Octagonal Domains for Continuous Constraints

Pelleau, Marie; Truchet, Charlotte; Benhamou, Frédéric

doi:10.1007/978-3-642-23786-7_53

Cited by 6 publications

(7 citation statements)

References 10 publications

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“…In Pelleau et al [19], the notion of box encountered in continuous constraint programming is called into question. Each pair (i, j) of variables is associated with an octagon.…”

Section: Related Workmentioning

confidence: 99%

An Interval Filtering Operator for Upper and Lower Bounding in Constrained Global Optimization

Sans¹,

Coletta²,

Trombettoni³

2016

2016 IEEE 28th International Conference on Tools With Artificial Intelligence (ICTAI)

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This paper presents a new interval-based operator for continuous constrained global optimization. It is built upon a new filtering operator, named TEC, which constructs a bounded subtree using a Branch and Contract process and returns the parallel-to-axes hull of the leaf domains/boxes. Two extensions of TEC use the information contained in the leaf boxes of the TEC subtree to improve the two bounds of the objective function value: (i) for the lower bounding, a polyhedral hull of the (projected) leaf boxes replaces the parallel-to-axes hull, (ii) for the upper bounding, a good feasible point is searched for inside a leaf box of the TEC subtree, following a look-ahead principle. The algorithm proposed is an auto-adaptive version of TEC that plays with both extensions according to the outcomes of the upper and lower bounding phases. Experimental results show a significant speed-up on several state-of-the-art instances.

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“…In Pelleau et al [19], the notion of box encountered in continuous constraint programming is called into question. Each pair (i, j) of variables is associated with an octagon.…”

Section: Related Workmentioning

confidence: 99%

An Interval Filtering Operator for Upper and Lower Bounding in Constrained Global Optimization

Sans¹,

Coletta²,

Trombettoni³

2016

2016 IEEE 28th International Conference on Tools With Artificial Intelligence (ICTAI)

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“…La plupart des résultats théoriques et pratiques des chapitres 3, 4, 5 et 6 font l'objet de publications dans des conférences ou journaux [Truchet et al, 2010], [Pelleau et al, 2011], [Pelleau et al, b] (accepté avec corrections), [Pelleau et al, a] (soumis).…”

Section: Nos Contributionsunclassified

Abstract Domains in Constraint Programming

2015

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La programmation par contraintes permet de formaliser et résoudre des problèmes fortement combinatoires, dont le temps de calcul évolue en pratique exponentiellement. Les méthodes développées aujourd'hui résolvent efficacement de nombreux problèmes industriels de grande taille dans des solveurs génériques. Cependant, les solveurs restent dédiés à un seul type de variables : réelles ou entières, et résoudre des problèmes mixtes discrets-continus suppose des transformations ad hoc. Dans un autre domaine, l'interprétation abstraite permet de prouver des propriétés sur des programmes, en étudiant une abstraction de leur sémantique concrète, constituée des traces des variables au cours d'une exécution. Plusieurs représentations de ces abstractions, appelées domaines abstraits, ont été proposées. Traitées de façon générique dans les analyseurs, elles peuvent mélanger les types entiers, réels et booléens, ou encore représenter des relations entre variables. Dans cette thèse, nous définissons des domaines abstraits pour la programmation par contraintes, afin de construire une méthode de résolution traitant indifféremment les entiers et les réels. Cette généralisation permet d'étudier des domaines relationnels, comme les octogones déjà utilisés en interprétation abstraite. En exploitant l'information spécifique aux octogones pour guider la recherche de solutions, nous obtenons de bonnes performances sur les problèmes continus. Dans un deuxième temps, nous définissons notre méthode générique avec des outils d'interprétation abstraite, pour intégrer les domaines abstraits existants. Notre prototype, AbSolute, peut ainsi résoudre des problèmes mixtes et utiliser les domaines relationnels implémentés.

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“…For non-relational domains we can use two classic strategies from CP: split each variable in turn, or split along a variable with maximal size (i.e., |S i | or b i − a i ). These strategies lift naturally to octagons by replacing the set of variables with the (finite) set of unit binary expressions (see also [20]). For polyhedra, one can bisect the segment between two vertices that are the farthest apart, in order to minimize τ p .…”

Section: Disjunctive Completion and Splitmentioning

confidence: 99%

A Constraint Solver Based on Abstract Domains

Pelleau

Miné

Truchet

et al. 2013

Lecture Notes in Computer Science

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In this article, we apply techniques from Abstract Interpretation (a general theory of semantic abstractions) to Constraint Programming (which aims at solving hard combinatorial problems with a generic framework based on first-order logics). We highlight some links and differences between these fields: both compute fixpoints by iteration but employ different extrapolation and refinement strategies; moreover, consistencies in Constraint Programming can be mapped to non-relational abstract domains. We then use these correspondences to build an abstract constraint solver that leverages abstract interpretation techniques (such as relational domains) to go beyond classic solvers. We present encouraging experimental results obtained with our prototype implementation.

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Octagonal Domains for Continuous Constraints

Cited by 6 publications

References 10 publications

An Interval Filtering Operator for Upper and Lower Bounding in Constrained Global Optimization

An Interval Filtering Operator for Upper and Lower Bounding in Constrained Global Optimization

Abstract Domains in Constraint Programming

A Constraint Solver Based on Abstract Domains

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