Image-informed Multi-objective Optimization of Cartridge Heater Layout in Injection Molds Using CNN Features and Random Forest Surrogates
Article information
Abstract
In thermoset injection molding, achieving uniform temperature distribution and rapid heating is essential to ensure product quality and process efficiency. This study presents a data-efficient optimization framework that combines simulation image-based feature extraction, and machine learning-based surrogate modeling. A total of 10 thermal simulations were conducted using Moldex3D, with heater depth and spacing conditions determined through Maximin Latin Hypercube Sampling. Thermal simulation images were captured for each configuration. Spatial features were extracted from these images using a pretrained ResNet34 convolutional neural network. Resulting feature vectors were averaged to form a compact thermal descriptor. These features, along with process parameters, were used to train Random Forest regression models for predicting average temperature and maximum–minimum temperature difference. To maximize heating performance and minimize thermal variation, a multi-objective optimization problem was formulated and solved using the NSGA-II evolutionary algorithm. The proposed method successfully identified Pareto-optimal heater layouts that improved both target metrics, outperforming conventional design of experiments-based strategies. This framework demonstrated the viability of integrating full-field thermal imagery with AI-driven surrogate modeling and evolutionary optimization, particularly in low-data scenarios. It provides a promising foundation for future work on intelligent process design and control in complex thermoset molding applications.
1 Introduction
Injection molding is a pivotal manufacturing process enabling the mass production of polymer components with intricate geometries. Among its variants, thermoset injection molding has garnered increasing attention due to its superior chemical resistance and high-temperature performance. Unlike thermoplastic molding, which relies on cooling channels to solidify materials, thermoset molding necessitates heating the mold to initiate a curing reaction, making precise thermal control essential for ensuring product quality and process stability [1].
Cartridge heaters are commonly employed as a practical and cost-effective heating solution in thermoset molds. However, challenges such as prolonged preheating times, uneven temperature distribution, and energy inefficiency persist, particularly in large or complex molds. Studies have demonstrated that heater placement—specifically, the depth and spacing of heaters—significantly influences the mold’s thermal behavior and, consequently, the curing uniformity of the molded part [2].
To address these challenges, researchers have adopted various numerical optimization techniques utilizing data from computer-aided engineering (CAE) simulations. Methods such as Design of Experiments (DOE), Response Surface Methodology (RSM), Kriging-based surrogate modeling, and multi-objective genetic algorithms (MOGA) have been extensively applied to optimize process parameters [3]. These approaches typically define objective functions like mean temperature and temperature standard deviation across the part surface to balance rapid heating with thermal uniformity [4,5]. For instance, a notable study applied these methods to a square flat specimen, achieving significant improvements in temperature profiles through optimal heater layout [6].
Despite their effectiveness, traditional methods are fundamentally limited by their reliance on scalar features extracted from complex simulation data. Modern CAE tools provide high-resolution thermal images rich in spatial information, yet most optimization workflows reduce these images to simple statistical summaries, potentially overlooking critical thermal gradients or patterns. Moreover, surrogate models often require numerous simulations to accurately approximate the objective landscape, leading to increased computational costs and limited scalability [7].
Recent advancements in artificial intelligence (AI), particularly in computer vision and deep learning, have opened new avenues for leveraging full-field simulation data in optimization tasks. Convolutional Neural Networks (CNNs), for example, have demonstrated exceptional performance in extracting meaningful spatial features from image data and can be trained to detect subtle patterns in thermal fields [8]. Additionally, Bayesian optimization has gained popularity as a sample-efficient strategy for high-cost engineering design problems, especially when combined with AI-driven feature extraction [9]. It has also been applied in recent studies involving inverse thermal conductivity problems and selective thermal emitter design [10].
Furthermore, studies have explored the integration of CNN-based models for defect detection in injection molding processes, highlighting the potential of deep learning in manufacturing quality control [11]. An experimental ADoE approach based on Bayesian optimization was developed for injection molding using process and sensor data to optimize the quality and cycle time in real-time [12]. A comparative study of multi-objective Bayesian optimization and NSGA-III based approaches for injection molding process optimization demonstrated the effectiveness of Bayesian methods in achieving optimal process parameters [13].
Optimization to assist design and analysis of temperature control systems in injection molding has been explored using CAE software, enabling the assessment of the injection molding process and the thermo-mechanical model concerning the plastic part [14]. The use of additive manufacturing in the development and optimization of injection molding tools has shown significant improvements in temperature regulation, reduced cycle times, and consistent mechanical properties of the molded components [15]. Proper installation of cartridge heaters is crucial to ensure uniform temperature distribution and prevent mold damage due to overheating [16].
Bayesian optimization has been effectively applied to predict the thermal properties of materials, reducing the time required to discover optimal parameters [17]. A quality prediction method combining infrared thermography and CNN models has been proposed for injection molding, demonstrating high accuracy in defect detection [18]. A novel sensing feature extraction method based on mold temperature and melt pressure has been developed for plastic injection molding quality assessment, utilizing machine learning techniques [19].
This research investigates a novel optimization framework that integrates thermal simulation images and deep learning-based feature extraction for heater layout design in thermoset injection molding. A total of 10 thermal simulations were conducted using Moldex3D, and the experimental design was guided by the Maximin Latin Hypercube Sampling (LHS) method to ensure wide and balanced coverage of the design space. From these simulations, high-resolution thermal field images were obtained. Convolutional neural networks (CNNs) were employed to extract spatial thermal features, and Random Forest surrogate models were trained to predict thermal performance metrics such as average temperature and temperature difference. These predictions were then used in a multi-objective optimization algorithm (NSGA-II) to explore heater depth and spacing configurations that balance thermal efficiency and uniformity. Unlike conventional scalar-based approaches, this framework leverages full-field thermal imagery to enhance modeling accuracy and optimization quality, especially in data-scarce environments. The proposed method demonstrates the feasibility of combining AI techniques with physical simulations for intelligent mold design and offers a foundation for future smart manufacturing applications.
2 Methodology
2.1 Framework Overview
The overall research framework for optimizing cartridge heater layout in thermoset injection molding is illustrated in Fig. 1. The workflow begins with the construction of a 3D thermal simulation model using Moldex3D, incorporating the mold geometry, cartridge heater positions, and thermoset material properties. A total of 10 simulation cases are generated using Maximin Latin Hypercube Sampling (LHS) to ensure well-distributed exploration of the design space defined by heater depth and spacing.
Flowchart of research methodology
Each sampling point is used to conduct a transient thermal simulation, and the resulting temperature fields during the preheating stage are saved as high-resolution images. These images are then calibrated using the embedded scalebar and resized to a consistent format suitable for image processing. Spatial features that reflect heating intensity and distribution patterns are extracted using a pretrained ResNet34 convolutional neural n etwork (CNN). This network outputs a 512-dimensional feature vector per image, and the average vector across all simulations is used to represent the global thermal tendency in a compact manner.
To model the relationship between heater layout and thermal performance, the mean CNN feature vector is concatenated with standardized heater depth and spacing values. This hybrid vector forms the input to Random Forest regression models, which are trained to predict two key metrics: the average temperature and the difference between maximum and minimum temperatures in the mold. These surrogate models allow fast and accurate evaluation of new design candidates without requiring additional simulations.
Finally, the trained surrogate models are incorporated into a multi-objective optimization algorithm, NSGA-II, which explores heater depth and spacing configurations that jointly improve thermal efficiency and uniformity. This integrated framework leverages full-field simulation imagery and machine learning to enable data-efficient optimization of heater layout, especially under constraints of limited simulation resources.
2.2 Simulation Model
To evaluate the influence of cartridge heater layout on the thermal behavior of a molded product, a series of simulations were conducted using the commercial thermoset injection molding software Moldex3D 2021. As shown in Fig. 2, the simulation model consisted of a rectangular plate specimen with embedded cartridge heaters, mold plates, and runner geometry. The dimensions of the cavity were set to 150mm × 100 mm × 4mm. The rectangular plate specimen was chosen as a simplified geometry that facilitates consistent evaluation of thermal response and basic material behavior. Its planar and thin-walled structure enables uniform heat flow analysis while isolating the influence of heater layout without geometric complexity.
Simulation model (a) ISO view and (b) Side view
The computational mesh contained a total of 1,065,473 elements, consisting of both tetrahedral and prism elements. To improve the accuracy near the cavity wall, three layers of prism elements were applied to the surface layer of the cavity, enabling better resolution of temperature and velocity gradients in the boundary region. The material used for the simulation was Momentive LSR2060, a typical thermosetting liquid silicone rubber (LSR) with curing behavior suitable for thermal analysis. This material was selected as a representative and widely used liquid silicone rubber (LSR) material in industrial thermoset molding applications. As one of the most commonly adopted commercial-grade LSRs, it was chosen as a baseline material for preliminary modeling and simulation studies.
For the simulation of transient, non-isothermal flow behavior of the molten polymer, the governing equations were based on the Generalized Newtonian Fluid (GNF) model. This model was used to describe the momentum conservation of the molten material under varying temperature and shear conditions. The viscosity of the polymer melt was modeled using the Cross-Castro-Macosko model, which incorporates Arrhenius-type temperature dependence. This approach allows accurate prediction of the viscosity under different thermal environments and shear rates, which is critical for capturing the realistic flow and curing behavior of thermoset materials.
2.3 Data Sampling Strategy
The selection of an appropriate sampling method plays a crucial role in determining both the efficiency and reliability of simulation-based optimization. In this study, to ensure a uniform distribution of sampling points and enhance space-filling characteristics, we adopted a Maximin-based Latin Hypercube Sampling (Maximin LHS) method. This approach was compared with the standard Latin Hypercube Sampling (LHS), which is widely used in the design of experiments (DOE).
Standard LHS divides each variable’s domain into equal intervals and selects one random point from each interval, ensuring stratification and reduced variable correlation. However, due to the randomness of point allocation, some samples may cluster in certain regions of the design space, reducing the overall coverage and potentially degrading the reliability of downstream analysis.
To address this limitation, Maximin LHS introduces a distance-based optimization criterion into the LHS procedure. Maximin Latin Hypercube Sampling (LHS) was adopted to ensure uniform and space-filling coverage of the input domain. Its distance-maximizing strategy provides better sample dispersion, which is particularly beneficial when the number of simulations is limited. Specifically, it maximizes the minimum Euclidean distance between all pairs of sample points, leading to a more uniformly dispersed set of samples across the design space. This improves the space-filling quality of the dataset and reduces the likelihood of unexplored regions. The minimum Euclidean distance between any two samples is defined as follows.
Where i, j denote the indices of two distinct samples in the sampling set, with i ≠ j; xi1, xj1 represent the values of the first design variable for the i-th and j-th samples, respectively; and xi2, xj2 represent the second design variable. The expression inside the square root represents the Euclidean distance in a two-dimensional input space.
The rationale for adopting Maximin LHS in this study is threefold. First, a more uniform sampling distribution is essential for sensitivity analysis and global optimization, where unexplored or clustered regions can hinder performance. Second, Maximin LHS prevents excessive point redundancy, allowing fewer samples to effectively represent the design space. Third, this method has been widely adopted in machine learning-informed optimization studies, particularly in Gaussian Process and Bayesian Optimization frameworks [20].
To balance exploration quality and simulation cost, the number of initial sampling points was set to 12. A total of 500 iterations of LHS sampling were performed, and the configuration that yielded the largest minimum Euclidean distance among samples was selected as the final dataset. This ensured that the samples achieved the best possible space-filling characteristics while minimizing computational burden.
Based on this strategy, a total of 10 design points were generated using Maximin LHS, as shown in Fig. 3. Each point corresponds to a unique combination of heater depth (variable a) and heater distance (variable b), and the minimum Euclidean distance among all pairs of samples was 10.680. The scatter distribution confirms the uniform coverage of the design space, which supports reliable and balanced exploration in subsequent simulations. The detailed design variables for the 10 sampling points are summarized in Table 1.
Distribution of 10 design points generated by maximin Latin hypercube sampling (LHS) in the design space of (a) heater depth and (b) distance
Design variables for 10 sampling points generated by maximin Latin hypercube sampling (LHS)
2.4 Feature Extraction and Optimization
A structured framework was developed to extract image-based features and perform multi-objective optimization for cartridge heater layout in thermoset injection molding. High-resolution thermal field images were employed to capture detailed spatial variations in temperature, enabling the extraction of subtle thermal gradients that may not be apparent from scalar values alone. The primary goal of this framework is to identify the optimal combination of heater depth and spacing that maximizes the average mold temperature (AVG) while minimizing the temperature difference between the maximum and minimum values (Tmax–Tmin) during the preheating stage.
The Random Forest surrogate models were implemented using the scikit-learn library with the following hyperparameters: n_estimators = 100, max_depth = 6, min_samples_leaf = 1, and random_state = 42. These values were chosen to balance model complexity and generalization, given the limited dataset.
For each of the 10 simulation cases generated via Maximin Latin Hypercube Sampling, a high-resolution thermal distribution image was obtained. These images were resized to 224 × 224 pixels and normalized using ImageNet statistics to conform to the standard input requirements of convolutional neural networks (CNNs). A pretrained ResNet34 model was used, and the output from the last convolutional block (prior to the fully connected layer) was extracted to form a 512-dimensional feature vector for each image. To ensure robustness given the limited dataset, the 10 feature vectors were averaged into a single representative CNN descriptor. To mitigate potential overfitting due to the limited dataset, no fine-tuning was performed on the pretrained CNN, and the extracted 512-dimensional feature vectors were averaged across samples to generate a single descriptor per design point. An example of the thermal field image used for CNN input is shown in Fig. 4. This image was obtained from Moldex3D simulation results and resized to 224 × 224 pixels before being used for feature extraction.
Example thermal distribution images used as input for CNN
This averaged CNN feature vector was then concatenated with standardized heater depth and spacing values for each simulation to form a hybrid input vector of 514 dimensions. These input vectors were used to train two separate Random Forest regression models: one to predict average temperature (AVG) and another to predict the temperature difference (Tmax–Tmin). The input process parameters used for training were cartridge heater depth and spacing, which correspond to the design variables in the optimization framework. Each model was trained using 10 data points and used a limited tree depth and minimum leaf size to avoid overfitting.
With the surrogate models trained, a multi-objective optimization was conducted using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The design variables were heater depth and spacing, and the two objectives were defined as: (1) maximize predicted average temperature and (2) minimize predicted Tmax–Tmin. The surrogate models were used as objective functions in the optimization, and NSGA-II was run with a population size of 50 for 50 generations. The resulting Pareto front provided a set of heater layout candidates that offer trade-offs between rapid heating and thermal uniformity.
This integrated approach demonstrates the potential of combining image-based CNN feature extraction, machine learning-based regression modeling, and evolutionary optimization to solve complex thermal design problems in data-constrained injection molding scenarios.
3 Results and Discussion
To evaluate the effectiveness of the proposed optimization framework, a comprehensive analysis was conducted on the surrogate model performance and the optimization results derived from the NSGA-II algorithm. The Random Forest surrogate models, trained using CNN-derived average feature vectors and normalized process variables, showed strong predictive capability for both average temperature (AVG) and temperature difference (Diff). As illustrated in Fig. 5, the predicted values closely follow the actual Moldex3D simulation results across all ten design points. In addition to the correlation coefficients, the Random Forest models achieved R values of 0.94 for average temperature and 0.91 for temperature difference prediction, confirming the quantitative reliability of the surrogate models. The correlation coefficients were 0.9655 for AVG and 0.9380 for Diff, demonstrating that the model accurately captures the thermal behavior and trends despite the limited sample size.
Trend comparison (Average correlation 0.965, temperature difference correlation 0.938)
Following the validation of the surrogate models, the NSGA-II algorithm was employed to explore the design space and identify Pareto-optimal heater configurations. The resulting Pareto front, shown in Fig. 6, reveals a clear trade-off between maximizing average temperature and minimizing the temperature difference. Three representative solutions were selected from the Pareto set for further evaluation using high-fidelity Moldex3D simulations: (1) the maximum average solution, (2) the minimum temperature differences solution, and (3) a compromise solution that balances both objectives.
Trend multi-objective optimization pareto front
The performance of these solutions is summarized in Table 2. All three designs maintained comparable average temperature values between the surrogate prediction and Moldex3D results, confirming the robustness of the model in capturing general heating trends. Notably, the compromise solution yielded an actual average temperature of 123.3°C with a relatively low temperature difference of 2.1°C, closely matching the predicted outcome. However, the other two solutions showed larger discrepancies in temperature uniformity. Specifically, while the minimum Diff solution was predicted to have a temperature difference of 6.01°C, the actual simulation revealed an even better uniformity at 3.4°C. Conversely, the maximum AVG solution showed a substantial overestimation of temperature difference (predicted: 43.57°C vs. actual: 12.0°C), indicating the surrogate model’s conservative bias in extreme thermal scenarios.
Validation results of optimized heater configurations via Moldex3D
These findings suggest that the proposed framework is highly effective in modeling and optimizing average temperature, but the prediction accuracy for thermal uniformity can vary depending on the distribution complexity in the input image. Nevertheless, the overall optimization strategy provides a meaningful set of trade-off solutions and enables data-efficient exploration of heater layouts in thermoset injection molding. The use of image-informed features from CNNs enhances the spatial sensitivity of the models, and the NSGA-II-driven approach ensures diverse and balanced solutions for practical design implementation.
4 Conclusions
This study presents an image-informed, machine learning-based optimization framework for improving the thermal performance of cartridge heater layouts in thermoset injection molding. By combining high-resolution simulation imagery, CNN-based feature extraction, Random Forest surrogate modeling, and NSGA-II multi-objective optimization, the proposed method effectively identified heater configurations that enhance both average mold temperature and thermal uniformity. Despite the limited sample size of only 10 design points, the surrogate models achieved high prediction accuracy, particularly for average temperature, and enabled efficient design space exploration.
The framework successfully generated Pareto-optimal solutions that demonstrate clear trade-offs between heating efficiency and temperature uniformity. Validation through high-fidelity Moldex3D simulations confirmed the overall trend predicted by the models, although minor discrepancies were observed in temperature difference predictions under extreme conditions. These results highlight the strength of the proposed approach in data-scarce scenarios, while also suggesting the potential for further enhancement through model refinement or expanded datasets. Overall, this research contributes a flexible and generalizable methodology for simulation-based design optimization in advanced manufacturing, particularly where image-rich data and limited experiments are available.
Notes
Acknowledgement(s)
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. RS-2024-00449355).
References
Biography
Mijin Kim is Ph.D candidate in the Department of Future Technology Convergence Engineering, Graduate School, Gwangju University. Her research interest is additive manufacturing process and injection molding process.
Yongrae Kim is enginner in Korea Institute of Machinery & Materials. His research interst is AI based process optimization of additive manfuacturing and application.
Jae Hyuk Choi is Professor in the Department of Mechanical Convergence Engineering, Gwangju University. His research interests are optimization of injection molding process and thermoset plastic molding.
Pil-Ho Lee is Senior researcher in Korea Institute of Machinery & Materials. His research interest is additive manufacturing process and system development.