# Evaluating Packaging Design Relative Feature Importance Using an Artificial Neural Network (ANN)
###### Abstract  
Packaging design plays a crucial role in ensuring the protective performance of packages. Various factors must be considered to ensure package strength during the packaging design process. Understanding the relative importance of each influencing factor or design feature provides valuable insights for optimizing packaging designs. However, traditional methods such as testing and numerical analysis have limitations in evaluating the relative significance of these parameters. To address this challenge, this work applied four distinct Artificial Neural Network (ANN)-based approaches, including connection weights, gradient-based, permutation, and Shapley additive explanations (SHAP) values, to explore the relative importance of different packaging design features on a given packaging property. In this study, box compression strength (BCS) was used as a representative packaging property, and the relative importance of up to six BCS features (edge crush test (ECT), perimeter, thickness, depth, and flexural stiffness in both the machine and cross-machine directions) were evaluated. The findings of this study demonstrate the effectiveness of artificial neural network (ANN)-based approaches in evaluating the relative importance of packaging design features. This approach can be readily applied to assess other packaging design features' importance beyond the studied features with significant potential for cost savings and material reduction in packaging design. in the results. Several new methods for assessing the importance of packaging design features have emerged in recent years. Techniques such as analytical hierarchy process (AHP) [1,2] and finite element analysis (FEA) [3, 4, 5] have been developed to optimize different packaging systems. However, these methods are not consistently applied or fully integrated into industry practices. For instance, a primary disadvantage of AHP is expert subjectivity [6]. AHP relies on expert input for pairwise comparisons between options, where experts evaluate the relative importance or performance of one option over another. These judgments, being influenced by personal opinions, can introduce subjectivity [1]. On the other hand, FEA requires material properties that are challenging to obtain due to the anisotropic and non-linear mechanical behavior exhibited by paper fibrous material [7,8]. Additionally, there are limited applications of these methods for systematically evaluating the importance of packaging design features. Therefore, there is a significant opportunity to develop a more efficient approach for assessing the feature importance for packaging design. Despite the limited advancement in methods for evaluating the feature importance of packaging design, researchers have extensively investigated various techniques for assessing the relative importance of input variables using machine learning (ML) techniques. According to a recent academic report, ML applications in the packaging industry highlight their transformative impact on operational optimization and process efficiency. Key application areas include packaging design optimization, quality control, predictive maintenance, and supply chain management. ML has significant potential to revolutionize traditional packaging processes by enhancing automation, precision, and decision-making [9]. In recent decades, artificial neural networks (ANNs), one subset of ML, have been a focal point due to their capability to generalize complex non-linear problems. ANNs are excellent at capturing non-linear relationships between input features and the outcomes. Compared with traditional physical testing methods or numerical (e.g., FEM) that might require explicit programming of relationships between features, ANN methods automatically learn the patterns in the data through training, which saves time and reduces the risk of human error in modeling complex engineering systems [10].