Global optimization method for finding dense packings of equal circles in a circle

Wenqi Huang and Tao Ye

European Journal of Operational Research, 2011, vol. 210, issue 3, 474-481

Abstract: This paper considers the problem of finding the densest packing of N (N = 1, 2, ...) equal circles in a circle. This problem is perhaps the most classical packing problem. It is also a natural and challenging test system for evaluating various global optimization methods. We propose a quasi-physical global optimization method by simulating two kinds of movements of N elastic disks: smooth movement driven by elastic pressures and abrupt movement driven by strong repulsive forces and attractive forces. The algorithm is tested on the instances of N = 1, 2, ... , 200. Using the best-known record of the radius of the container as an upper bound, we find 63 new packings better than the best-known ones reported in literature.

Keywords: Packing; Global; optimization; Heuristic; Quasi-physical; approach (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:210:y:2011:i:3:p:474-481

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