Adapting Consistency in Constraint Solving

Abstract

State-of-the-art constraint solvers uniformly maintain the same level of local consistency (usually arc consistency) on all the instances. We propose two approaches to adjust the level of consistency depending on the instance and on which part of the instance we propagate. The first approach, parameterized local consistency, uses as parameter the stability of values, which is a feature computed by arc consistency algorithms during their execution. Parameterized local consistencies choose to enforce arc consistency or a higher level of local consistency to a value depending on whether the stability of the value is above or below a given threshold. In the adaptive version, the parameter is dynamically adapted during search, and so is the level of local consistency. In the second approach, we focus on partition-one-AC, a singleton-based consistency. We propose adaptive variants of partition-one-AC that do not necessarily run until having proved the fixpoint. The pruning can be weaker than the full version, but the computational e↵ort can be significantly reduced. Our experiments show that adaptive parameterized maxRPC and adaptive partition-one-AC can obtain significant speed-ups over arc consistency and over the full versions of maxRPC and partition-one-AC. ⇤ The results contained in this chapter have been presented in [BBCB13] and [BBBT14]. This work has been funded by the EU project ICON (FP7-284715).

Reasoning and inference for (Maximum) satisfiability: new insights

“…In contrast, MAB frameworks were extensively used in the context of Constraint Programming (CP) and specifically the Constraint Satisfaction Problem (CSP) 62 . In particular, MAB frameworks were used to select the consistency level of propagation [BBP15] or a restart strategy [GS07] for CSP solving. In terms of heuristics, CHB was also implemented in the context of CSP [Sch18] and was further adapted to this problem in the form of a new heuristic, called Conflict-History Search (CHS), which similarly adopts a constraint weighting scheme on the basis of ERWA [HT21].…”

Arc-consistency and linear programming duality: an analysis of reduced cost based filtering

“…See for instance the discussion in [Cauwelaert and Schaus, 2017] where the arc-consistency algorithm for MinWAllDiff is found too costly and the filtering of [Focacci et al, 2002] used as a baseline is too weak. Reduced costs based filtering techniques could be a very good framework to design anytime and adaptive consistency algorithms [Balafrej et al, 2016].…”