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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Six Ways of Integrating Symmetries within Non-overlapping Constraints
verfasst von : Magnus Ågren, Nicolas Beldiceanu, Mats Carlsson, Mohamed Sbihi, Charlotte Truchet, Stéphane Zampelli
Erschienen in: Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Verlag: Springer Berlin Heidelberg
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This paper introduces six ways for handling a
chain of lexicographic ordering (lex-chain)
constraint between the origins of identical orthotopes (e.g., rectangles, boxes, hyper-rectangles) subject to the fact that they should not pairwise overlap. While the first two ways deal with the integration of a
lex-chain
constraint within a generic geometric constraint kernel, the four latter ways deal with the conjunction of a
lex-chain
constraint and a
non-overlapping
or a
cumulative
constraint. Experiments on academic two and three dimensional placement problems as well as on industrial problems show the benefit of such a strong integration of symmetry breaking constraints and non-overlapping ones.