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

Abstract

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