Multi-objective multi-population simplified swarm optimization for container loading optimization with practical constraints

Abstract

The container loading problem (CLP) holds significant importance in logistics and supply chain management due to its direct influence on transportation costs and times, thereby impacting the competitive advantages of enterprises across industries. Although there are existing studies for CLP, there remains a gap in addressing the optimization of multiple objectives while satisfying practical constraints. Moreover, container loading methods must also meet performance requirements such as high computational speed, explainability, and implementation capability. Although meta-heuristic-based algorithms have shown effective computational capabilities and performance, such algorithms often being trapped in the local optima especially when searching in the vast solution space of the CLP, particularly as the quantity and diversity of cargo sizes and shapes increase. Motivated by realistic needs, this study aims to develop a UNISON-based framework that integrates the merging spaces algorithm, a novel simple but effective hybrid simplified swarm optimization genetic algorithm (SSO-GA), and a multi-populations co-evolution strategy to determine the loading sequence of parcels to maximize space utilization and weight balance while satisfying to practical constraints. Specifically, the merging spaces algorithm merges fragmented small spaces resulting from loaded parcels into larger spaces, thereby facilitating the accommodation of additional parcels. The hybrid SSO-GA splits encoded solutions and updates segment using novel strategies resulting in the rearrangement of a group of parcels and their corresponding layouts for better space utilization. Furthermore, the multi-populations co-evolution strategy enhances the diversity of the search space and stabilizes solution quality by simultaneously exploiting the best solutions and exploring alternative solutions during the solution update process. An empirical study was conducted by using a public benchmark dataset which demonstrated the practical effectiveness of the proposed framework by significantly improving average space utilization while ensuring center balance and satisfying practical constraints. Furthermore, this study can also serve as a digital support system capable of assisting decision-makers in optimizing container loading operations, thereby improving productivity and saving valuable time.