# Evaluating Packaging Design Relative Feature Importance Using an Artificial Neural Network (ANN)
## 4 Discussion  
The findings of this study demonstrate the effectiveness of artificial neural network (ANN)-based approaches in evaluating the relative importance of packaging design features. By applying four ANN-based methods--connection weights, gradient-based, permutation, and SHAP values, the study successfully assessed the significance of six design features influencing box compression strength (BCS). The validation of these ANN-derived feature importance rankings against theoretical values obtained from the McKee formula further supports the reliability of this approach. The results consistently indicated that the edge crush test (ECT) is the most influential factor for BCS, followed by perimeter, thickness, and flexural stiffness in both machine and cross-machine directions. These rankings were largely consistent across the synthetic and real datasets, confirming the robustness of the ANN-based methods. Additionally, the study highlights that the permutation and gradient-based methods yield reliable rankings, whereas the connection weights method showed inconsistencies when applied to features theoretically deemed insignificant, such as depth. Another strength lies in the versatility of the ANN framework. The adaptability of these methods enables their application beyond BCS to other packaging design properties, allowing for a more comprehensive and data-driven optimization of packaging performance. This approach could serve as a valuable tool for material cost reduction while maintaining structural integrity. Despite the promising results, certain limitations exist. First, while the ANN-based feature importance rankings aligned well with theoretical calculations, the study was limited to six packaging design features. Other relevant factors, such as environmental conditions (humidity, temperature), dynamic load considerations, and secondary packaging  
Figure 14: Comparison of the average ANN-evaluated BCS feature importance of the real dataset and theoretical BCS feature importance calculated using the improved McKee formula. influences, were not included in the analysis. Future studies should explore the integration of these additional variables to refine and enhance the accuracy of ANN-based feature importance evaluations. Second, the study relied on two datasets--one synthetic and one real--but both were constrained to commonly used commercial packaging formats. The generalizability of the findings to more diverse or unconventional packaging structures remains uncertain. Expanding the dataset to include a broader range of packaging designs could further validate the applicability of the proposed methodology. Additionally, while ANN models provide valuable insights into feature importance, they operate as \"black box\" models, making the direct interpretation of their inner workings challenging. The reliance on SHAP values and permutation techniques mitigates this issue to some extent, but further work is needed to enhance the interpretability of ANN-derived insights in the packaging domain. For future research, several promising directions could further enhance packaging design optimization. 1. Expanding Input Features: Incorporating additional packaging parameters, such as material properties, environmental factors, and manufacturing processes, could improve model accuracy and provide a more comprehensive understanding of factors influencing BCS. These aspects were not fully explored in this study but could significantly impact packaging performance. 2. Enhancing Model Generalizability: Broadening the range of package types and materials in the dataset would improve the ANN model's applicability across various industries, making it more versatile and widely usable. 3. Improving Data Quality and Expanding Data: Utilizing numerical methods to generate higher-quality synthetic data or collecting real-world data from diverse sources, such as physical tested data from different companies, would enhance the model's reliability and robustness. 4.