Carlsson, Mats and Beldiceanu, Nicolas and Martin, Julien (2008) A geometric constraint over k-dimensional objects and shapes subject to business rules. [SICS Report]
This report 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 efficient and effective filtering of the domain variables of the k-dimensional object, without the need to use spatial data structures. The constraint was used to directly encode the packing knowledge of a major car manufacturer and tested on a set of real packing problems under these rules, as well as on a packing-unpacking problem.
|Item Type:||SICS Report|
|Uncontrolled Keywords:||Global Constraint, Geometric Constraint, Rule, Sweep, Quantifier-Free Presburger Arithmetic|
|Deposited By:||Vicki Carleson|
|Deposited On:||24 Apr 2008|
|Last Modified:||18 Nov 2009 16:15|
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