A Tree Search Algorithm for Solving the Container Loading Problem

Authors:
Tobias Fanslau;Andreas Bortfeldt
Affiliations:
Department of Information Systems, University of Hagen, 58084 Hagen, Germany;Department of Information Systems, University of Hagen, 58084 Hagen, Germany
Venue:
INFORMS Journal on Computing
Year:
2010

Citing 4
Cited 15

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A Maximal-Space Algorithm for the Container Loading Problem

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Two natural heuristics for 3D packing with practical loading constraints

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A parallel multi-population biased random-key genetic algorithm for a container loading problem

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An iterated construction approach with dynamic prioritization for solving the container loading problems

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A priority-considering approach for the multiple container loading problem

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A two-stage tabu search algorithm with enhanced packing heuristics for the 3L-CVRP and M3L-CVRP

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A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints

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A global search framework for practical three-dimensional packing with variable carton orientations

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A heuristic block-loading algorithm based on multi-layer search for the container loading problem

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Multi-container loading with non-convex 3D shapes using a GA/TS hybrid

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The six elements to block-building approaches for the single container loading problem

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A beam search approach to the container loading problem

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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. Omega23(4) 377--390] with reasonable computing time.