On the multiple optimal solutions and patterns of the pallet loading problem

The Pallet Loading Problem is a common optimization issue in the fields of manufacturing, transportation, and logistics. It involves placing as many identical rectangular boxes as possible onto a rectangular pallet. As methods for solving this problem continue to advance and gain widespread adoption, it has become common to find multiple optimal solutions for various pallet-loading scenarios. However, this phenomenon remains underexplored in literature. This study identifies and analyzes the characteristics of multiple optimal solutions for the Pallet Loading Problem, offering insights into their patterns, transformations, and practical applications, thus bridging the gap in the current literature. We present a substantial number of instances, solutions, and practical examples by analyzing the results in relation to the identified pattern features. We also identify the conditions for achieving single optimal patterns and perfect patterns while exploring the concepts and applications of perfect partitions, perfect contours, and perfect patterns. This study aimed to enhance the understanding of the solutions and loading patterns of the problem, ultimately facilitating the generation and implementation of perfect or near-perfect pallet loading patterns for real-world logistics applications.