A new load balance methodology for container loading problem in road transportation

The load balance aspect of the Container Loading Problem (CLP) has been handled in an simplified way in the literature. Either load balance has been treated as a soft constraint or the geometrical centre of the container has been assumed to be the ideal location for the centre of gravity of the cargo, or both, which does not meet regulatory directives and transportation legislation. In this paper, we treat load balance as a hard constraint and adopt vehicle specific diagrams that define the feasibility domain for the location of the centre of gravity of the cargo, according to the vehicle specific technical characteristics, thus fulfilling and complying with real-world regulations and legislation. We propose a multi-population biased random-key genetic algorithm (BRKGA), with a new fitness function that takes static stability and load balance into account. Extensive computational experiments were performed with different variants of the proposed approach. Also solutions taken from the literature were evaluated in terms of load balance. The computational results show that it is possible to obtain stable and load balanced solutions without compromising the performance in terms of container volume utilization, and demonstrate also the advantage in incorporating load balance in the packing generation algorithm.