A Tree Search Algorithm for Solving the Container Loading Problem

Abstract

This 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 packing volume is maximized. The method includes two variants: the full-support variant guarantees full support from below for all packed boxes, although this constraint is not taken into account by the nonsupport 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 are blocks of identical boxes in the same spatial orientation 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 partition-controlled tree search. 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 [Bischoff, E. E., M. S. W. Ratcliff. 1995. Issues in the development of approaches to container loading. Omega 23(4) 377–390] with reasonable computing time.

A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint

“…To solve the CLP instances the tree search algorithm CLTRS (Container Loading by Tree Search) by Fanslau and Bortfeldt (2010) is used. CLTRS generates guillotine packing patterns throughout, i.e.…”

“…constraint (C2) is always satisfied, while orientation and support constraint (C1) and (C3), respectively, are optionally observed. Below we give an extended outline of algorithm CLTRS; for a comprehensive description we refer the reader to Fanslau and Bortfeldt (2010).…”

“…3.1). For the parameters of method CLTRS the original settings as described in Fanslau and Bortfeldt (2010) were adopted. However, a pair of reduced time limits for the search stages (10 seconds for stage 1, 20 seconds for stage 2) was applied throughout.…”

“…The TRSA results by a straightforward adaptation of a tree search algorithm for the 3D container loading problem (CLP) that was proposed by Fanslau and Bortfeldt (2010). Note that in the 3D-CLP (considered here) a box set and one container with fixed dimensions are given and the aim is to maximize the volume (or value) of the packed boxes while generally not all given boxes can be packed.…”

Una revisión literaria del Problema de Carga del Pallet

“…Thus, there is also a contribution in the use of natural resources economically, in the limitation of already complicated traffic, and, as a whole, in the careful treatment of the environment. Evidently, it all can be translated into monetary savings [28].…”