Hybrid Evolutionary-Heuristic Framework for Multi-Objective 3D Container Loading Problem

Efficiently packing heterogeneous cargo into containers remains a fundamental challenge in logistics optimization, directly influencing transportation costs, resource utilization, and supply chain efficiency. This study addresses the three-dimensional container loading problem (3D-CLP) by proposing a hybrid multi-objective framework that explicitly decouples global sequence optimization from local geometric feasibility. The framework integrates a non-dominated sorting genetic algorithm (NSGA-II) to evolve item loading sequences with an enhanced Deepest-Bottom-Left-Fill (E-DBLF) heuristic that serves as a free-space-aware decoder, enforcing collision-free placement through systematic space splitting and explicit residual-volume management. Unlike conventional approaches that intertwine search and placement, this separation-of-roles strategy preserves structural integrity during decoding and stabilizes evolutionary exploration. The framework jointly optimizes space utilization and total packed weight, with performance assessed using Pareto-based metrics including hypervolume (HV) and Pareto front (PF) analysis. Extensive experiments on benchmark (BR) and synthetic instances demonstrate that the proposed method consistently produces well-distributed Pareto fronts and exhibits remarkable robustness as item heterogeneity increases, maintaining space utilization above 87% even under strongly heterogeneous conditions, where competing algorithms degrade sharply. An ablation study isolates the contribution of the E-DBLF component, confirming a 7–10% improvement in space utilization over the standard DBLF within the same optimization framework, with no increase in the number of packed items. These findings establish that performance gains in heterogeneous container loading are driven primarily by the synergy between sequence optimization and structured free-space decoding, rather than by increasingly complex evolutionary operators. The proposed framework offers a transparent, reproducible, and computationally tractable solution for offline and tactical loading planning, contributing a generalizable hybridization principle for packing and cutting problems in operations research.