Solving the Pallet Loading Problem with Deep Reinforcement Learning

Because of its complexity and prominence in the logistic field, the Pallet Loading Problem (PLP) has caught the attention of academics and practitioners as one of the most challenging cutting and packing optimization problems. To solve the PLP, several state-of-the-art Operations Research techniques have been used in the existing literature. This study evaluates the capacity of Deep Reinforcement Learning (DRL), one of the trendiest techniques of machine learning. Actually, the DRL is a combination of the Reinforcement Learning (RL) approach with Deep Neural Network (DNN). A specification phase of the DRL training process and the DNN input/output nodes embedded to solve this NP-hard combinatorial optimization problem is provided. We have used the UML standard to formally specify the complex sequential interaction between the different components of the DRL architecture during the training process. Thus, the DRL was tailored to solve the PLP with and without taking into account the practical stability constraints. The proposed approach was implemented, and computational experimentation was conducted on 16 Benchmark instances from the literature. Numerical results demonstrate that the DRL approach effectively solves the PLP with an average volume utilization of nearly 99%. To ensure package stability, realistic full support conditions were incorporated into the loading process algorithm, successfully resolving the corresponding PLP. Despite the time-consuming nature of the training process, the DRL approach consistently achieves competitive results, with a total average volume utilization of approximately 98%.