SODA

A geometric constraint over k-dimensional objects and shapes subject to business rules

Carlsson, Mats and Beldiceanu, Nicolas and Martin, Julien (2008) A geometric constraint over k-dimensional objects and shapes subject to business rules. [SICS Report]

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Abstract

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
ID Code:2903
Deposited By:Vicki Carleson
Deposited On:24 Apr 2008
Last Modified:18 Nov 2009 16:15

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