Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Using a tabu search approach for solving the two-dimensional irregular cutting problem
Annals of Operations Research - Special issue on Tabu search
Strategic directions in constraint programming
ACM Computing Surveys (CSUR) - Special ACM 50th-anniversary issue: strategic directions in computing research
Solution Techniques for Constraint Satisfaction Problems: Advanced Approaches
Artificial Intelligence Review
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Mixed Global Constraints and Inference in Hybrid CLP–IP Solvers
Annals of Mathematics and Artificial Intelligence
An Open-Ended Finite Domain Constraint Solver
PLILP '97 Proceedings of the9th International Symposium on Programming Languages: Implementations, Logics, and Programs: Including a Special Trach on Declarative Programming Languages in Education
Sweep as a Generic Pruning Technique Applied to the Non-overlapping Rectangles Constraint
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Non-overlapping Constraints between Convex Polytopes
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Branch and Infer: a Unifying Framework for Integer and Finite Domain Constraint Programming
INFORMS Journal on Computing
The Role of Integer Programming Techniques in Constraint Programming's Global Constraints
INFORMS Journal on Computing
Optimization in computer-aided pattern packing (marking, envelopes)
Optimization in computer-aided pattern packing (marking, envelopes)
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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.