A Genetic Algorithm with Lower Neighborhood Search for the Three-Dimensional Multiorder Open-Size Rectangular Packing Problem

This paper addresses the multiorder open-dimension three-dimensional rectangular packing problem (3D-MOSB-ODRPP), which involves packing rectangular items from multiple orders into a single, size-adjustable container. We propose a novel metaheuristic approach combining a genetic algorithm with the Gurobi solver. The algorithm incorporates a lower neighborhood search strategy and is underpinned by a mathematical model representing the multiorder open-dimension packing scenario. Extensive experiments validate the effectiveness of the proposed approach. The LNSGA algorithm outperforms Gurobi and the traditional genetic algorithm in solution quality and computational efficiency. For small-scale instances, LNSGA achieves optimal values in most cases. LNSGA demonstrates significant optimization improvements over Gurobi and the genetic algorithm for large-scale instances. The superior performance is attributed to the effective integration of the lower neighborhood search mechanism and the Gurobi solver. This study offers valuable insights for optimizing the packing process in e-commerce warehousing and logistics operations.