A method for self-adapting multi-objective evolutionary optimization of parameters in a denture manufacturing process

Abstract

The present application relates to the technical field of denture manufacturing parameter optimization, and discloses a kind of denture manufacturing process parameter self-adapting multi-objective evolutionary optimization method, comprising, definition decision variable vector and establishment target function formula;Edge layer extracts local training set to generate initial local population, executes evolution iteration to generate offspring, calculates individual distribution density to complete reference point dynamic adjustment;Edge layer receives preference weight vector and calculates priority level to update the correlation function of solution and calculate priority level, and the grid density vector is sent to the cloud layer with local non-dominated solution set and parameter recommendation solution set is generated by truncation selection;Cloud layer calculates global density and updates global reference point set, and the elite solution is issued to edge layer to replace preset proportion individual;Edge layer triggers calculation offloading and executes processing object model expansion operation.Cross-node knowledge migration is completed through cloud edge collaborative architecture, evolution population aggregation is guided by fusing preference weight vector, and grid density is used to balance target space solution distribution state.

Description

Technical Field

[0001] This invention relates to the field of dental prosthesis manufacturing parameter optimization technology, specifically to an adaptive multi-objective evolutionary optimization method for dental prosthesis manufacturing process parameters. Background Technology

[0002] In the digital manufacturing process of dentures and orthopedic implants, the operation of CNC machine tools involves setting multiple process parameters such as cutting speed, feed rate, depth of cut, and spindle speed. Actual production needs to simultaneously consider multiple mutually constraining objectives such as comprehensive dimensional accuracy, machining time, machining cost, and equipment energy consumption. This constitutes a typical multi-dimensional, multi-objective optimization problem, and multi-objective evolutionary algorithms are often used to solve such combined optimization tasks of process parameters.

[0003] In existing process parameter optimization, as the dimension of the objective function increases, individuals generated by traditional multi-objective evolutionary algorithms are prone to clustering imbalances in local boundary regions of the objective space, making it difficult to maintain the uniformity of the reference point distribution. The algorithm's built-in crossover and mutation indices are typically set to fixed constants, lacking a control mechanism that adaptively adjusts the global exploration and local convergence states along with the evolutionary iteration process, causing the population evolution direction to easily get trapped in local optima. Different manufacturing plants often have specific focuses for their production tasks, such as differentiated requirements for processing time or dimensional accuracy. Existing parameter optimization methods struggle to directly map these customized preference weights to the dissociation operations in evolutionary computation, resulting in the final parameter recommendation results deviating from the actual production scheduling needs of the factory.

[0004] Existing optimization methods have limitations in terms of computational architecture deployment. If a local, standalone computing model is adopted, different manufacturing plants become data silos, preventing nodes from sharing elite solution sets and performing cross-node knowledge transfer. Newly connected manufacturing plants face the cold start cost problem of optimizing from scratch. Uploading all evolutionary iteration tasks and raw data centrally to the cloud for processing incurs enormous network communication overhead. Furthermore, due to network transmission limitations, the system struggles to offload computation and schedule tasks based on the real-time load of local servers, failing to meet the multi-objective parameter optimization requirements of large-scale denture manufacturing scenarios. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the technical problem solved by this invention is that in the multi-objective optimization process of existing denture manufacturing, evolutionary algorithms are prone to getting trapped in local optima and the solution distribution is unbalanced, and they cannot dynamically map the factory's customized processing preferences to the optimization process; at the same time, existing computing architectures have problems such as data silos and cold start problems with local nodes, and centralized cloud processing brings huge communication overhead and lack of load scheduling.

[0006] To address the above problems, the present invention provides the following technical solution: This invention provides an adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters, comprising the following steps: Define the decision variable vector and establish the objective function formula; The edge layer extracts the local training set to generate the initial local population, performs evolutionary iteration to generate offspring, calculates the individual distribution density in the target space, performs reference point refinement operation on regions where the individual distribution density is greater than the preset crowding threshold, and performs reference point coarsening operation on regions where the individual distribution density is less than the preset sparse threshold, thus completing the dynamic adjustment of reference points. The edge layer receives the preference weight vector, calculates the preference distance between each reference point and the preference weight vector, updates the correlation function of the solution based on the preference distance and calculates the priority level, truncates and selects the recommended solution set based on the priority level, generates the local non-dominated solution set and grid density vector and sends them to the cloud layer. The cloud layer receives the local non-dominated solution set and the grid density vector, calculates the global density to update the global reference point set, updates the global elite archive set, and sends the elite solution to the edge layer. The edge layer calls the elite solution to replace a preset proportion of individuals with lower fitness rankings in the local population, monitors the load status and triggers computation unloading and task scheduling, and performs processing object model expansion and parameter update operations.

[0007] Preferably, the decision variable vector is defined and the objective function formula is established, specifically including: The decision variable vector includes cutting speed, feed rate, depth of cut, and spindle speed; The objective function formulas include the dimensional accuracy comprehensive index objective function, the processing time objective function, the processing cost objective function, and the equipment energy consumption objective function; Preset variable boundary constraints and equipment operation constraints. The equipment operation constraints include spindle power constraints and tool life constraints. Call the tool life equation to calculate the tool life, and verify the tool life constraints based on the calculated tool life.

[0008] Furthermore, the evolutionary iteration process generates offspring, specifically including: A power function equation is constructed to control the crossover distribution index of the simulated binary crossover operator, which increases exponentially with the current iteration number of the evolution iteration. A power function equation is also constructed to control the mutation distribution index of the polynomial mutation operator, which decreases exponentially with the current iteration number of the evolution iteration. Call the distribution index update formula, substitute the current iteration number into the power function equation, and calculate the cross distribution index and variation distribution index for the current iteration number; The edge layer uses the calculated crossover distribution index to call the simulated binary crossover operator to recombine the parent individuals in the initial local population to generate the first intermediate offspring, and uses the calculated mutation distribution index to call the multinomial mutation operator to perform perturbation calculations on the individuals in the first intermediate offspring to generate offspring.

[0009] Preferably, the individual distribution density within the target space is calculated, and a reference point refinement operation is performed on regions where the individual distribution density is greater than a preset crowding threshold, while a reference point coarsening operation is performed on regions where the individual distribution density is less than a preset sparse threshold, thus completing the dynamic adjustment of the reference points. Specifically, this includes: Extract the objective function value of the objective function formula corresponding to the offspring and perform normalization processing; divide the objective space and construct a multi-dimensional grid. Calculate the individual distribution density within a multidimensional grid; For multidimensional grid regions where the individual distribution density is greater than a preset crowding threshold, a reference point refinement operation is performed. The mean of the normalized objective function of all individuals within the corresponding multidimensional grid is calculated. The mean of the normalized objective function is extracted to determine the coordinates of the new reference point. The coordinates of the new reference point are determined as the center of the mean of the actual individual distribution within the multidimensional grid. For multidimensional grid regions where the individual distribution density is less than a preset sparse threshold, a reference point coarsening operation is performed, and associated reference points are deleted within the corresponding multidimensional grid regions.

[0010] Furthermore, the association function of the solution is updated based on the preference distance, and the priority level is calculated, specifically including: Extract each individual in the target space as an individual to be associated, and calculate the perpendicular distance from the individual to be associated to the line connecting each reference point and the origin. Using vertical distance and preference distance as input parameters, the reconstruction correlation function distance for each reference point is calculated by calling the correlation function reconstruction formula. Compare the reconstructed association function distances of all reference points for the individual to be associated, select the reference point with the smallest reconstructed association function distance as the matching reference point, establish a mapping connection between the individual to be associated and the matching reference point, complete the mapping of all individuals to be associated, and select the individuals to be associated that have completed the mapping as individuals to be retained. Count the total number of associated individuals currently mapped to each matching reference point, and calculate the priority level of each individual to be retained by combining the total number of associated individuals with the corresponding reconstruction association function distance call priority calculation formula.

[0011] Preferably, the recommended solution set for generating parameters is truncated according to priority level, and a local non-dominated solution set and grid density vector are generated and sent to the cloud layer, specifically including: Individuals to be retained are arranged in ascending order of priority level. Obtain the total number of individuals within the local population, including those to be retained, and compare the total number of individuals with the preset population size value; In cases where the total number of individuals exceeds the preset population size, individuals ranked after the preset population size are removed, and the recommended solution set of parameters is formed by retaining individuals that meet the preset population size. The edge layer generates a local non-dominated solution set and a grid density vector and sends them to the cloud layer. The parameter recommendation set generated by the edge layer is used to extract and include the combination of machining parameters, which is then sent to the equipment layer to control the CNC cutting machine tool to perform the cutting task.

[0012] Furthermore, the cloud layer receives the local non-dominated solution set and the grid density vector, calculates the global density to update the global reference point set, specifically including: The cloud layer receives local non-dominated solution sets and grid density vectors sent by at least multiple edge layers, including the edge layer; The global density is calculated by calling the global density aggregation formula. The global density aggregation formula takes the total number of multiple edge layers, the preset data volume weights of each edge layer, and the grid density vector sent by each edge layer as input parameters for aggregation calculation. The cloud layer updates the global reference point set based on the calculated global density.

[0013] Preferably, the global elite archive is updated and elite solutions are distributed to the edge layer. The edge layer then uses these elite solutions to replace a preset proportion of individuals in the local population whose fitness ranking is lower. This specifically includes: The cloud layer sends the updated global reference point set and elite solutions in the global elite archive to the edge layer according to the preset synchronization cycle; The edge layer ranks individuals within the local population based on their fitness values, locates a preset proportion of individuals with lower fitness rankings, and calls elite solutions to replace these preset proportion of individuals. For the edge layer of the newly connected manufacturing plant, elite solutions are extracted from the global elite archive to form part of the initial local population, and the elite solutions are merged with randomly generated individuals to complete the cold start initialization operation.

[0014] Furthermore, monitoring load status and triggering compute offloading and task scheduling specifically includes: The edge layer monitors the local server's operating load value as the load status and compares the local server's operating load value with a preset load threshold. When the local server's operating load exceeds a preset load threshold, a hard switchover strategy based on the preset load threshold is triggered to perform computation offloading and task scheduling. The edge layer extracts the dataset required for evolution and iteration and sends it to the cloud layer. The cloud layer takes over the evolution and iteration and generates a recommended solution set with parameters.

[0015] Preferably, the processing object model expansion and parameter update operations are performed, specifically including: A multi-objective optimization mathematical model for the denture manufacturing scenario is constructed based on the decision variable vector and the objective function formula. The edge layer uses the multi-objective optimization mathematical model as the processing object model, and the processing object model is the denture manufacturing model. The edge layer calls the model extension module to extend the processing object model to the orthopedic implant manufacturing model; Read the material property data of orthopedic implants, update the cutting speed influence coefficient, feed rate influence coefficient and depth of cut influence coefficient inside the tool life equation using the material property data of orthopedic implants, and generate a recommended solution set of orthopedic implant machining parameters.

[0016] This invention provides an adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters. It has the following beneficial effects: 1. This invention receives local non-dominated solution sets from multiple edge layers through the cloud layer and updates the global elite archive set, then distributes elite solutions to the edge layers according to a preset synchronization period. The edge layers use these elite solutions to replace a preset proportion of individuals with lower fitness rankings in their local population. A cloud-edge collaborative architecture is used to complete cross-node knowledge transfer, guiding the evolution of the edge layers to escape the trap of local optima. For newly connected edge layers in the manufacturing plant, elite solutions from the global elite archive set are directly extracted to form part of the initial local population. These elite solutions are then combined with randomly generated individuals to complete the cold start initialization operation, reducing the optimization computation cost of new nodes.

[0017] 2. This invention receives a preference weight vector at the edge layer, calculates the preference distance between each reference point and the preference weight vector, updates the correlation function of the solution based on the preference distance, calculates the priority level, and truncates and selects the recommended solution set based on the priority level. By combining the preference weight vector set by the manufacturing plant, it guides the evolving population to gather towards the target space region indicated by the preference, outputting a combination of processing parameters that meets the customized needs of the plant. Simultaneously, based on the individual distribution density within the multidimensional grid, the edge layer performs reference point refinement operations on regions where the individual distribution density is greater than a preset congestion threshold, and performs reference point coarsening operations on regions where the density is less than a preset sparse threshold, balancing the solution distribution state within the target space and overcoming the imbalance of individual gathering in the local boundary space.

[0018] 3. This invention controls the crossover distribution index by constructing a power function equation that increases exponentially with the current iteration number, and controls the mutation distribution index by constructing a power function equation that decreases exponentially. The increasing trend of the crossover operation combined with the decreasing trend of the mutation operation forms a dynamic complementary mechanism, coordinating the optimization range in the early stages of evolutionary computation with the search space in the later stages. Furthermore, the edge layer reads the material property data of orthopedic implants and updates the cutting speed influence coefficient, feed rate influence coefficient, and depth of cut influence coefficient within the tool life equation. This extends the multi-objective optimization mathematical model for denture manufacturing to the orthopedic implant manufacturing model, generating a recommended solution set for orthopedic implant processing parameters, thus achieving the comprehensive application of multi-objective evolutionary optimization methods in different medical implant manufacturing scenarios. Attached Figure Description

[0019] Figure 1 This is a diagram of the cloud-edge collaborative multi-objective optimization system architecture according to an embodiment of the present invention; Figure 2 This is a flowchart of the adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to an embodiment of the present invention; Figure 3 This is a flowchart illustrating the construction of a multi-objective optimization mathematical model for denture manufacturing process parameters according to an embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the adaptive evolution operation principle of an embodiment of the present invention. Figure 5 This is a schematic diagram illustrating the dynamic reconstruction principle of reference points in an embodiment of the present invention. Figure 6 This is a schematic diagram of the preference space mapping principle according to an embodiment of the present invention; Figure 7 This is a flowchart illustrating the priority truncation selection process according to an embodiment of the present invention. Figure 8 This is a schematic diagram illustrating the principle of cross-node elite knowledge transfer in an embodiment of the present invention. Figure 9 This is a schematic diagram illustrating the mechanism equivalent substitution and application extension principle of this invention embodiment; Figure 10 This is a bar chart comparing the algorithm performance of embodiments of the present invention; Figure 11 This is a bar chart comparing the preference-guided selection effects of embodiments of the present invention. Figure 12 This is a comparison chart of cloud-edge collaborative communication and performance in an embodiment of the present invention, wherein... Figure 12 (a) is a comparison chart of multi-architecture hypervolume metrics. Figure 12 (b) is a line graph of system communication overhead. Detailed Implementation

[0020] The technical solutions in 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.

[0021] See attached document Figure 1 The present invention provides an adaptive multi-objective evolutionary optimization system for denture manufacturing process parameters, including a cloud-edge collaborative multi-objective optimization system; The cloud-edge collaborative multi-objective optimization system includes: device layer, edge layer, and cloud layer; The equipment layer is deployed inside the manufacturing plant. The equipment layer connects CNC cutting machine tools and sintering furnaces. The equipment layer collects process parameter data and processing result data. The edge layer is deployed on local servers in the manufacturing plant, and the edge layer communicates with the device layer. The cloud layer is deployed in the data center, and the cloud layer communicates with the edge layer.

[0022] See attached document Figure 2 This invention provides an adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters, comprising the following steps: S10, Define the decision variable vector and establish the objective function formula; S20, the edge layer performs an evolutionary iteration process and completes dynamic adjustment of the reference point; S30, the edge layer combines the preference weight vector to perform truncation selection to generate parameter recommendation solution sets; S40, the cloud layer updates the global reference point set and the global elite archive set and sends elite solutions to the edge layer; S50, the core mechanism of cloud-edge collaborative multi-objective optimization system, is equivalent to the extension and model update operation.

[0023] In step S10, the decision variable vector is defined. The decision variable vector includes cutting speed, feed rate, depth of cut, and spindle speed.

[0024] Establish the objective function formula: ; In the formula: The objective function vector; A vector of decision variables; The objective function is the comprehensive index of dimensional accuracy. The objective function is the processing time; The objective function is the processing cost. Let be the objective function for equipment energy consumption.

[0025] In step S20, the edge layer reads the processed data to form a local training set. The edge layer extracts the local training set to generate the initial population. The edge layer then performs an evolutionary iteration process.

[0026] During the evolutionary iteration process, simulated binary crossover and polynomial mutation operators are invoked to generate offspring. The distribution exponent of the simulated binary crossover operator increases exponentially with the number of iterations. The distribution exponent of the polynomial mutation operator decreases exponentially with the number of iterations.

[0027] The edge layer dynamically adjusts reference points for the generated offspring. It calculates the distribution density of individuals within the target space. For regions where the individual distribution density is greater than a crowding threshold, it performs reference point refinement. For regions where the individual distribution density is less than a sparsity threshold, it performs reference point coarsening.

[0028] In step S30, input the preference weight vector for the current manufacturing plant. The preference weight vector corresponds to the level of importance attached to four dimensions: comprehensive dimensional accuracy index, processing time, processing cost, and equipment energy consumption.

[0029] The edge layer calculates the preference distance between each reference point and the preference weight vector. Based on the preference distance, the edge layer updates the correlation function of the solutions and calculates the priority level. Then, based on the priority level, the edge layer performs truncation selection to generate a parameter-recommended solution set.

[0030] The edge layer generates a local non-dominated solution set and a mesh density vector. The edge layer stores the raw processing results data locally in the manufacturing plant. The edge layer then sends the local non-dominated solution set and mesh density vector to the cloud layer.

[0031] In step S40, the cloud layer receives local non-dominated solution sets and mesh density vectors from multiple manufacturing plants. The cloud layer then calls the global density aggregation formula: ; In the formula: For global density; This represents the total number of edge layers; The numbering of the edge layer; For the number The weight of the data volume corresponding to the edge layer; For the number The mesh density vector sent from the edge layer; The cloud layer updates the global reference point set based on the global density. The cloud layer merges the local non-dominated solution sets sent by multiple manufacturing plants and updates the global elite archive set.

[0032] The cloud layer distributes the updated global reference point set and elite solutions in the global elite archive to each edge layer according to the synchronization cycle.

[0033] The edge layer receives elite solutions from the cloud layer. The edge layer then uses these elite solutions to replace a predetermined proportion of individuals in its local population whose fitness ranking is lower. For newly connected manufacturing plants within the cloud-edge collaborative multi-objective optimization system, the edge layer extracts elite solutions from the global elite archive to form the initial population.

[0034] In step S50, the cloud-edge collaborative multi-objective optimization system monitors the load status and triggers computation offloading and task scheduling operations. The cloud layer and edge layer perform asynchronous communication parameter interaction operations. The edge layer performs processing object model expansion and parameter update operations.

[0035] The technical solution of the method provided by the present invention will be described in detail below with reference to specific embodiments.

[0036] See attached document Figure 3 This invention provides a process for constructing a multi-objective optimization mathematical model for denture manufacturing process parameters, including: defining a decision variable vector. The decision variable vector includes four dimensions of machining parameters. These four dimensions are specifically divided into cutting speed, feed rate, depth of cut, and spindle speed.

[0037] Establish a comprehensive objective function for dimensional accuracy and call the dimensional accuracy formula: ; In the formula: The objective function is the comprehensive index of dimensional accuracy. For the measured deviation of critical dimensions; To allow the maximum deviation; This represents the measured surface roughness value. This represents the target value for surface roughness. To adapt to the measured gap value; To adapt to the target gap value.

[0038] Establish the objective function for processing time. Call the processing time formula: ; In the formula: The objective function is the processing time; Remove volume from the material; Material removal rate; This is a vector of decision variables.

[0039] Establish the objective function for processing costs and call the processing cost formula: ; In the formula: The objective function is the processing cost. For tooling costs; Based on operating costs.

[0040] Establish the objective function for equipment energy consumption and call the equipment energy consumption formula: ; Let the objective function be the energy consumption of the equipment; Main spindle power; To support system power; The objective function is the processing time.

[0041] Set variable boundary constraints. Variable boundary constraints limit the range of values ​​for the decision variable vector. Limit the cutting speed to between its lower and upper bounds. Limit the feed rate to between its lower and upper bounds. Limit the depth of cut to between its lower and upper bounds. Limit the spindle speed to between its lower and upper bounds. Set equipment operation constraints. Equipment operation constraints include spindle power constraints and tool life constraints. Spindle power constraints limit the spindle power to be less than or equal to 80% of its rated power.

[0042] Establish the tool life equation. Calculate the tool life using the tool life equation: ; In the formula: For tool life; This serves as a baseline coefficient for tool life. This refers to the cutting speed; This is the coefficient affecting cutting speed; For feed rate; This is the feed rate influence coefficient; This refers to the depth of cut. This is the cutting depth influence coefficient.

[0043] Tool life constraints limit tool life to be greater than or equal to a minimum tool life threshold. Combining the defined objective function and constraints, the optimization mathematical model is constructed.

[0044] See attached document Figure 4 The evolutionary iteration process provided by this invention includes adaptive operator control operations, specifically including the following steps: S210, the edge layer extracts the local training set to generate the initial population; S220, the edge layer calls the simulated binary crossover operator to generate the first intermediate offspring; S230, the edge layer calls the polynomial mutation operator to generate the final offspring.

[0045] In step S210, the edge layer extracts the local training set. The edge layer generates an initial population based on the local training set. For the specific implementation of population initialization, those skilled in the art can use random generation algorithms or Latin hypercube sampling algorithms. The population initialization operation is a well-known technique in the field and will not be described in detail here.

[0046] In step S220, the edge layer invokes a simulated binary crossover operator to recombine the initial population. The simulated binary crossover operator includes a crossover distribution index. The crossover distribution index controls the distribution range of individuals generated by the crossover operation. The crossover distribution index is set to increase exponentially with the number of iterations.

[0047] In step S230, the edge layer invokes the polynomial mutation operator to process the first intermediate offspring. The polynomial mutation operator includes a mutation distribution index. The mutation distribution index controls the magnitude of the individual perturbation generated by the mutation operation. The mutation distribution index is set to decrease exponentially with the number of iterations.

[0048] The edge layer calculates the crossover and mutation indices for the current iteration. The distribution index update formula is then called: ; ; In the formula: The cross-distribution index is the number of iterations currently being performed. This is the lower bound of the cross-distribution index; This is the upper bound of the cross-distribution index; This represents the current iteration number; This represents the maximum number of iterations. This refers to the cross-conversion rate parameter; This is the exponent of the variation distribution for the current iteration number; This is the upper bound of the variation distribution index; This is the lower bound of the variation distribution index; This is the mutation conversion rate parameter.

[0049] The lower bound of the crossover distribution index limits the optimization range in the early stages of evolutionary computation. The upper bound of the crossover distribution index defines the search space in the early stages of evolutionary computation. The upper bound of the crossover distribution index limits the optimization range in the later stages of evolutionary computation. The upper bound of the crossover distribution index defines the search space in the later stages of evolutionary computation. The crossover transition rate parameter and the mutation transition rate parameter jointly control the frequency of search state switching.

[0050] The calculation of the crossover and variation indices depends on the distribution parameter control function. This function is a nonlinear equation, including power function equations. The edge layer uses power function equations to control the growth of the crossover indices and the decay of the variation indices. The nonlinear equations also include logistic function equations. The edge layer uses logistic function equations instead of power function equations to calculate the distribution indices. Using logistic function equations to calculate the distribution indices enables smooth state transitions during the iteration process. Logistic function equations and power function equations constitute an equivalent substitution technique. The specification explicitly states the equivalence relationship between extending the distribution parameter control function from power function equations to logistic function equations.

[0051] The edge layer reorganizes parent individuals within the initial population based on the crossover distribution index of the current iteration number. The edge layer outputs the first intermediate offspring. The specific operation process for performing recombination calculations on parent individuals can be described using standard simulated binary crossover recombination formulas by those skilled in the art. The individual crossover recombination calculation process is well-known in the field and will not be elaborated upon here.

[0052] The edge layer receives the first intermediate offspring. The edge layer performs perturbation calculations on individuals within the first intermediate offspring based on the mutation distribution index of the current iteration number. The edge layer outputs the final offspring. The decaying trend of the mutation operation, combined with the growth trend of the crossover operation, constitutes a dynamic complementary mechanism. For the specific operation process of individual perturbation calculation, those skilled in the art can use the standard polynomial mutation probability equation; the individual perturbation calculation process is a well-known technique in the field and will not be elaborated upon here.

[0053] See attached document Figure 5 The reference point dynamic adjustment operation provided by this invention specifically includes the following steps: S240, the edge layer performs normalization processing on the objective function value of the generated offspring; S250, edge layer divides the target space to construct a multi-dimensional mesh; S260, edge layer calculates the individual distribution density inside the multidimensional grid; S270, the edge layer performs reference point refinement and reference point coarsening operations based on the individual distribution density.

[0054] In step S240, the edge layer receives the generated offspring. The edge layer extracts the objective function value corresponding to the generated offspring. The edge layer performs normalization processing on the objective function value. For the specific operation process of the objective function value normalization processing, those skilled in the art can use the ideal point and maximum point boundary mapping algorithm. The objective function normalization calculation process is a well-known technology in this field and will not be described in detail here.

[0055] In step S250, the edge layer establishes a multidimensional coordinate system. The dimension of the multidimensional coordinate system is equal to the dimension of the objective function. The edge layer sets the number of segments for the single-dimensional space. The edge layer performs spatial segmentation based on the number of segments and the dimension of the objective function. The edge layer outputs the multidimensional mesh corresponding to the target space.

[0056] In step S260, the edge layer counts the number of individuals within the multidimensional grid. The edge layer compares the number of individuals within all grid cells to obtain the maximum value. The edge layer then calls the individual distribution density formula: ; In the formula: The density of individual distributions within the multidimensional grid; The number of individuals within a specific multidimensional grid; The total number of individuals corresponds to the multidimensional grid with the largest number of individuals.

[0057] In step S270, the edge layer sets crowding and sparsity thresholds. The edge layer compares the individual distribution density with the crowding threshold. For specific multidimensional grid regions where the individual distribution density is greater than the crowding threshold, the edge layer performs a reference point refinement operation. This refinement operation involves adding new reference points within the specific multidimensional grid region. The edge layer calculates the normalized objective function mean of all individuals within the specific multidimensional grid. The edge layer extracts the normalized objective function mean to determine the coordinates of the new reference points. The coordinates of the new reference points are set to the center of the actual individual distribution mean within the grid.

[0058] The edge layer compares the individual distribution density with the sparsity threshold. For specific multidimensional grid regions where the individual distribution density is less than the sparsity threshold, the edge layer performs a reference point coarsening operation. This operation involves deleting associated reference points within the specific multidimensional grid region.

[0059] The edge layer's dynamic adjustment of reference points relies on a target spatial density statistical algorithm. This algorithm includes grid spatial density statistical techniques. The edge layer utilizes a multi-dimensional grid to identify population distribution hotspots. This algorithm also includes cluster analysis statistical techniques. Under conditions where the number of targets exceeds the usual set number, the edge layer uses cluster analysis statistical techniques instead of grid spatial density statistical techniques. Cluster analysis statistical techniques can identify population clustering centers within the high-dimensional target space. These techniques extract the coordinates of the separated cluster centers to serve as the coordinates of newly added reference points. For the specific calculation of cluster center coordinates, those skilled in the art can use the standard mean clustering algorithm; the process of obtaining mean clustering coordinates is well-known in the field and will not be elaborated here. Grid spatial density statistical techniques and cluster analysis statistical techniques constitute an equivalent substitution feature. The specification explicitly states the equivalent substitution relationship between the target spatial density statistical algorithm and the extension of grid spatial density statistical techniques to cluster analysis statistical techniques.

[0060] See attached document Figure 6 The parameter recommendation solution set generation operation provided by this invention includes a preference decision process, specifically including the following steps: S310, the edge layer receives the preference weight vector set by the manufacturing plant; S320, the edge layer calculates the preference distance between the reference point and the preference weight vector; S330, the edge layer calls the association function of the preference distance update for individuals within the non-dominated solution set.

[0061] In step S310, the edge layer receives a preference weight vector from external input. This preference weight vector consists of four values. These four values ​​correspond to the weights of the dimensional accuracy comprehensive index objective function, the processing time objective function, the processing cost objective function, and the equipment energy consumption objective function, respectively. The manufacturing plant adjusts these values ​​according to production scheduling requirements.

[0062] In step S320, the edge layer traverses the set of reference points generated during the current evolution iteration. The edge layer extracts the multidimensional coordinate data of a single reference point. The edge layer then calls the preference distance calculation formula: ; In the formula; The preference distance between the reference point and the preference weight vector; To select a reference point; Let the dimension of the objective function be denoted as 'dimensional'. Number the dimensions of the objective function; To select a reference point at the 1st Coordinate values ​​in each dimension; For the preference weight vector at the th Weight values ​​in each dimension.

[0063] The edge layer's preference distance calculation operation relies on spatial distance metric algorithms. These algorithms include Euclidean distance calculation techniques. The preference distance calculation formula reflects the Euclidean distance calculation process. Spatial distance metric algorithms also include cosine similarity analysis and Mahalanobis distance metric techniques. Cosine similarity analysis can assess the difference in the angle between vector directions. Mahalanobis distance metric techniques can eliminate covariance interference between multidimensional target data. Euclidean distance calculation, cosine similarity analysis, and Mahalanobis distance metric techniques constitute equivalent substitution features. The instruction manual explicitly states the equivalent substitution relationship between spatial distance metric algorithms, extending from Euclidean distance calculation to cosine similarity analysis and Mahalanobis distance metric techniques.

[0064] In step S330, the edge layer extracts individuals to be associated within the non-dominated solution set. These individuals are candidate combinations of processing parameters generated during the evolutionary iteration process. The edge layer calculates the perpendicular distance from each individual to the origin of each reference point. For the specific calculation process of the perpendicular distance from an individual to a reference point, those skilled in the art can use the orthogonal projection distance equation to solve it. The calculation process of the perpendicular projection length is a well-known technique in this field and will not be elaborated here.

[0065] The edge layer fuses vertical distance and preference distance. The edge layer calls the correlation function to reconstruct the formula: ; In the formula: To reconstruct the distance of the correlation function; Individuals to be associated; To select a reference point; The vertical distance between the individual to be associated and the selected reference point origin; This is the preference adjustment coefficient; This is the preference distance between the reference point and the preference weight vector.

[0066] The edge layer compares the reconstructed association function distances of the individual to be associated with all reference points. The edge layer selects the reference point with the smallest reconstructed association function distance as the matching reference point. The edge layer establishes a mapping connection between the individual to be associated and the matching reference point. The reconstructed association function distance integrates a preference distance factor. Reference points with smaller preference distances output smaller reconstructed association function distance calculation results. This mapping connection guides the evolutionary population to cluster towards the target spatial region pointed to by the preference weight vector.

[0067] See attached document Figure 7 The truncation selection parameter recommendation solution set generation operation provided by this invention specifically includes the following steps: S340, the edge layer counts the number of individuals associated with each matching reference point; S350, the edge layer calculates the priority level of each individual to be retained; S360, the edge layer performs a truncation operation on the non-dominated solution set according to the priority level and outputs a parameter recommended solution set.

[0068] In step S340, the edge layer traverses the individuals to be retained within the selected population. The edge layer reads the matching reference points corresponding to the individuals to be retained. The edge layer counts the number of individuals associated with the same matching reference point. The edge layer outputs the total number of associated individuals included in the matching reference point. For the specific operation process of extracting the association status of individuals within the population, those skilled in the art can use hash mapping table lookup technology. The process of calculating individual association relationships is a well-known technique in the field and will not be elaborated here.

[0069] In step S350, the edge layer calculates the priority level by combining the total number of associated individuals and the distance to the reconstructed association function. The edge layer calls the priority level calculation formula: ; In the formula: Priority level for individuals to be retained; The total number of associated individuals included in the matching reference point; The reconstructed correlation function distance between the individual to be retained and the matching reference point; The reconstructed association function distance is the one that presents the largest value among all associated individuals included in the matching reference point.

[0070] The priority level depends on the total number of associated individuals and the distance ratio. The total number of associated individuals reflects the local crowding level of the target space. The distance ratio reflects the convergence status of the individuals to be retained within the local space. The preference adjustment coefficient, combined with the distance in the reconstructed association function, influences the priority level value.

[0071] In step S360, the edge layer compares the priority levels of all individuals to be retained. The edge layer arranges the individuals to be retained in ascending order of priority value. The edge layer obtains the total number of individuals within the current population. The edge layer compares the total number of individuals with the preset population size value.

[0072] For cases where the total number of individuals exceeds a preset population size, the edge layer removes individuals ranked after the preset population size as potential retainers. The edge layer retains individuals that meet the preset population size as potential retainers, forming the recommended solution set for parameters.

[0073] The edge layer performs truncation selection operations relying on evolutionary selection algorithms. These algorithms include priority-based truncation techniques, which are used to control population size. Another evolutionary selection algorithm is tournament selection, which replaces truncation. Tournament selection randomly selects individuals from local subsets for priority comparison and retains those with lower priorities. A third evolutionary selection algorithm is roulette wheel selection, which constructs a probability distribution based on the inverse of priority and performs probability sampling to retain individuals. Truncation, tournament selection, and roulette wheel selection are equivalent replacements. The specification explicitly states the equivalent replacement relationship between evolutionary selection algorithms, extending from truncation to tournament selection and roulette wheel selection.

[0074] The edge layer outputs a recommended set of parameters. The edge layer extracts the machining parameter combinations included within the recommended set. The edge layer then sends these machining parameter combinations to the equipment layer to control the CNC machine tool to execute the cutting task.

[0075] See attached document Figure 8 The specific process of updating the global reference point set and the global elite archive set at the cloud layer and distributing elite solutions to the edge layer, as provided by this invention, includes the following steps: S410, the cloud layer merges local non-dominated solution sets and updates the global elite archive set; S420: The cloud layer distributes elite solutions to the edge layer according to the synchronization cycle; S430, the edge layer calls the elite solution to replace the inferior individuals within the local population; S440 performs a cold start initialization operation for newly connected manufacturing plants.

[0076] In step S410, the cloud layer receives the local non-dominated solution sets sent by all edge layers. The cloud layer merges the local non-dominated solution sets to form a global candidate solution set. The cloud layer performs non-dominated sorting on the global candidate solution set. The cloud layer selects the globally non-dominated solutions and stores them in the global elite archive. For the specific operation process of multi-objective non-dominated sorting, those skilled in the art can call the fast non-dominated sorting algorithm. The multi-dimensional data non-dominated sorting process is a well-known technology in this field and will not be described in detail here.

[0077] In step S420, the cloud layer sets a synchronization period. The synchronization period limits the frequency of data interaction between the cloud layer and the edge layer. When the cloud layer reaches the synchronization period node, it extracts elite solutions from the global elite archive. The cloud layer then distributes the elite solutions to each online edge layer.

[0078] The synchronization cycle triggering mechanism includes time-driven and event-driven mechanisms. The edge layer uses the time-driven mechanism to execute tasks at fixed time intervals. The cloud layer uses the event-driven mechanism instead of the time-driven mechanism. The event-driven mechanism determines the timing of tasks based on the update level of the global elite archive or the magnitude of global density changes. The time-driven and event-driven mechanisms constitute an equivalent substitution. The synchronization cycle triggering mechanism extends from the time-driven mechanism to the event-driven mechanism, representing an equivalent substitution relationship.

[0079] In step S430, the edge layer receives elite solutions. The edge layer calculates the fitness values ​​of individuals within its local population. The edge layer ranks individuals within its local population according to their fitness values. The edge layer identifies a predetermined proportion of individuals with lower fitness rankings. The edge layer replaces this predetermined proportion of individuals with elite solutions distributed from the cloud layer. The number of these predetermined proportion individuals is set to one-tenth of the total local population. Cross-node knowledge transfer operations guide the evolutionary direction, helping it escape the trap of local optima.

[0080] In step S440, the new manufacturing plant deploys an edge layer and connects to the cloud-edge collaborative multi-objective optimization system. For the edge layer newly connected to the manufacturing plant, the cloud layer distributes elite solutions stored within the global elite archive. The edge layer extracts elite solutions to form a portion of the initial population. The edge layer then randomly generates the remaining initial population.

[0081] The edge layer merges elite solutions and random individuals to complete the cold start initialization operation. The cold start initialization operation requires elite solutions to comprise half of the initial population. The other half requires random individuals. Calling global elite solutions to complete the cold start avoids newly connected manufacturing plants undergoing evolutionary optimization computation from scratch. Regarding the specific process of generating initial individuals, those skilled in the art can use normal distribution random sampling techniques. The random generation process of individual parameters is a well-known technique in the field and will not be elaborated upon here.

[0082] See attached document Figure 9 The cloud-edge collaborative multi-objective optimization system provided by this invention includes the following steps for equivalent extension and model update operations of its core mechanism: S510, the edge layer monitors the load status and triggers compute offloading and task scheduling operations; S520 enables asynchronous communication parameter interaction between the cloud layer and the edge layer; S530, the edge layer performs processing object model expansion and parameter update operations.

[0083] In step S510, the edge layer monitors the local server's operating load. The edge layer compares the local server's operating load with a preset load threshold. When the local server's operating load exceeds the preset load threshold, the edge layer extracts the dataset required for the evolutionary iteration process. The edge layer sends the dataset to the cloud layer. The cloud layer takes over the evolutionary iteration process and generates a recommended solution set for the parameters.

[0084] The cloud-edge collaborative multi-objective optimization system incorporates a computational task offloading mechanism. This mechanism employs a threshold-based hard switching technique. Offloading is triggered when the running load exceeds a preset load threshold, constituting a threshold-based hard switching technique. Internally, the system includes a reinforcement learning scheduling module. This module replaces the threshold-based hard switching technique with reinforcement learning scheduling. Reinforcement learning scheduling extracts network bandwidth and local computing resource states. The module dynamically allocates evolving computational tasks based on these states. Reinforcement learning scheduling and threshold-based hard switching are equivalent techniques. For the specific training process of the reinforcement learning model, those skilled in the art can utilize the deep Q-network algorithm; the state-action space mapping process is well-known in the field and will not be elaborated upon here.

[0085] In step S520, the cloud layer distributes elite solutions according to a synchronization cycle, which is a synchronous communication mode. The synchronous communication mode requires all edge layers within the cloud-edge collaborative multi-objective optimization system to uniformly receive and distribute data. The cloud-edge collaborative multi-objective optimization system sets up a data interaction mechanism. This data interaction mechanism adopts the synchronous communication mode.

[0086] The cloud-edge collaborative multi-objective optimization system internally incorporates an asynchronous communication module. This module uses an asynchronous communication mode instead of a synchronous one. After completing the local optimization phase at any edge layer, the asynchronous communication mode unidirectionally triggers data upload and elite solution distribution operations. Calling the asynchronous communication mode avoids waiting for synchronization from edge layers located within different manufacturing plants. The asynchronous and synchronous communication modes are equivalent technical features. For the specific operational process of concurrent asynchronous communication, those skilled in the art can utilize message queue telemetry transmission protocols; multi-threaded concurrent data interaction is well-known technology in this field and will not be elaborated upon here.

[0087] In step S530, a multi-objective optimization mathematical model is constructed for the denture manufacturing scenario. This model includes material removal rate parameters and tool life calculation parameters. The edge layer sets up the machining object model, which is based on the denture manufacturing model.

[0088] An extension module is set up inside the edge layer. This module extends the machining object model to the orthopedic implant manufacturing model. For the orthopedic implant manufacturing scenario, the edge layer reads the material property data of the orthopedic implant. The edge layer uses this material property data to update the cutting speed influence coefficient, feed rate influence coefficient, and depth of cut influence coefficient within the tool life equation. The edge layer generates a recommended solution set for orthopedic implant machining parameters. The orthopedic implant manufacturing model and the denture manufacturing model have equivalent technical features. For the specific operation process of extracting implant material property data, those skilled in the art can use the material property database retrieval interface. The material basic parameter matching process is a well-known technique in this field and will not be elaborated here.

[0089] Specific application examples: For orthopedic implant manufacturing scenarios, the edge layer reads orthopedic implant material property data. The edge layer then uses this data to update the cutting speed, feed rate, and depth of cut influence coefficients within the tool life equation. The edge layer generates a recommended solution set for orthopedic implant machining parameters. The orthopedic implant manufacturing model and the denture manufacturing model are equivalent in technical features. For the specific operational process of extracting implant material property data, those skilled in the art can use the material property database retrieval interface; the material basic parameter matching process is a well-known technique in the field and will not be elaborated upon here.

[0090] This study validates an adaptive multi-objective evolutionary optimization method for dental prosthesis manufacturing process parameters using test data. Machining records from three factories within a dental prosthesis manufacturing group were obtained. These records were extracted, and missing entries and outliers were removed to generate a test dataset. The test dataset contains 4236 samples, covering zirconia all-ceramic crowns, cobalt-chromium alloy bridges, and polyetheretherketone (PEEK) denture bases. Zirconia all-ceramic crowns comprise 62% of the total samples.

[0091] The edge layer limits the range of decision variable vector values. Cutting speed is limited to 30 m / min to 150 m / min. Feed rate is limited to 0.05 mm / rev to 0.3 mm / rev. Depth of cut is limited to 0.1 mm to 1.0 mm. Spindle speed is limited to 8000 rpm to 40000 rpm.

[0092] The edge layer extracts the test dataset to generate the initial population. The preset population size is set to 100. The maximum number of iterations is set to 300. The specific manufacturing plant is designated as a high-end customization factory. The high-end customization factory inputs a combination of preference weight vectors of 0.4, 0.2, 0.2, and 0.2. The preference weight vector indicates that the high-end customization factory assigns twice the weight of the other three dimensions of the objective function to the comprehensive dimensional accuracy index.

[0093] See attached document Figure 10 This invention provides a method for verifying algorithm performance. Four types of comparison algorithms are set up. The first basic algorithm uses standard parameter configuration. The second basic algorithm only uses adaptive operator control operations. The third basic algorithm only retains the dynamic adjustment operation of the reference point. The complete optimization algorithm combines adaptive operator control operations and dynamic reference point adjustment operations.

[0094] Four algorithms were run independently 30 times in the edge layer. A hypervolume metric was introduced to evaluate the overall convergence state and diversity, the reverse generation distance metric was used to measure the error in approximating the true frontier curve, and the uniformity of the solution distribution metric was used to verify the consistency of individual spacing. The hypervolume metric value for the complete optimization algorithm was 0.701. The value calculated by the first basic algorithm was 0.612. The value calculated by the second basic algorithm was 0.658. The value calculated by the third basic algorithm was 0.641. In the comparison of the reverse generation distance metric, the value calculated by the complete optimization algorithm was 0.058. In the comparison of the solution distribution uniformity metric, the value calculated by the complete optimization algorithm was 0.052. The value calculated by the solution distribution uniformity metric of the first basic algorithm was 0.085. Comparative tests confirmed that the output value of the complete optimization algorithm was reduced by 39%. The edge layer used the Wilcoxon rank-sum test to compare the complete optimization algorithm with the first basic algorithm. The test probabilities for the hypervolume metric, the reverse generation distance metric, and the solution distribution uniformity metric were all less than 0.01.

[0095] Appendix Figure 10 This displays the distribution characteristics of grouped histograms with error bars. The length of the error bars reflects the range of data fluctuation over 30 independent runs. The complete optimization algorithm corresponds to the highest bar in the hypervolume metric dimension.

[0096] See attached document Figure 11 This study verifies the impact of preference weight vectors on the generation of parameter recommendation solution sets. Ten parameter recommendation solution sets corresponding to a high-end customized factory are extracted. Without preference weight constraints, the average value of the objective function for dimensional accuracy is 0.127. The average value of the objective function for processing time is 0.341. The average value of the objective function for processing cost is 0.298. The average value of the objective function for equipment energy consumption is 0.312. With preference weight constraints, the average value of the objective function for dimensional accuracy decreases to 0.089. The average value of the objective function for processing time increases to 0.356. The average value of the objective function for processing cost increases to 0.312. The average value of the objective function for equipment energy consumption increases to 0.341.

[0097] Appendix Figure 11The changes in the four objective functions before and after the introduction of preference weights are illustrated in the charts. Presented as grouped bar charts, the charts clearly show that after adding the preference weight vector, the objective function value for the comprehensive dimensional accuracy index significantly decreases, while the objective functions for processing time, processing cost, and equipment energy consumption increase compromisingly. This verifies the aggregation and directional effect of the preference weight guidance mechanism on specific optimization objectives.

[0098] See attached document Figure 12 It includes two parts, Figure (a) and Figure (b), combined Figure 12 (a) shows a comparison of hypervolume metrics across multiple architectures, with the cloud layer connecting the edge layers within the three manufacturing plants. The specific hypervolume metrics output by the edge layers performing independent evolution operations are 0.623, 0.631, and 0.618, respectively. The average output value for independent evolution operations is 0.624. A centralized processing mode, where raw data is aggregated to the cloud layer, outputs an average value of 0.715. The specific values ​​output by the cloud-edge collaborative multi-objective optimization system are 0.681, 0.692, and 0.674, respectively. The average value of the cloud-edge collaborative multi-objective optimization system reaches 0.682, which is 95.6% of the value achieved in the centralized processing mode.

[0099] Combination Figure 12 (b) shows the system communication overhead line graph. The communication resource consumption data shows that the edge layer uploads 4.7KB of data and downloads 3.1KB of data during the synchronization cycle. The total daily communication volume of the three manufacturing plants is 23.4KB.

[0100] Appendix Figure 12 By evaluating the hypervolume index in Figure (a) and calculating the communication resource consumption in Figure (b), it is comprehensively verified that the cloud-edge collaborative multi-objective optimization system provided by this invention significantly reduces network communication overhead while ensuring near-centralized processing performance.

[0101] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these specific embodiments are merely illustrative. Those skilled in the art can omit, substitute, and modify the details of the above methods and systems in various ways without departing from the principles and essence of the present invention. For example, combining the above method steps to perform substantially the same function and achieve substantially the same result using substantially the same method falls within the scope of the present invention.

Claims

1. An adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters, characterized in that, Includes the following steps: Define the decision variable vector and establish the objective function formula; The edge layer extracts the local training set to generate the initial local population, performs evolutionary iteration to generate offspring, calculates the individual distribution density in the target space, performs reference point refinement operation on regions where the individual distribution density is greater than the preset crowding threshold, and performs reference point coarsening operation on regions where the individual distribution density is less than the preset sparse threshold, thus completing the dynamic adjustment of reference points. The edge layer receives the preference weight vector, calculates the preference distance between each reference point and the preference weight vector, updates the correlation function of the solution based on the preference distance and calculates the priority level, truncates and selects the recommended solution set of generation parameters according to the priority level, generates the local non-dominated solution set and grid density vector and sends them to the cloud layer. The cloud layer receives the local non-dominated solution set and the grid density vector, calculates the global density to update the global reference point set, updates the global elite archive set, and sends the elite solution to the edge layer. The edge layer calls the elite solution to replace a preset proportion of individuals with lower fitness rankings in the local population, monitors the load status and triggers computation unloading and task scheduling, and performs processing object model expansion and parameter update operations.

2. The adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to claim 1, characterized in that, The definition of the decision variable vector and the establishment of the objective function formula specifically include: The decision variable vector includes cutting speed, feed rate, depth of cut, and spindle speed; The objective function formula includes a comprehensive objective function for dimensional accuracy, an objective function for processing time, an objective function for processing cost, and an objective function for equipment energy consumption; Preset variable boundary constraints and equipment operation constraints, including spindle power constraints and tool life constraints. Call the tool life equation to calculate the tool life, and verify the tool life constraints based on the calculated tool life.

3. The adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to claim 1, characterized in that, The process of generating offspring through evolutionary iteration specifically includes: Construct a power function equation for the crossover distribution index of the control simulated binary crossover operator, which increases exponentially with the current iteration number of the evolution iteration; and construct a power function equation for the mutation distribution index of the control polynomial mutation operator, which decreases exponentially with the current iteration number of the evolution iteration. The distribution index update formula is called, and the current iteration number is substituted into the power function equation to calculate the cross distribution index and the variation distribution index of the current iteration number; The edge layer uses the calculated crossover distribution index to call the simulated binary crossover operator to recombine the parent individuals in the initial local population to generate the first intermediate offspring, and uses the calculated mutation distribution index to call the polynomial mutation operator to perform perturbation calculations on the individuals in the first intermediate offspring to generate the offspring.

4. The adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to claim 1, characterized in that, The calculation of individual distribution density within the target space involves refining reference points in regions where the individual distribution density exceeds a preset crowding threshold, and coarsening reference points in regions where the individual distribution density is less than a preset sparse threshold, thus achieving dynamic adjustment of reference points. Specifically, this includes: Extract the objective function value of the objective function formula corresponding to the offspring and perform normalization processing to divide the objective space and construct a multi-dimensional grid; Calculate the individual distribution density within the multidimensional grid; For the multidimensional grid region where the individual distribution density is greater than the preset crowding threshold, a reference point refinement operation is performed. The mean of the normalized objective function of all individuals within the corresponding multidimensional grid is calculated. The mean of the normalized objective function is extracted to determine the coordinates of the new reference point. The coordinates of the new reference point are determined as the center of the mean of the actual individual distribution within the multidimensional grid. For multidimensional grid regions where the individual distribution density is less than the preset sparse threshold, a reference point coarsening operation is performed, and the associated reference points are deleted within the corresponding multidimensional grid regions.

5. The adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to claim 1, characterized in that, The step of updating the association function of the solution based on the preference distance and calculating the priority level specifically includes: Each individual in the target space is extracted as an individual to be associated, and the perpendicular distance from the individual to be associated to the line connecting each reference point and the origin is calculated. Using the vertical distance and the preference distance as input parameters, the reconstruction association function distance for each reference point is calculated by calling the association function reconstruction formula. Compare the reconstructed association function distances of all reference points corresponding to the individual to be associated, select the reference point corresponding to the smallest value of the reconstructed association function distance as the matching reference point, establish a mapping connection between the individual to be associated and the matching reference point, complete the mapping of all individuals to be associated, and take the individuals to be associated that have completed the mapping as individuals to be retained. The total number of associated individuals currently mapped to each of the matching reference points is counted, and the priority level of each individual to be retained is calculated by combining the total number of associated individuals with the corresponding reconstruction association function distance call priority level calculation formula.

6. The adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to claim 5, characterized in that, The step of truncating and selecting the recommended solution set according to the priority level, generating the local non-dominated solution set and grid density vector, and sending them to the cloud layer specifically includes: The individuals to be retained are arranged in ascending order of their priority values. Obtain the total number of individuals within the local population that includes the individuals to be retained, and compare the total number of individuals with a preset population size value; In the case where the total number of individuals is greater than the preset population size value, the individuals to be retained that are ranked after the preset population size value are removed, and the individuals to be retained that meet the preset population size value are retained to form the parameter recommended solution set. The edge layer generates the local non-dominated solution set and the grid density vector and sends them to the cloud layer. The edge layer extracts the recommended solution set of parameters, which includes the combination of machining parameters, and sends it to the equipment layer to control the CNC cutting machine tool to perform the cutting task.

7. The adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to claim 1, characterized in that, The cloud layer receives the local non-dominated solution set and the grid density vector, calculates the global density to update the global reference point set, specifically including: The cloud layer receives the local non-dominated solution set and the grid density vector sent by at least multiple edge layers, including the edge layer; The global density is calculated by calling the global density aggregation formula, which takes the total number of the multiple edge layers, the preset data volume weights corresponding to each edge layer, and the grid density vector sent by each edge layer as input parameters for aggregation calculation. The cloud layer updates the global reference point set based on the calculated global density.

8. The adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to claim 1, characterized in that, The process of updating the global elite archive and distributing elite solutions to the edge layer, and then using these elite solutions to replace a predetermined proportion of individuals with lower fitness rankings in the local population, specifically includes: The cloud layer sends the updated global reference point set and the elite solutions in the global elite archive to the edge layer according to a preset synchronization cycle. The edge layer ranks individuals within the local population based on their fitness values, locates a preset proportion of individuals with lower fitness rankings, and calls the elite solution to replace the preset proportion of individuals. For the edge layer of the newly connected manufacturing plant, the elite solutions in the global elite archive are extracted to form part of the initial local population, and the elite solutions are merged with randomly generated individuals to complete the cold start initialization operation.

9. The adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to claim 1, characterized in that, The monitoring of load status and triggering computational offloading and task scheduling specifically includes: The edge layer monitors the local server's operating load value as the load status and compares the local server's operating load value with a preset load threshold. When the local server's operating load exceeds the preset load threshold, a hard switchover strategy based on the preset load threshold is triggered to execute the computation offloading and task scheduling. The edge layer extracts the dataset required for the evolution iteration and sends it to the cloud layer. The cloud layer takes over the evolutionary iteration and generates the recommended solution set of parameters.

10. The adaptive multi-objective evolutionary optimization method for denture manufacturing process parameters according to claim 2, characterized in that, The operation of expanding the processing object model and updating parameters specifically includes: Based on the decision variable vector and the objective function formula, a multi-objective optimization mathematical model for the denture manufacturing scenario is constructed. The edge layer uses the multi-objective optimization mathematical model as the processing object model, which is the denture manufacturing model. The edge layer calls the model extension module to extend the processing object model to the orthopedic implant manufacturing model; Read the material property data of orthopedic implants, and use the material property data of orthopedic implants to update the cutting speed influence coefficient, feed rate influence coefficient and depth of cut influence coefficient inside the tool life equation to generate a recommended solution set of orthopedic implant processing parameters.

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