1. Disk Packing in a Square: A New Global Optimization Approach.
- Author
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Addis, B., Locatelli, M., and Schoen, F.
- Subjects
- *
STOCHASTIC processes , *FUNCTIONAL analysis , *MATHEMATICAL analysis , *MATHEMATICAL optimization , *COMPUTER programming , *COMPUTER algorithms , *MATHEMATICAL models , *ALGORITHMS - Abstract
We present a new computational approach to the problem of placing n identical nonoverlapping disks in the unit square in such a way that their radii are maximized. The problem has been studied in a large number of papers, from both a theoretical and a computational point of view. In this paper, we conjecture that the problem possesses a so-called funneling landscape, a feature that is commonly found in molecular conformation problems. Based on this conjecture, we develop a stochastic search algorithm that displays excellent numerical performance. Thanks to this algorithm, we could improve over previously known putative optima in the range n ≤ 130 in as many as 32 instances, the smallest of which is n=53. [ABSTRACT FROM AUTHOR]
- Published
- 2008
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