New filtering for the \it cumulative constraint in the context of non-overlapping rectangles

Nicolas Beldiceanu 1, 2 Mats Carlsson 3 Sophie Demassey 1, 2 Emmanuel Poder 1
2 TASC - Theory, Algorithms and Systems for Constraints
LINA - Laboratoire d'Informatique de Nantes Atlantique, Département informatique - EMN, Inria Rennes – Bretagne Atlantique
Abstract : This article describes new filtering methods for the cumulative constraint. The first method introduces the so called longest closed hole and longest open hole problems. For these two problems it first provides bounds and exact methods and then shows how to use them in the context of the non-overlapping constraint. The second method introduces balancing knapsack constraints which relate the total height of the tasks that end at a specific time-point with the total height of the tasks that start at the same time-point. Experiments on tight rectangle packing problems show that these methods drastically reduce both the time and the number of backtracks for finding all solutions as well as for finding the first solution. For example, we found without backtracking all solutions to 65 perfect square instances of order 22-25 and sizes ranging from 192×192 to 661×661.
Type de document :
Article dans une revue
Annals OR, 2011, 184 (1), pp.27-50. <10.1007/s10479-010-0731-0>
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https://hal.archives-ouvertes.fr/hal-00485563
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Soumis le : vendredi 21 mai 2010 - 09:29:40
Dernière modification le : lundi 5 octobre 2015 - 16:58:51

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Nicolas Beldiceanu, Mats Carlsson, Sophie Demassey, Emmanuel Poder. New filtering for the \it cumulative constraint in the context of non-overlapping rectangles. Annals OR, 2011, 184 (1), pp.27-50. <10.1007/s10479-010-0731-0>. <hal-00485563>

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