# Sustainable Optimization of the Injection Molding Process Using Particle Swarm Optimization (PSO)
## 4 Result
### Taguchi Optimization Results  
Using the Taguchi L\({}_{9}\) 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 [PERSON]' 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-inefficiency. 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 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 \({}^{\circ}\)C to 245 \({}^{\circ}\)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 Tables 2 and 3 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(2\({}^{3}\)) 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.