Abstract
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.
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Ågren, M., Beldiceanu, N., Carlsson, M., Sbihi, M., Truchet, C., Zampelli, S. (2009). Six Ways of Integrating Symmetries within Non-overlapping Constraints. In: van Hoeve, WJ., Hooker, J.N. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2009. Lecture Notes in Computer Science, vol 5547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01929-6_3
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DOI: https://doi.org/10.1007/978-3-642-01929-6_3
Publisher Name: Springer, Berlin, Heidelberg
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