A container loading algorithm with static mechanical equilibrium stability constraints

Abstract

The Container Loading Problem (CLP) literature has traditionally guaranteed cargo static stability by imposing the full support constraint for the base of the box. Used as a proxy for real-world static stability, this constraint excessively restricts the container space utilization and has conditioned the algorithms developed for this problem. In this paper we propose a container loading algorithm with static stability constraints based on the static mechanical equilibrium conditions applied to rigid bodies, which derive from Newton’s laws of motion. The algorithm is a multi-population biased random-key genetic algorithm, with a new placement procedure that uses the maximal-spaces representation to manage empty spaces, and a layer building strategy to fill the maximal-spaces. The new static stability criterion is embedded in the placement procedure and in the evaluation function of the algorithm. The new algorithm is extensively tested on well-known literature benchmark instances using three variants: no stability constraint, the classical full base support constraint and with the new static stability constraint—a comparison is then made with the state-of-the-art algorithms for the CLP. The computational experiments show that by using the new stability criterion it is always possible to achieve a higher percentage of space utilization than with the classical full base support constraint, for all classes of problems, while still guaranteeing static stability. Moreover, for highly heterogeneous cargo the new algorithm with full base support constraint outperforms the other literature approaches, improving the best solutions known for these classes of problems.