A multi-objective optimization method for injection molding process parameters

Abstract

This invention discloses a multi-objective optimization method for injection molding process parameters. First, simulation results datasets are obtained based on Moldflow simulation analysis and CCF. Then, an injection molding quality optimization model is constructed using NGO-XGBoost. Next, the SHAP method is used to interpret and analyze the NGO-XGBoost model, obtaining the importance and positive / negative impact of each optimization design variable on the predicted quality optimization objective. The Pareto front is obtained through multi-objective optimization using MOMVO. Finally, the optimal combination of process parameters is determined using the CRITIC-TOPSIS evaluation method. This invention can effectively reduce the warpage and volume shrinkage of ABS plastic injection molded parts, thereby obtaining high-quality ABS plastic products. It provides a theoretical basis and data support for obtaining the optimal combination of process parameters for ABS plastic injection molding.

Description

Technical Field

[0001] This invention relates to a multi-objective optimization method for injection molding process parameters, specifically a multi-objective optimization method for injection molding process parameters based on SHAP-NGO-XGBoost and MOMVO, belonging to the field of injection molding technology. Background Technology

[0002] ABS plastic is a terpolymer of acrylonitrile, butadiene, and styrene. It possesses excellent toughness, heat resistance, and good processing properties. It is a readily available, high-performance, inexpensive, and widely used "tough, hard, and rigid" material, finding extensive applications in machinery, electrical, textile, automotive, aircraft, shipbuilding, and chemical industries. Sensor housings are typically made of ABS plastic. For example, in automotive parts, ABS plastic sensor housings are used in anti-lock braking systems to improve braking performance and vehicle stability; in electronic products, they protect sensor components and ensure their proper operation. However, ABS plastic inevitably suffers from injection molding defects such as warpage and volume shrinkage, especially in thin-walled parts. Therefore, adjusting and optimizing process parameters such as temperature, time, and pressure to improve part quality, reduce defects, and achieve dimensional accuracy, appearance quality, and stable physical properties is a crucial aspect of ABS plastic injection molding research.

[0003] Currently, combining simulation analysis and mathematical model prediction is a common method for optimizing process parameters. Generally, the injection molding process of thin-walled plastic parts is first simulated using Moldflow software to analyze cooling effects and flow properties. Then, a mathematical model is constructed based on the simulation data to establish the relationship between quality objectives and process parameters. Finally, a search-based optimization algorithm is used to obtain the optimal combination of process parameters. For example, Cao Y et al. constructed an Adaptive Network Fuzzy Inference System (ANFIS) between warpage deformation and process parameters, and used a Genetic Algorithm (GA) to obtain the optimal process parameter scheme; Sun Zheng et al. constructed a mathematical proxy model between warpage deformation, volume shrinkage rate, and process parameters based on a gradient-enhanced Kriging (GEK) model, used a multi-objective differential evolution (MODE) algorithm to search for Pareto solutions, and determined the optimal process parameter scheme based on weighted coefficients; Liu X et al. used a GA-optimized Extreme Learning Machine (ELM) model to construct a mathematical proxy model between warpage deformation, volume shrinkage rate, and process parameters, applied a multi-objective firefly algorithm combined with the GRA-TOPSIS multi-objective decision-making method to determine the final optimal process parameter scheme.

[0004] In the study of practical injection molding problems, multiple interrelated objectives and constraints often need to be considered and weighed comprehensively. For example, warpage and volume shrinkage defects: while minimizing warpage by reducing the cooling rate will also increase volume shrinkage due to the extended cooling time. Multi-objective optimization, as a method for solving optimization problems involving multiple conflicting objectives, aims to find reasonable trade-offs among these objectives and generate a Pareto front of a set of multi-objective optimal values. Current research on multi-objective optimization often transforms multi-objective problems into single-objective problems using the idea of ​​weighted combination. Commonly used methods include Grey Relational Analysis (GRA), Top-Order Solution Approximation (TOPSIS), Entropy Weight, and Fuzzy Comprehensive Evaluation (FCE). However, from the perspective of multiple objectives, all objectives are usually mutually restrictive, and improving one objective often comes at the expense of others. Therefore, a multi-objective optimization problem usually generates a large number of non-dominated solutions (Pareto solutions). Currently, in the research on multi-objective optimization of injection molding process parameters, researchers often determine the final Pareto optimal solution based on engineering experience and repeated experiments. How to determine the optimal trade-off scheme to achieve the best comprehensive objective remains a challenge in the industry. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a multi-objective optimization method for injection molding process parameters, which can effectively reduce the warpage and volume shrinkage of ABS plastic injection molded parts, thereby obtaining high-quality ABS plastic parts. This method can provide a theoretical basis and data support for obtaining the optimal combination of process parameters for ABS plastic injection molding.

[0006] To achieve the above objectives, this multi-objective optimization method for injection molding process parameters specifically includes the following steps:

[0007] Step 1: Using warpage deformation and volume shrinkage rate as quality optimization targets, select process parameters that affect these two targets as optimization design variables, determine the range of process parameters based on recommended values, and use the range of each process parameter as the experimental design space to design CCF experiments. Then, perform injection molding simulation based on Moldflow to obtain the experimental results of the quality optimization targets.

[0008] Step 2: Based on the simulation test results, the XGBoost model is optimized using the NGO optimization algorithm to construct the NGO-XGBoost injection molding quality prediction model.

[0009] Step 3: Analyze the NGO-XGBoost model using the SHAP interpretation method to obtain the importance and positive and negative impact of each optimization design variable on the predicted quality optimization objective, and obtain the Pareto front of the quality optimization objective through multi-objective optimization using MOMVO.

[0010] Step 4: Determine the optimal combination of process parameters in the Pareto front of the obtained quality optimization objectives using the CRITIC-TOPSIS evaluation method.

[0011] Furthermore, in Step 2, the objective function obj of the XGBoost model is defined as follows:

[0012]

[0013] In the formula: Let y be the loss function, where y i This represents the actual value of sample i. Ω(f) represents the predicted value of sample i; k ) represents the regularization term, indicating the model complexity of the k-th decision tree, where f K This represents the Kth decision tree;

[0014] The regularization term of the objective function in the XGBoost model is defined as follows:

[0015]

[0016] In the formula: γ is the difficulty coefficient of node splitting; T is the depth of the current subtree; λ is the regularization parameter that controls the weight size; ω is the weight of the leaf node.

[0017] Furthermore, in Step 2, when optimizing the XGBoost model using the NGO optimization algorithm, the learning rate, the maximum depth of the tree, and the minimum weight of the leaf nodes are used as the hyperparameters to be optimized. The initial value of the number of hyperparameter combinations and the maximum number of iterations of the NGO optimization algorithm are set. The XGBoost model is trained by using the number of hyperparameter combinations initialized with the number of hyperparameter combinations in each iteration. Finally, the fitness value of the corresponding hyperparameter combination is calculated based on the model performance index. The lower the fitness value, the better the hyperparameter combination.

[0018] Furthermore, Step 3 analyzes the NGO-XGBoost model using the SHAP interpretation method, as detailed below:

[0019] ① Use TreeExplainer as the SHAP interpreter;

[0020] ②Calculate the SHAP value of each feature by providing dataset samples of the NGO-XGBoost model;

[0021] ③ The visualization function of the SHAP interpretability tool is used to explain the prediction logic of the model and generate a SHAP summary diagram.

[0022] Furthermore, in Step 3, multi-objective optimization is performed using MOMVO to obtain the Pareto front for the quality optimization objective, as detailed below:

[0023] ① Set the MOMVO parameters, define the objective function, and initialize relevant variables and archives;

[0024] ② Calculate the wormhole existence probability (WEP), travel distance rate (TDR), and fitness value in the main loop;

[0025] ③ Sort the solutions according to their fitness values, select non-dominated solutions, update the solution set and save it in the archive.

[0026] ④ Check if the file size of the current solution set exceeds the limit. If the file size exceeds the predetermined range, perform a trimming operation to remove the excess solution.

[0027] ⑤ Use the roulette wheel method to select a solution from the archive and update its position;

[0028] ⑥ Check the termination condition. If the maximum number of iterations has not been reached, continue the loop until the end to obtain the Pareto front.

[0029] Furthermore, in Step 4, when determining the optimal combination of process parameters in the Pareto front of the obtained quality optimization target using the CRITIC-TOPSIS evaluation method, firstly, weights are assigned to each evaluation index using the CRITIC method, and the weights of warpage deformation and volume shrinkage rate are calculated based on the correlation coefficient and standard deviation between each target; then, following the steps of the TOPSIS method, the degree of closeness between each evaluation object and the ideal target is calculated based on the obtained weights, and a comprehensive evaluation score is obtained.

[0030] Compared with existing technologies, this multi-objective optimization method for injection molding process parameters first obtains a simulation result dataset based on Moldflow simulation analysis and center composite surface design (CCF). Then, it constructs an injection molding quality optimization model using Northern Eagle Optimized Extreme Gradient Enhancement (NGO-XGBoost) based on dataset fitting. The NGO algorithm is used to explore the hyperparameter space, which can improve the model's prediction accuracy, balance model complexity, and prevent overfitting, thereby determining the most effective configuration of the XGBoost model. Then, the SHAP (SHapley Additive exPlanations) method is used to interpret and analyze the NGO-XGBoost model to obtain the importance and positive and negative impact of each optimization design variable on the prediction quality optimization objective. The Pareto front is obtained through multi-objective optimization using the Multi-Objective Multiverse Cosmic Optimization (MOMVO) algorithm. Finally, the optimal combination of process parameters is determined by the CRITIC-TOPSIS evaluation method. Simulation verification shows that the prediction error of the NGO-XGBoost model for warpage deformation and volume shrinkage rate is controlled within 5%, and the model prediction accuracy is good. Moreover, the optimized warpage deformation and volume shrinkage rate are significantly reduced compared with the simulation results before optimization. This can provide theoretical basis and data support for obtaining the optimal combination of process parameters for ABS plastic injection molding. Attached Figure Description

[0031] Figure 1 This is a 3D model of a sensor housing made of ABS plastic injection molding, where (a) is a front view of the sensor housing and (b) is a back view of the sensor housing.

[0032] Figure 2 These are the model diagrams for the model flow simulation analysis, where (a) is the front view of the model flow simulation analysis and (b) is the back view of the model flow simulation analysis.

[0033] Figure 3 These are simulation views of warpage deformation and volume shrinkage rate based on the process parameter combination recommended by Moldflow software before optimization, where (a) is the simulation view of warpage deformation and (b) is the simulation view of volume shrinkage rate.

[0034] Figure 4 This is a diagram illustrating the iterative convergence of NGOs;

[0035] Figure 5 These are SHAP summary diagrams, where (a) is a SHAP summary diagram of warpage deformation and (b) is a SHAP summary diagram of volume shrinkage rate;

[0036] Figure 6 This is a flowchart of multi-objective optimization based on the MOMVO algorithm;

[0037] Figure 7 This is a Pareto front diagram obtained after multi-objective optimization based on the MOMVO algorithm;

[0038] Figure 8 These are simulation views of the optimal combination of warping deformation and volume shrinkage rate after optimization, where (a) is the simulation view of warping deformation and (b) is the simulation view of volume shrinkage rate. Detailed Implementation

[0039] This multi-objective optimization method for injection molding process parameters aims to optimize the warpage and volume shrinkage of ABS plastic products. First, it obtains a dataset of simulation results based on Moldflow simulation analysis and center composite surface design (CCF). Then, it constructs an injection molding quality optimization model using Northern Eagle Optimized Extreme Gradient Enhancement (NGO-XGBoost) based on dataset fitting. Next, it interprets and analyzes the NGO-XGBoost model using the SHAP (SHapley Additive exPlanations) method, and obtains the Pareto front through multi-objective multivariate universe optimization (MOMVO). Finally, it determines the optimal combination of process parameters using the CRITIC-TOPSIS evaluation method.

[0040] The present invention will be specifically described below using an ABS plastic injection-molded sensor housing as an example.

[0041] The geometric model of the sensor housing made of ABS plastic injection molding is as follows: Figure 1 (a) Figure 1 As shown in (b), the sensor housing requires adequate heat dissipation and a lightweight design. The dimensions of the plastic part are 216mm × 154mm × 50mm, and its volume is 239292mm². 3 The average wall thickness is 2.16 mm. The interior and edges of the plastic part utilize a reinforcing rib structure to distribute external loads and reduce localized stress concentration. Simultaneously, strict surface quality requirements are imposed on the mating posts and holes to ensure the precision and stability of mating with other components. This plastic part is required to have a warpage deformation and volume shrinkage rate not exceeding 0.584 mm and 7%, respectively.

[0042] The 3D model of the plastic part was imported into Moldflow software for mesh generation. The mesh was created using triangular elements. Because flow analysis may involve drastic changes in flow pressure, temperature, and velocity, potentially leading to analysis failure, long and thin elements should be avoided as much as possible. Mesh statistics show that free edges and multi-edges are 0, connected components are 1, misaligned elements are 0, and the aspect ratio is less than 6.00. The mesh generation meets the requirements of the 3D model, ensuring the accuracy of the analysis results. It is also important to note that the mesh matching rate of the surface mesh model must reach at least 85% for flow + pressure holding analysis, and for warpage deformation analysis, the matching rate must reach at least 90%.

[0043] After the mesh is generated, establish as follows: Figure 2 (a) Figure 2 (b) shows the mold flow simulation analysis model including the gating system and the cooling system. The red pipes represent the gating system, which consists of the gate and the main runner. It can smoothly fill the mold cavity with the molten plastic to obtain plastic products with clear outlines and excellent internal quality. The blue pipes represent the cooling system, which consists of straight-through channels and circumferential channels. In the molding cycle of plastic parts, the cooling time of the mold accounts for more than 2 / 3 of the entire cycle. Therefore, the quality of the cooling effect has a great impact on the molding efficiency and the quality of the plastic parts.

[0044] The Moldflow simulation analysis sequence was set as: cooling-filling-holding-warpage. The ABS material grade was PA-757, and the software-recommended process parameter combination was: melt temperature 210℃, mold temperature 45℃, holding pressure 80MPa, and molding cycle time 30s. After the analysis was completed, as follows... Figure 3 (a) Figure 3 As shown in (b), the quality target warpage deformation and volume shrinkage rate are 0.7645 mm and 7.124%, respectively, which do not meet the requirements of the plastic part product.

[0045] Step 1: Determine the quality optimization target, select the injection molding process parameters and their value ranges, use the value ranges of each process parameter as the experimental design space, design CCF experiments based on the value ranges of each process parameter, and perform injection molding simulation based on Moldflow to obtain the experimental results of the quality optimization target.

[0046] Warpage deformation (W / mm) and volume shrinkage rate (V / %) were used as quality optimization targets. Based on the process parameters recommended by Moldflow software and the influencing factors of the mold flow analysis process, the process parameters were subdivided into melt temperature (A / ℃), mold temperature (B / ℃), injection pressure (C / MPa), holding pressure (D / MPa), injection time (E / s), holding time (F / s), and cooling time (G / s). These seven process parameters were used as input variables for CCF design, and warpage deformation (W / mm) and volume shrinkage rate (V / %) were used as output variables.

[0047] The process parameters are referenced from the commonly used range for injection molding. The upper limit of the parameters is (230, 70, 90, 70, 5, 30, 30), and the lower limit is (180, 50, 70, 50, 3, 15, 15). The experimental level arrangement must not exceed the cube boundary; therefore, the value of 'a' is taken as 0.6, making the parameter level (-1, -a, 0, a, 1). This ensures that the experimental design fully considers the high and low levels of the process parameters and achieves the required accuracy within the design range.

[0048] As shown in Table 1, the CCF experimental design was divided using Minitab software, and the entire experimental arrangement consisted of the following three experimental points:

[0049] ① Cube point, where the coordinates of each point are either 1 or -1, is part of the composition factor experiment.

[0050] ②The center point, where the three-dimensional coordinates of all points are 0.

[0051] ③ Axial point: except for one coordinate which is ±0.6, all other coordinates are 0.

[0052] Table 1. Experimental Design and Simulation Results

[0053]

[0054]

[0055] Step 2: Based on the simulation test results, the Northern Eagle Optimized Extreme Gradient Enhancement (NGO-XGBoost) based on dataset fitting is used to construct an injection molding quality prediction model.

[0056] The XGBoost model is a supervised learning algorithm that integrates multiple CART trees using Gradient Tree Boosting. In the CART tree generation algorithm, the regression tree with the smallest sum of squared errors is selected as the optimal split point. After a tree is generated, it is pruned to improve generalization ability. The tree generated in the k-th round learns the "residual" between the true value and the model's predictions in the (k-1)-th round, causing the model's predictions to gradually approach the true values.

[0057] The objective function obj of the XGBoost model is defined as follows:

[0058]

[0059] In the formula: Let y be the loss function, where y i This represents the actual value of sample i. Ω(f) represents the predicted value of sample i; k ) represents the regularization term, indicating the model complexity of the k-th decision tree, where f K Let K represent the Kth decision tree.

[0060] Unlike the AdaBoost model, which only has a loss function as its objective function, the XGBoost model's objective function consists of two terms: a loss function and a regularization term. The loss function is used to evaluate the error or loss between the model's predictions and the true values, while the regularization term is used to control the model's complexity, tending to select a simpler model to avoid overfitting.

[0061] The regularization term is defined as follows:

[0062]

[0063] In the formula: γ is the difficulty coefficient of node splitting; T is the depth of the current subtree; λ is the regularization parameter that controls the weight size; ω is the weight of the leaf node.

[0064] In the above formula, the first term γT controls the complexity of the tree through the number of leaf nodes and its coefficient; the larger the value, the larger the objective function, thereby suppressing the complexity of the model. The second term... The L2 regularization term is used to control the weight scores of leaf nodes (i.e., the weights of leaf nodes are controlled by the regularization parameter), making the model less susceptible to data noise.

[0065] NGO is a group-based metaheuristic algorithm that mimics the hunting behavior of the northern goshawk, which consists of two main actions: prey identification and attack, and pursuit and escape. These two actions also correspond to the exploration and development phases, respectively.

[0066] ① Prey identification and attack

[0067] As a northern goshawk soars through the air, it searches for potential prey. Once it spots a target, it adjusts its position to attack. In optimization algorithms, solutions are considered potential prey, and the goal is to find the optimal solution—the most nutritious prey. Therefore, during the search phase, randomly selecting prey within the search space enhances the algorithm's global exploration capability to determine the best area.

[0068] ② Chase and escape operations

[0069] After a northern goshawk attacks its prey, the prey attempts to escape. Therefore, in a series of chases and escapes, the northern goshawk continues to pursue its prey. Due to its high speed and maneuverability, the northern goshawk can hunt its prey in almost any situation and eventually capture it. This behavioral simulation enhances the algorithm's ability to perform local searches within the search space.

[0070] To determine the most efficient configuration of the XGBoost model, the NGO algorithm was used to explore the hyperparameter space, thereby improving model prediction accuracy, balancing model complexity, and preventing overfitting. As shown in Table 2, the learning rate, maximum tree depth, and minimum sum of weights of leaf nodes are the hyperparameters to be optimized, with values ​​ranging from (0, 100), (1, 8), and (1, 3), respectively. Therefore, the population size (number of hyperparameter combinations) of the NGO optimization algorithm was initialized to 50, and the maximum number of iterations was set to 100. The XGBoost model was trained for each of the 50 hyperparameter combinations in each iteration. Finally, the fitness value of the corresponding hyperparameter combinations was calculated based on model performance metrics (RMSE, MAE, MAPE). A lower fitness value indicates a better hyperparameter combination. Figure 4 As shown, it is clear that after 40 iterations, the fitness value of the model reached the lowest point of 0.0872, which indicates that the hyperparameter combination has reached the optimal configuration at this time.

[0071] Table 2 Hyperparameter Combinations

[0072]

[0073] The R-values ​​of the four models NGO-XGBoost, XGBoost, AdaBoost-SVM, and AdaBoost-ELM are compared. 2 Comparison of RMSE, MAE, and MAPE, R 2 The R-squared values ​​reflect the linear relationship between predicted and simulated values; the closer to 1, the better. RMSE, MAE, and MAPE reflect the first and second order relative errors between predicted and simulated values; the smaller the error value, the better the model fit. As shown in Table 3, in the prediction model for warping deformation, the R-squared value of the model... 2The ranking is: NGO-XGBoost > XGBoost > AdaBoost-SVM > AdaBoost-ELM, and the ranking of the RMSE, MAE and MAPE of the models is: NGO-XGBoost < XGBoost < AdaBoost-SVM < AdaBoost-ELM. As shown in Table 4, in the prediction model of volume shrinkage, the R 2 The ranking is: NGO-XGBoost > XGBoost > AdaBoost-SVM > AdaBoost-ELM, and the ranking of the RMSE, MAE and MAPE of the models is: NGO-XGBoost < XGBoost < AdaBoost-SVM < AdaBoost-ELM. In summary, the NGO-XGBoost model has the best prediction ability in the prediction of warpage deformation and volume shrinkage.

[0074] Table 3 Comparison of warpage deformation prediction models

[0075]

[0076] Table 4 Comparison of volume shrinkage prediction models

[0077]

[0078] Step 3: Use the SHAP (SHapley Additive exPlanations) method to interpret and analyze the NGO-XGBoost model, and perform multi-objective optimization through the multi-objective multi-universe optimization algorithm (MOMVO) to obtain the Pareto front of the quality optimization objective.

[0079] SHAP is a method for interpreting the predictions of machine learning models. It is based on the concept of Shapley values in cooperative game theory and quantifies the contribution of parameters to the model predictions. Perform SHAP interpretation on the NGO-XGBoost model to obtain the contribution of each process parameter to the prediction quality objective, that is, the SHAP value. Moreover, if the SHAP value is positive, the quality objective increases; if the SHAP value is negative, the quality objective decreases. Use red to represent the low level of the parameter and blue to represent the high level of the parameter. For the warpage deformation amount and volume shrinkage rate, the smaller the two, the better the quality of the plastic part.

[0080] Analyze the NGO-XGBoost model through the SHAP interpretation method as follows:

[0081] ① Constructing the SHAP Explainer: To explain the decision-making process of the NGO-XGBoost model, the SHAP tree model explainer (TreeExplainer) is used. This explainer is specifically designed for tree structure models and is the core tool in SHAP for explaining tree models (such as XGBoost and LightGBM). TreeExplainer can quickly and efficiently calculate the SHAP values ​​of each feature by analyzing the split nodes of the tree model.

[0082] ② Calculate SHAP values: After the SHAP interpreter is built, the SHAP value of each feature can be calculated by providing a dataset sample of the NGO-XGBoost model. The SHAP value reflects the positive or negative contribution of process parameters to the model's prediction results and is a core indicator for quantifying the influence of process parameters.

[0083] ③ Visualization Analysis: To intuitively display the distribution of SHAP values ​​and the contribution of each process parameter to the model, the visualization function of the SHAP interpretability tool is used to interpret the prediction logic of the model and generate a SHAP summary diagram.

[0084] Generate a SHAP digest image as follows Figure 5 As shown, Figure 5 As shown in (a), in the NGO-XGBoost warpage prediction model, the importance ranking is: melt temperature (A) > holding pressure (D) > injection pressure (C) > injection time (E) > cooling time (G) > holding time (F) > mold temperature (B). Explaining the significance of melt temperature, a low melt temperature increases warpage, while a high melt temperature decreases warpage. Figure 5 As shown in (b), in the NGO-XGBoost volume shrinkage prediction model, the importance ranking is: melt temperature (A) > injection time (E) > holding pressure (D) > cooling time (G) > holding time (F) > mold temperature (B) > injection pressure (C). Similarly, the significant factor of melt temperature is explained: a low melt temperature reduces volume shrinkage, while a high melt temperature increases volume shrinkage. SHAP analysis shows that a high melt temperature reduces warpage but increases volume shrinkage. Therefore, the prediction model must incorporate multi-objective optimization methods to find the optimal combination of process parameters.

[0085] MOMVO is a multi-objective MVO algorithm inspired by the multiverse theory, in which white holes, black holes, and wormholes are three core elements. In the MOMVO algorithm, white holes represent points where new solutions are generated, which are potentially optimal solutions in the search space; black holes are used to eliminate bad solutions, which are suboptimal or invalid solutions in multi-objective optimization problems; wormholes are seen as a mechanism for jumping or exchanging solutions, allowing solutions to move and exchange rapidly in the search space to accelerate the optimization process or avoid local optimum traps.

[0086] Based on the constructed NGO-XGBoost model, the MOMVO algorithm is used for global optimization. For example... Figure 6As shown, firstly, the initial parameters of MOMVO are set, including the population size, the number of universes (i.e., solutions), the probability of white holes / black holes, the number of iterations, etc. The maximum number of iterations is set to 150, the initial number of universes is 100, and the maximum file storage is 100. The objective function is defined, and the relevant variables and files are initialized. Then, in the main loop, the wormhole existence probability (WEP), travel distance rate (TDR), and cosmic expansion rate (i.e., fitness value) are calculated. The wormhole existence probability (WEP) and travel distance rate (TDR) are the two core coefficients of MOMVO, which affect the iteration and optimization process, enabling the MOMVO algorithm to perform more accurate exploration and local search around the optimal universe. WEP represents the probability of white hole existence. As the iteration progresses, the WEP value will gradually increase, which means that the influence of white holes is greater in the later stages. TDR is used to control the wormhole traversal distance between black holes and white holes. Calculating the cosmic expansion rate (i.e., fitness value) means calculating the fitness value or objective function value of each solution, with the purpose of evaluating the quality of the solution. Then, an elitist strategy is used to update the optimal solution. Specifically, the universe (i.e., the solution) is sorted according to its expansion rate (i.e., fitness value), and a non-dominated solution is selected (a solution that has no better alternatives on all objectives). The solution set is updated and saved in a file. During the update process, the possibility of a full file needs to be addressed. The file size of the current solution set is checked to see if it exceeds a limit. If the file size exceeds the predetermined range, the excess solutions are pruned and removed to maintain a reasonable file size. This update is performed through ranking and pruning. Finally, a roulette wheel method is used to... The algorithm selects a universe (i.e., a solution) from the archive and updates its position. A roulette wheel mechanism is used to select different universes (i.e., solutions) to determine which universes can be preserved and optimized. Then, through the white hole and black hole mechanism, the algorithm simulates the passage of matter from one universe to another, thereby generating new solutions. Finally, the algorithm checks the termination condition. The algorithm starts from the initial number of iterations. After completing one iteration, the number of iterations is incremented by 1, and the above steps are repeated until the preset maximum number of iterations is reached. If the current number of iterations is less than the maximum number of iterations, the algorithm continues to execute; otherwise, it terminates and outputs the Pareto front.

[0087] The final Pareto front is as follows Figure 7 As shown.

[0088] Step 4: Determine the optimal combination of process parameters using the CRITIC-TOPSIS evaluation method.

[0089] To meet the product requirements that the warpage and volume shrinkage of the ABS plastic part must not exceed 0.584 mm and 7% respectively, 13 Pareto solutions meeting the requirements were selected, and the optimal combination of process parameters was determined using the CRITIC-TOPSIS evaluation method. In the evaluation process, the CRITIC-TOPSIS method fully leverages the advantages of both the CRITIC and TOPSIS methods. First, weights are assigned to each evaluation index using the CRITIC method, and the weights for warpage and volume shrinkage are calculated based on the correlation coefficient and standard deviation between each objective, resulting in [0.566, 0.434]. Then, following the steps of the TOPSIS method, the degree of closeness between each evaluated object and the ideal target is calculated based on the obtained weights, thereby deriving a comprehensive evaluation score. As shown in Table 5, the fifth group has the highest score, with optimal warpage deformation and volume shrinkage rates of 0.528 mm and 6.504%, respectively. The corresponding process parameter combination is as follows: melt temperature (A) = 207.783℃, mold temperature (B) = 59.739℃, injection pressure (C) = 82.767 MPa, holding pressure (D) = 69.559 MPa, injection time (E) = 4.358 MPa, holding time (F) = 29.352 s, and cooling time (G) = 22.804 s.

[0090] Table 5. Comprehensive Evaluation Results of CRITIC-TOPSIS

[0091]

[0092] The highest-scoring parameter combination obtained from the CRITIC-TOPSIS evaluation was used for Moldflow simulation analysis, such as... Figure 8 As shown, the warpage deformation and volume shrinkage rate were 0.506 mm and 6.675%, respectively, while the model's predicted values ​​were 0.528 mm and 6.504%, respectively. The deviations between the two values ​​were 4.3% and 2.6%, respectively, with the error controlled within 5%, indicating that the model's prediction accuracy was good. Furthermore, compared to the initial combination of process parameters, the warpage deformation and volume shrinkage rate were reduced by 30.9% and 8.7%, respectively, achieving a simultaneous reduction in warpage deformation and volume shrinkage rate, indicating a good optimization effect.

Claims

1. A multi-objective optimization method for injection molding process parameters, characterized in that, Specifically, the following steps are included: Step 1: Using warpage deformation and volume shrinkage rate as quality optimization targets, select process parameters that affect these two targets as optimization design variables, determine the range of process parameters based on recommended values, and use the range of each process parameter as the experimental design space to design CCF experiments. Then, perform injection molding simulation based on Moldflow to obtain the experimental results of the quality optimization targets. Step 2: Based on the simulation test results, the XGBoost model is optimized using the NGO optimization algorithm to construct the NGO-XGBoost injection molding quality prediction model. Step 3: Analyze the NGO-XGBoost model using the SHAP interpretation method to obtain the importance and positive and negative impact of each optimization design variable on the predicted quality optimization objective, and obtain the Pareto front of the quality optimization objective through multi-objective optimization using MOMVO. Step 4: Determine the optimal combination of process parameters in the Pareto front of the obtained quality optimization objectives using the CRITIC-TOPSIS evaluation method.

2. The multi-objective optimization method for injection molding process parameters according to claim 1, characterized in that, In Step 2, the objective function obj of the XGBoost model is defined as follows: In the formula: Let y be the loss function, where y i This represents the actual value of sample i. Ω(f) represents the predicted value of sample i; k ) represents the regularization term, indicating the model complexity of the k-th decision tree, where f K This represents the Kth decision tree; The regularization term of the objective function in the XGBoost model is defined as follows: In the formula: γ is the difficulty coefficient of node splitting; T is the depth of the current subtree; λ is the regularization parameter that controls the weight size; ω is the weight of the leaf node.

3. The multi-objective optimization method for injection molding process parameters according to claim 2, characterized in that, In Step 2, when optimizing the XGBoost model using the NGO optimization algorithm, the learning rate, the maximum depth of the tree, and the minimum weight of the leaf nodes are used as the hyperparameters to be optimized. The initial values ​​of the number of hyperparameter combinations and the maximum number of iterations for the NGO optimization algorithm are set. The XGBoost model is trained by using the number of hyperparameter combinations initialized with the number of hyperparameter combinations in each iteration. Finally, the fitness value of the corresponding hyperparameter combination is calculated based on the model performance index. The lower the fitness value, the better the hyperparameter combination.

4. The multi-objective optimization method for injection molding process parameters according to claim 3, characterized in that, Step 3 analyzes the NGO-XGBoost model using the SHAP interpretation method, as detailed below: ① Use TreeExplainer as the SHAP interpreter; ②Calculate the SHAP value of each feature by providing dataset samples of the NGO-XGBoost model; ③ The visualization function of the SHAP interpretability tool is used to explain the prediction logic of the model and generate a SHAP summary diagram.

5. The multi-objective optimization method for injection molding process parameters according to claim 4, characterized in that, In Step 3, multi-objective optimization is performed using MOMVO to obtain the Pareto front for the quality optimization objective, as detailed below: ① Set the MOMVO parameters, define the objective function, and initialize relevant variables and archives; ② Calculate the wormhole existence probability (WEP), travel distance rate (TDR), and fitness value in the main loop; ③ Sort the solutions according to their fitness values, select non-dominated solutions, update the solution set and save it in the archive; ④ Check if the file size of the current solution set exceeds the limit. If the file size exceeds the predetermined range, perform a trimming operation to remove the excess solution. ⑤ Use the roulette wheel method to select a solution from the archive and update its position; ⑥ Check the termination condition. If the maximum number of iterations has not been reached, continue the loop until the end to obtain the Pareto front.

6. The multi-objective optimization method for injection molding process parameters according to claim 1, characterized in that, In Step 4, when determining the optimal combination of process parameters in the Pareto front of the obtained quality optimization target using the CRITIC-TOPSIS evaluation method, firstly, weights are assigned to each evaluation index using the CRITIC method, and the weights of warpage deformation and volume shrinkage are calculated based on the correlation coefficient and standard deviation between each target; then, following the steps of the TOPSIS method, the degree of closeness between each evaluation object and the ideal target is calculated based on the obtained weights, and a comprehensive evaluation score is obtained.

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