# Sustainable Optimization of the Injection Molding Process Using Particle Swarm Optimization (PSO)
## 4 Result
### 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 \({}^{\circ}\)C, and melt temperature at 234.8 \({}^{\circ}\)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 Tables 5 and 6. Figure 3: Factor response diagram. 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 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