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Article Dans Une Revue Engineering Applications of Artificial Intelligence Année : 2009

How to take into account piecewise constraints in constraint satisfaction problems

Élise Vareilles
Michel Aldanondo
Paul Gaborit

Résumé

A particular data structure named a Quad Tree allows a better representation of solution space of binary continuous constraints C(x(1), x(2)), than classical continuous consistencies. The generation and integration of this data structure do not raise any particular problem for continuous constraints defined by only one mathematical formula [Sam, D., 1995. Constraint consistency techniques for continuous domains. Ph.D. Thesis, Ecole Polytechnique Federale de Lausanne]. In this paper, we propose to extend the method of generating Quad Trees in order to take into account, in CSPs, binary continuous constraints defined by a piecewise constraint, i.e. a set of functions defined on intervals. The first section presents the industrial requirements which led us to take into account this type of constraint in CSP. The second section recalls the principles of the Quad Tree. The last section describes our contributions relevant to Quad Tree extensions dealing with piecewise constraints.
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Dates et versions

hal-01599441 , version 1 (13-11-2018)

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Élise Vareilles, Michel Aldanondo, Paul Gaborit. How to take into account piecewise constraints in constraint satisfaction problems. Engineering Applications of Artificial Intelligence, 2009, 22 (4-5), pp.778-785. ⟨10.1016/j.engappai.2009.01.004⟩. ⟨hal-01599441⟩
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