By Marie Pelleau
Constraint Programming goals at fixing challenging combinatorial difficulties, with a computation time expanding in perform exponentially. The equipment are this present day effective sufficient to unravel huge commercial difficulties, in a general framework. even if, solvers are devoted to a unmarried variable style: integer or genuine. fixing combined difficulties is dependent upon advert hoc alterations. In one other box, summary Interpretation deals instruments to end up application homes, by means of learning an abstraction in their concrete semantics, that's, the set of attainable values of the variables in the course of an execution. a variety of representations for those abstractions were proposed. they're referred to as summary domain names. summary domain names can combine any form of variables, or even characterize kinfolk among the variables.
In this paintings, we outline summary domain names for Constraint Programming, which will construct a well-known fixing process, facing either integer and genuine variables. We additionally learn the octagons summary area, already outlined in summary Interpretation. Guiding the hunt through the octagonal family members, we receive strong effects on a continual benchmark. We additionally outline our fixing process utilizing summary Interpretation thoughts, that allows you to comprise present 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 equipment 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 info for Abstract Domains in Constraint Programming
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. Different propagation strategies are possible.
Note that this is not always the case, as the HC4-Revise algorithm can compute an approximation of the HC. For instance, when there exist multiple occurrences of a variable in the constraint, the result obtained with the HC4-Revise algorithm can be an overapproximation of the hull-consistent domains. 16. 5(b), the points correspond to the Cartesian product of the consistent domains. There are three solution points and are represented by crosses. 5(b)), we obtain 15 points. We can deduce that the stronger the chosen consistency is, the higher the ratio of number of solution points on the total number of points is.
In the case of an integer variable vi , the domain can be represented as a subset of points Di or as a subinterval of Di . – Let v1 , . . , vn be the ˆ 1, . . , D ˆ n . We call integer variables with discrete ﬁnite domains D ˆ Cartesian product any Cartesian product of any integer set in D. – Let v1 , . . , vn be the variables with ˆ 1, . . , D ˆ n . We call integer box any Cartesian discrete ﬁnite domains D State of the Art 29 ˆ Integer boxes of D ˆ form a ﬁnite lattice product of integer intervals in D.
Abstract Domains in Constraint Programming by Marie Pelleau