By Marie Pelleau
Constraint Programming goals at fixing difficult combinatorial difficulties, with a computation time expanding in perform exponentially. The equipment are this day effective sufficient to unravel huge commercial difficulties, in a ordinary framework. besides the fact that, solvers are devoted to a unmarried variable kind: integer or actual. fixing combined difficulties will depend on advert hoc differences. In one other box, summary Interpretation bargains instruments to turn out application houses, through learning an abstraction in their concrete semantics, that's, the set of attainable values of the variables in the course of an execution. a number of representations for those abstractions were proposed. they're known as summary domain names. summary domain names can combine any kind of variables, or even signify family among the variables.
In this paintings, we outline summary domain names for Constraint Programming, with the intention to construct a known fixing procedure, facing either integer and actual variables. We additionally research the octagons summary area, already outlined in summary Interpretation. Guiding the quest by way of the octagonal family, we receive solid effects on a continuing benchmark. We additionally outline our fixing strategy utilizing summary Interpretation options, in an effort to contain present summary domain names. Our solver, AbSolute, is ready to clear up combined difficulties and use relational domains.
- Exploits the over-approximation easy methods to combine AI instruments within the tools of CP
- Exploits the relationships captured to unravel 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
16 (D1 = [0, 4], D2 = [−1, 1]). – 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. 5(c) shows the hull-consistent box. The solutions correspond to the diagonal in the box. The solutions are also represented and correspond to the diagonal line in the box. We can see that in this box there are more non-solution points than solution points. For a given constraint C, an algorithm taking the domains as input and removing from them the inconsistent values is called a propagator and is denoted by ρC .
1. Introduction In CP, solving techniques strongly depend on the type of variables, and are even dedicated to a type of variables (integer or real). If a problem contains both integer and real variables, there are no solving methods. There are three possible solutions to this kind of problem with CP: the integers are transformed into real variables and integrity constraints are added to the problem (the propagation of these new constraints reﬁne the bound of the integer variables [GRA 06]); the real varibales are discretized, the possible values for the real variables are enumerated with a given step [CHO 10]; or a discrete and a continuous solver are combined [COL 94, FAG 14] By looking more closely, we can see that regardless of the resolution method used, it alternates between propagation and 54 Abstract Domains in Constraint Programming exploration phases.
Abstract Domains in Constraint Programming by Marie Pelleau