Six Ways of Integrating Symmetries within Non-overlapping Constraints

Abstract: This paper introduces six ways for handling a chain of lexicographic ordering 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 chain of lexicographic ordering constraint within a generic geometric constraint kernel, the four latter ways deal with the conjunction of a chain of lexicographic ordering 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.

• Type: Conference
• Year: 2009
• Where: CPAIOR
• Authors: Magnus Ågren, Nicolas Beldiceanu, Mats Carlsson, Mohamed Sbihi, Charlotte Truchet, Stéphane Zampelli
• Keywords: CPAIOR 2009, Cumulative Constraint, Discrete Geometry, Generic Geometric Constraint, Lexicographic Ordering Constraint