Simultaneous containment of several polygons
SCG '87 Proceedings of the third annual symposium on Computational geometry
Annals of Operations Research - Special issue on Tabu search
Using a tabu search approach for solving the two-dimensional irregular cutting problem
Annals of Operations Research - Special issue on Tabu search
Rounding arrangements dynamically
Proceedings of the eleventh annual symposium on Computational geometry
Snap rounding line segments efficiently in two and three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
The irregular cutting-stock problem mdash; a new procedure for deriving the no-fit polygon
Computers and Operations Research
Polygon decomposition for efficient construction of Minkowski sums
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
Computational Geometry: Theory and Applications
Bin Packing with Adaptive Search
Proceedings of the 1st International Conference on Genetic Algorithms
Optimization in computer-aided pattern packing (marking, envelopes)
Optimization in computer-aided pattern packing (marking, envelopes)
A New Placement Heuristic for the Orthogonal Stock-Cutting Problem
Operations Research
An efficient solution method for relaxed variants of the nesting problem
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Mixed-integer programming models for nesting problems
Journal of Heuristics
On Packing 2D Irregular Shapes
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem
INFORMS Journal on Computing
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
A genetic programming hyper-heuristic approach for evolving 2-D strip packing heuristics
IEEE Transactions on Evolutionary Computation
Irregular stock cutting system based on AutoCAD
Advances in Engineering Software
Computers and Operations Research
Automating the packing heuristic design process with genetic programming
Evolutionary Computation
Algorithms for nesting with defects
Discrete Applied Mathematics
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This paper presents a new heuristic algorithm for the two-dimensional irregular stock-cutting problem, which generates significantly better results than the previous state of the art on a wide range of established benchmark problems. The developed algorithm is able to pack shapes with a traditional line representation, and it can also pack shapes that incorporate circular arcs and holes. This in itself represents a significant improvement upon the state of the art. By utilising hill climbing and tabu local search methods, the proposed technique produces 25 new best solutions for 26 previously reported benchmark problems drawn from over 20 years of cutting and packing research. These solutions are obtained using reasonable time frames, the majority of problems being solved within five minutes. In addition to this, we also present 10 new benchmark problems, which involve both circular arcs and holes. These are provided because of a shortage of realistic industrial style benchmark problems within the literature and to encourage further research and greater comparison between this and future methods.