A Tree Search Algorithm for Solving the Container Loading Problem

The paper presents a tree search algorithm for the three-dimensional container loading problem (3D-CLP). The 3D-CLP is the problem of loading a subset of a given set of rectangular boxes into a rectangular container so that the packed volume is maximized. The method has two variants: the packing variant guarantees full support from below for all packed boxes, while this constraint is not taken into account by the cutting variant. The guillotine cut constraint is considered by both variants. The method is mainly based on two concepts. On the one hand the block building approach is generalized. Not only blocks of identical boxes in the same spatial orientation are applied but also blocks of different boxes with small inner gaps. On the other hand the tree search is carried out in a special fashion called a partitioncontrolled tree search (PCTRS). This makes the search both efficient and diverse, enabling a sufficient search width as well as a suitable degree of foresight. The approach achieves excellent results for the well-known 3D-CLP instances suggested by Bischoff and Ratcliff with reasonable computing time.