By Marie Pelleau
Constraint Programming goals at fixing difficult combinatorial difficulties, with a computation time expanding in perform exponentially. The tools are this day effective sufficient to resolve huge commercial difficulties, in a known framework. in spite of the fact that, solvers are devoted to a unmarried variable variety: integer or actual. fixing combined difficulties will depend on advert hoc differences. In one other box, summary Interpretation bargains instruments to turn out application homes, via learning an abstraction in their concrete semantics, that's, the set of attainable values of the variables in the course of an execution. quite a few representations for those abstractions were proposed. they're referred to as summary domain names. summary domain names can combine any kind of variables, or even characterize family members among the variables.
In this paintings, we outline summary domain names for Constraint Programming, which will construct a widely used fixing strategy, facing either integer and actual variables. We additionally learn the octagons summary area, already outlined in summary Interpretation. Guiding the quest through the octagonal family, we receive reliable effects on a continual benchmark. We additionally outline our fixing procedure utilizing summary Interpretation strategies, so one can contain latest summary domain names. Our solver, AbSolute, is ready to remedy combined difficulties and use relational domains.
- Exploits the over-approximation how you can combine AI instruments within the tools of CP
- Exploits the relationships captured to resolve non-stop difficulties extra effectively
- Learn from the builders of a solver in a position to dealing with essentially all summary domains
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Extra resources for Abstract Domains in Constraint Programming
12), forms ﬁnite complete lattices for inclusion, it is sufﬁcient to compute the consistency for each constraint until the ﬁxpoint is reached. It was demonstrated by Apt in 1999 [APT 99] and Benhamou in 1996 [BEN 96] that the order in which the consistences are applied is irrelevant. Indeed, as the lattices are complete, any subset has a unique least element: the consistent ﬁxpoint. State of the Art 39 However, the order in which the consistencies, and therefore the propagators, are applied inﬂuences the speed of convergence, that is, the number of iterations required to reach the ﬁxpoint.
Indeed, we need to know some characteristics of the chosen representation, such as the size to cut into smaller elements. Similarly, the consistency used strongly depends on the chosen representation. In fact, the generalized arc consistency would not be used if the domains are represented using integer intervals. If domains are represented using integer intervals, the bound consistency is used. If the integer Cartesian product is used, then the generalized arc consistency is more appropriate. And if the domains are represented using ﬂoating point intervals, the hull consistency is more suitable.
In both solving methods, the selection criterion of the variable to instantiate or domain to cut is not explicitly given. This is because there is no unique way to choose the domain to be cut or the variable to instantiate, and it often depends on the problem to solve. The next State of the Art 43 section describes some of the choice strategies or existing exploration strategies. 5. Exploration strategies Several choice strategies have been designed to determine the order in which the variables should be instantiated or the domains should be split.
Abstract Domains in Constraint Programming by Marie Pelleau