Using a tabu search approach for solving the two-dimensional irregular cutting problem
Annals of Operations Research - Special issue on Tabu search
Exact Solution of the Two-Dimensional Finite Bon Packing Problem
Management Science
Efficient nesting of congruent convex figures
Communications of the ACM
Determining the minimum-area encasing rectangle for an arbitrary closed curve
Communications of the ACM
The irregular cutting-stock problem mdash; a new procedure for deriving the no-fit polygon
Computers and Operations Research
Genetic Algorithm Coding Methods for Leather Nesting
Applied Intelligence
A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums
Computers and Operations Research
Benders decomposition, Lagrangean relaxation and metaheuristic design
Journal of Heuristics
A Generic Approach for Leather Nesting
ICNC '09 Proceedings of the 2009 Fifth International Conference on Natural Computation - Volume 05
Matheuristics: Optimization, Simulation and Control
HM '09 Proceedings of the 6th International Workshop on Hybrid Metaheuristics
Mathematical model and efficient algorithms for object packing problem
Computational Geometry: Theory and Applications
A beam search implementation for the irregular shape packing problem
Journal of Heuristics
Irregular Packing Using the Line and Arc No-Fit Polygon
Operations Research
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The nesting problem is an irregular two-dimensional cutting problem where the shapes of the pieces to cut and the master surfaces are irregular in shape and different in size. In particular, we consider nesting problems where the master surface could contain defects. Some of them can be accepted (i.e., incorporated) in certain types of pieces, while other defected areas must be avoided. The problems considered in this paper arise in the leather garment and furniture industry. First, we solve nesting problems involving a single master surface (Irregular Single Knapsack Problem) for which we propose three different constructive (placement) procedures for the pieces. These procedures generate sets of cutting patterns, which are global configurations of the pieces, as sets on the master surface, and are included in an iterative algorithm motivated by a Lagrangean relaxation approach, where the Lagrangean dual seeds a Guided Local Search hybrid. Finally, we embed this iterative algorithm into a heuristic for solving the problem of cutting more than one master surface for producing all of the requested pieces, minimizing the total waste (Irregular Multiple Stock-Size Cutting Stock Problem). We test our algorithms on three sets of test problem instances. In order to validate the new heuristics for the nesting problem involving a single master surface we use a set of well-known irregular strip packing instances from the literature, where defects are not considered. The new heuristics for the nesting problem involving multiple master surfaces are then tested on a set of rectangular bin-packing instances and on a set of real-world instances obtained from leather garment and furniture industries with defects in the master surface.