A Global Constraint for Nesting Problems

• Type: Article in International Scientific Journal
• Date: 2008

Authors

Cristina Ribeiro (Author) FEUP; Maria Antónia Carravilla (Author) FEUP

Journal

Title: Artificial Intelligence Review

Vol. 30 No. 1-4

Pages: 99-118

ISSN: 0269-2821

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 3 Citations

ISI Web of Science

Scopus - 4 Citations

COMPENDEX

INSPEC

Scientific classification

FOS: Engineering and technology > Other engineering and technologies

CORDIS: Physical sciences > Computer science

Other information

Authenticus ID: P-003-TBA

DOI: 10.1007/s10462-009-9120-y

Abstract (EN): Nesting problems are particularly hard combinatorial problems. They involve the positioning of a set of small arbitrarily-shaped pieces on a large stretch of material, without overlapping them. The problem constraints are bidimensional in nature and have to be imposed on each pair of pieces. This all-to-all pattern results in a quadratic number of constraints. Constraint programming has been proven applicable to this category of problems, particularly in what concerns exploring them to optimality. But it is not easy to get effective propagation of the bidimensional constraints represented via finite-domain variables. It is also not easy to achieve incrementality in the search for an improved solution: an available bound on the solution is not effective until very late in the positioning process. In the sequel of work on positioning non-convex polygonal pieces using a CLP model, this work is aimed at improving the expressiveness of constraints for this kind of problems and the effectiveness of their resolution using global constraints. A global constraint “outside” for the non-overlapping constraints at the core of nesting problems has been developed using the constraint programming interface provided by Sicstus Prolog. The global constraint has been applied together with a specialized backtracking mechanism to the resolution of instances of the problem where optimization by Integer Programming techniques is not considered viable. The use of a global constraint for nesting problems is also regarded as a first step in the direction of integrating Integer Programming techniques within a Constraint Programming model.

Language: English

Type (Professor's evaluation): Scientific