Abstract Domains in Constraint Programming by Marie Pelleau

By Marie Pelleau

Constraint Programming goals at fixing difficult combinatorial difficulties, with a computation time expanding in perform exponentially. The equipment are this present day effective sufficient to unravel huge business difficulties, in a primary framework. in spite of the fact that, solvers are devoted to a unmarried variable sort: integer or genuine. fixing combined difficulties depends on advert hoc alterations. In one other box, summary Interpretation deals instruments to end up software 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 kind of variables, or even characterize kinfolk among the variables.

In this paintings, we outline summary domain names for Constraint Programming, in order to construct a popular fixing strategy, facing either integer and actual variables. We additionally examine the octagons summary area, already outlined in summary Interpretation. Guiding the hunt through the octagonal kin, we receive strong effects on a continuing benchmark. We additionally outline our fixing strategy utilizing summary Interpretation recommendations, with a purpose to comprise latest summary domain names. Our solver, AbSolute, is ready to clear up 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 unravel non-stop difficulties extra effectively
  • Learn from the builders of a solver in a position to dealing with virtually all summary domains

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Another alternative is to add discrete global constraints to a continuous solver [BER 09] or to create mixed global constraints [CHA 09b] to treat within the same constraint both continuous and discrete variables. Thus, each variable benefits from a suitable constraint for its type (discrete or continuous). However, this method depends on the problem and demands the necessary global constraints as well as an ad hoc consistency for each problem. 7. Conclusion CP can efficiently solve CSPs. While solving methods do not depend on the problem at hand, they are highly dedicated to the type of variables (discrete or continuous) of the problem.

The earlier this constraint generates a failure, the bigger is the subtree cut from the search tree. Other heuristics as a survey are given in [GEE 92, GEN 96, BEE 06]. 2. A classical continuous solver. 7. Comparison between the strategy instantiating variables with the biggest domains first a) and the first-fail strategy b) 46 Abstract Domains in Constraint Programming Once the variable to instantiate is chosen, we need to choose to which value it should be instantiated. Here too, many strategies have been developed, choosing the value maximizing the number of possible solutions [DEC 87, KAS 04], the product of the domains size (promise) [GIN 90] and the sum of the domains size (min-conflicts) [FRO 95].

In addition, we are no longer restricted to existing Cartesian representations, but can define new representations in the same way as in AI. 2. Unified components To begin with, we define all the necessary bricks for the development of a unique solving method, namely, the consistency, the splitting operator and of course the abstract domains for CP. These definitions are based on notions of order, lattices and fixpoints. 1. Consistency and fixpoint Given a partially ordered set with the inclusion and a constraint, we can define the consistent element as the least element of the partially ordered set if it exists.

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