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Computing Maximum Polygonal Packings in Convex Polygons Using Best-Fit, Genetic Algorithms and ILPs (CG Challenge)

Authors Alkan Atak, Kevin Buchin , Mart Hagedoorn , Jona Heinrichs, Karsten Hogreve, Guangping Li , Patrick Pawelczyk

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Author Details

Alkan Atak
  • TU Dortmund, Germany
Kevin Buchin
  • TU Dortmund, Germany
Mart Hagedoorn
  • TU Dortmund, Germany
Jona Heinrichs
  • TU Dortmund, Germany
Karsten Hogreve
  • TU Dortmund, Germany
Guangping Li
  • TU Dortmund, Germany
Patrick Pawelczyk
  • TU Dortmund, Germany

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Alkan Atak, Kevin Buchin, Mart Hagedoorn, Jona Heinrichs, Karsten Hogreve, Guangping Li, and Patrick Pawelczyk. Computing Maximum Polygonal Packings in Convex Polygons Using Best-Fit, Genetic Algorithms and ILPs (CG Challenge). In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 83:1-83:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SoCG.2024.83

Abstract

Given a convex region P and a set of irregular polygons with associated profits, the Maximum Polygon Packing Problem seeks a non-overlapping packing of a subset of the polygons (without rotations) into P maximizing the profit of the packed polygons. Depending on the size of an instance, we use different algorithmic solutions: integer linear programs for small instances, genetic algorithms for medium-sized instances and a best-fit approach for large instances. For packing rectilinear polygons we provide a dedicated best-fit algorithm.

Subject Classification

ACM Subject Classification
  • Theory of computation → Packing and covering problems
Keywords
  • Polygon Packing
  • Nesting Problem
  • Genetic Algorithm
  • Integer Linear Programming

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Supplementary Materials

References

  1. Brenda Baker, Ed Coffman, and Ronald Rivest. Orthogonal packings in two dimensions. SIAM J. Comput., 9:846-855, November 1980. URL: https://doi.org/10.1137/0209064.
  2. Julia A. Bennell and Xiang Song. A comprehensive and robust procedure for obtaining the nofit polygon using minkowski sums. Computers & Operations Research, 35(1):267-281, 2008. Part Special Issue: Applications of OR in Finance. URL: https://doi.org/10.1016/j.cor.2006.02.026.
  3. Edmund K. Burke, Graham Kendall, and Glenn Whitwell. A new placement heuristic for the orthogonal stock-cutting problem. Operations Research, 52(4):655-671, 2004. URL: https://doi.org/10.1287/opre.1040.0109.
  4. Luiz H. Cherri, Leandro R. Mundim, Marina Andretta, Franklina M.B. Toledo, José F. Oliveira, and Maria Antónia Carravilla. Robust mixed-integer linear programming models for the irregular strip packing problem. European Journal of Operational Research, 253(3):570-583, 2016. URL: https://doi.org/10.1016/j.ejor.2016.03.009.
  5. Richard Cottle, Mukund N. Thapa, et al. Linear and nonlinear optimization, volume 253. Springer, 2017. URL: https://doi.org/10.1007/978-1-4939-7055-1.
  6. Guilherme Dias da Fonseca and Yan Gerard. Shadoks approach to knapsack polygonal packing. In Symposium on Computational Geometry (SoCG), volume 293 of LIPIcs, pages 84:1-84:9, 2024. URL: https://doi.org/10.4230/LIPIcs.SoCG.2024.84.
  7. Sándor P. Fekete, Phillip Keldenich, Dominik Krupke, and Stefan Schirra. Maximum polygon packing: The cg:shop challenge 2024, 2024. URL: https://arxiv.org/abs/2403.16203.
  8. Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2023. URL: https://www.gurobi.com.
  9. Africa Gómez and Daniel de la Fuente. Resolution of strip-packing problems with genetic algorithms. Journal of the Operational Research Society, 51(11):1289-1295, November 2000. URL: https://doi.org/10.1057/palgrave.jors.2601019.
  10. Martin Held. Priority-driven nesting of irregular polygonal shapes within a convex polygonal container based on a hierarchical integer grid. In Symposium on Computational Geometry (SoCG), volume 293 of LIPIcs, pages 85:1-85:6, 2024. URL: https://doi.org/10.4230/LIPIcs.SoCG.2024.85.
  11. Elizabeth Hopper and Brian C.H. Turton. A review of the application of meta-heuristic algorithms to 2d strip packing problems. Artificial Intelligence Review, 16(4):257-300, December 2001. URL: https://doi.org/10.1023/A:1012590107280.
  12. Yannan Hu, Hideki Hashimoto, Shinji Imahori, and Mutsunori Yagiura. Efficient implementations of construction heuristics for the rectilinear block packing problem. Computers & Operations Research, 53:206-222, 2015. URL: https://doi.org/10.1016/j.cor.2014.06.021.
  13. Yannan Hu, Hideki Hashimoto, Shinji Imahori, and Mutsunori Yagiura. Practical algorithms for two-dimensional packing of general shapes. In Teofilo F. Gonzalez, editor, Handbook of Approximation Algorithms and Metaheuristics, Second Edition, Volume 1: Methologies and Traditional Applications, pages 585-609. Chapman and Hall/CRC, 2018. URL: https://doi.org/10.1201/9781351236423-33.
  14. Juan J. Lastra-Díaz and María Teresa Ortuño. Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts. European Journal of Operational Research, 313(1):69-91, 2024. URL: https://doi.org/10.1016/j.ejor.2023.08.009.
  15. Canhui Luo, Zhouxing Su, and Zhipeng Lü. A general heuristic approach for maximum polygon packing. In Symposium on Computational Geometry (SoCG), volume 293 of LIPIcs, pages 86:1-86:9, 2024. URL: https://doi.org/10.4230/LIPIcs.SoCG.2024.86.
  16. Rodrigues, Marcos O., Cherri, Luiz H., and Mundim, Leandro R. MIP models for the irregular strip packing problem: new symmetry breaking constraints. ITM Web Conf., 14:05, 2017. URL: https://doi.org/10.1051/itmconf/20171400005.
  17. The CGAL Project. CGAL User and Reference Manual. CGAL Editorial Board, 5.6 edition, 2023. URL: https://doc.cgal.org/5.6/Manual/packages.html.
  18. Ron Wein, Alon Baram, Eyal Flato, Efi Fogel, Michael Hemmer, and Sebastian Morr. 2D minkowski sums. In CGAL User and Reference Manual. CGAL Editorial Board, 5.6 edition, 2023. URL: https://doc.cgal.org/5.6/Manual/packages.html#PkgMinkowskiSum2.
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