Six Ways of Integrating Symmetries within Non-overlapping Constraints

Authors:
Magnus Ågren;Nicolas Beldiceanu;Mats Carlsson;Mohamed Sbihi;Charlotte Truchet;Stéphane Zampelli
Affiliations:
SICS, Kista, Sweden SE-164 29;École des Mines de Nantes, LINA UMR CNRS 6241, Nantes, France FR-44307;SICS, Kista, Sweden SE-164 29;École des Mines de Nantes, LINA UMR CNRS 6241, Nantes, France FR-44307;Université de Nantes, LINA UMR CNRS 6241, Nantes, France FR-44322;École des Mines de Nantes, LINA UMR CNRS 6241, Nantes, France FR-44307
Venue:
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2009

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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.