Computing Maximum Polygonal Packings in Convex Polygons using Best-Fit, Genetic Algorithms and Integer Linear Programs
DOI:
https://doi.org/10.57717/cgt.v5i5.87Abstract
Given a convex region \(C\) and a set of simple polygons with associated profits, the Maximum Polygon Packing Problem seeks a non-overlapping packing of a subset of the polygons (without rotations) into \(C\), such that the total profit of the packed polygons is maximized.
To handle instances of various sizes and properties, we present a collection of algorithms for this problem. For large instances, we utilize a greedy best-fit placement strategy. For instances consisting exclusively of rectilinear polygons, we use a specialized greedy best-fit algorithm which handles rectilinear shapes efficiently. For medium-sized instances, we provide a genetic algorithm. Finally, for the smallest instances, we employ an integer linear programming model to obtain near-optimal solutions.
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Copyright (c) 2026 Alkan Atak, Kevin Buchin, Mart Hagedoorn, Jona Heinrichs, Karsten Hogreve, Guangping Li, Patrick Pawelczyk
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