Solving set-valued constraint satisfaction problems

Luc Jaulin (1, 2)

1 Lab-STICC_ENSTAB_CID_IHSEV
2 Pôle STIC_OSM

In this paper, we consider the resolution of constraint satisfaction problems in the case where the variables of the problem are subsets of Rn. In order to use a constraint propagation approach, we introduce set intervals (named i-sets), which are sets of subsets of Rn with a lower bound and an upper bound with respect to the inclusion. Then, we propose basic operations for i-sets. This makes possible to build contractors that are then used by the propagation to solve problem involving sets as unknown variables. In order to illustrate the principle and the efficiency of the approach, a testcase is provided.

Mots clés: Set intervals; Constraint propagation; Constraint satisfaction; Contractors; Interval analysis; Set intervals.

Domaines: Automatique / Robotique

Luc Jaulin. Solving set-valued constraint satisfaction problems. Computing, 2012, 94 (2), pp.297-311. ⟨10.1007/s00607-011-0169-5⟩. ⟨hal-00686856⟩