Real-Time Optimal Parameter Recommendation for Injection Molding Machines Using AI with Limited Dataset

Abstract

This paper presents an efficient parameter optimization approach to the plastic injection molding process to achieve high productivity. In collaboration with a company specializing in plastic injection-mold-based production, real process data was collected and used in this research. The result is an integrated framework, combining a genetic algorithm (GA) with a CatBoost-based surrogate model for multi-objective optimization of the injection molding machine parameters. The aim of the optimization is to minimize the cycle time and cycle energy while maintaining the product quality. Ten process parameters were optimized, which are machine-specific. An evolutionary optimization using the NSGA-II algorithm is used to generate the recommended parameter set. The proposed GA-surrogate hybrid approach produces the optimal set of parameters that reduced the cycle time by 4.5%, for this specific product, while maintaining product quality. Cycle energy was evaluated on an hourly basis; its variation across candidate solutions was limited, but it was retained as an optimization objective to support energy-based process optimization. A total of 95% of the generated solutions satisfied industrial quality constraints, demonstrating the robustness of the proposed optimization framework. While classical Design of Experiment (DOE) approaches require sequential physical trials, the proposed GA-surrogate framework achieves convergence in computational iterations, which significantly reduces machine usage for optimization. This approach demonstrates a practical way to automate data-driven process optimization in an injection mold machine for an industrial application, and it can be extended to other manufacturing systems that require adaptive control parameters.

1. Introduction

The injection molding process is one of the most widely used manufacturing methods for the production of complex high-volume plastic components [1,2]. To optimize process parameters, it is crucial to achieve sustainability goals, since it enables minimal energy and material input [3]. Obtaining optimal process parameters is a major challenge due to the high nonlinear and independent relationships between different process parameters, such as injection pressure, temperature, holding pressure, and cooling time [4]. An improper set of parameters can result in several defects, such as warpage, sink marks, improper filling, and flush formation, including high cycle time and increased energy consumption [5]. Systematic adjustment of melt temperature, mold temperature, and packing pressure can significantly reduce surface and dimensional defects, though precise control is required to avoid residual stresses that lead to warpage [5]. Traditional parameter-tuning methods are based on expert knowledge and numerous trial-and-error steps that are time-consuming, costly, and difficult to scale.Manual tuning typically stops once acceptable part quality is reached with a workable parameter set, and further fine-tuning is rarely pursued due to time constraints. Consequently, there is growing research interest in alternative approaches for process optimization that enable automated and data-driven parameter adjustment [6]. Moreover, recent studies emphasize that comprehensive analyses of parameter interactions, including melt temperature, mold temperature, and cooling time effects, are necessary to understand their collective influence on warpage and other critical defects [7].

In industry, the standard is first to establish an initial good state, which is a baseline parameter configuration derived from the operator’s experience in previous production runs or mold setup sheets [8]. However, converging to a good state can be challenging, especially when processing with a new mold, where there is no historical machine–mold fingerprint and operators must determine suitable process windows from scratch [9]. Even when re-setting an existing mold, where technicians rely on documented “golden settings” or previously validated process parameters, stable operation is not always guaranteed due to mold-specific rheology, machine-induced variations, material batch fluctuations (i.e., viscosity, moisture content), and thermal history effects [10].

These machine–mold-material interactions introduce dynamic variations in resulting part quality. Compensating these effects would require constant monitoring and parameter correction, if needed, by an operator. This makes manual parameter tuning, based on operator skill, insufficient to efficiently achieve consistent global optimal states in terms of quality, cycle time, and energy consumption. Time and resource constraints for the operator, who, in practice, often supervises multiple machines at the same time, prevent exhaustive monitoring and correction. This highlights the need for an adaptive autonomous approach that continuously adjusts parameters based on real-time feedback to maintain optimal production conditions despite these fluctuations.

Previous research on injection molding optimization has explored statistical and machine learning techniques such as Design of Experiments (DOE), response surface methodology (RSM), and Artificial Neural Networks (ANNs) to model and predict process behavior. In recent years, evolutionary and multi-objective optimization algorithms have been increasingly applied for the optimization of the injection molding process due to their ability to handle nonlinear, high-dimensional, and conflicting objectives. Genetic algorithm (GA)-based approaches remain prevalent, with several studies integrating surrogate models to reduce experimental cost. Early hybrid Artificial Neural Network–Genetic Algorithm (ANN-GA) approaches demonstrated the ability to capture nonlinear relationships between parameters of the injection molding process and part quality [11]. More recent studies have extended these frameworks to optimize quality-related objectives such as warpage and shrinkage, demonstrating strong modeling capabilities [12]. However, these methods typically rely on extensive offline datasets and simulation-driven evaluations, which limit their scalability and suitability for real-time, adaptive industrial deployment. Pascoschi et al. employed unsupervised learning techniques based on autoencoders and clustering to analyze energy consumption patterns in industrial injection molding, demonstrating the potential of machine learning to understand processes and improve energy efficiency [13]. However, such approaches focus primarily on analysis rather than on closed-loop parameter optimization and require expert interpretation of the extracted patterns. Kariminejad et al. proposed a Bayesian adaptive design of experiments that reduces the number of required trials compared to classic NSGA-II and desirability methods; however, it still depends on structured sampling strategies and assumes surrogate models that may not generalize well in highly dynamic production environments [6]. Hong et al. combined the response surface methodology (RSM) with a backpropagation (BP) neural network and NSGA-II to optimize process parameters via simulation, but the approach is largely validated using numerically generated data, which may not fully capture the complexities of real machine behavior or support online optimization [14]. Narowski and Wilczyński developed a global injection molding model that incorporates the plasticizing system and mold flow using detailed numerical simulations and experimental validation [15]. Such models improve simulation fidelity but remain computationally intensive and are not designed for real-time optimization or adaptive control.

Recently, multi-objective evolutionary algorithms (MOEAs) have gained attention due to their ability to handle nonlinear, high-dimensional, and conflicting objectives in injection molding. Among these, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) [16], Non-dominated Sorting Genetic Algorithm III (NSGA-III) [17], Strength Pareto Evolutionary Algorithm 2 (SPEA2) [18], and Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D) [19] are widely used in engineering optimization problems. Other works have adopted MOEAs such as NSGA-II in combination with deep neural networks or response surface models to jointly optimize cycle time, energy consumption, and quality metrics [20,21,22]. While these approaches achieve improved Pareto-optimal solutions in simulation environments, they typically focus on a single evolutionary strategy and lack systematic comparisons with alternative MOEAs. Experimental comparisons of classical MOEAs, such as NSGA-II, SPEA2, and MOEA/D, on benchmark problems have shown that each method exhibits distinct strengths and weaknesses with respect to convergence and solution diversity [23]. Benchmark studies in the evolutionary optimization literature highlight that algorithm performance can vary significantly depending on problem structure, objective dimensionality, and constraint handling [24]. This suggests that algorithm selection remains problem-dependent. Real-time optimization studies emphasize the importance of adaptive feedback and online learning but often avoid multi-objective trade-offs or evolutionary comparisons due to computational complexity [6]. Gaspar-Cunha et al. provided a comprehensive survey of optimization strategies in injection molding, covering surrogate modeling, evolutionary algorithms, and multi-objective formulations [25]. The authors highlight that despite methodological advances, most studies rely on offline simulations and lack a systematic experimental comparison of alternative MOEAs under industrial conditions.

Table 1. Summary of related works.

Ref.	Algorithm	Application/Objective	Limitations
Shen et al. (2007) [11]	ANN + GA	Prediction and optimization of injection molding process parameters for quality improvement	Requires large offline datasets; no real-time capability; limited industrial validation
Ghadoui et al. (2023) [12]	ANN + GA	Minimization of warpage and shrinkage through parameter optimization	Simulation-heavy; offline training; limited adaptability to process drift
Kariminejad et al. (2024) [6]	Bayesian adaptive DOE + surrogate modeling	Single- and multi-objective real-time optimization of an industrial injection molding process	Structured sampling; assumes surrogate model generalization; sensitive to dynamic environments
Hong et al. (2025) [14]	RSM + BP Neural Network + NSGA-II	Simultaneous optimization of multiple quality metrics	Primarily numerical data; limited representation of real machine disturbances
Guo et al. (2024) [20]	DNN + GA + Monte Carlo simulation (MCS)	Multi-objective optimization of injection molding parameters	High computational cost; simulation-driven; offline training
Janmanee et al. (2024) [21]	GA	Improvement in part quality through GA-based parameter tuning	Limited objective scope; simple GA; no online adaptation
Rajani & Prakash (2017) [23]	NSGA-II vs SPEA2 vs MOEA/D (benchmark comparison)	Comparative performance evaluation on benchmark problems	Not injection-molding-specific; limited benchmark diversity
Ishibuchi et al. (2025) [24]	Multiple MOEAs (survey and benchmark study)	Comprehensive performance comparison across benchmark suites	Generic benchmarks; not domain-specific
Pascoschi et al. (2024) [13]	Hybrid AI (Autoencoder + K-Means)	Energy consumption analysis and optimization in industrial plastic injection molding	Unsupervised outputs require expert interpretation; focus on energy only; not real-time
Narowski et al. (2024) [15]	Comprehensive simulation modeling (Moldex3D + experimental validation)	Global injection molding process modeling, including plasticizing and mold flow	Simulation-driven; detailed data requirements; not a parameter optimization method
Gaspar-Cunha et al. (2025) [25]	Survey of optimization approaches (surrogate models, multi-objective algorithms)	Review of advanced optimization techniques for injection molding design and efficiency	Review paper; no new empirical evaluation; broad trends without performance metrics
Vega et al. (2024) [26]	Random Forest, Logistic Regression	Process state prediction and classification to improve production efficiency	Focus on classification, not direct parameter optimization; dependent on labeled features

summarizes these works, highlighting the problems addressed, techniques used, limitations, and remarks regarding industrial and real-time applicability. Some recent works move closer to industrial deployment by leveraging real production data. Vega et al. used machine learning classifiers such as random forests and logistic regression to predict and classify injection molding process states with high accuracy using real machine data [26]. Nevertheless, these studies focus on process monitoring and classification rather than multi-objective parameter optimization or adaptive decision making. While surrogate-based, hybrid, and MOEA approaches have provided valuable insights into parameter interactions, most methods rely on offline data, are computationally intensive, and lack the flexibility needed for adaptive, real-time optimization in industrial contexts. NSGA-II remains a practical choice due to robustness and relatively low computational overhead, but alternative algorithms may offer advantages in many-objective or structured problems, albeit with higher complexity.

To address these limitations, this study integrates expert knowledge into a hybrid data-driven optimization framework to answer the following research questions:

1.

What system components are needed for a real-time optimization, and how can they be integrated into the production process?

2.

Can AI provide better settings to a human expert, and where do they differ?

3.

How much data is needed for good quality predictions?

4.

How should limitations be handled due to real-world production?

The effectiveness of the proposed framework is then shown based on a case study of a real-world mold-machine use case.

Figure 1 shows the high-level overview of the proposed system and its interactions with the injection molding machine. The blue blocks highlight the main components required for the solution.

The objective is to enable data-driven process optimization in injection molding by combining digital process monitoring, smart data acquisition, and AI-supported decision systems. The goal is to optimize the process and help avoid production defects and cycle-dependent variability through the development of automated parameter recommendation systems and closed-loop optimization workflows. The optical quality inspection module was developed in [27,28]. This paper focuses on the different modules: data-acquisition and preprocessing framework, the surrogate-modeling methodology, the multi-objective NSGA-II-based optimizer, and the rule-based feedback interface. The workflow developed is validated in an industrial injection-molding case study at a local production company (KHW [29]), demonstrating the applicability of automated optimization in a real production environment. Changes in the recommended parameters as well as the input parameters to the workflow are visualized via Grafana [30] for testing and validation.

In contrast to the existing work in the injection molding optimization framework, which focuses on process-parameter tuning using simulation-based surrogate models [11,14] or real-time machine-level adjustments without multi-objective trade off [4,6], this work introduces an integrated end-to-end optimization framework that directly connects industrial machine data, surrogate modeling, multi-objective optimization, and defect-based feedback. Several contributions lead to the first research question. These include (1) the development of a fully data-driven surrogate modeling pipeline based on industrial machine logs, rather than the simulation-derived datasets commonly used in prior studies. This work also (2) introduces a classifier-constrained NSGA-II algorithm that jointly optimizes cycle time and energy consumption while enforcing a learned quality constraint, an approach not found in the existing literature, where quality is usually modeled as an objective rather than a feasibility condition. Finally, this project (3) integrates this optimization into a closed-loop workflow that incorporates inline defect detection from the visual inspection pipeline, allowing automated parameter suggestion under real production conditions. To the best of our knowledge, no existing work has described a workflow that combines real machine data, defect-aware surrogate modeling, multi-objective evolutionary optimization, and rule-based system feedback in a single operational framework suitable for deployment on industrial shop floors.

The rest of this paper is structured as follows: Section 2 introduces the use-case for this research and the general working process of the machine. Section 3 describes the concept and implementation workflow, including data acquisition, preprocessing, and optimization architecture. Section 4 reports the experimental results. Section 5 discusses the benefits, compares the proposed approach with alternative methods, and highlights limitations. Finally, Section 6 concludes and describes future directions.

2. Example Injection Molding Task

2.1. Injection Molding Process Background

There are three main parts to be considered as input for optimization: (1) the machine and its properties, (2) the specific mold, and (3) the material. All three together define the process and its characteristics. A typical injection mold consists of two primary halves, the stationary half and the moving half, mounted, respectively, on the fixed and moving plates of the injection molding machine. During each cycle, the mold closes, the molten polymer is injected under high pressure, the part cools and solidifies, and the mold opens to allow ejection of the part.

The default injection molding process is executed as follows:

(1)

The mold is closed.

(2)

The molten plastic is injected.

(3)

The machine applies holding pressure to ensure good filling.

(4)

The machine waits for the part to cool.

(5)

The mold opens, the handling removes the ready part, and then the process is repeated at step (1).

These steps form a cycle, called a shot, that produces one part. The cycle time is defined from mold closing to mold closing. There are additional things that happen in parallel. After step (2), the machine starts dosing and melting the amount of plastic needed for the next shot, and after step (5), handling moves the part from the mold and then puts it down before moving back to the mold to remove the next finished part (step 5). This is a general process description that happens irrespective of the produced part. The timing varies, as well as the number of parts produced, depending on the individual molds.

2.2. Sleigh Mold

In this research work, the industrial case study focuses on a large single-cavity mold used for the production of plastic sleigh components at KHW. Such molds belong to the thermoplastic injection mold class and are engineered to withstand high mechanical loads, rapid thermal cycling, and precise dimensional requirements typical of large structural parts.

Figure 2 shows and highlights the mold used for the product sled, mounted on the injection molding machine during production. The mold follows a conventional two-plate design, consisting of a stationary plate mounted on the right-hand side and a movable plate mounted on the left-hand side. The stationary plate is connected to the machine nozzle, through which the molten thermoplastic is injected into the mold via the sprue and runner system. The movable plate retracts along the tie bars to open the mold after cooling. The tie bars, marked in the figure, indicate the clamping structure and opening direction of the mold. The highlighted cavity pattern defines the final sled geometry and is responsible for the shape and surface quality. In this case, the resulting product is a sled for children, shown in Figure 3, which is a large part that takes around 56s to produce in one cycle. The material was kept constant throughout our tests and data collection.

The machine is equipped with an EUROMAP77 interface and a corresponding OPCUA server to access settable machine parameters as well as measured values [31]. At machine startup, the system connects to the EUROMAP77 interface as an OPCUA client and subscribes to the desired parameters and measurements. This data is stored in a local database accessible using the machine learning approach.

The EUROMAP77 interface provides access to machine internal measurements and settings. No additional external sensors were added to the setup. This, on one hand, enables the reuse of the approach for other machine–mold combinations using the same interface, but on the other hand, limits the available details on the actual measurement equipment. Details such as accuracy, precision, and detailed sensor specifications are not available via the interface. The data collected corresponds to that available to the human operator at his monitoring panel. The lack of these details is therefore not crucial for the given approach.

3. Concept and Implementation

3.1. Workflow

Figure 4 illustrates the overall workflow developed within this research study, integrating data acquisition, surrogate modeling, multi-objective optimization, and rule-based post-processing into a closed-loop framework. It depicts the interdependency of different modules. The process begins with the extraction of historical machine data in .csv format, followed by manual and automated labeling of shot-wise quality information. These labeled datasets serve as the basis for training the surrogate models, which subsequently act as fast evaluators during the optimization stage. In parallel with surrogate construction, the optimization pipeline defines the feasible control-parameter search space and employs an NSGA-II algorithm to minimize cycle time and energy consumption while satisfying classifier-based quality constraints. The resulting Pareto front is then filtered using domain-specific feasibility criteria, including pressure-profile monotonicity and holding-pressure–time characteristics, to obtain practically applicable parameter sets. These candidate solutions are forwarded to the inline quality-inspection module for final validation before being deployed on the injection-molding machine. The refined optimal settings are then iteratively fed back into the surrogate and rule modules, enabling continuous improvement. A detailed description of each component, which includes (1) data acquisition and pre-processing, (2) surrogate model framework, (3) optimization framework, and (4) post-processing, is provided in the subsequent sections.

3.2. Data Acquisition and Pre-Processing

Data used for the research project was collected from the industrial injection molding machine at KHW. Data for the sledge mold, as introduced in the previous Section 2.2, was considered as the case study. Process data for production was extracted directly from the machine’s built-in sensors and control systems, which record operational parameters for each production cycle via the EUROMAP-77 interface. The dataset was collected over several months of testing and production cycles on the machine. The raw data collected was pre-processed and exported to a usable ċsv file containing 31 process parameters along with time stamps.

The recorded parameters were categorized into two main groups: control parameters and measured parameters. Control parameters are machine settings that need to be modified by an expert to produce a good mold part from the machine. Measured parameters are automatically captured by machine sensors for the process and sent out as feedback. These sets of parameters are unique to different injection mold machines. Listed in

Table 2. List of process parameters, types, data types, and units.

No.	Parameter Name	Type	Data Type	Units
1	JobCycleCounter	Measured	Integer	Count
2	LastCycleTime	Measured	Float	s
3	DosingTime	Measured	Float	s
4	InjectionTime	Control	Float	s
5	CushionVolume	Measured	Float	cm3
6	PlastificationHydraulicPressureAverage	Control	Float	bar
7	TransferHydraulicPressure	Measured	Float	bar
8–13	ActualTemperature_1–ActualTemperature_6	Control	Float	°C
14	InjectionSpeed	Control	Float	mm/s
15	VPChangeOverPosition	Control	Float	mm
16	Maximum_injection_pressure	Control	Integer	bar
17	Switch_point	Control	Integer	mm
18	Holding_pressure	Control	Integer	bar
19	Holding_pressure_time	Control	Float	s
20	Cooling_time	Control	Float	s
21–25	Holding_pressure_point_1–5	Control	Integer	bar
26–30	Holding_pressure_time_point_1–5	Control	Float	s
31	Energy_per_hour_estimated	Measured	Float	kWh

is the set of parameters acquired after pre-processing of raw sensor data from the machine.

The dataset represents a mixture of temporal process information and cycle-based performance indicators. Based on modification limitations, mold-specific information, and expert knowledge, the control parameters were selected, which include 10 control parameters Holding_pressure_point_1–5 and Holding_pressure_time_point_1–5. This formed the basis for subsequent optimization modeling. Several challenges were encountered during data collection and preparation. The raw machine data were time-structured, but lacked direct assignment to individual shots, except for certain job parameters (e.g., JobCycleCounter, InjectionTime, DosingTime, CushionVolume, LastCycleTime, TransferHydraulicPressure), which occur exactly once per shot and serve as reference points. Other parameters, such as temperature zones and potmeter positions, were recorded multiple times per shot. The number of measurements per temperature zone varied from shot to shot, creating irregularities in the raw dataset. To associate each measurement with a specific shot, an adaptive shot time window was defined using the timestamps of JobCycleCounter and LastCycleTime. The start and end times for each shot were calculated dynamically, accounting for irregularities in parameter logging. This approach ensured that all cyclic and non-cyclic parameters were correctly mapped to their corresponding shot IDs. A data mapper was implemented to compute the average values for cyclic parameters (e.g., temperature zones) within each shot window and to extract job and machine parameters into a consolidated shot-level dataset. First, the limited variability in the machine logs restricted coverage of the full parameter optimization space. Additionally, the dataset was imbalanced, with a higher proportion of successful (“good”) cycles compared to defective ones (“bad”), making classifier training more difficult. The manual labeling process of defective data also required significant expert input, increasing the data preparation time. Due to the complexity of the injection molding process and the high dimensionality of the parameters, scaling the data to broader parameter ranges remains a challenge and motivates the use of surrogate modeling and optimization algorithms described in the following sections.

3.3. Surrogate Model Framework

In the proposed system design, a data-driven surrogate model is developed to approximate the underlying relationships between the injection molding control parameters and the process result. These surrogate models replace the need for direct physical simulation or repeated machine trials, significantly reducing computational and experimental costs. Three surrogate models are constructed:

(1)

A binary classifier to distinguish feasible (defect-free) and infeasible (defective) operating conditions.

(2)

Two regression models to predict the cycle time and energy consumption for feasible samples.

The process control vector is defined as follows:

$$\mathbf{x}={\left[\begin{array}{c}{x}_1,x_2,\dots ,x_d\end{array}\right]}^{\top }\in {\mathbb{R}}^d,$$

(1)

where each variable $x_i$ corresponds to a control parameter (e.g., holding pressure or holding time at each point), bounded by predefined limits:

$$x_i\in [x_i^L,x_i^U],i=1,2,\dots ,d.$$

(2)

Given the historical dataset,

$$D={\left\{\left({\mathbf{x}}_i,y_i^{\left(q\right)},y_i^{\left(t\right)},y_i^{\left(e\right)}\right)\right\}}_{i=1^{\prime }}^N$$

(3)

where

$$\begin{array}{cccc}\hfill y_i^{\left(q\right)}& \in \{0,1\}\hfill & \hfill & \mathrm{denotes}\mathrm{the}\mathrm{quality}\mathrm{label} (0:\mathrm{defect}\text{-}\mathrm{free},1:\mathrm{defective}).\hfill \end{array}$$

(4)

$$\begin{array}{cccc}\hfill y_i^{\left(t\right)}& \in {\mathbb{R}}^{+}\hfill & \hfill & \mathrm{is}\mathrm{the}\mathrm{measured}\mathrm{cycle}\mathrm{time}.\hfill \end{array}$$

(5)

$$\begin{array}{cccc}\hfill y_i^{\left(e\right)}& \in {\mathbb{R}}^{+}\hfill & \hfill & \mathrm{is}\mathrm{the}\mathrm{estimated}\mathrm{cycle}\mathrm{energy}\mathrm{consumption}.\hfill \end{array}$$

(6)

Missing or invalid entries are removed according to the condition:

$$D^{\prime }=\left\{\left(x_i,y_i^{\left(q\right)},y_i^{\left(t\right)},y_i^{\left(e\right)}\right)\in D|\neg \mathrm{isNaN}\left(y_i^{\left(q\right)},y_i^{\left(t\right)},y_i^{\left(e\right)}\right)\right\}.$$

(7)

3.3.1. Classification Model

A CatBoost classifier [32] $f_{\mathrm{cls}}(·)$ is trained to predict the quality state of each parameter vector:

$${\widehat{y}}^{\left(q\right)}=f_{\mathrm{cls}}(\mathbf{x};{\mathrm{\Theta }}_{\mathrm{cls}}),$$

(8)

where ${\mathrm{\Theta }}_{\mathrm{cls}}$ denotes the model parameters optimized via gradient boosting.

The loss function minimized during training is the standard logistic loss:

$$L_{\mathrm{cls}}=-{\displaystyle \frac{1}{N}}\sum _{i=1}^N\left[y_i^{\left(q\right)}log{\widehat{y}}_i^{\left(q\right)}+(1-y_i^{\left(q\right)})log(1-{\widehat{y}}_i^{\left(q\right)})\right].$$

(9)

The classifier is trained on the dataset $D^{\prime }$ and gives a binary decision that identifies the feasible (${\widehat{y}}^{\left(q\right)}=0$) and infeasible (${\widehat{y}}^{\left(q\right)}=1$) regions in the design space.

3.3.2. Regression Models for Feasible Samples

Only defect-free samples ($y_i^{\left(q\right)}=0$) are considered for regression modeling. Let the feasible subset be defined as

$$D_{\mathrm{valid}}=\{({\mathbf{x}}_i,y_i^{\left(t\right)},y_i^{\left(e\right)})\mid y_i^{\left(q\right)}=0\}.$$

(10)

Two independent CatBoost regressors are trained to predict cycle time and energy consumption:

$$\begin{array}{c}{\widehat{y}}^{\left(t\right)}=f_{\mathrm{time}}(\mathbf{x};{\mathrm{\Theta }}_{\mathrm{time}}),\hfill \end{array}$$

(11)

$$\begin{array}{c}{\widehat{y}}^{\left(e\right)}=f_{\mathrm{energy}}(\mathbf{x};{\mathrm{\Theta }}_{\mathrm{energy}}),\hfill \end{array}$$

(12)

where $f_{\mathrm{time}}$ predicts the cycle time, and $f_{\mathrm{energy}}$ predicts the energy consumption.

Both models minimize the mean squared error (MSE) loss:

$$L_{\mathrm{reg}}={\displaystyle \frac{1}{N_{\mathrm{valid}}}}\sum _{i=1}^{N_{\mathrm{valid}}}{({\widehat{y}}_i-y_i)}^2.$$

(13)

Each regressor is implemented using a CatBoost ensemble with 500 iterations, a depth of 6, and a learning rate of 0.1, consistent with common surrogate modeling practices for moderate-dimensional nonlinear processes.

3.4. Surrogate-Based Prediction Workflow

During optimization, the surrogate prediction pipeline operates as follows for a set of candidate parameters $\mathbf{x}$:

$$\left\{\begin{array}{cc}{\widehat{y}}^{\left(q\right)}=f_{\mathrm{cls}}\left(\mathbf{x}\right),\hfill & \mathrm{if}{\widehat{y}}^{\left(q\right)}=1, \mathrm{sample}\mathrm{deemed}\mathrm{infeasible},\hfill \\ ({\widehat{y}}^{\left(t\right)},{\widehat{y}}^{\left(e\right)})=(f_{\mathrm{time}}\left(\mathbf{x}\right),f_{\mathrm{energy}}\left(\mathbf{x}\right)),\hfill & \mathrm{if}{\widehat{y}}^{\left(q\right)}=0, \mathrm{sample}\mathrm{feasible}.\hfill \end{array}\right.$$

(14)

This framework enables the optimizer to efficiently evaluate multiple candidate solutions without requiring new physical measurements with feasibility constraints during the classification stage.

3.5. Optimization Framework

The multi-objective optimization framework is developed to identify optimal injection molding control parameters that simultaneously minimize cycle time and energy consumption while ensuring product quality. The optimization problem is expressed as

$$\begin{array}{c}\underset{\mathbf{x}\in \mathcal{X}}{min}{f}_1\left(\mathbf{x}\right)={\widehat{y}}^{\left(t\right)}=f_{\mathrm{time}}\left(\mathbf{x}\right),\hfill \end{array}$$

(15)

$$\begin{array}{c}\underset{\mathbf{x}\in \mathcal{X}}{min}{f}_2\left(\mathbf{x}\right)={\widehat{y}}^{\left(e\right)}=f_{\mathrm{energy}}\left(\mathbf{x}\right),\hfill \end{array}$$

(16)

$$\begin{array}{c}\mathrm{s}.\mathrm{t}.{\widehat{y}}^{\left(q\right)}=f_{\mathrm{cls}}\left(\mathbf{x}\right)=0,\hfill \end{array}$$

(17)

$$\begin{array}{cc}\hfill & x_i^L\le x_i\le x_i^U,i=1,2,\dots ,d,\hfill \end{array}$$

(18)

where $\mathbf{x}$ is the vector of $d=10$ control parameters, $\mathcal{X}$ denotes the feasible search space defined by the parameter bounds $x_i^L$ and $x_i^U$, $f_{\mathrm{time}}(·)$ and $f_{\mathrm{energy}}(·)$ are surrogate regressors, and $f_{\mathrm{cls}}(·)$ is the surrogate classifier. The classifier acts as a quality constraint, ensuring only defect-free parameter sets are evaluated in the objective space.

3.5.1. Initialization via Latin Hypercube Sampling

The initial population is generated using Latin Hypercube Sampling (LHS) [33], which ensures a well-distributed coverage of the multi-dimensional search space.

$$P_0=\{{\mathbf{x}}_1,{\mathbf{x}}_2,\dots ,{\mathbf{x}}_{N_{\mathrm{pop}}}\},{\mathbf{x}}_i\sim \mathrm{LHS}\left(\mathcal{X}\right),$$

(19)

where $N_{\mathrm{pop}}=100$ is the population size.

3.5.2. NSGA-II Algorithm

A Non-dominated Sorting Genetic Algorithm II (NSGA-II) [16] is used to perform multi-objective optimization. NSGA-II iteratively evolves the population by applying selection, crossover, and mutation operators to generate offspring. The main steps are summarized as follows:

• Selection: Tournament selection based on non-dominated rank and crowding distance.
• Crossover: Simulated Binary Crossover (SBX) with probability $p_c=0.9$ and distribution index ${\eta }_c=15$.
• Mutation: Polynomial mutation with distribution index ${\eta }_m=40$.
• Elitism: Non-dominated sorting and crowding distance ensure diversity along the Pareto front.

For each candidate ${\mathbf{x}}_i$ generated by NSGA-II, the surrogate classifier evaluates the feasibility. Only feasible solutions are passed to the regressors to compute objective values $f_1\left({\mathbf{x}}_i\right)$ and $f_2\left({\mathbf{x}}_i\right)$. If a candidate is classified as infeasible (${\widehat{y}}^{\left(q\right)}=1$), a large penalty is assigned.

$$f_1\left({\mathbf{x}}_i\right)=f_2\left({\mathbf{x}}_i\right)=+\infty .$$

(20)

3.5.3. Convergence

The optimization process ends after a predefined number of generations, $N_{\mathrm{gen}}=200$. At convergence, the algorithm produces a Pareto-optimal front of feasible solutions:

$$F^{\ast }=\{({\mathbf{x}}_i,f_1\left({\mathbf{x}}_i\right),f_2\left({\mathbf{x}}_i\right))\mid {\mathbf{x}}_i\in \mathcal{X}, {\widehat{y}}^{\left(q\right)}\left({\mathbf{x}}_i\right)=0, i=1,\dots ,N_{\mathrm{pop}}\},$$

(21)

which represents the trade-off between cycle time and energy consumption. Further post-processing, based on additional manufacturing constraints filters, ranks these solutions.

3.6. Post-Processing and Adaptive Refinement

To further enhance performance, the workflow incorporates an adaptive rule-based post-processing stage. The optimization process generates 100 solutions. Since not all solutions are feasible, a rule-based filtering strategy is applied to refine the solutions based on expert knowledge and iterative testing. First, the monotonicity in the holding-pressure profile (Holding_pressure_point_1–5) is checked, ensuring a physically consistent pressure trajectory. Second, the remaining solutions are ranked by predicted cycle time, prioritizing configurations that meet productivity requirements. Third, solutions are sorted according to the cumulative holding-pressure times (Holding_pressure_time_point_1–5), removing parameter combinations that violate feasible pressure–time relationships.

Through these sequential filtering steps, infeasible, unstable, or operationally impractical settings are removed, yielding a compact, high-quality candidate set suitable for real-machine validation. During industrial testing, the measured cycle time, energy consumption, and defect occurrence associated with each selected solution are fed back into the system to support adaptive model refinement. This feedback mechanism enables periodic updates of the surrogate regressors and the quality classifier, ensuring that the predictive models remain aligned with the actual process dynamics. In this way, the framework realizes the principles of intelligent and data-driven manufacturing promoted in Industry 4.0 research [4,14]. This framework effectively combines surrogate modeling, classifier-based feasibility filtering, and NSGA-II multi-objective optimization to efficiently explore high-dimensional, nonlinear injection molding process spaces while reducing the need for costly experimental trials.

4. Results

4.1. Surrogate Model Performance

The surrogate modeling framework consists of a binary quality classifier to predict defect occurrence, a cycle-time regressor, and an energy-consumption regressor. All models were trained with CatBoost using historical process data collected from the industrial injection–molding machine. The data was collected during normal production, machine setup, and optimization trial runs as described in Section 3.2. The complete dataset consists of 5545 injection-molding shots and was split into a training set of 4436 samples and a test set of 1109 samples. The test set also served as the evaluation set during training to enable early stopping. Early stopping was implemented by monitoring performance on the test set and terminating training when no improvement was observed for 50 consecutive iterations. The final model was rolled back to the iteration achieving the best performance on this test set.

The classifier achieved an overall accuracy of 97% on the test set of 1109 shots. Class-wise performance was well balanced, with precision, recall, and F1-scores of 0.94, 1.00, and 0.97 for ”good” shots. For ”defective” shots, the values for precision, recall, and F1-scores were 1.00, 0.93, and 0.97. This shows a robust separation between feasible and infeasible regions of the parameter space. The performance metrics of the classifier, as summarized in

Table 3. Performance metrics of the surrogate models trained on industrial injection molding data. Exact values are reported for the test datasets.

Surrogate Model	Metric	Value	Notes
Classifier	Accuracy	0.97	Test set of 1109 samples
Classifier	Precision	0.94 (defective), 1.00 (good)	–
Classifier	Recall	1.00 (defective), 0.93 (good)	–
Classifier	F1-score	0.97 (both classes)	–
Cycle-time Regressor	RMSE	9.82 s	Test set 1109 samples
Cycle-time Regressor	Iterations	26	CatBoost early stopping
Energy Regressor	RMSE	8.21 Wh	Test set 1109 samples)
Energy Regressor	Iterations	46	CatBoost early stopping

, correspond to the single best iteration in the evaluation set during this training run. This is critical for the optimization pipeline because NSGA-II evaluates thousands of candidate configurations. Early rejection of infeasible solutions significantly accelerates convergence and prevents exploration of defect-prone zones. The performance metrics of the surrogate models are summarized in Table 3, and the confusion matrix of the classifier is shown in Figure 5. During offline evaluation, the surrogate models were integrated into the optimization and feedback loop, where the predictions were used to select the process parameters.

The cycle-time regressor achieved an RMSE of 2.03 s across a target range of approximately 23–61 s, with CatBoost early stopping, which reduced the model to 26 effective iterations. This corresponds to a relative prediction error of roughly 3.3%, indicating that the deviation is small compared to the predicted value scale. Although the absolute error remains non-negligible due to limited training samples, the model exhibits consistent monotonic trends and stable generalization, enabling NSGA-II to reliably estimate relative improvements.

The energy regressor achieved an RMSE of 9.01 Wh in the target range of 26–106 Wh, converging after 46 iterations. This corresponds to a relative error of approximately 8.5%, reflecting moderate accuracy given the larger natural variability in energy consumption. Despite the small training dataset of 5545 shots, the model captures sensitivity to parameter changes, particularly in the cooling and holding phases where most energy fluctuations occur, providing sufficiently descriptive behavior for guiding the multi-objective search. This data was obtained from 3–4 trial runs covering normal production, machine setup, and the test runs of the optimization. No formal DoE was performed. Therefore, the system is able to use normal machine activity for data collection and setup.

4.2. Multi-Objective Optimization Results (NSGA-II)

The NSGA-II run produced a smooth, concave Pareto front, shown in Figure 6, between cycle time and energy consumption. The Pareto set shows a clear trade-off: reductions in cycle time incur small increases in energy use, and vice versa. The distribution of the solution was uniform, without artificial clustering, providing a good set of alternatives for decision making.

To assess the effectiveness of the proposed optimization framework, NSGA-II was compared against other methods: NSGA-III, MOEA/D, and SPEA2. The performance of the algorithms was evaluated using the hypervolume (HV), inverted generational distance (IGD), and the number of Pareto-optimal solutions. The HV indicator measures the size of the portion of the objective space that is dominated by the obtained Pareto set with respect to a given reference point. Larger HV values indicate a better approximation of the true Pareto front, reflecting both convergence toward the optimal front and diversity along the trade-off surface. The IGD indicator evaluates how far the reference Pareto front is from the obtained solution set by computing the average distance from each point on the reference front to its nearest neighbor in the approximated set. Lower IGD values correspond to solutions that more closely approximate the reference front. The number of Pareto-optimal solutions indicates the richness of the solution set by counting distinct non-dominated solutions produced by an algorithm. A larger number of Pareto-optimal solutions provides greater flexibility for decision making by offering a broader set of trade-offs among objectives.

The quantitative results are summarized in

Table 4. Performance comparison of multi-objective optimization algorithms.

Algorithm	HV (Mean ± Std)	IGD	# Pareto Solutions
NSGA-II	$725.61\pm 3.23$	0.143	100
NSGA-III	$715.61\pm 4.52$	0.457	13
MOEA/D	$524.01\pm 120.12$	6.704	11
SPEA2	$727.22\pm 0.00$	0.000	100

. NSGA-II achieved a high mean HV of $725.61\pm 3.23$ with low variance, indicating a strong balance between convergence and diversity of the Pareto front. In contrast, NSGA-III obtained a lower HV of $715.61\pm 4.52$, and MOEA/D produced substantially inferior performance, with a mean HV of $524.01\pm 120.12$ and fewer Pareto-optimal solutions. This indicates reduced robustness under classifier-based feasibility filtering. SPEA2 achieved the highest HV value ($727.22\pm 0.00$), but with a lack of variance. In terms of convergence accuracy, NSGA-II achieved an IGD of 0.143, indicating a close approximation to the reference Pareto front. NSGA-III and MOEA/D exhibited higher IGD values of 0.457 and 6.704, respectively. This shows inferior convergence under the same feasibility handling strategy. Although SPEA2 achieves an IGD of 0.000, indicating convergence to the best-known Pareto front, NSGA-II offers a favorable balance between convergence, diversity, and solution richness. This is evident from its higher HV value and larger number of Pareto-optimal solutions.

Industrial expertise knowledge (e.g., monotonic pressure decay, minimum holding-time windows) and rule-based filters removed approximately 80% of solutions, demonstrating the importance of combining a data-driven search with domain expertise. From the filtered set, operators selected the most promising settings, balancing a short cycle time with a low defect likelihood and practical implementability on the machine.

4.3. Iterative Testing

To verify the practical applicability and robustness of the proposed framework, a series of iterative machine tests was conducted on the industrial injection molding machine at KHW. Figure 7 illustrates the sequence of iterative machine trials performed during the validation of the optimized parameter sets. The plot shows the LastCycleTime with respect to the JobCycleCounter, which represents the uniqueID for each cycle, highlighting how different events and parameter adjustments affected cycle behavior during the experiment. Each point corresponds to one of the candidate solutions selected from the filtered Pareto-optimal set.

The left region of the Figure 7 represents some test values, where the cycle time fluctuates around approximately 55–57 s. This range is close to the baseline working values used by KHW machine operators before optimization. A short period marked in red indicates a short-shot event, where the cycle time drops significantly due to incomplete filling. This confirms that a certain set of optimized parameters can occasionally produce critical defects. The area marked as “Machine working values” is the baseline working values generally used by KHW operators during production.

Further into the sequence in Figure 7, an isolated spike above 65s occurs, annotated as a “Spike in Dosing Time”. This event reflects an instantaneous disturbance in the plastification behavior, typical of the variability of the machine–material relationship observed during long production runs. To the right of this disturbance, there is a more iterative evaluation of optimized parameters. These tests were applied sequentially on the real machine during live production. The figure shows that these optimized settings initially increased the cycle time variance, which is expected because the hold-pressure and cooling-time profiles differ from the historically stable configuration of the machine. Highlighted in green are some of the best working sets of optimized parameters. Here, the cycle time consistently converges toward approximately 53.5 s, improving upon the original 56 s baseline. A brief red zone labeled Flash indicates an over-packing incident produced by one of the more aggressive parameter sets, and the huge fluctuations in cycle time again illustrate the importance of the rule-based filtering steps, described in detail in Section 4.4.

Toward the end of the sequence in Figure 7, a green-highlighted region labeled Lower Cooling Time (19 s) demonstrates the best-performing optimized solution. Modification of the cooling time was applied only during testing, since it depends on the material type and product thickness. This is a high-risk adjustment with insufficient information to adjust this specific control parameter. Overall, this figure demonstrates how iterative machine testing, guided by the surrogate model and NSGA-II optimization, validates and refines parameter candidates under real production conditions.

4.4. Closed-Loop Feedback Performance

The rule-based feedback module played a central role in stabilizing the optimization-to-machine workflow. The system incorporates the folling:

• Machine-specific pressure monotonicity constraints;
• Minimum holding-time thresholds;
• Operator-validated feasibility rules;
• Digital defect detection feedback.

Thus, the system automatically pruned infeasible or high-risk configurations. This reduced the combinations of invalid parameters by approximately 80%, substantially decreasing the number of physical machine trials required. When the optical inspection system detects defects, the feedback logic is reverted to the previously accepted solution, ensuring uninterrupted production.

4.5. Comparison Against Industrial Baseline

Following NSGA-II optimization and subsequent rule-based post-processing, three representative parameter sets were selected from the filtered Pareto front. These solutions were chosen because they satisfied the classifier-based quality constraint, exhibited monotonic pressure profiles, and demonstrated favorable trade-offs between cycle time and energy consumption.

Table 5. Comparison of baseline machine settings and representative Pareto-optimal solutions obtained using NSGA-II optimization.

Parameter	Baseline	Pareto Solution A	Pareto Solution B	Pareto Solution C
Holding Pressure Point 1 (bar)	65	81	81	76
Holding Pressure Point 2 (bar)	58	59	62	62
Holding Pressure Point 3 (bar)	55	57	59	59
Holding Pressure Point 4 (bar)	46	49	49	47
Holding Pressure Point 5 (bar)	43	46	40	39
Holding Pressure Time 1 (s)	1.00	0.31	0.31	1.82
Holding Pressure Time 2 (s)	1.00	1.15	1.15	4.19
Holding Pressure Time 3 (s)	1.00	0.08	0.08	0.08
Holding Pressure Time 4 (s)	1.00	2.60	3.44	3.48
Holding Pressure Time 5 (s)	6.00	4.18	4.99	4.99
Cycle Time (s)	∼56	∼53.5	∼55	∼60

Pareto solutions were selected after classifier-based feasibility filtering and rule-based constraints enforcing monotonic pressure decay and valid timing windows.

summarizes the baseline machine settings used in production and the three optimized configurations.The optimized sets show adjustments across control variables, most notably reshaping of the holding pressure levels (points 1–5) and modification of the corresponding timing parameters. These patterns reflect the optimizer’s ability to exploit regions of the search space associated with shorter cycle times or reduced energy usage while still maintaining the feasibility as learned by the classifier. Compared to the expert’s baseline, these values also show the ability of the Artificial Intelligence (AI) system to explore further options, especially with fractions of a second for the timing parameters. These fine sets are typically not explored during human trials.

Table 5 shows the optimized configurations that correspond to the top three distinct trade-off solutions selected from the filtered Pareto front. From Table 5, the following conclusion is drawn:

• Baseline cycle time: ∼56 s.
• Optimized cycle time: $53.5$ s.
• Improvement: ≈4.5% reduction.

For energy consumption, surrogate-predicted improvements were directed toward the measured values during production trials. Although the surrogate cannot fully capture mold- and material-specific thermal behavior due to limited training data, predicted and measured trends matched closely. The first real-machine trial using NSGA-II settings produced a nearly optimal result, demonstrating the practical utility of surrogate-assisted optimization in an industrial injection-molding environment.

4.6. Real-Machine Validation and Defect Behavior

A set of 200 optimized parameters, obtained using the NSGA-II algorithm, was evaluated on the KHW injection mold machine. Only two sets of parameters resulted in defects, both detected by the optical inspection system, confirming that the solution is repeatable and practically feasible. The surrogate classifier correctly identified feasible regions in most cases, validating its usefulness as a feasibility filter. The surrogate predictions did not show measurable drift, which is an important factor in data-scarce industrial environments. The measured cycle times and energy values closely matched the surrogate predictions, reinforcing the reliability of the model for real-world deployment. Overall, the end-to-end framework demonstrated a successful deployment of AI-assisted optimization in a real industrial setting.

5. Discussion

This work demonstrates that real-time optimization in injection molding relies on the integration of four core components: machine-level data acquisition, a preprocessing and feature-engineering pipeline, surrogate models with a feasibility classifier, and a multi-objective optimizer. Through the implementation and validation of this workflow, this study successfully addressed all research questions introduced in the article. The final implemented workflow shows the real-time optimization capability and is seamlessly integrated into the production environment with minimal operational impact. The iterative testing phase provides key information on the interaction between AI-generated recommendations and expert knowledge. The AI-based method efficiently explored the parameter space and proposed performance-enhancing settings, while human-defined rule-based filtering remains essential for enforcing production constraints and ensuring machine-safe operation. Despite the limited size of the training dataset, iterative machine feedback compensates for data sparsity and leads to stable surrogate model performance. In this use case, 60–80 representative cycles were sufficient for reliable predictions, with further refinement achieved by continuously comparing optimized predictions to real measured results. The best performing results emerged when AI-driven exploration was constrained by domain knowledge, indicating that AI serves as a complementary tool that enhances, rather than replaces, expert-driven process design.

Compared to the recent literature, the proposed framework explicitly incorporates classifier-based feasibility handling and real-machine validation, which are often omitted in simulation-driven studies. Although alternative optimization algorithms such as NSGA-III, MOEA/D, and SPEA2 are widely used, the comparative evaluation conducted in this study demonstrates that NSGA-II offers a more robust balance between convergence accuracy, solution diversity, and feasibility under industrial constraints. This positions the proposed approach as a practical and scalable optimization strategy for real-world injection molding processes.

Nevertheless, several limitations and challenges remain. The precision and generalization capability of the surrogate models and the feasibility classifier depend on the quality and representativeness of the collected production data. Abrupt changes in material properties, machine conditions, or mold configuration are not formulated in the problem configuration. The classifier-based feasibility filtering may restrict the exploration of unexplored regions of the design space, potentially excluding unconventional but viable solutions. In addition, the computational overhead associated with surrogate training, classifier updates, and multi-objective optimization limits scalability. This requires retraining for high-dimensional parameter spaces. The proposed framework has been validated on a specific industrial injection molding setup. Direct transferability to other machines, materials, or processes would require additional calibration and domain-specific adjustments. Furthermore, due to ongoing production constraints at KHW, only a limited number of real-machine validation trials could be conducted within the available testing time. These trials were sufficient to confirm the practical feasibility and performance trends of the proposed approach, but more extensive, long-term testing would be required to fully assess robustness under varying production conditions.

The scientific contribution of this work lies not in proposing a new optimization algorithm but in systematically evaluating and validating multi-objective optimization strategies under realistic industrial constraints. By combining classifier-based feasibility handling, surrogate-assisted optimization, and real-machine validation, this study identifies an optimization procedure that is both effective and practically deployable for injection molding processes. This approach advances current practice by bridging the gap between theoretical optimization methods and industrial applicability.

6. Conclusions and Future Work

This research demonstrates the successful implementation of a data-driven optimization framework for an industrial injection-molding process using a large mold at KHW. The complexity of the mold, characterized by extended flow paths, asymmetric cooling behavior, and high sensitivity to pressure and profile variations, makes manual parameter optimization challenging. The machine-implemented tests confirmed that optimized solutions lead to consistent improvements in cycle time and energy consumption, with only minimal defect occurrence.

NSGA-II–based optimization achieved a reduction in cycle time from approximately 56 s in the baseline configuration to 53.5 s for the best optimized setting, corresponding to an improvement of approximately 4.5%. The trend in energy consumption was also reduced according to surrogate predictions, but not according to production trials. Comparative evaluation against NSGA-III, MOEA/D, and SPEA2 demonstrated that NSGA-II provided the most robust balance between convergence accuracy, solution diversity, and feasibility handling, achieving a high mean hypervolume of 725.61 with low variance and an IGD of 0.143. Although SPEA2 achieved zero IGD, it exhibited reduced solution diversity and premature convergence, whereas NSGA-III and MOEA/D showed inferior convergence and significantly fewer Pareto-optimal solutions.

Although this project demonstrates the effectiveness of the proposed approach, several opportunities remain for future work. Feedback-based refinement can be expanded beyond rule-based filtering toward more expressive approaches such as regression-based adaptive weighting of parameters or large language model (LLM)-assisted rule generation, enabling dynamic interpretation of machine behavior and operator feedback. Additional experimental campaigns are planned using different molds and product geometries to systematically evaluate the transferability and robustness of the framework beyond the single industrial use case presented in this study. Expanding the dataset across multiple molds, materials, and machine types would support generalization and enable the development of mold-independent base models. Future iterations of the system will shift toward continuous learning paradigms, where the surrogate updates itself automatically based on each production cycle. The long-term goal is a fully automated closed-loop optimization architecture in which the optimizer directly communicates with the machine control system to autonomously adjust parameters, verify results, and refine models without human intervention. Such advances would bring industrial injection molding closer to self-optimizing, intelligent manufacturing systems capable of adapting to mold wear, material variability, and environmental changes in real time.