A Geometric Constraint over k-Dimensional Objects and Shapes Subject to Business Rules

Abstract

Abstract. This paper presents a global constraint that enforces rules written in a language based on arithmetic and first-order logic to hold among a set of objects. In a first step, the rules are rewritten to Quantifier-Free Presburger Arithmetic (QFPA) formulas. Secondly, such formulas are compiled to generators of k-dimensional forbidden sets. Such generators are a generalization of the indexicals of cc(FD). Finally, the forbidden sets generated by such indexicals are aggregated by a sweep-based algorithm and used for filtering.The business rules allow to express a great variety of packing and placement constraints, while admitting effective filtering of the domain variables of the k-dimensional object, without the need to use spatial data structures.

From Rules to Constraint Programs with the Rules2CP Modelling Language

“…Furthermore, a large subset of PKML has been shown in [16] to be efficiently compilable with indexicals within the geometrical kernel of the global constraint geost.…”

“…A large subset of PKML rules restricted to linear constraints has been shown in [16] to be compilable with indexical constraints in the geometrical kernel of the global constraint geost [17] for higher-dimensional placement problems. Here we define PKML as a library of Rules2CP declarations and rules.…”

Toward sustainable development in constraint programming

“…However, it turned out that indexicals could not replace or encode the propagators associated to global constraints. After initial work on the efficient compilation of indexicals (for instance [13]), very little work was done in the spirit of indexicals, exceptions being [9,22]. On the one hand, classical indexicals have a number of known limitations:…”

Sweeping with Continuous Domains

“…This technique has been fruitfully applied in the context of placement problems (rectangle packing, container loading, warehouse management). In particular, the filtering algorithm of the geost constraint [5,8,6], today implemented in different systems like Choco [1], JaCop [10] or SICStus [9], is based on a sweeping loop. Propagation (e.g., AC3 [11]) requires a propagator for each constraint, that is, an operator that removes inconsistent values.…”

“…However, such brute force methods, apart from being inefficient, are not possible with continuous domains (that are not countable). In previous publications, inflaters have been proposed for several important classes of constraints: rectangle inclusion and non-overlapping [5], linear equations, distance equations [2] as well as constraints derived from business rules [8]. The method in [8] is generic as it addresses a class of first-order formulae with linear constraints by way of predicates.…”