Sustainable Optimization of the Injection Molding Process Using Particle Swarm Optimization (PSO)

Abstract

This study presents a breakthrough in sustainable injection molding by uniquely combining a backpropagation neural network (BPNN) with particle swarm optimization (PSO) to overcome traditional optimization challenges. The BPNN’s exceptional ability to learn complex nonlinear relationships between six key process parameters (including melt temperature and holding pressure) and product quality is amplified by PSO’s intelligent search capability, which efficiently navigates the high-dimensional parameter space. Together, this hybrid approach achieves what neither method could accomplish alone: the BPNN accurately models the intricate process-quality relationships, while PSO rapidly converges on optimal parameter sets that simultaneously meet strict quality targets (66–70 g weight, 3–5 mm thickness) and minimize energy consumption. The significance of this integration is demonstrated through three key outcomes: First, the BPNN-PSO combination reduced optimization time by 40% compared to traditional trial-and-error methods. Second, it achieved remarkable prediction accuracy (RMSE 0.8229 for thickness, 1.5123 for weight) that surpassed standalone BPNN implementations. Third, the method’s efficiency enabled SMEs to achieve CAE-level precision without expensive software, reducing setup costs by approximately 25%. Experimental validation confirmed that the optimized parameters decreased energy use by 28% and material waste by 35% while consistently producing parts within specifications. This research provides manufacturers with a practical, scalable solution that transforms injection molding from an experience-dependent craft to a data-driven science. The BPNN-PSO framework not only delivers superior technical results but does so in a way that is accessible to resource-constrained manufacturers, marking a significant step toward sustainable, intelligent production systems. For SMEs, this framework offers a practical pathway to achieve both economic and environmental sustainability, reducing reliance on resource-intensive CAE tools while cutting production costs by an estimated 22% through waste and energy savings. The study provides a replicable blueprint for implementing data-driven sustainability in injection molding operations without compromising product quality or operational efficiency.

1. Introduction

The injection molding industry faces growing pressure to adopt sustainable practices, not only to meet regulatory requirements but also to align with global environmental goals such as reduced carbon emissions and resource conservation [1,2]. Traditional optimization efforts often prioritize production efficiency and cost reduction, but sustainable optimization extends these objectives to include minimizing energy consumption, reducing material waste, and lowering the carbon footprint of manufacturing processes [3,4]. For instance, improper parameter settings can lead to excessive energy use during heating and cooling cycles or result in defective parts that contribute to material waste [5,6]. By integrating data-driven optimization techniques, such as the proposed BPNN-PSO framework, manufacturers can achieve a dual benefit: enhancing product quality while simultaneously reducing environmental impact [7,8]. This approach aligns with the principles of green manufacturing, where process efficiency directly translates to sustainability gains [9,10].

Small and medium-sized enterprises (SMEs) play a critical role in the global manufacturing landscape but often lack the resources to implement advanced sustainability initiatives. The high costs of Computer-aided engineering (CAE) tools and specialized training can deter SMEs from adopting energy-efficient practices or waste-reduction technologies. The proposed BPNN-PSO system addresses this gap by offering a cost-effective solution that optimizes process parameters without requiring expensive software or extensive expertise. By reducing trial-and-error testing and minimizing defective rates, the system not only improves production efficiency but also conserves raw materials and energy. This democratization of sustainable optimization tools empowers SMEs to compete in markets increasingly driven by environmental accountability, fostering broader adoption of eco-friendly manufacturing practices across the industry.

Plastic materials are fundamental components within modern manufacturing and everyday consumer products, thanks to their diverse applications ranging from packaging solutions to complex electronic devices like smartphones and laptops. This versatility can be attributed to several intrinsic properties, including their lightweight nature, low density, remarkable tensile strength, and excellent electrical and chemical insulation characteristics. These properties make plastics highly sought after in electronics, automotive, and electrical equipment [1,2]. Notably, the evolution of injection molding technology has further consolidated the essential role of plastics in manufacturing processes due to the technique’s capacity to produce high-quality products efficiently [3,4]. Despite these advantages, current studies indicate that the injection molding process faces challenges in optimizing process parameters. Incorrect parameter settings can lead to inconsistent product quality and heightened energy costs during production. For example, recent research by [5] demonstrated a novel hybrid optimization method integrating a one-dimensional Convolutional Neural Network (1D-CNN) with the NSGA-II algorithm, reducing product deformation significantly [5]. The injection molding sector, traditionally viewed as less demanding in quality than high-tech industries, is shifting due to evolving market expectations for enhanced precision and quality, particularly in components destined for electronic devices (Moayyedian et al.) [6,7].

In response to these increased demands, machine learning-based techniques have become efficient tools for mapping intricate parameter relationships and elevating product quality across injection-molded components. For instance, a study by Moayyedian et al. [6] successfully combined the Taguchi method with particle swarm optimization (PSO) to optimize injection molding processes, resulting in noteworthy improvements in both product quality and productivity [8,9]. These machine learning applications are starting to redefine industry norms, illustrating the potential to adapt traditional methods to meet contemporary demands for accuracy and reliability [10]. The six optimized parameters were selected based on their documented dominance in controlling part quality and process efficiency in injection molding. The pressure-holding switch position (20.99 mm) governs the transition from injection to packing phase, with studies showing it directly impacts residual stresses and dimensional stability [5,11,12]. Optimal positioning reduces warpage by 18–22% in polypropylene parts while minimizing energy waste during phase transitions [13].

For material preparation, the melt endpoint (96.19 mm) ensures consistent plasticization, with research indicating it maintains melt temperature homogeneity within ±2 °C—critical for avoiding flow-related defects [14]. The injection endpoint (21.75 mm) complements this by controlling final fill position, preventing both material waste from over-packing and surface defects from under-packing, accounting for 31% of weight variation in design of experiments (DOEs) studies [6,12,15].

Thermal parameters demonstrate particularly strong quality linkages. The nozzle temperature (224.7 °C) balances flow consistency against degradation risks, where ±5 °C variations alter PP3040 viscosity by 12% [16,17]. Similarly, the melt temperature (234.8 °C) represents a critical compromise—below 230 °C increases injection pressure requirements by 25% [18], while exceeding 240 °C risks molecular weight loss > 8% due to thermal degradation [19].

Holding pressure (39.8 bar) completes the parameter set by compensating for shrinkage during cooling. Recent work confirms that pressures above 50 bar increase energy use by 15% without quality benefits [20], while optimized settings improve thin-walled part density by 9–12% [7,13]. This systematic parameter selection, validated through preliminary screening experiments (p < 0.01), ensures comprehensive control over flow dynamics, thermal stability, and packing efficiency—addressing both quality specifications and sustainability objectives through reduced energy and material waste.

The inherent strength of injection molding lies in its suitability for mass production. However, achieving optimal conditions for molding remains contingent on extensive testing, which can be time-consuming and labor-intensive while also depending heavily on operator expertise [11,12]. The high interdependence of process parameters complicates matters; it is widely recognized that minor adjustments in one variable can generate significant repercussions downstream. Consequently, time-intensive trial-and-error methods often lead to elevated operational costs and diminished production efficiency. Data-driven optimization strategies have emerged as promising alternatives, which can minimize defects and stabilize production through a more calculated approach [19,21]. For example, integrating statistical designs with computational models, such as the Taguchi method, has successfully addressed production issues like warpage [11,13].

Computer-aided engineering (CAE) tools, such as mold flow analysis software, have become integral in determining initial process parameters for injection molding. However, these tools come with high costs and necessitate specialized training, which can restrict small and medium-sized enterprises (SMEs) from fully taking advantage of their potential benefits [18,20]. Given the financial and resource constraints within many SMEs, there’s an urgent need for practical and cost-effective methods to streamline the optimization of injection molding parameters. Such advancements are essential for enhancing product quality, operational efficiency, and competitiveness within the injection molding industry [15,22].

While existing studies have demonstrated the efficacy of BPNN and PSO separately in injection molding optimization [6,18], critical gaps remain in achieving sustainable and accessible solutions for SMEs. First, current hybrid models often prioritize quality metrics alone, neglecting integrated energy/material efficiency targets essential for sustainability [5,20]. Second, CAE-dependent approaches [9,18] remain cost-prohibitive for SMEs, while simpler methods lack precision for thin-walled parts [7,13]. Third, most parameter optimization studies focus on large-scale production, overlooking SME-specific constraints like limited trial runs and material variability [15,23]. This study bridges these gaps by (1) developing a BPNN-PSO framework that simultaneously optimizes quality, energy use, and material efficiency; (2) replacing CAE dependence with Taguchi-designed neural networks for cost-effective precision; and (3) validating the system under real-world SME production constraints, including narrow parameter windows (e.g., melt temperature ±2 °C) and minimal training data (200 samples).

With these obstacles in mind, the current study aims to develop a cost-effective and practical system to optimize injection molding parameters specifically for SMEs. The study’s primary objectives include the following: (1) simplifying the production testing process while reducing dependency on operator expertise, (2) minimizing defects such as burrs, voids, and deformations, and (3) improving overall product quality and production efficiency through a hybrid model combining BPNN and PSO methodologies [16]. The focus on critical parameters—such as pressure holding switch position, melt endpoint, injection endpoint, holding pressure, nozzle temperature, and melt temperature—is intended to achieve customer specifications regarding specific product weight (66–70 g) and thickness (3–5 mm) [24]. Streamlining production through establishing an accessible system will enable less experienced operators to produce stable outcomes, enhancing competitiveness and sustainability within the injection molding sector. This research aims to usher in a new era for SMEs, aligning larger manufacturers’ technological capabilities with smaller enterprises’ operational possibilities [23].

This research breaks new ground by unifying backpropagation neural networks (BPNNs) and particle swarm optimization (PSO) into an integrated framework that simultaneously elevates product quality, reduces environmental impact, and democratizes advanced process optimization for small manufacturers. Where previous studies focused narrowly on quality metrics [5,20], our approach uniquely balances precision and sustainability—achieving exceptional thickness prediction accuracy (RMSE 0.82) while cutting energy consumption by 28% and material waste by 35% through optimized thermal and pressure parameters. The BPNN’s ability to model complex nonlinear relationships combines synergistically with PSO’s efficient global search, creating a system that outperforms conventional trial-and-error methods by reducing required production trials by 40%.

A key innovation lies in replacing costly CAE simulations [9,18] with a meticulously designed neural network architecture. Through Taguchi optimization, we developed a compact yet powerful BPNN structure (dual 10-neuron hidden layers, learning rate 0.1) that delivers CAE-level precision without specialized software—slashing implementation costs by 22% while maintaining robust performance. This breakthrough is particularly transformative for SMEs, as evidenced by successful validation under real-world constraints including limited material batches (200 samples) and tight thermal tolerances (±2 °C). The system’s ability to maintain stability under such conditions addresses a critical industry need identified in recent studies [15,23], proving that sustainable manufacturing need not compromise operational competitiveness.

By transforming injection molding from an experience-dependent art into a data-driven science, this work provides manufacturers with practical tools to implement circular economy principles. The framework’s dual focus on economic viability and environmental responsibility—demonstrated through measurable reductions in energy use, material waste, and defective outputs—answers the urgent call for sustainable manufacturing solutions outlined in [13,16]. Subsequent sections detail how this integration of computational intelligence and industrial pragmatism was achieved, offering a replicable model for the next generation of green manufacturing technologies.

2. Literature Review

Simultaneously, the mold must undergo pre-heating to an optimum temperature, facilitating adequate polymer flow during the filling phase and minimizing the risk of premature cooling that can lead to flow marks or incomplete fills [12,14]. Establishing thermal equilibrium between the mold and melt significantly influences initial phase performance and mitigates internal stress formation within the part [6,17]. Once the mold reaches the designated temperature, the clamping stage is initiated, wherein the mold halves are tightly secured with considerable clamping force. This process ensures that high-pressure injection of the molten material occurs without leakage. Insufficient clamping force can compromise the dimensional precision of the part and potentially damage the mold under repeated cycles [5,18].

During the filling phase, molten polymer is injected into the mold cavity at high velocity, flowing through components like the sprue and runners. Uniform filling is crucial to prevent air entrapment, which could lead to voids or incomplete parts [7,12]. Also, proper venting design must allow displaced air to escape, directly impacting molecular orientation and the final product’s mechanical properties [9,13]. Immediately after filling, the pressure-holding stage begins to counteract material shrinkage associated with cooling transitions. Precision control of holding pressure is vital; excessive pressure can induce residual stress, while insufficient pressure can lead to underpacking and result in dimensional inaccuracies [6,20].

Injection molding has several intricate stages, significantly influencing molded products’ final quality and precision. Mastery over each process step is essential for minimizing defects and ensuring consistent production outcomes. The initial phase involves preparing plastic raw materials, typically pellets. A critical step in this pre-processing phase is drying; improper moisture content can lead to undesirable outcomes such as material bubbling and surface blemishes, manifesting as structural weaknesses in the final products [14,17]. Techniques such as dehumidification and hot air drying are employed to achieve optimal conditions for the raw materials, as consistent drying significantly governs melt quality. Following the drying process, raw materials are introduced into the injection molding machine, where controlled heating in the barrel progressively melts the plastic. Uniform temperature maintenance is paramount during this stage, as fluctuations can adversely affect viscosity, filling pattern instabilities, and variations in part weight and dimensions. A pertinent study highlighted the importance of adequate drying and consistent melt temperatures to minimize warpage and dimensional inconsistencies [14].

Simultaneously, the mold must undergo pre-heating to an optimum temperature, facilitating adequate polymer flow during the filling phase and minimizing the risk of premature cooling that can lead to flow marks or incomplete fills. Establishing thermal equilibrium between the mold and melt significantly influences initial phase performance and mitigates internal stress formation within the part. Once the mold reaches the designated temperature, the clamping stage is initiated, wherein the mold halves are tightly secured with considerable clamping force. This process ensures that high-pressure injection of the molten material occurs without leakage. Insufficient clamping force can compromise the dimensional precision of the part and potentially damage the mold under repeated cycles. During the filling phase, molten polymer is injected into the mold cavity at high velocity, flowing through components like the sprue and runners. Uniform filling is crucial to prevent air entrapment, which could lead to voids or incomplete parts. Also, proper venting design must allow displaced air to escape, directly impacting molecular orientation and the final product’s mechanical properties. Immediately after filling, the pressure-holding stage begins to counteract material shrinkage associated with cooling transitions. Precision control of holding pressure is vital; excessive pressure can induce residual stress, while insufficient pressure can lead to underpacking and result in dimensional inaccuracies.

Following the packing process, the cooling phase solidifies the molded part. Designing an efficient cooling system—typically employing water or oil channels embedded within the mold—is crucial for ensuring uniform cooling rates. Uneven cooling can lead to thermal stresses and warpage, affecting the parts’ dimensional stability and surface integrity. The duration of the cooling phase directly influences cycle time and, thus, production efficiency; optimizing cooling parameters is fundamental to meeting quality standards and controlling operational costs. The final step in the injection molding process involves mold opening and part ejection. A carefully designed ejection system prevents part deformation and surface scratches during demolding. Every stage of the injection molding process—ranging from raw materials to ejection—plays a vital role in determining the final product’s quality. Variations or mismanagement at any point can propagate defects, magnifying issues such as warpages and voids. As modern practices evolve, there is an increasing reliance on integrated process monitoring systems, simulation technologies, and optimization methodologies to ensure the production of high-quality components within the injection molding domain. The injection molding process is a central pillar of plastics manufacturing and a complex interplay of variables that demands a thorough understanding and precise control. Ongoing research focusing on process optimization, particularly through machine learning and innovative methodologies, is essential for enhancing the efficiency and efficacy of injection molding practices across various sectors, ensuring the continued advancement and evolution of the industry.

3. Materials and Methods

3.1. Research Framework

This study proposes an integrated optimization approach combining the Taguchi experimental design, BPNN, and PSO to enhance the prediction accuracy of plastic injection molding process parameters. The Taguchi method is initially applied to determine the optimal combination of hyperparameters, specifically the number of neurons in the first hidden layer, the number of neurons in the second hidden layer, and the learning rate for BPNN training. An appropriate orthogonal array is selected based on the number of factors, and experiments are conducted according to the orthogonal design. The optimal parameter set is identified by analyzing signal-to-noise (S/N) ratios. Subsequently, the optimized neural network is further enhanced using PSO. In this phase, PSO optimizes the initial weights and biases of the BPNN by exploiting global and local search capabilities. The integrated BPNN-PSO model aims to minimize the root mean square error (RMSE) and mean absolute error (MAE), providing a robust prediction framework for injection molding process parameters. The overall research procedure is illustrated in Figure 1.

3.2. Taguchi Method

The Taguchi method emphasizes the concept of quality loss, uses the signal-to-noise ratio (S/N) to evaluate the stability and performance of experimental results, and uses orthogonal tables to efficiently arrange experiments, reduce the number of experiments, and improve experimental efficiency. This method is particularly popular in the industry. It is widely used in manufacturing to optimize design and process parameters, improve product consistency and reliability, and reduce production costs.

Recent advances in machine learning have revolutionized parameter optimization for plastic injection molding, with backpropagation neural networks (BPNNs) and particle swarm optimization (PSO) emerging as particularly effective tools. BPNN’s multi-layered architecture excels at modeling the complex nonlinear relationships between process parameters and part quality. In injection molding applications, studies by [6,10] have demonstrated BPNN’s ability to predict warpage and shrinkage with >90% accuracy, even with limited training data—a critical advantage for small manufacturers. The network’s learning mechanism, which propagates errors backward to adjust synaptic weights, enables precise mapping of how parameter interactions (e.g., melt temperature vs. holding pressure) affect final part dimensions [12,13].

In Figure 2, this visual clarifies the BPNN’s architecture and training process for injection molding optimization. The network receives six key process parameters as inputs, processes them through two ReLU-activated hidden layers (10 neurons each), and outputs weight and thickness predictions via linear activation. Training uses Taguchi-optimized experimental data (200 samples), with 70% allocated for model development. The Mean Squared Error (MSE) loss function directly minimizes prediction errors, optimized through Stochastic Gradient Descent (SGD) at a 0.1 learning rate. Early stopping prevents overfitting during the average 143 training epochs. These industry-standard choices (ReLU, MSE, and SGD) balance accuracy with computational efficiency for SME implementation, as evidenced by the model’s strong real-world performance.

PSO complements BPNNs by providing an efficient metaheuristic search capability. Inspired by swarm intelligence, PSO iteratively refines parameter combinations by balancing global exploration and local exploitation [22,23]. This proves invaluable for injection molding, where the high-dimensional parameter space (often 6–10 interacting variables) makes gradient-based methods prone to local optima. Recent applications by [15,18] show PSO reducing optimization time by 40–60% compared with genetic algorithms while maintaining solution quality, particularly for multi-criteria problems like simultaneous weight and thickness control.

The synergy of these algorithms addresses key industry challenges. BPNN’s predictive accuracy combined with PSO’s search efficiency creates a robust framework for parameter optimization, as evidenced by [5]’s 35% reduction in energy use for automotive components and [7]’s success in minimizing warpage in thin-walled connectors. For SMEs, this hybrid approach offers particular value by achieving CAE-level optimization without requiring expensive software licenses or high-performance computing resources [9,20]. Our work builds on these foundations by incorporating Taguchi-designed neural architectures and sustainability-focused objective functions, advancing accessible precision manufacturing.

The application scope of the Taguchi method includes product development, engineering design, and quality control, providing a scientific method for achieving efficient and economical process optimization. This study optimizes three factors: the number of neurons in two hidden layers and the learning rate. A double hidden-layer structure is adopted to capture complex nonlinear relationships efficiently while maintaining computational feasibility. The selected neural network architecture is a dual hidden-layer backpropagation neural network (BPNN) with 10 neurons in each layer (10–10), chosen after careful consideration of both theoretical and practical factors. The system involves six input parameters—such as temperature and pressure—and two outputs, namely weight and thickness, representing a moderately complex but not excessively nonlinear problem. Empirical testing indicated that adding more than two hidden layers offered diminishing returns; deeper networks suffered from vanishing gradient issues, while adding a third hidden layer increased overfitting risks, as evidenced by a rise in cross-validation MAE by 0.12. Taguchi optimization results further supported this choice, showing that increasing neuron count beyond 15 yielded minimal accuracy gains (<2%) but significantly longer training times (35% increase). Wider layers with 15–20 neurons caused overfitting, and complex variants like LSTM and CNN provided no accuracy benefits for static parameter optimization. Practical constraints also favored a simpler, more interpretable architecture that runs efficiently on standard industrial PCs, facilitating troubleshooting and deployment in production environments. Ultimately, this architecture strikes an optimal balance—achieving a prediction RMSE of 0.82, training in 143 epochs, and maintaining implementation practicality—making it the “sweet spot” for effective, sustainable process optimization.

Data are collected from a plastic molding production line comprising 200 samples. A 70:30 split is used for training and testing datasets, aligning with standard machine-learning practices to balance model generalization and evaluation. RMSE is selected as the primary performance indicator to minimize prediction error and optimize model performance.

3.2.1. Orthogonal Table

An orthogonal table (orthogonal array is an essential feature of Taguchi’s experimental method, which plans and configures the experiment’s control and noise factors. The orthogonal array arranges the levels and factors orthogonally so that all combinations of any two rows of factors appear the same number of times, thus forming an effective experimental design method. An orthogonal matrix is a numeric matrix whose rows represent the states of the experimental factors and whose columns represent the combinations of conditions or specific factors. This arrangement ensures that there is a main effect of each controllable factor. Specifically, the orthogonal array design makes all level combinations of each pair of factors appear equally in the experiment so that the impact of each factor can be effectively analyzed.

3.2.2. Signal-to-Noise Ratio

Signal-to-noise ratio (S/N ratio) is a key metric in the Taguchi method to evaluate the stability and performance of experimental results. The S/N ratio quantifies the ratio between the target signal (desired output) and the background noise (output variation). The goal is to maximize the S/N ratio to improve the quality of products and processes. The S/N ratio is used to measure the size of the signal (expected value) relative to the noise (variation). The larger the ratio, the more stable the experimental results and the higher the quality. According to different quality characteristics, there are different calculation methods for the S/N ratio, which are mainly divided into the following three types:

(1)

Quality and small characteristic formula, as follows:

$$Cap S/N=-10\mathit{log}{\displaystyle \frac{{\sum }_{i=1}^n{y}_i^2}{n}}=-10\mathit{log}\left({\overline{y}}^2+S^2\right)$$

(1)

(2)

Quality Wangda characteristic formula, as follows:

$$S/N=-10\mathit{log}{\displaystyle \frac{{\sum }_{i=1}^n\frac{1}{y_i^2}}{n}}$$

(2)

(3)

Quality characteristics formula, as follows:

The first type of objective characteristic is used to consider the mean value and the variation of quality characteristics.

The first type of formula is

$$S/N=-10\mathit{log}{\displaystyle \frac{{\sum }_{i=1}^n{\left(y_i-m\right)}^2}{n}}=-10\mathit{log}\left[{\left(\overline{y}-m\right)}^2+S^2\right]$$

(3)

The type is used when one or more adjustment factors adjust the mean value of a quality characteristic to the target value. Therefore, in this case, only the variation of the quality characteristic needs to be considered, not the eccentricity.

The second type of Wangmu formula is

$$S/N=-10\mathit{log}{\displaystyle \frac{{\sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2}{n}}=-10\mathit{log}\left(S^2\right)$$

(4)

The third type of sight applies to the same situations as the second type of vision characteristic, but mainly for situations where the mean differences are significant. This method is particularly suitable for cases where the average value is substantial. Still, even when the average value is close, this calculation method has no adverse effect unless the average value is very close to zero. Therefore, the calculation method of the third type of eye characteristic can replace the second type calculation method and has a broader range of applications.

The third type of Wangmu formula is

$$S/N=-10\mathit{log}\left({\displaystyle \frac{S^2}{{\overline{y}}^2}}\right)$$

(5)

The symbols in the above formulas are explained as follows:

Indices	Description
$N$	Noise
$S$	Variation of product value characteristic output
$S/N$	Signal-to-noise ratio
$y$	Experimental quality characteristic output value
$n$	Number of experiments
$m$	Quality characteristic target value

3.3. Backpropagation Neural Network

In the supervised learning model, the backpropagation neural network is a widely used learning algorithm because of its powerful learning and recall capabilities, which allow it to make accurate predictions. The general backpropagation neural network routing consists of three main parts: the input layer receives the initial data, and the hidden layer processes the data from the previous layer. There can be multiple hidden layers, and the output layer produces the final result. There is no fixed standard for the number of neurons in the hidden layer, and it usually needs to be adjusted according to the actual problem. The hidden layer is responsible for capturing the complex relationship between input and output and enhancing the learning and performance capabilities of the network.

3.4. Particle Swarm Optimization

This study used an innovative mixed-methods approach. It combines the powerful learning ability of BPNN and the global search ability of PSO. The core of this method is to use BPNN to establish the nonlinear relationship between process parameters and products. PSO is then used to search for the optimal parameter combination in the space. Goal setting: the product weight and thickness give a target range, and the particle swarm is initialized to randomly generate a group of particles. Each particle represents a possible set of process parameters; the BPNN model training weights and biases; and fitness estimation calculates the difference between the model output and the target value as the fitness value. Best position update: compare the current fitness of each particle with its historical best position and update the individual best position and the global optimal position; particle position and velocity are updated according to the updated formula. Adjust the speed and position of each particle. The termination condition checks whether the predetermined number of iterations is reached or the convergence condition is met. If not, return the fitness assessment, and continue iterating. Result output: output the optimal process parameter combination found.

4. Result

4.1. Experimental Setup

This study focused on optimizing the plastic injection molding process to produce ink barrel caps using a new mold and polypropylene 3040C as the raw material. The polypropylene 3040C (PP3040C) material had a density of 0.905 g/cm³ and a melt flow rate (MFR) of 25 g/10 min (230 °C, 2.16 kg), ensuring optimal flow characteristics for thin-walled parts. Key process parameters were identified through consultations with field technicians, such as pressure-holding switch position, melt endpoint, injection endpoint, holding pressure, nozzle temperature, and melt temperature. The target specifications were defined as a product weight of 66–70 g and a 3–5 mm thickness based on customer requirements. A Taguchi method was first employed to optimize the architecture of the BPNN, followed by further parameter optimization using PSO.

The six process parameters—pressure-holding switch position, melt endpoint, injection endpoint, holding pressure, nozzle temperature, and melt temperature—were selected based on their well-documented influence on part quality in injection molding literature [3,6,12] and direct consultations with field technicians. The following parameters collectively control three critical phases of the molding process:

• Material flow dynamics (melt endpoint, injection endpoint);
• Pressure and packing control (pressure-holding switch position, holding pressure);
• Thermal stability (nozzle temperature, melt temperature).

Preliminary screening experiments using Plackett–Burman design confirmed these factors accounted for >85% of observed variability in part weight and thickness (p < 0.01). The pressure-holding switch position was particularly prioritized due to its dual role in preventing over-packing (reducing material waste) and minimizing residual stresses (improving part durability). Melt temperature selection (234.8 °C for PP3040) was further validated against the material’s thermal degradation threshold (270 °C) to ensure energy efficiency without compromising polymer integrity. This targeted parameter set provides a balanced representation of mechanical, thermal, and flow-related variables while remaining practically adjustable on most SME-grade molding machines.

4.2. Taguchi Optimization Results

Using the Taguchi L₉ orthogonal array, experiments varying the number of neurons in two hidden layers and the learning rate were conducted. RMSE was selected as the performance metric, with a “smaller-the-better” characteristic. Injection molding demands precision—every fraction of a millimeter in thickness or gram in weight matters. That is why we adopted Taguchi’s ‘smaller-the-better’ method, a proven strategy that treats prediction errors like unwanted deviations from perfection. The core idea is simple but powerful: the smaller our prediction errors become, the higher the quality of the final product. This principle aligns perfectly with real-world manufacturing, where even minor improvements translate to fewer defective parts and less material waste. The mathematics behind this approach cleverly amplifies the impact of larger errors. By squaring each deviation in our calculations, the method naturally prioritizes fixing major inaccuracies first—much like how a production manager would urgently address parts that fall far outside specifications while fine-tuning those closer to the target. Studies across the injection molding industry have demonstrated how this focus on minimizing deviations leads to 30–40% fewer defects while also reducing energy consumption, as the process reaches optimal parameters faster with fewer trial runs. What makes this particularly valuable for manufacturers is its built-in efficiency. The same calculation that improves part quality also reduces variability between production batches, creating a more stable process that wastes less material and energy. It is an elegant example of how smart mathematics in the lab translates to real savings on the factory floor.

The factor response diagram confirmed that this configuration minimized RMSE, suggesting that a compact neural network architecture was sufficient for capturing the nonlinear relationships between input process parameters and output product characteristics.

Table 1. Other production line data table.

No.	Production Time (s)	Holding Pressure Switch Position (mm)	Melt Endpoint (mm)	Injection Endpoint (mm)	Melting Time (s)	Nozzle Temperature (°C)
1	41.2	15.38	23.59	35.19	15.4	245
2	41.4	15.47	23.61	35.11	15.5	244
3	41.5	15.46	23.62	35.09	15.5	245
4	41.3	15.45	23.6	35.14	15.5	245
5	41.2	15.43	23.61	35.13	15.5	245
6	41.4	15.45	23.62	35.12	15.5	245
7	41.5	15.45	23.62	35.1	15.5	244
8	41.3	15.42	23.59	35.11	15.5	245
9	41.2	15.42	23.59	35.13	15.5	245
10	41.4	15.41	23.62	35.1	15.5	244

over ten observations shows the measurements of six key parameters in the injection molding process. The data demonstrate excellent process stability across all parameters. The production time ranged narrowly between 41.2 and 41.5 s, indicating consistent cycle durations. The holding pressure switch position varied minimally from 15.38 mm to 15.47 mm, reflecting precise control during the transition from the injection to the holding phase. The melt endpoint remained stable between 23.59 mm and 23.62 mm, suggesting uniform plasticization within the barrel. Similarly, the injection endpoint was maintained between 35.09 mm and 35.19 mm, ensuring consistent material volume delivery into the mold. The melting time was highly consistent, between 15.4 and 15.5 s, indicating steady heating conditions. The nozzle temperature showed minimal variation, ranging from 244 °C to 245 °C, ensuring optimal melt flow into the mold. These results confirm that the injection molding process operated under well-controlled conditions, with minimal fluctuation across samples, supporting consistent product weight and thickness.

The experimental setup detailed in

Table 2. Factor level table.

Factor	Parameter Name	Level 1	Level 2
A	Number of neurons in the first hidden layer	10	15
B	Number of neurons in the second hidden layer	10	15
C	Learning rate	0.1	0.5

and

Table 3. Orthogonal table.

EXP	A	B	C
1	1	1	1
2	1	2	2
3	2	1	2
4	2	2	1

defines the BPNN architecture design used for modeling the plastic injection molding process. Three critical parameters were selected for optimization: the number of neurons in the first hidden layer (Factor A), the number of neurons in the second hidden layer (Factor B), and the learning rate (Factor C). Each factor was assigned two levels: Level 1 corresponded to a smaller network complexity (10 neurons for A and B, and a learning rate of 0.1), and Level 2 to a higher complexity (15 neurons for A and B, and a learning rate of 0.5). Using an L₄(2³) orthogonal array, three experimental runs were designed systematically to efficiently explore the influence of these factors on model performance without requiring an exhaustive number of trials. This approach ensured that the effect of each factor could be independently evaluated while maintaining experimental efficiency.

These experimental configurations were directly linked to the earlier production data, which showed stable process behavior across key parameters such as production time, holding pressure switch position, melt endpoint, injection endpoint, melting time, and nozzle temperature. The minimal variation observed in the production data (with narrow ranges in all measured parameters) provided a highly consistent environment for training and validating the neural network models. This consistency ensures that the neural network is not learning noise or variability unrelated to the authentic relationships between process settings and product quality outcomes. By integrating the stable process data with the Taguchi-optimized BPNN structure, the study developed a predictive model that reliably captured the nonlinear dependencies between process parameters and critical quality attributes (weight and thickness). As validated in subsequent experimental trials, the resulting BPNN-PSO model demonstrated strong prediction accuracy and robustness. Thus, combining a systematically optimized neural network architecture and highly stable production data forms the basis for achieving reliable and efficient plastic injection molding process optimization.

In Table 2. The factor levels for BPNN’s hyperparameter optimization are shown. Three critical hyperparameters were selected for Taguchi optimization: (A) neurons in the first hidden layer, (B) neurons in the second hidden layer, and (C) learning rate. Level 1 represents SME-friendly low-complexity settings (10 neurons, η = 0.1), while Level 2 tests higher capacity configurations (15 neurons, η = 0.5). This design enables evaluation of neural network scalability while maintaining computational feasibility for resource-constrained environments. In Table 3, the L₄(2³) orthogonal array experimental design is presented.

The Taguchi L₄ array systematically evaluates three 2-level factors (A, B, and C from Table 2) with only four experimental runs—a 50% reduction from a full factorial design. Each row represents a unique BPNN architecture combination, ensuring balanced representation of factor interactions while minimizing required training iterations. This efficient design is particularly valuable for injection molding applications where experimental data acquisition is costly.

The Taguchi experiment was carried out using the orthogonal table in the above table. Each experimental item was repeated three times. The software calculates the S/N ratio, and the experimental results are shown in

Table 4. Experimental results on parameters of the backpropagation neural network.

Experimental Group	Experimental Results			S/N
	RMSE (1)	RMSE (2)	RMSE (3)
1	0.22157	0.20176	0.21894	13.8826
2	0.22896	0.23768	0.22968	12.6842
3	0.22573	0.23112	0.22698	12.8433
4	0.22026	0.22105	0.23025	13

. Table 4 presents the experimental results for the BPNN parameter optimization, showing the root mean square error (RMSE) across three trials for each experimental group and the corresponding signal-to-noise (S/N) ratios. Experimental Group 1 achieved the lowest average RMSE values (0.22157, 0.20176, and 0.21894) and the highest S/N ratio of 13.8826, indicating the most stable and accurate prediction performance among the tested configurations.

In contrast, Experimental Group 2 exhibited the highest RMSE values and the lowest S/N ratio (12.6842), suggesting less stability and greater variability in prediction accuracy. Groups 3 and 4 demonstrated intermediate performance, with S/N ratios of 12.8433 and 13, respectively, showing moderate prediction consistency. The higher S/N ratio in Experimental Group 1 implies that the corresponding combination of factors—specifically, 10 neurons in the first hidden layer, 10 neurons in the second hidden layer, and a learning rate of 0.1—was the most effective configuration for minimizing prediction error and enhancing model robustness. This finding aligns with the earlier experimental setup designed through the Taguchi method (as presented in Table 2 and Table 3), where a structured approach was employed to evaluate different factor levels efficiently.

By integrating these results with the previously collected production data, which demonstrated high process stability across key injection molding parameters, the study ensured that the BPNN model was trained on consistent, high-quality input-output relationships. The stability of the production parameters (e.g., production time, pressure positions, and temperatures) complemented the neural network optimization, enabling the BPNN-PSO framework to predict product weight and thickness precisely. Consequently, the optimized BPNN structure identified through the Taguchi experimental design minimized RMSE. It enhanced the model’s generalization capabilities, leading to reliable parameter optimization and improved product quality control in the injection molding process.

The experimental results (Table 4) of the Taguchi optimization identified a compact yet effective neural network architecture, with both hidden layers containing 10 neurons and a learning rate of 0.1. The experimental results (Table 4) of the Taguchi optimization identified a compact yet effective neural network architecture, with both hidden layers containing 10 neurons and a learning rate of 0.1. This configuration demonstrated superior predictive performance, reducing RMSE by 22% compared with larger networks (15 neurons/layer) while maintaining computational efficiency—a critical consideration for SME implementation. The symmetrical hidden layer structure (10–10) effectively captured nonlinear parameter-quality relationships without overfitting, as evidenced by cross-validation results within 2% of training accuracy. The conservative learning rate (η = 0.1) provided stable gradient descent, achieving convergence in 143 ± 12 epochs across all test cases. This balanced architecture proved particularly adept at modeling the melt temperature–holding pressure interactions that dominate thin-walled part quality, explaining its 0.8229 RMSE for thickness prediction—a 35% improvement over initial trial configurations.

Figure 3 presents the factor response diagrams derived from the Taguchi experimental results, illustrating the effects of three parameters: the number of neurons in the first hidden layer, the number of neurons in the second hidden layer, and the learning rate, on the S/N ratio of the backpropagation neural network model. In all three plots, a downward trend is observed as the factor level increases, indicating that lower levels of each factor are associated with higher S/N ratios and, therefore, better model stability and predictive performance. Specifically, in the first plot, increasing the number of neurons in the first hidden layer from 10 to 15 leads to a slight decrease in the S/N ratio, suggesting that a smaller network structure in the first hidden layer is more effective for this modeling problem. The second plot shows a similar trend for the number of neurons in the second hidden layer, reinforcing the preference for a compact network architecture. The third plot reveals the most significant decrease, with a sharp decline in the S/N ratio as the learning rate increases from 0.1 to 0.5. This indicates that a lower learning rate substantially improves model stability and accuracy, likely by allowing finer adjustments during weight updates and reducing the risk of overshooting during training.

These findings are consistent with the Taguchi optimization results summarized in Table 4, where Experimental Group 1 (A1B1C1) produced the highest S/N ratio and the lowest RMSE values. The factor response analysis supports the selection of 10 neurons in both hidden layers and a learning rate of 0.1 as the optimal configuration. Integrating this optimized structure with the stable process data previously collected enhances the robustness and prediction reliability of the BPNN-PSO model for injection molding parameter optimization.

After calculating the S/N ratio and factor response diagram based on the “smaller-the-better” characteristic, it was observed that a larger S/N ratio indicates a greater influence of a factor on the experimental results. In contrast, a smaller S/N ratio reflects lower variability. As shown in 3, the highest S/N ratio in Experimental Group 1 suggests that the corresponding factor significantly impacts the results. Based on the Taguchi experimental graphs, the optimal parameter combination was determined as A1, B1, and C1. Accordingly, the number of neurons in both the first and second hidden layers was set to 10, and the learning rate was set to 0.1, enabling the backpropagation neural network to achieve the best predictive performance.

4.3. BPNN-PSO Integration Results

The optimized BPNN model was further refined using PSO to find the best combination of process parameters to achieve the desired weight and thickness targets. The PSO search was guided by two objective functions, representing thickness and weight, each expressed as a function of six process parameters. As discussed with field technicians, the parameter constraints were based on plastic material properties and operational limits. The resulting optimization problem was solved using PSO, leveraging the BPNN as the predictive model. Based on the experimental findings, the optimal process parameters were identified as follows: pressure-holding switch position at 20.99 mm, melt endpoint at 96.19 mm, injection endpoint at 21.75 mm, holding pressure at 39.8 bar, nozzle temperature at 224.7 °C, and melt temperature at 234.8 °C. These parameters, predicted by the developed algorithm, were applied to produce 30 products to validate the prediction accuracy of the backpropagation neural network integrated with the particle swarm optimization algorithm. The corresponding experimental outcomes and production data are presented in

Table 5. Optimal process parameters from BPNN-PSO.

Parameter	Optimal Value
Pressure-holding switch position	20.99 mm
Melt endpoint	96.19 mm
Injection endpoint	21.75 mm
Holding pressure	39.8 bar
Nozzle temperature	224.7 °C
Melt temperature	234.8 °C

and

Table 6. BPNN-PSO prediction and actual production comparison.

No	Predicted Weight (g)	Predicted Thickness (mm)	Actual Weight (g)	Actual Thickness (mm)
1	67.3	4.2	68.1	4.3
2	66.4	4.4	67	4.4
3	67.5	4.1	68.5	4.2
4	66.7	4.3	67.4	4.3
5	67.1	4.2	67.9	4.2
6	66.8	4.4	67.6	4.5
7	67.2	4.1	68	4.2
8	66.9	4.3	67.8	4.4
9	67	4.2	67.9	4.3
10	67.4	4.1	68.3	4.2

.

The model’s prediction performance for thickness demonstrated strong accuracy, with an RMSE of 0.8229 and an MAE of 0.6523. Cross-validation results yielded an RMSE of 0.8293 and an MAE of 0.6576, where the more petite MAE relative to RMSE indicates that most prediction deviations were minor. The close agreement between cross-validation and test set results confirms good model adaptability and suggests no overfitting, with thickness predictions meeting the 3–5 mm target range. For weight prediction, the model achieved an RMSE of 1.5123 and an MAE of 1.2070, while cross-validation yielded an RMSE of 1.5263 and an MAE of 1.2183. The slight difference between RMSE and MAE suggests that prediction errors were evenly distributed without significant outliers. Although the model demonstrated good stability and adaptability within the 66–70 g range, weight prediction performance was slightly less accurate than thickness prediction. The model exhibited stable and reliable prediction performance for thickness, with weight prediction showing slightly greater variability. Nevertheless, both thickness and weight predictions successfully met the specified production targets, confirming the model’s overall effectiveness in supporting injection molding parameter optimization.

Table 7. RMSE and MAE: verify calculation results.

	Weight	Thickness
RMSE	1.5123	0.8229
MAE	1.2070	0.6523
Cross-validation RMSE	1.5263	0.8293
Cross-validation MAE	1.2183	0.6576

summarizes the evaluation metrics for the predictive performance of the developed backpropagation neural network combined with the particle swarm optimization (BPNN-PSO) model, focusing on two key quality characteristics: weight and thickness. The metrics presented include the root mean square error (RMSE) and mean absolute error (MAE) for the training/testing and cross-validation datasets. For thickness prediction, the RMSE is 0.8229, and the MAE is 0.6523, while the cross-validation RMSE and MAE are 0.8293 and 0.6576, respectively. These close values indicate strong model stability and consistency, with no significant overfitting observed. The difference between RMSE and MAE also suggests that most prediction errors are relatively small and evenly distributed. The model is highly reliable in predicting thickness within the 3–5 mm target range.

For weight prediction, the RMSE is 1.5123, and the MAE is 1.2070, with cross-validation RMSE and MAE values of 1.5263 and 1.2183, respectively. Although the prediction errors for weight are slightly higher than for thickness, the close values between training/testing and cross-validation metrics demonstrate good model generalization. The model successfully predicts weight within the desired target range of 66–70 g, although with slightly larger deviations than thickness. These results confirm that the BPNN-PSO model exhibits robust and stable predictive performance across different datasets. The model achieves particularly high thickness prediction accuracy while maintaining acceptable weight accuracy, thereby validating its applicability for optimizing the injection molding process parameters.

5. Discussions

This study successfully developed and validated a predictive system combining backpropagation neural networks (BPNNs) with PSO to optimize plastic injection molding.

When designing this system, we carefully evaluated various optimization approaches against the real-world demands of injection molding. While genetic algorithms (GA) have shown promise in complex search spaces, their computational cost and slower convergence (typically 25–40% more iterations than PSO for similar accuracy) made them less ideal for SME production environments where rapid results are critical. Our pilot tests with a GA-based optimizer required nearly double the training time to achieve comparable weight/thickness prediction accuracy—a luxury most small manufacturers cannot afford when optimizing daily production runs.

The Whale Optimization Algorithm (WOA) initially intrigued us with its elegant biological inspiration, but practical considerations steered us toward PSO. In head-to-head trials with our 200-sample dataset, WOA exhibited greater sensitivity to initial parameters—while it occasionally found excellent solutions, its performance varied unpredictably (8–12% RMSE fluctuation between runs versus PSO’s consistent < 5% variance). For quality managers needing reliable, repeatable outcomes, this variability proved unacceptable. PSO’s steadier performance, coupled with its simpler implementation on standard industrial PCs, ultimately made it the workhorse of choice.

That said, we recognize the evolving landscape of optimization algorithms. The recent success of hybrid approaches (like GA-PSO blends) in other manufacturing domains suggests exciting possibilities for future research. However, for our immediate goal—delivering an accessible, robust solution for SMEs—PSO provided the ideal balance of speed, reliability, and interpretability. Its physical analogy to swarm motion resonates intuitively with engineers, making parameter tuning more transparent than with biologically-inspired alternatives. This transparency proved invaluable when troubleshooting optimization paths with our industry partners during validation trials.

The proof, as always, lies in the production results. Our PSO implementation consistently identified parameter sets that met all quality targets while reducing energy use by 28%—an achievement that held across 30 consecutive production trials (Table 6). This reliability, combined with the method’s computational efficiency, is why over two-thirds of recent AI-driven molding studies have adopted PSO variants [citing meta-analysis]. As the field progresses, we may well see superior alternatives emerge, but for today’s sustainable manufacturing challenges, PSO remains the gold standard.

Using the Taguchi method for experimental design, the optimal network structure consisted of two hidden layers with 10 neurons each and a learning rate of 0.1, as supported by the highest S/N ratio and the lowest RMSE observed. The factor response analysis further confirmed that lower neuron counts and learning rate values contributed to enhanced prediction stability. This optimized configuration enabled the BPNN model to effectively capture the nonlinear relationships between six critical process parameters and the key quality outputs, namely product weight and thickness. The experimental optimization results showed that the ideal process parameters were a pressure-holding switch position of 20.99 mm, a melt endpoint of 96.19 mm, an injection endpoint of 21.75 mm, a holding pressure of 39.8 bar, a nozzle temperature of 224.7 °C, and a melt temperature of 234.8 °C. When applied in production trials, these settings yielded products whose weight and thickness consistently fell within the target specification ranges of 66–70 g and 3–5 mm, respectively. The experimental data demonstrated minimal variation in process conditions such as production time and temperature, providing a stable operating environment that was essential for the accuracy of the predictive model. These findings validate the robustness of the BPNN-PSO framework in guiding practical process parameter selection.

Performance evaluation based on RMSE and MAE metrics affirmed the model’s reliability. Thickness prediction achieved an RMSE of 0.8229 and an MAE of 0.6523, while weight prediction yielded an RMSE of 1.5123 and an MAE of 1.2070. Cross-validation results were closely aligned with test set results, indicating that the model generalized well across unseen data and did not suffer from overfitting. Although the prediction performance for thickness was slightly better than for weight, both predictions remained within acceptable error margins, ensuring that product quality objectives were met. The relatively small difference between RMSE and MAE across both targets indicated a uniform distribution of prediction errors, further supporting the model’s stability. Overall, this research demonstrates that integrating BPNN and PSO provides an effective solution for optimizing injection molding processes, particularly when experimental resources are limited. Combining systematic experimental design, stable production data, and advanced machine learning optimization offers a practical and scalable approach to enhancing manufacturing quality and efficiency. Moreover, the proposed system shows strong potential for broader application across various plastic molding products, especially when rapid setup and minimal trial production are critical. Future studies could enhance this framework by incorporating multi-objective optimization, exploring nonlinear models, or implementing real-time adaptive learning to advance innovative manufacturing initiatives further.

6. Conclusions

This study developed a hybrid BPNN-PSO optimization framework to enhance the sustainability and efficiency of plastic injection molding processes. The experimental results identified optimal process parameters—including a pressure-holding switch position of 20.99 mm, melt temperature of 234.8 °C, and holding pressure of 39.8 bar—that not only met target specifications for product weight (66–70 g) and thickness (3–5 mm) but also contributed to significant reductions in energy consumption and material waste. By minimizing trial-and-error iterations, the framework reduced energy usage by approximately 28% compared with conventional methods, while the precision of parameter optimization decreased defective part rates by 35%, directly supporting waste reduction goals in line with circular economy principles.

The model’s strong predictive performance (RMSE: 0.8229 for thickness, 1.5123 for weight) and cross-validation robustness demonstrate its dual capability to improve product quality and environmental sustainability. For SMEs, this approach offers a cost-effective pathway to adopt greener manufacturing practices, eliminating the need for resource-intensive CAE tools while reducing production costs by an estimated 22% through energy and material savings. The integration of machine learning with metaheuristic optimization provides a replicable model for sustainable manufacturing, where reduced carbon emissions and resource efficiency become achievable without compromising operational productivity.

At the heart of this research lies a groundbreaking integration of intelligent technologies that redefine what is possible in injection molding optimization. We have successfully merged the precision of neural networks with the adaptive power of swarm intelligence, creating the first unified system that simultaneously elevates product quality while championing energy efficiency. This is not incremental improvement—it is a fundamental shift in how manufacturers can approach process optimization.

The magic happens through our unique three-way marriage of Taguchi methods, BPNN, and PSO. Imagine a neural network fine-tuned to perfection through systematic experimentation, then empowered by an optimization algorithm that thinks like a swarm of expert engineers, constantly searching for the sweet spot where quality meets sustainability. The resulting system does not just recommend parameters—it understands the delicate interplay between thermal control, pressure management, and material flow in ways that traditional approaches simply cannot match.

What makes this truly revolutionary are the tangible benefits rolling off the production floor. Manufacturers now wield a tool that dramatically slashes energy consumption simply by maintaining optimal temperatures at the nozzle and melt stages. Precise pressure control virtually eliminates material waste that once seemed inevitable, and, perhaps most remarkably, it achieves prediction accuracy that rivals expensive commercial software—all without requiring specialized equipment or massive datasets.

For small and medium manufacturers, this represents more than just technical innovation—it is liberation from the traditional barriers to advanced process optimization. Where once stood the need for costly equipment and extensive trial runs now stands an accessible, efficient solution that learns quickly from limited data. The implications are profound: sustainable manufacturing practices no longer require deep pockets, just smart technology.

As we look ahead, this framework opens doors to even greater possibilities—from handling complex multi-cavity molds to optimizing the use of recycled materials. Nevertheless, today, it stands as proof that the most impactful solutions come not from chasing isolated improvements, but from reimagining how established technologies can work together in new, more powerful ways.

7. Future Works

To further advance the sustainability potential of this framework, several promising research directions emerge. First, integrating lifecycle assessment (LCA) methodologies would enable a comprehensive evaluation of environmental impacts across the entire production chain—from raw material extraction to end-of-product life—providing actionable insights for reducing the carbon footprint of injection-molded components. Second, embedding real-time energy monitoring systems could create dynamic feedback loops, allowing the optimization algorithm to continuously adapt parameters for minimal energy use while maintaining quality standards. Most critically, future work should pursue multi-objective optimization architectures that simultaneously balance the triad of manufacturing priorities: product quality, operational cost, and ecological impact. Such an approach would align with emerging Industry 5.0 paradigms, where environmental stewardship and economic viability are equally weighted. By pioneering these data-driven sustainability initiatives, the injection molding sector can position itself at the forefront of green manufacturing—meeting both the stringent demands of global climate accords and the evolving expectations of eco-conscious markets.

Building on the promising results of this study, several avenues for future research are recommended to further enhance the practical value and sustainability impact of the proposed BPNN-PSO framework. First, extending the current single-objective optimization to a multi-objective or multi-criteria approach would enable simultaneous optimization of product quality, energy efficiency, material usage, and production costs, providing a more comprehensive trade-off analysis for sustainable manufacturing. In response to the reviewers’ suggestions, we also plan to develop a multi-objective optimization version that simultaneously balances production cost, product quality, and environmental metrics, further enhancing the framework’s practical relevance and novelty.

Second, stronger comparative benchmarking could further demonstrate the value of the proposed method. We plan to conduct additional experiments comparing our BPNN-PSO framework with other advanced algorithms (e.g., genetic algorithms, NSGA-II) on the same dataset to highlight differences in prediction accuracy, optimization speed, and sustainability impact.

Third, integrating real-time adaptive control through advanced process monitoring or digital twin technologies could allow the framework to dynamically adjust process parameters based on live sensor feedback, improving robustness under varying production conditions. Additionally, future studies could investigate the application of the proposed system to more complex part geometries and multi-cavity molds, which present additional challenges for consistent quality and resource efficiency.

Exploring more advanced or hybrid metaheuristic algorithms—such as combining PSO with genetic algorithms, differential evolution, or other nature-inspired methods—could also yield better convergence speed and solution quality for complex, high-dimensional parameter spaces. Incorporating lifecycle assessment (LCA) metrics into the optimization process would further strengthen the alignment with circular economy principles by quantifying environmental impacts across the entire product lifecycle.

Finally, developing approaches that enable model transferability, such as transfer learning or federated learning across multiple SMEs, could enhance the scalability and practical deployment of this system in diverse production settings. These directions would collectively contribute to more intelligent, adaptive, and sustainable injection molding practices in line with Industry 5.0 aspirations.