New Lower Bounds of Constraint Violations for Over-Constrained Problems

Régin, Jean‐Charles; Petit, Thierry; Bessière, Christian; Puget, Jean‐François

doi:10.1007/3-540-45578-7_23

Cited by 13 publications

(15 citation statements)

References 4 publications

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“…A set of disjoint conict sets is then obtained by repeating the previous algorithm on the constraints that are not yet member of a computed conict set (each computation starts from scratch). It is also possible to rene this detection of conict as mentioned in [5].…”

Section: Conict Set Based Lteringmentioning

confidence: 99%

“…Therefore another ltering algorithm based on successive computations of disjoint conict sets were proposed in [5].…”

Section: Ssc: Conict Set Based Filteringmentioning

confidence: 99%

“…Only two existing approaches exploit the structure of the constraints: the search for conict sets (i.e. a set of soft constraints which leads to a failure if all these constraints are considered hard) [5] and the design of specic ltering algorithms for global soft constraints [3], for instance the alldi constraint. Our goal is to explain how a ltering algorithm associated with a constraint can be used in an ecient way even if the constraint can be violated.…”

Section: Introductionmentioning

confidence: 99%

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Using Hard Constraints for Representing Soft Constraints

Régin

2011

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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Abstract. Most of the current algorithms dedicated to the resolution of over-constrained problems, as PFC-MRDAC, are based on the search for a support for each value of each variable taken independently. The structure of soft constraints is only used to speed-up such a search, but not to globally deduce the existence or the absence of support. These algorithms do not use the ltering algorithms associated with the soft constraints. In this paper we present a new schema where a soft constraint is represented by a hard constraint in order to automatically benet from the pruning performance of the ltering algorithm associated with this constraint and from the incremental aspect of these ltering algorithms. In other words, thanks to this schema every ltering algorithm associated with a constraint can still be used when the constraint is soft. The PFC-MRDAC (via the Satisability Sum constraint) algorithm and the search for disjoint conict sets are then adapted to this new schema.

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Section: Conict Set Based Lteringmentioning

confidence: 99%

“…Therefore another ltering algorithm based on successive computations of disjoint conict sets were proposed in [5].…”

Section: Ssc: Conict Set Based Filteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Using Hard Constraints for Representing Soft Constraints

Régin

2011

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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“…Moreover, the best algorithms to solve over-constrained problems like PFC-MRDAC (Larrosa et al, 1998) and the ones based on conflict-sets detection Régin et al, 2001) can be implemented as specific filtering algorithms associated with this constraint. A filtering algorithm based on a PFC-MRDAC version dealing only with the boundaries of the domain of the variable has also been described .…”

Section: If a Value Is Assigned To S I ∈ S[c]mentioning

confidence: 99%

Global Constraints and Filtering Algorithms

Régin¹

2004

Constraint and Integer Programming

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Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algorithms establishing arc consistency for two useful constraints, the alldiff and the global cardinality constraints, are fully detailed. Filtering algorithms are also considered from a theoretical point of view: three different ways to design filtering algorithms are described and the quality of the filtering algorithms studied so far is discussed. A categorization is then proposed. Over-constrained problems are also mentioned and global soft constraints are introduced.

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“…As we shall see in Section 2, three distance metrics were defined in the original paper on partial constraint satisfaction [7] that define various ways in which a problem can be relaxed 1 . The most popular of these distance metrics is known as Max-CSP: find an assignment of values to the variables that maximizes the number of constraints that are satisfied [8,10,14].…”

Section: Introductionmentioning

confidence: 99%