A beam search implementation for nesting problems

Bennell, Julia A. and Song, X. (2006) A beam search implementation for nesting problems. 3rd ESICUP Meeting: The EURO Special Interest Group on Cutting and Packing, Porto, Portugal. 16 - 18 Mar 2006.

Abstract

The paper will present a constructive approach for nesting problems that utilises beam search to guide the generation of efficient layouts. In order to design an effective constructive heuristic it is important to consider two key features; the placement rule and the intelligent search strategy. Many placement heuristics have been investigated by researchers with the majority favouring some variant of the left most strategy. In our implementation we base the placement rule on the TOPOS algorithm which permits the layout to grow from a floating origin rather than from left to right. We include some improvements in the scope of placements via a more powerful nofit polygon generator that can efficiently represent holes in the partial solution. The role of the intelligent search strategy is to determine the order in which the pieces should be placed. Searching a permutation has a natural tree search structure. However, the combinatorial nature of the problem prevents exhaustive search and reasonable bounds are difficult to define. As a result a beam search approach is proposed where the beam width can constrain the number of branches searched. Empirical results are presented.

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