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

Multi-Objective Optimization of Container Loading: Balancing Space Utilization, Unloading Obstacles, and Cargo Stability | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Multi-Objective Optimization of Container Loading: Balancing Space Utilization, Unloading Obstacles, and Cargo Stability Mahboob Elahi, Wael Mohammed, Samuel Olaiya Afolaranmi, Jose Luis Martinez Lastra, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7712709/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract 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. container loading problem cargo balance metaheuristic optimization genetic algorithm multi-drop deliveries stability constraints Full Text Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major Revision 16 Dec, 2025 Reviewers agreed at journal 13 Oct, 2025 Reviewers invited by journal 13 Oct, 2025 First submitted to journal 25 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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