Decomposing Global Cost Functions

Christian Bessiere (1) , Patrice Boizumault (2) , Simon de Givry (3) , Patricia Guttiriez (4) , Samir Loudni (2) , Jean-Philippe Metivier (2) , Thomas Schiex (3)

1 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 Equipe CODAG - Laboratoire GREYC - UMR6072
3 UBIA - Unité de Biométrie et Intelligence Artificielle (ancêtre de MIAT)
4 UAB - Universitat Autònoma de Barcelona = Autonomous University of Barcelona = Universidad Autónoma de Barcelona

Similarly to what has been done with Global Constraints in Constraint Programming, different results have been recently published on Global Cost Functions in weighted CSPs, defining the premises of a Cost Function Programming paradigm. In this paper, in the spirit of Berge-acyclic decompositions of global constraints such as Regular, we explore the possibility of decomposing Global Cost Functions in such a way that enforcing soft local consistencies on the decomposed cost function offers guarantees on the level of consistency enforced on the original global cost function. We show that an extension of Directional Arc Consistency to arbitrary arities and Virtual Arc Consistency offer specific guarantees.We conclude by preliminary experiments on Weighted Regular decompositions that show that decompositions may be very useful to easily integrate global cost functions in existing solvers with good efficiency.

Domaines: Intelligence artificielle [cs.AI]; Traitement du texte et du document

Christian Bessiere, Patrice Boizumault, Simon de Givry, Patricia Guttiriez, Samir Loudni, et al.. Decomposing Global Cost Functions. 11th Workshop on Preferences and Soft Constraints (Soft'11) in 17th Int. Conf. on Principles and Practice of Constraint Programming, Sep 2011, Perugia, Italy. pp.16-30. ⟨hal-01017977⟩