# Sustainable Optimization of the Injection Molding Process Using Particle Swarm Optimization (PSO)
## 4 Result
### Taguchi Optimization Results
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  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No. **} & **Production** & **Holding Pressure** & **Melt Endpoint** & **Injection** & **Melting** & **Nozzle** \\  & **Time (s)** & **Switch Position (mm)** & **(mm)** & **Endpoint (mm)** & **Time (s)** & **Temperature (\({}^{\circ}\)C)** \\ \hline
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  
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, \(\eta\) = 0.1), while Level 2 tests higher capacity configurations (15 neurons, \(\eta\) = 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. 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. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factor** & **Parameter Name** & **Level 1** & **Level 2** \\ \hline 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 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Factor level table.