A Hybrid Approach for the Container Loading Problem for Enhancing the Dynamic Stability Representation

In the container loading problem (CLP), the construction of packing patterns is driven by the maximization of the volume occupied, and comprises several constraints such as loading feasibility, weight balance, cargo stability, operational safety, material handling, and the prevention of cargo damage during container shipping. Previous works introduced dynamic stability indicators using simulation or statistical approaches. However, this firstly exponentially increases the computational burden, and secondly misrepresents the essential kinetic mechanical aspects. This paper presents a hybrid scheme to solve the CLP by embedding a mechanical model into a reactive GRASP algorithm, leading to two main novelties; namely, the substitution of the physics simulation engine to find the dynamic stability of the packing patterns, and a modified structure of the metaheuristic, guaranteeing specified minimum stability while achieving efficient packing patterns. The mechanical model dynamically analyzes the forces and accelerations acting on the cargo to predict loss of support, overturning, or critical velocity deltas that would damage it. At the same time, the reactive GRASP algorithm considers the dynamic stability indicators in the improvement steps. The stability indicators are obtained from the mechanical model, allowing the user to know the percentage of damaged boxes in a packing pattern. The effectiveness of the proposed approach is tested using a set of classical benchmark instances, obtaining adequately accurate solutions within a short computational time. The resulting scheme integrates real-world problem conditions and achieves dynamic stability solutions at an acceptable computational cost; it is programmed in C++ instead of relying on proprietary simulation tools.