three aspects: 1. Traditional heuristic rules: These methods rely on simple, fixed priority rules for immediate decision-making, resulting in a "short-sighted" flaw. They cannot predict the competition for resources (machines / workers) in subsequent processes, the sudden changes in energy consumption caused by speed switching, or the cumulative effect of carbon emissions. When multiple objectives conflict, they are prone to bias towards a single objective and getting trapped in local optima, making it difficult to obtain high-quality solutions. 2. Standard multi-objective evolutionary algorithms: Although these algorithms have global search potential, their general design is seriously out of touch with the specific structure of DRCFJSP. Standard genetic operators such as crossover and mutation lack an understanding of the physical constraints and decision-making logic of the scheduling problem (they do not understand "process sequence constraints" or "resource compatibility," and the offspring often violate process logic after crossover. Mutation may randomly change the speed level, disrupting the energy efficiency-time balance). They are unable to effectively utilize the domain knowledge of the problem, resulting in low search efficiency, slow convergence speed, and unstable solution quality, making it difficult to balance convergence and solution diversity. 3. Lack of structured knowledge representation and reuse mechanisms: Existing models typically treat resources such as processes, machines, and workers as isolated data points, ignoring the rich semantic relationships and dynamic constraints between resources. Due to the lack of effective knowledge representation and reasoning tools (such as knowledge graphs), the algorithm cannot efficiently reason about the multi-dimensional constraint network composed of "machine-worker-process," nor can it transform the high-quality scheduling patterns accumulated in historical optimization into reusable prior knowledge. This results in a blind search process with poor adaptability, making it difficult to cope with dynamic and ever-changing flexible production environments.

[0004] Therefore, there is an urgent need for a new optimization method that can deeply integrate domain knowledge and achieve efficient search and decision-making collaboration in order to systematically solve this problem and provide enterprises with a set of Pareto optimal scheduling schemes that take into account completion time, total cost and total carbon emissions. Summary of the Invention

[0005] To address the above technical problems, this invention proposes a flexible scheduling method for human-machine dual-resource collaborative workshops based on industrial knowledge graphs, comprising: S1. Obtain the workshop instance data to be scheduled, including the workpiece's process priority, process-machine processing constraint matrix, worker-machine operation permission matrix, and set the genetic algorithm parameters: population size, maximum number of function evaluations, and niche radius; S2. Based on process priority, worker-machine operation permission matrix, and process-machine processing constraint matrix, construct a workshop scheduling knowledge graph. With workpieces, processes, machines, and workers as nodes, establish edges between operable worker-machine node pairs, between processable process-machine node pairs, and between adjacent process nodes of the same workpiece. Create resource attributes for nodes, including idle power of machine nodes and unit labor cost of worker nodes. Create object attributes for edges, including processing time and instantaneous power of processes at different speeds on different machines. S3. Based on the constraints of the workshop scheduling knowledge graph and individual encoding rules, initialize a global population P1 and a local population P2 of size N. Each individual in the population is encoded by a gene vector of the same value range length, as follows: The process ordering vector is used to represent the priority of each process for each workpiece; Machine selection vector is used to select the processing machine for each process step; The worker selection vector is used to select operators for the machines assigned to a process. The speed selection vector is used to select the processing speed level for the corresponding process on the selected machine; S4. Decode and simulate scheduling of individuals through semantic retrieval based on the workshop scheduling knowledge graph, including: performing sorting operation on the process sorting vector to obtain the process priority sequence; according to the priority sequence, and based on the node paths connected by edges provided by the workshop scheduling knowledge graph, selecting machines, workers and speed levels for each process in sequence; under the premise of satisfying process priority constraints and machine health and worker attendance status constraints, using an active scheduling strategy to simulate scheduling of all processes of the individual, obtaining the start time and completion time of each process of the individual; and calculating the three target values ​​of maximum completion time, total cost and total carbon emissions based on the simulation results. S5. For individuals in the global population P1, the final fitness is calculated using the strength value based on the dominance relationship and the decision space density; for individuals in the local population P2, the dominance relationship is calculated using the niche radius constraint based on the Euclidean distance of the decision space encoding vector, so as to retain heterogeneous individuals with similar target performance but different resource utilization patterns. S6. When the maximum number of function evaluations is not reached, the global population P1 and the local population P2 perform an evolutionary cycle: parent selection is performed based on the fitness of individuals selected from the global population P1, and individuals with lower fitness enter the mating pool; parent selection is performed based on the dominance relationship of individuals selected from the local population P2, and individuals that dominate other individuals enter the mating pool. Genetic operations are performed on the two parent individuals to generate two offspring individuals, and S4 and S5 are called on the offspring individuals to complete decoding and fitness evaluation. Based on the migration probability p migrateElite individuals in the global population P1 are migrated to the local population P2, and exploratory individuals in the local population P2 with crowded decision spaces are migrated to the global population P1; the migration probability p migrate The weights are dynamically adjusted based on the update frequency of the edge weights in the workshop scheduling knowledge graph. The SPEA2 environment selection strategy was adopted in the global population P1, the offspring population and the merged population of exploratory individuals migrating from the local population P2, respectively. The Epsilon non-dominated sorting and double crowding control strategy was adopted in the local population P2, the offspring population and the merged population of elite individuals migrating from the global population P1, respectively, to construct a new generation of global population P1 and local population P2. S7. Output the non-dominant individuals in the local population P2 at the time of termination as the final solution set, and give their maximum completion time, total cost and total carbon emission index values. Identify the high-frequency and high-performance process-machine-worker combinations in the final solution set to improve the weight of the corresponding relationship edges in the workshop scheduling knowledge graph.

[0006] Further, in step S1, and in step S3, the gene vector of the individual is... The total length is 4*J, where J is the total number of processes. , , , All are real number vectors of length J and value range [0,1], corresponding to the process sorting vector, machine selection vector, worker selection vector and speed selection vector, respectively.

[0007] Furthermore, in step S2, high-frequency process-machine-worker combinations are statistically analyzed based on historical high-quality scheduling schemes, and the initial weight of the corresponding relationship edge is set to a preset weight value higher than that of other ordinary edges. In step S3, the relevant encoding dimensions of some individuals are biased and initialized using edges in the workshop scheduling knowledge graph that have a weight ranking greater than a preset proportion. For process-machine-worker combinations in the workshop scheduling knowledge graph that have an edge weight ranking greater than a preset proportion, the encoding values ​​of the relevant dimensions are biased and sampled so that the frequency of this type of path in the initial population is higher than that of uniform random sampling.

[0008] Further, in step S4, the decoding process specifically includes: The process sorting vector in the encoding vector Convert to a global priority sequence π for the process; For each process in sequence π, the set of available machines is determined by querying the machine-processable relationships associated with that process in the workshop scheduling knowledge graph, and then based on the machine selection vector... The value is used to select a machine; After selecting a machine, the set of workers capable of operating the machine is determined by querying the worker-operable machine relationships associated with that machine in the workshop scheduling knowledge graph, and then based on the worker selection vector. Select a worker from the values; Select vector based on velocity The value is used to select a processing speed for the process on the selected machine; Based on the global priority sequence π of the process, the selected machine, worker and speed, the start time and completion time of each process are determined through active scheduling simulation, and a complete feasible scheduling scheme is generated. Process O ij The start time is , Let j-1 be the completion time of the process for workpiece i. It is agreed that the completion time of the -1st process for each workpiece is 0; FT M [k] represents the earliest available time for machine k; FT W [l] represents the earliest available time for worker l; Process O ij The completion time is , For process O ij The completion time for processing at speed s on machine k; Update the next available time for the relevant machines and workers as follows: , ; Maximum completion time is This refers to the time of the last completed process in the entire production batch. Total cost includes the sum of machine operating costs calculated based on machine usage time, labor costs calculated based on worker occupancy time, and energy costs calculated based on energy consumption. Total carbon emissions are calculated using the following formula or its equivalent: the summation of the products of the processing time of all processes at the selected machine and speed level and the corresponding unit power carbon emission factor over the entire scheduling cycle.

[0009] Further, in step S5: For individuals in the global population P1, the final fitness F(i) is calculated using the strength value of dominance relations and the density of the decision space: Where D(i) is the density information based on K nearest neighbors (K=1), and R(i) is the initial fitness of an individual, which is the sum of the strengths of all other individuals that dominate individual i: ; The condition for individual i to dominate individual j is that individual i is not inferior to individual j in all objectives, and is strictly superior to j in at least one objective; When calculating dominance relationships for individuals in the local population P2, using a niche radius constraint based on the Euclidean distance of the decision space encoding vector: If individual i is not inferior to individual j on all objectives, and the Euclidean distance between the decision space encoding vectors of individuals i and j is less than the preset niche radius. If so, then individual i dominates individual j in a local sense.

[0010] Further, in step S6, the migration probability p migrate The dynamic adjustment rule is as follows: The weights of the edges in the workshop scheduling knowledge graph are dynamically adjusted based on their overall change. When the overall change in the weights of the edges in the workshop scheduling knowledge graph exceeds a preset threshold, p is increased. migrate When the change is lower than a preset threshold, decrease p. migrate .

[0011] Further, in step S6: The SPEA2 environment selection strategy is adopted, which includes ranking candidate individuals by strength and measuring their crowding. Individuals located on the Pareto front and evenly distributed in the decision space are preferentially retained. The crowding of the decision space is combined with truncation and filling until the number of individuals is N. Truncation refers to removing the most crowded individual among the candidate individuals, and filling refers to selecting individuals with the highest difference between fitness and the harmonic average crowding of the decision space from the dominated solutions. An Epsilon non-dominated sorting and dual crowding control strategy is adopted, which includes performing non-dominated sorting on the merged population to obtain the first non-dominated front solution set. From the remaining individuals excluding the first non-dominated frontier, select those that meet the following criteria: Individuals with approximately non-adverse conditions, the The approximate non-dominated condition is: there is no individual in the first non-dominated front that allows for all objectives. Even after the proportions are relaxed, the individual can still be controlled. The first non-dominated front solution set is combined with the... A temporary population is obtained by merging approximately non-dominant individuals; When the number of individuals in the temporary population exceeds the preset size, the crowding degree is calculated based on the nearest neighbor distance between the target space and the decision space, and the two crowding degrees are normalized and fused to obtain the comprehensive crowding degree. The individual with the smallest comprehensive crowding degree is removed cyclically until the preset size is met. When the number of individuals in the temporary population is less than the preset size, the remaining individuals that were not selected are supplemented to the preset size according to the rule of prioritizing non-dominant frontier level and sparser decision space.

[0012] Further, in step S7, the specific operation of enhancing the weights is as follows: for specific machine-worker-process combinations that frequently occur in the Pareto optimal solution set, count the occurrence frequency of each edge in the Pareto optimal solution set, denoted as... Update the weights of the corresponding edges in the workshop scheduling knowledge graph according to the following formula: In the formula, The knowledge reward factor is set to 0.5. The size of the Pareto optimal solution set. The edge weights before the update. This represents the updated edge weights.

[0013] Furthermore, during the initialization in step S3, a roulette wheel selection strategy based on edge weights is used to select the next node.

[0014] Compared with the prior art, the beneficial effects of the present invention are: By implicitly reflecting the differences in resource paths of different scheduling schemes in the graph through real-number encoding differences, it can effectively identify and protect high-quality heterogeneous solutions with similar target performance but different resource allocation patterns, thereby enhancing the algorithm's ability to cope with multimodal optimization problems.

[0015] By dynamically adjusting the migration probability between populations based on changes in knowledge graph weights, information exchange is strengthened when exploring new regions, while independent search is maintained when developing stable regions. This intelligently balances "exploration" and "development," improves global optimization efficiency, and avoids premature convergence.

[0016] The optimal solution obtained through optimization is fed back into the knowledge graph as experience, reinforcing the weight of high-quality resource paths. When faced with new tasks, the system can prioritize the use of these accumulated "golden paths" for initialization, significantly accelerating convergence and enabling self-learning and continuous optimization.

[0017] By using knowledge graphs to simultaneously achieve "hard" encoding of physical constraints and "soft" memorization of optimization patterns, the system can ensure the feasibility of scheduling schemes while accumulating and adapting to efficient production logic, thereby significantly improving its adaptability to multi-batch, variable-parameter production tasks and overall scheduling performance. Attached Figure Description

[0018] Figure 1 This is a flowchart of the present invention; Figure 2 This is the Gantt chart of the final optimized solution based on the algorithm of this invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0020] This invention provides a flexible scheduling method for human-machine dual-resource collaborative workshops based on industrial knowledge graphs. For example... Figure 1 As shown, this method deeply integrates semantic modeling of knowledge graphs with a dual-population co-evolutionary algorithm. Through a closed loop of "hard constraint encoding - co-optimization - knowledge feedback", it efficiently solves the scheduling problem of green flexible workshops with dual resource constraints and multiple rotation speeds.

[0021] The steps of the method of the present invention will be described in detail below with reference to a specific embodiment.

[0022] Step S1: Encoding and Parameter Settings First, we define the scheduling problem model to be solved. The dual-resource-constrained multi-speed green flexible job shop scheduling problem (DRCFJSP) aims to allocate appropriate machines, workers, and processing speeds to a set of jobs containing multiple processes, with the objective of minimizing a three-objective vector. ,in: (1) Indicates the maximum completion time (Makespan): ,in It is the completion time of the j-th process of workpiece i. This refers to the time taken for the final step in a production batch. Suppose there are j workpieces to be produced. Workpieces 1 through j-1 are completed within one hour, but workpiece j requires 10 hours. Therefore, the entire batch of work in the workshop is not finished within one hour, but rather delayed until 10 hours. The goal is to pinpoint the final step in the entire production batch and bring it forward as early as possible. Minimizing this value means shortening the overall production cycle and improving production efficiency.

[0023] (2) Total Cost: In the formula, This represents the total machine cost, of which The total working hours of machine k. Let k be the processing cost per unit time for machine k; This represents the total labor cost, of which For workers l Total working hours For workers l The unit time cost; This represents the total energy cost, of which For electricity prices.

[0024] (3) Total Carbon Emission: ,in As a carbon emission factor, Total energy consumption.

[0025] Total energy consumption In the formula, Total processing energy consumption, of which For process O ij The processing time on machine k at speed s. For process O ij The instantaneous power processed at speed s on machine k; Total idle energy consumption, of which Let be the idle power of machine k.

[0026] Define the core encoding method of the algorithm. A feasible scheduling scheme (i.e., an individual) is encoded as a real vector X of length 4*J (where J is the total number of operations), with the following structure: In the formula, Corresponding process sorting vector, The corresponding machine selects the vector. Corresponding worker selection vector The corresponding velocity selection vectors are all real subvectors of length J with a value range of [0,1].

[0027] At the same time, the algorithm parameters are set, including population size N=100, maximum function evaluation times maxFE=50000, and niche radius. =0.1 etc. The niche radius is a distance threshold in the normalized objective space. If the distance between two solutions in the normalized three-objective space is ≤0.1, they are considered too close and a diversity penalty is required.

[0028] Step S2: Construct a multi-dimensional knowledge graph for workshop scheduling Before the algorithm starts, a workshop scheduling knowledge graph is constructed based on the production tasks to be processed and resource constraints. This knowledge graph uses workpieces, processes, machines, and workers as core entities, resource attributes (such as energy consumption factors and processing unit prices) as data attributes, and "process sequence relationships," "machine processability relationships," and "worker-operable machine relationships" as object attributes, forming a multi-dimensional semantic network. This graph provides structured semantic support for subsequent decoding and evaluation.

[0029] This step uses a graph theory-based algorithm to parse and instantiate the input scheduling instance data. The input data typically includes a worker-machine operation permission matrix (as shown in Table 1.1) and a process machine processing constraint matrix (as shown in Table 1.2). The construction process is as follows: S21. First, initialize an empty directed attribute graph G=(V,E). V is the set of nodes, containing four core entities: workpiece, process, machine, and worker. E is the set of edges, representing the semantic relationships between entities and carrying attribute information. S22. Node Instantiation and Attribute Injection: Traverse the machine node set M, worker node set W, workpiece node set J, and process node set O, create a corresponding node for each machine, and define its static data attribute: machine idle power. The unit time processing cost of machine k Create a corresponding node for each worker and define its static data attribute: the worker's unit hourly cost. Create a workpiece node for each workpiece, and a process node for each process.

[0030] S23. Edge generation for resource matching relationships: Analyze the worker-machine operation permission matrix (Table 1.1). If the elements in the matrix... Then at the worker node With machine nodes Establish a directed edge between the worker and the machine, allowing the worker to operate the machine. Initialize the edge weight to 1.0, indicating that the operation is feasible. Analyze the machine processing constraint matrix for each process (Table 1.2). If the process... Available in machine If the upper processing (i.e., the corresponding value of the matrix is ​​1) is then established point to The machine can process a directed edge, and the edge is associated with an attribute list containing the processing time of the process at different speeds s of machine k. and instantaneous power .

[0031] Edge weights: During the first run of the algorithm, the weights of all resource matching edges in the workshop scheduling knowledge graph are initialized to the baseline value. After the algorithm terminates, iterate through the final output set of Pareto optimal solutions. Each "worker" in the statistical solution set Operating the machine "relationship side" The number of times it appears is denoted as Update the weights of the corresponding edges in the workshop scheduling knowledge graph according to the following formula: In the formula, The knowledge reward factor is set to 0.5. This represents the size of the Pareto solution set. The physical meaning of this formula is: the higher the probability of a resource combination appearing in the optimal solution set, the greater the weight increment it receives. The edge weights before the update. This represents the updated edge weights.

[0032] When using the workshop scheduling knowledge graph to guide population initialization, this invention abandons the traditional "completely random selection" and instead adopts a "weighted roulette wheel selection strategy," specifically implemented as follows: When the decoding process requires a certain machine... When assigning a worker, the first step is to query the workshop scheduling knowledge graph to obtain relevant information. All connected feasible worker sets and the corresponding edge weights Next, calculate the probability of each worker being selected. The formula is: Finally, a random number in the interval [0, 1] is generated. The final worker is determined based on the cumulative probability distribution.

[0033] S24. Edge generation of process sequence relationships: Based on the process route constraints of the workpiece, for the same workpiece... Adjacent processes within and Establish a directed edge of type process sequence to establish topological order constraints during decoding.

[0034] Through the above procedural steps, the originally discrete two-dimensional matrix data is transformed into a knowledge graph with explicit topological structure and semantic attributes, enabling the decoder to quickly obtain the set of optional resources and corresponding physical parameters for any process in subsequent steps through graph traversal algorithms (such as neighbor node query).

[0035] in: a. Entities, including: Jobs: such as J1, J2, J3, J4, J5, J6, J7, J8, J9, J10.

[0036] Operations: such as O11, O12... O106.

[0037] Machines: such as M1, M2, M3, M4, M5, M6.

[0038] Workers: such as W1, W2, W3, W4, W5.

[0039] Performance metrics (Objectives): (Completion time) (cost), (Carbon emissions).

[0040] b. Relations, including: Process sequence relationship: (O ij )--[Next_Op]-->(O i,j+1 ).

[0041] Resource matching relationships: (Machine)--[Operable_By]-->(Worker); (Op)--[Can_Be_Processed_On]-->(Machine).

[0042] Real-time state relationship: (Machine)--[Has_Idle_Power]-->(Value).

[0043] Step S3: Population Initialization Initialize two independent populations: a global population P1 and a local population P2, each with a size of N. Individuals are generated by randomly generating real number vectors X that meet the range requirements. To improve the quality of the initial solution, the generation of some individuals can be guided by historical high-quality paths with higher weights in the workshop scheduling knowledge graph (such as the "M3-W3" combination).

[0044] Step S4: Decoding and Evaluation This step uses a decoder based on semantic retrieval from a workshop scheduling knowledge graph to map the encoded vector X into an executable scheduling plan and a sequence of process priorities. And calculate its three target vector values: a. Process sorting decoding (OS): This is achieved through the argsort operation. Convert to global priority sequence , For example, if = [0.8, 0.2, 0.9], then = [1, 0, 2] means that process 1 has the highest priority, followed by process 0, and then process 2.

[0045] b. Resource and speed selection decoding (MA, WA, SS): When allocating machines and workers, the decoder performs semantic constraint retrieval by accessing a pre-built knowledge graph.

[0046] Machine selection semantic verification: By retrieving the directed edge [(Op)--[Can_Be_Processed_On]-->(Machine)] in the workshop scheduling knowledge graph, all possible machine sets for the current process are automatically identified.

[0047] Dual-resource coupling verification: After selecting a machine, the directed edges [(Machine)--[Operable_By]-->(Worker)] in the shop floor scheduling knowledge graph are further retrieved to ensure that the assigned worker has the legal qualifications to operate the specific machine. This retrieval process is essentially a search of directed edges in the shop floor scheduling knowledge graph that sequentially connect process, machine, and worker nodes [(Op)-[Can_Be_Processed_On]->(Machine)-[Operated_By]->(Worker)]. Only when the path formed by the directed edge exists in the shop floor scheduling knowledge graph topology and its "state attributes" (such as machine health and worker attendance status) are available, is the path formed by the directed edge (also known as the assignment decision) approved.

[0048] This retrieval method based on the knowledge graph relationship of workshop scheduling eliminates the possibility of generating "infeasible solutions" from the logical source, ensuring that the random values ​​generated by the genetic operator after mutation can always be mapped to the physical real resource combination.

[0049] For priority sequence The j-th process (global index j) in the process, after retrieval, yields the following optional set: Machine (MA): ,in Let k be the number of available machines for process j, and k be the index of the selected machine.

[0050] Worker (WA): ,in Let l be the number of available workers for process j on machine k, and l be the index of the selected worker.

[0051] Speed ​​(SS): ,in Let be the number of selectable speeds for process j on machine k, and s be the index of the selected speed.

[0052] c. Active scheduling simulation: according to Priority scheduling of each process O ij (It selects machine k, worker l, and speed s), and the decoder uses an active scheduling generation strategy to calculate O for each process. ij Start time S ij Completion time C ij : Start time S ij : , ( It is agreed that the completion time of the -1st process of each workpiece is 0, indicating that the first process has no predecessor constraints. Completion time C ij : ; FT M [k]: Earliest available time for machine k; FT W [l]: The earliest available time for worker l; Process O ij The completion time.

[0053] Resource Update: , .

[0054] d. Target value calculation: After the scheduling simulation is completed, the target value is calculated according to the formula. Priority order scheduling of all processes O ij The three objective values ​​f of the composed scheduling scheme 1 ,f 2 ,f 3 .

[0055] Step S5: Calculate fitness A fitness assessment strategy based on SPEA2 was adopted, but the two populations were differentiated: For an individual i in population P, the strength S(i): In the formula, S(i) represents the number of individuals controlled by i. This means that i is no worse than j on all objectives, and is strictly better than j on at least one objective. Dominate .

[0056] Domination means that if all the objective solutions of a feasible individual are not inferior to all the objective solutions of another individual, and the feasible individual is superior to the other individual in at least one objective, then the individual dominates the other individual. Non-dominance means that if there is no situation where one individual dominates another individual, and one individual is inferior to another individual in at least one objective and the other individual is inferior to one individual in at least one objective, then the relationship between the two individuals is said to be non-dominant. The fitness (Normal) of the global population P1: Calculate the initial fitness R(i) of an individual, which is the sum of the strengths of all other individuals that dominate individual i: Final fitness F(i): , where D(i) is based on the density information of K nearest neighbors (K=1), used to distinguish individuals with the same R(i). The smaller, the better. The fewer individuals that control it, The better. When multiple individuals have the same (As they are all on the Pareto frontier), through Prioritize retaining individuals in sparse regions to avoid unpacking and clustering. Smaller individuals are generally better; Fitness of the local population P2 (LocalC): To protect the diversity of the decision space when calculating R(i), a decision space niche mechanism is introduced: If and only if The condition for determining whether individual i dominates individual j in a local sense is: i is not inferior to j on all objectives and the Euclidean distance between their decision space encoding vectors is equal. .

[0057] in, It is the Euclidean distance between the decision vectors. It is the radius of the niche habitat.

[0058] When calculating the distance between individuals in the decision space, the similarity of the graph structure is implicitly represented by the differences in real-number encoding. Since each scheduling scheme corresponds to a semantic path in the pre-constructed workshop scheduling knowledge graph, consisting of specific resource nodes (machines, workers) and process nodes, the Euclidean distance in the encoding space... This actually reflects the degree of overlap in the topological structure of the workshop scheduling knowledge graph across different schemes. Since the real vectors of different individuals correspond to drastically different node connection orders in the graph, the Euclidean distance in the encoding space... This actually reflects the non-overlapping degree of scheduling logic on resource occupation paths. This ensures that the local population P2 can protect "heterogeneous solutions" that, although similar in performance, are completely different in resource utilization patterns (i.e., the topological subgraph of the workshop scheduling knowledge graph), thus effectively addressing the challenges of multimodal optimization.

[0059] This multimodal evaluation method based on knowledge association mapping enables the algorithm to effectively protect and maintain multiple distinct high-quality production modes in a complex solution space through numerical evolution without increasing additional graph computation overhead.

[0060] Step S6: Evolutionary Cycle Set up a loop that repeats the following sub-steps until the function evaluation count has not reached maxFE: Step S6.1: Selection of mating pool A tournament selection process is performed on the global population P1 and the local population P2 respectively. Several individuals are randomly selected each time. Individuals selected from the global population P1 with lower fitness are entered into the mating pool. Individuals selected from the local population P2 that dominate other individuals are also entered into the mating pool. A set of parent individuals for reproduction is then selected.

[0061] Step S6.2: Genetic Operator The parent individuals selected from the global population P1 and the local population P2 are subjected to operation operators to generate offspring sets Offspring1 and Offspring2. The offspring are then decoded in step S4 and evaluated in step S5 to transform them into feasible scheduling schemes, and the three objective values ​​are calculated. The operation operators include crossover and mutation.

[0062] Step S6.3: Guiding Knowledge Transfer This step enables adaptive information exchange between populations: Select the elite individuals with the lowest fitness from P1; Select the most crowded (i.e., most exploratory potential) individual from P2 in the decision space (encoding vector); Based on the dynamic migration probability p migrate Perform the exchange of the aforementioned individuals. migrate The system adaptively adjusts the weights of the "resource-process" edges in the workshop scheduling knowledge graph based on their update frequency. When the update frequency of the workshop scheduling graph is high (drastic changes), it indicates that the system is in the exploratory phase, and the weights should be increased accordingly. This forces the global population P1 and the local population P2 to frequently exchange "exploration individuals" and "elite individuals" to prevent either population from getting stuck in a local optimum. When the graph update frequency is low (stable), it indicates that the system has entered the development phase, at which point the frequency should be reduced. This reduces external interference and allows each subpopulation to conduct refined searches within its designated advantageous area.

[0063] In the process of co-evolution between two populations, this invention introduces an adaptive migration mechanism based on the evolutionary density of the workshop scheduling knowledge graph. The migration probability p is defined as follows: migrate This probability is used to control the frequency of individual exchange between the global population P1 and the local population P2. It is dynamically adjusted by monitoring the update frequency of edge weights in the shop floor scheduling knowledge graph: when the weight distribution representing "resource-process" associations in the shop floor scheduling knowledge graph undergoes a drastic change, it indicates that the system is in a critical period of exploring new search areas, and at this time, p is automatically increased. migrate To enhance knowledge flow between populations and prevent local traps; conversely, when weights tend to stabilize, the migration probability is reduced to maintain the independent development capabilities of each subpopulation.

[0064] This mechanism, which adjusts the migration intensity through feedback from the workshop scheduling knowledge graph, ensures the algorithm's search flexibility in complex solution spaces.

[0065] The above-mentioned introduction of workshop scheduling knowledge graph evolution momentum As a quantitative measure of "update frequency", "drastic change", and "stability", it is used to characterize the update status of knowledge in the workshop scheduling knowledge graph.

[0066] 1. Quantitative measurement standards: The update frequency (i.e., evolutionary momentum) of edge weights in a workshop scheduling knowledge graph is defined as the relative rate of change of the total weights of the knowledge graph between two adjacent generations. Let the sum of all edge weights in the t-th generation workshop scheduling knowledge graph be... Then the formula for calculating the evolutionary momentum of generation t is: .

[0067] That is, the cumulative weight of all "worker-machine" and "process-machine" related edges in the graph. Formula expression: in: : Represents the set of all edges in the graph that have "learning ability", specifically referring to the two types of edges: (Machine)-[Operable_By]->(Worker) and (Op)-[Can_Be_Processed_On]->(Machine).

[0068] : indicates the first At that time, a certain edge The current weight value.

[0069] "Abrupt Change" Criterion: Setting Evolutionary Thresholds =0.05. When The workshop scheduling knowledge graph is determined to be in a state of "drastic change". Physically, this means that the algorithm is discovering a large number of new high-quality resource combinations (Pareto solutions), and the structure of the workshop scheduling knowledge graph is undergoing rapid reorganization.

[0070] "Stability" standard: when At this point, the workshop scheduling knowledge graph is determined to be in a "stable" state. This means that high-quality machine-worker paths have basically converged, and the increase in weight only comes from repeated confirmation of known paths, indicating that the structure of the workshop scheduling knowledge graph is becoming solidified.

[0071] 2. The mapping between the relationship of "update frequency", "drastic change", and "stability" and the transition probability: transition probability The update frequency (evolutionary momentum) of the workshop scheduling knowledge graph They show a positive correlation. The specific relationship is defined using the Sigmoid function or a linear mapping function: Step S6.4: Environment Selection This step selects a new generation of individuals from the merged population.

[0072] Environment Selection 1 (Global): Merge the original global population P1, the two offspring populations (Offspring1, Offspring2), and the explorers migrating from the local population, and execute multi-objective environment selection strategy 1 (environmental_selection_1). This selection is based on the R value of SPEA2 and truncates the decision space based on its crowding, generating a new generation P1. This maintains global convergence and the diversity of the decision space.

[0073] R-value calculation: Calculating merged populations The fitness R(i).

[0074] Extracting the non-dominated solution set: This refers to the first non-dominant frontier in the current merged population.

[0075] if Then execute the following loop to truncate and merge the population: Calculate each individual The distances of K nearest neighbors (K=3) in the decision space (Xi) and .

[0076] Remove the most crowded people .

[0077] Repeat until .

[0078] if Then perform the following operation to populate the merged population: Calculate the average congestion of the decision space harmonics .

[0079] .

[0080] From the perspective of being dominated In the middle, according to Sort, select Individuals are added to make up a total of N individuals.

[0081] Environment Selection 2 (Local): Merge the original local population P2, the two offspring populations (Offspring1, Offspring2), and elite individuals migrated from the global population, and execute multi-objective environment selection strategy 2. This selection is based on Epsilon dominance and truncation combining the dual crowding of the objective / decision space, generating a new generation of P2. This maintains diversity in both local exploration and the objective space.

[0082] Epsilon Dominant Choice: For merged populations Perform a non-dominated sort (NDSort).

[0083] First, take the first non-dominated frontier. .

[0084] Select again Approximate non-dominated solution .

[0085] merge and , .

[0086] if Then execute the following loop to truncate and merge the population: Calculate individuals The distances to K nearest neighbors (K=3) in the target space and .

[0087] Calculate individuals In the decision space, the distances of K nearest neighbors (K=3) and... .

[0088] Calculate the overall congestion level .

[0089] Remove the most crowded people .

[0090] if Then perform the following operation to populate the merged population: From the remaining solutions In the middle, according to Sort by prioritizing those with earlier frontiers and sparser encoding spaces. Individuals are added.

[0091] Step S7: Dynamic feedback of scheduling knowledge After the algorithm terminates, the final Pareto optimal solution set recorded in P2 is fed back to the shop floor scheduling knowledge graph as "empirical knowledge." Each high-quality scheduling pattern (such as a low-energy, high-parallel machine-worker combination) establishes weighted enhanced connections between relevant nodes in the shop floor scheduling knowledge graph. When the system receives a new task, the algorithm prioritizes retrieving high-weight "golden resource paths" (i.e., historically high-performing machine-worker-speed combinations) from the shop floor scheduling knowledge graph and uses them as the prior distribution for population initialization, thus significantly shortening the algorithm's convergence time. This closed-loop mechanism of "algorithm optimization - knowledge accumulation - feedback decision-making" enables the scheduling system to learn, providing more valuable prior knowledge for subsequent similar green and flexible shop floor scheduling tasks.

[0092] Step S8: Output The output local population P2 records the non-dominated solution set throughout the entire evolution process, which is the final Pareto front approximation found by the algorithm, providing users with a set of scheduling schemes that are balanced and optimized in terms of completion time, cost and carbon emissions.

[0093] To verify the effectiveness of the present invention, a comparative experiment was conducted.

[0094] Table 1.1 Worker Machine Operation Authority Matrix Table 1.2 Machining Constraint Matrix As can be seen from Tables 1.1 and 1.2, if the machine selects M1, this list only contains [W5], then regardless of... No matter how the gene changes (0.1, 0.5, 0.9), the result will always be W5.

[0095] If the machine selects M3, then this list contains [W1, W2, W3], then Only a change in the gene (0.1 -> 0.5 -> 0.8) would lead to the selection change from W1 to W2 to W3. Therefore, there will be no infeasible solutions.

[0096] Table 2.1 Optimal scheme for random initialization Table 2.2 Specific steps of the optimal random initialization scheme Based on Tables 2.1 and 2.2, perform f 1 f 2 f 3 Step-by-step calculation and analysis: f 1 The shortest completion time (Makespan) is the latest completion time among all 55 operations after the scheduling simulator runs. Referring to the table above, the completion time of operation J3's O35 is 92, thus yielding f. 1 = = = =92.00.

[0097] According to the above f 2 Total Cost and f 3 The formula for calculating total carbon emissions can be implemented through the following calculation steps: Step 1: Calculate CM (Total Machine Cost) and CW (Total Labor Cost) First, calculate the total processing time for each machine and each worker from the table above. .

[0098] (Total machine hours): M1: 26 (O14+O23+... a total of 11 processes) M2: 70 (O105 + O21 + ... a total of 15 processes) M3: 36 (O11+O12+... a total of 14 processes) M4: 14 (O16 + O106 + ... a total of 5 processes) M5: 8 (O103+O35+O51) M6: 30 (O101+O32+... a total of 10 processes) (Total working hours): W1: 26 (O12+O15+... a total of 8 processes) W2: 24 (O101+O25+... a total of 10 processes) W3: 20 (O11+O22+... a total of 7 processes) W4: 68 (O105+O21+... a total of 17 processes) W5: 46 (O14+O23+... a total of 13 processes) CM= CM=(26*55)+(70*52)+(36*60)+(14*48)+(8*43)+(30*55)=9896 CW= CW=(26*25)+(24*34)+(20*25)+(68*42)+(46*33)=6340 Step 2: Calculation (Total processing energy consumption) = .

[0099] calculate: O11 (M3, S1): O12 (M3, S1): O13 (M3, S2): ... (Do this for all 55 steps) (Total) = 2807.10 Step 3: Calculation (Total idle energy consumption) = Calculation, where : M1: M2: M3: M4: M5: M6: (Total) = 808.24 Step 4: Summarize and calculate f 2 and f 3 TEC (Total Energy Consumption) = =2807.10 + 808.24 = 3615.34 CE (Total Energy Cost) = =2892.27 f 2 (Total Cost) = CM + CW + CE = 9896.00 + 6340.00 + 2892.27 = 19128.27 f 3 (Total carbon emissions) = = =2169.20 Table 3.1 Final solution after algorithm optimization in this invention Table 3.2 Specific steps of the final scheme after algorithm optimization in this invention According to Tables 3.1, 3.2 and Figure 2 f after algorithm optimization 1 f 2 f 3 Step-by-step calculation and analysis: f 1 The shortest completion time (Makespan) is the latest completion time among all 55 operations after the scheduling simulator runs. Looking at the table above, the completion times for operations J10 (O106), J7 (O75), and J8 (O85) are all 38. That is, f1 = = =38.00. f 1 The number of processes decreased from 92 to 38. The algorithm evenly distributed the processes across all 6 machines, achieving a high degree of parallelism.

[0100] b. Based on the above f 2 Total Cost and f 3 The formula for calculating total carbon emissions can be implemented through the following calculation steps: Step 1: Calculate CM (Total Machine Cost) and CW (Total Labor Cost) First, calculate the total processing time for each machine and each worker from the table above. .

[0101] (Total machine hours): M1: 17 (O14+O23+... a total of 13 processes) M2: 38 (O12+O21+... a total of 13 processes) M3: 30 (O11+O15+... a total of 14 processes) M4: 23 (O16+O105+... a total of 8 processes) M5: 1 (O74) M6: 20 (O13+O101+... a total of 12 processes) (Total working hours): W1: 30 (O16+O105+... a total of 9 processes) W2: 12 (O101+O32+... a total of 6 processes) W3: 26 (O11+O15+... a total of 11 processes) W4: 42 (O12+O21+... a total of 16 processes) W5: 19 (O13+O14+... a total of 13 processes) CM= CM=(17*55)+(38*52)+(30*60)+(23*48)+(1*43)+(20*55)=6958 CW= CW=(30*25)+(12*34)+(26*25)+(42*42)+(19*33)=4199 Step 2: Calculation (Total processing energy consumption) = .

[0102] calculate: O11 (M3, S2): O12 (M2, S1): O13 (M6, S2): ... (Do this for all 55 steps) (Total) = 1583.50 Step 3: Calculation (Total idle energy consumption) = Calculation, where : M1: M2: M3: M4: M5: M6: (Total) = 222.64 Step 4: Summarize and calculate f 2 and f 3 TEC (Total Energy Consumption) = =1583.50 + 222.64 = 1806.14 CE (Total Energy Cost) = =1444.91 f 2 (Total Cost) = CM + CW + CE = 6958.00 + 4199.00 + 1444.91 = 12601.91 f 3 (Total carbon emissions) = = =1083.68 Table 4.1 Comparison of solutions before and after algorithm optimization This invention abstracts the complex dual-resource-constraint scheduling process into a path search problem using a workshop knowledge graph. The graph construction before algorithm execution achieves hard modeling of the workshop's physical constraints; the weight feedback after algorithm execution achieves soft memorization of the optimal scheduling logic. This closed loop of "hard constraints + soft memorization" enables the scheduling system to exhibit significant adaptive and learning capabilities when facing flexible production tasks with multiple batches and varying parameters.

[0103] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A flexible scheduling method for human-machine dual-resource collaborative workshops based on industrial knowledge graphs, characterized in that, include: S1. Obtain the workshop instance data to be scheduled, including the workpiece's process priority, process-machine processing constraint matrix, worker-machine operation permission matrix, and set the genetic algorithm parameters: population size, maximum number of function evaluations, and niche radius; S2. Based on process priority, worker-machine operation permission matrix, and process-machine processing constraint matrix, construct a workshop scheduling knowledge graph. With workpieces, processes, machines, and workers as nodes, establish edges between operable worker-machine node pairs, between processable process-machine node pairs, and between adjacent process nodes of the same workpiece. Create resource attributes for nodes, including idle power of machine nodes and unit labor cost of worker nodes. Create object attributes for edges, including processing time and instantaneous power of processes at different speeds on different machines. S3. Based on the constraints of the workshop scheduling knowledge graph and individual encoding rules, initialize a global population P1 and a local population P2 of size N. Each individual in the population is encoded by a gene vector of the same value range length, as follows: The process ordering vector is used to represent the priority of each process for each workpiece; Machine selection vector is used to select the processing machine for each process step; The worker selection vector is used to select operators for the machines assigned to a process. The speed selection vector is used to select the processing speed level for the corresponding process on the selected machine; S4. Decode and simulate scheduling of individuals through semantic retrieval based on the workshop scheduling knowledge graph, including: performing sorting operation on the process sorting vector to obtain the process priority sequence; according to the priority sequence, and based on the node paths connected by edges provided by the workshop scheduling knowledge graph, selecting machines, workers and speed levels for each process in sequence; under the premise of satisfying process priority constraints and machine health and worker attendance status constraints, using an active scheduling strategy to simulate scheduling of all processes of the individual, obtaining the start time and completion time of each process of the individual; and calculating the three target values ​​of maximum completion time, total cost and total carbon emissions based on the simulation results. S5. For individuals in the global population P1, the final fitness is calculated using the strength value based on the dominance relationship and the decision space density; for individuals in the local population P2, the dominance relationship is calculated using the niche radius constraint based on the Euclidean distance of the decision space encoding vector, so as to retain heterogeneous individuals with similar target performance but different resource utilization patterns. S6. When the maximum number of function evaluations is not reached, the global population P1 and the local population P2 perform an evolutionary cycle: parent selection is performed based on the fitness of individuals selected from the global population P1, and individuals with lower fitness enter the mating pool; parent selection is performed based on the dominance relationship of individuals selected from the local population P2, and individuals that dominate other individuals enter the mating pool. Genetic operations are performed on the two parent individuals to generate two offspring individuals, and S4 and S5 are called on the offspring individuals to complete decoding and fitness evaluation. Based on the migration probability p migrate Elite individuals in the global population P1 are migrated to the local population P2, and exploratory individuals in the local population P2 with crowded decision spaces are migrated to the global population P1; the migration probability p migrate The weights are dynamically adjusted based on the update frequency of the edge weights in the workshop scheduling knowledge graph. The SPEA2 environment selection strategy was adopted in the global population P1, the offspring population and the merged population of exploratory individuals migrating from the local population P2, respectively. The Epsilon non-dominated sorting and double crowding control strategy was adopted in the local population P2, the offspring population and the merged population of elite individuals migrating from the global population P1, respectively, to construct a new generation of global population P1 and local population P2. S7. Output the non-dominant individuals in the local population P2 at the time of termination as the final solution set, and give their maximum completion time, total cost and total carbon emission index values. Identify the high-frequency and high-performance process-machine-worker combinations in the final solution set to improve the weight of the corresponding relationship edges in the workshop scheduling knowledge graph.

2. The method according to claim 1, characterized in that, In step S3, the gene vector of the individual is The total length is 4*J, where J is the total number of processes. , , , All are real number vectors of length J and value range [0,1], corresponding to the process sorting vector, machine selection vector, worker selection vector and speed selection vector, respectively.

3. The method according to claim 1, characterized in that, In step S2, high-frequency process-machine-worker combinations are statistically analyzed based on historical high-quality scheduling schemes, and the initial weight of the corresponding relationship edge is set to a preset weight value higher than that of other ordinary edges. In step S3, the relevant encoding dimensions of some individuals are biased and initialized using edges in the workshop scheduling knowledge graph that have a weight ranking greater than a preset proportion. For process-machine-worker combinations in the workshop scheduling knowledge graph that have an edge weight ranking greater than a preset proportion, the encoding values ​​of the relevant dimensions are biased and sampled so that the frequency of this type of path in the initial population is higher than that of uniform random sampling.

4. The method according to claim 1, characterized in that, In step S4, the decoding process specifically includes: The process sorting vector in the encoding vector Convert to a global priority sequence π for the process; For each process in sequence π, the set of available machines is determined by querying the machine-processable relationships associated with that process in the workshop scheduling knowledge graph, and then based on the machine selection vector... The value is used to select a machine; After selecting a machine, the set of workers capable of operating the machine is determined by querying the worker-operable machine relationships associated with that machine in the workshop scheduling knowledge graph, and then based on the worker selection vector. Select a worker from the values; Select vector based on velocity The value is used to select a processing speed for the process on the selected machine; Based on the global priority sequence π of the process, the selected machine, worker and speed, the start time and completion time of each process are determined through active scheduling simulation, and a complete feasible scheduling scheme is generated. Process O ij The start time is , Let j-1 be the completion time of the process for workpiece i. It is agreed that the completion time of the -1st process for each workpiece is 0; FT M [k] represents the earliest available time for machine k; FT W [l] represents the earliest available time for worker l; Process O ij The completion time is , For process O ij The completion time for processing at speed s on machine k; Update the next available time for the relevant machines and workers as follows: , ; Maximum completion time is This refers to the time taken for the last process to be completed in the entire production batch. Total cost includes the sum of machine operating costs calculated based on machine usage time, labor costs calculated based on worker occupancy time, and energy costs calculated based on energy consumption. Total carbon emissions are calculated using the following formula or its equivalent: the summation of the products of the processing time of all processes at the selected machine and speed level and the corresponding unit power carbon emission factor over the entire scheduling cycle.

5. The method according to claim 1, characterized in that, In step S5: For individuals in the global population P1, the final fitness F(i) is calculated using the strength value of dominance relations and the density of the decision space: Where D(i) is the density information based on K nearest neighbors (K=1), and R(i) is the initial fitness of an individual, which is the sum of the strengths of all other individuals that dominate individual i: ； The condition for individual i to dominate individual j is that individual i is not inferior to individual j in all objectives, and is strictly superior to j in at least one objective; When calculating dominance relationships for individuals in the local population P2, using a niche radius constraint based on the Euclidean distance of the decision space encoding vector: If individual i is not inferior to individual j on all objectives, and the Euclidean distance between the decision space encoding vectors of individuals i and j is less than the preset niche radius. If individual i dominates individual j in a local sense, then individual i dominates individual j.

6. The method according to claim 1, characterized in that, In step S6, the migration probability p migrate The dynamic adjustment rule is as follows: The weights of the edges in the workshop scheduling knowledge graph are dynamically adjusted based on their overall change. When the overall change in the weights of the edges in the workshop scheduling knowledge graph exceeds a preset threshold, p is increased. migrate When the change is lower than a preset threshold, decrease p. migrate .

7. The method according to claim 1, characterized in that, In step S6: The SPEA2 environment selection strategy is adopted, which includes ranking candidate individuals by strength and measuring their crowding. Individuals located on the Pareto front and evenly distributed in the decision space are preferentially retained. The crowding of the decision space is combined with truncation and filling until the number of individuals is N. Truncation refers to removing the most crowded individual among the candidate individuals, and filling refers to selecting individuals with the highest difference between fitness and the harmonic average crowding of the decision space from the dominated solutions. An Epsilon non-dominated sorting and dual crowding control strategy is adopted, including performing non-dominated sorting on the merged population to obtain the first non-dominated front solution set; From the remaining individuals excluding the first non-dominated frontier, select those that meet the following criteria: Individuals with approximately non-adverse conditions, the The approximate non-dominated condition is: there is no individual in the first non-dominated front that allows for all objectives. Even after the proportions are relaxed, the individual can still be controlled. The first non-dominated front solution set is combined with the... A temporary population is obtained by merging approximately non-dominant individuals; When the number of individuals in the temporary population exceeds the preset size, the crowding degree is calculated based on the nearest neighbor distance between the target space and the decision space, and the two crowding degrees are normalized and fused to obtain the comprehensive crowding degree. The individual with the smallest comprehensive crowding degree is removed cyclically until the preset size is met. When the number of individuals in the temporary population is less than the preset size, the remaining individuals that were not selected are supplemented to the preset size according to the rule of prioritizing non-dominant frontier level and sparser decision space.

8. The method according to claim 1, characterized in that, In step S7, the specific operation of enhancing the weights is as follows: for specific machine-worker-process combinations that frequently occur in the Pareto optimal solution set, count the occurrence frequency of each edge in the Pareto optimal solution set, denoted as... Update the weights of the corresponding edges in the workshop scheduling knowledge graph according to the following formula: In the formula, The knowledge reward factor is set to 0.

5. The size of the Pareto optimal solution set. The edge weights before the update. This represents the updated edge weights.

9. The method according to claim 1, characterized in that, During initialization in step S3, a roulette wheel selection strategy based on edge weights is used to select the next node.

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