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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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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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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.

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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

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

Supplementary Materials

References

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