# Sustainable Optimization of the Injection Molding Process Using Particle Swarm Optimization (PSO)
## 4 Result
### Taguchi Optimization Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**EXP** & **A** & **B** & **C** \\ \hline
3 & 2 & 1 & 2 \\
4 & 2 & 2 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Orthogonal table. 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 Tables 2 and 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 (n = 0.1) provided stable gradient descent, achieving convergence in 143 \(\pm\) 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