Problèmes de placement 2D et application à l'ordonnancement : modélisation par la théorie des graphes et approches de programmation mathématique

Cédric Joncour 1, 2
1 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : The two dimensional orthogonal packing problem consists in deciding whether there exists a packing of rectangular items in a given bin. This is a hard combinatorial problem (In addition to capacity constraints add the items positionning complexity). In this thesis, we consider the case where item rotation is not allowed and with or without packing value optimization. In this study, we compare literature formulations and we propose new ones. We develop and test two resolution approaches. The first is based on Dantzig-Wolfe decomposition associated with a branching on no-overlapping disjunctive constraints. The second establish a combinatorial approach based on multiple interval graph caracterization (modelling the item no-overlapping according to each axis).
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Cédric Joncour. Problèmes de placement 2D et application à l'ordonnancement : modélisation par la théorie des graphes et approches de programmation mathématique. Recherche opérationnelle [cs.RO]. Université Sciences et Technologies - Bordeaux I, 2011. Français. ⟨tel-00661534⟩

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