LIPIcs.SoCG.2024.83.pdf
- Filesize: 0.68 MB
- 9 pages
Document
Computing Maximum Polygonal Packings in Convex Polygons Using Best-Fit, Genetic Algorithms and ILPs (CG Challenge)
Authors
Kevin Buchin 
,
Mart Hagedoorn ,
Guangping Li ,
-
Part of:
Volume:
40th International Symposium on Computational Geometry (SoCG 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-06-06
File
Document Identifiers
Author Details
Cite As Get BibTex
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
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads
Supplementary Materials
-
Software (Source Code)
https://github.com/traMectory/MPP
browse
archived version
-
Software (Source Code)
https://github.com/Alkan-Atak/AtrisBlockPacking
browse
archived version
References
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2023. URL: https://www.gurobi.com.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.