Multi-Objective Optimization of Container Loading: Balancing Space Utilization, Unloading Obstacles, and Cargo Stability

The Container Loading Problem (CLP) involves arranging rectangular boxes within a container while satisfying practical constraints such as dimensional fit, weight capacity, stackability, delivery order, customer priorities, and cargo stability. In real-world multi-drop delivery scenarios, additional considerations include minimizing unloading obstacles (ULOs) and maintaining cargo balance to ensure transport safety. This study formally defines a tri-objective CLP through a mathematical model that (i) maximizes space utilization, (ii) minimizes ULOs, and (iii) constrains the center of gravity (CG) of the loaded cargo within specified limits along each axis. The model integrates diverse practical constraints into a unified formulation. However, due to its complexity, it is used here for problem definition rather than being solved directly to optimality. A constraint-aware variant of the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is developed to generate high-quality feasible solutions. Computational results on benchmark instances from Bischoff and Ratcliff, adapted to include CG balance requirements, demonstrate that the algorithm can efficiently capture trade-offs between volume utilization, unloading efficiency, and cargo balance. The approach addresses current limitations of CLP studies by jointly considering multiple operational objectives and stability constraints, providing realistic insight into how different priorities affect container space use.