Artificial Bee Colony Algorithm with Pareto-Based Approach for Multi-Objective Three-Dimensional Single Container Loading Problems

The ongoing container shortage crisis has presented significant challenges for the freight forwarding industry, requiring companies to implement adaptive measures in order maintain peak operational efficiency. This article presents a novel mathematical model and artificial bee colony algorithm (ABC) with Pareto-based approach solve single-container-loading problems. goal is fit set of boxes strongly heterogeneous into specific dimension minimize broken space maximize profits. Furthermore, proposed incorporates bottom-left fill method, which heuristic strategy packing containers. We conducted numerical testing identify optimal parameters using C~ metric method. Subsequently, we evaluated performance our by comparing it other heuristics meta-heuristic approaches relative improvement (RI) value. Our analysis showed that outperformed achieved best results. These results demonstrate effectiveness solving real-world problems companies.