Hard problems of discrete geometry may be formulated as a global optimization problems, which may be solved by general purpose solvers implementing branch-and-bound (B&B) algorithm. A problem of densest packing of...
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ISBN:
(纸本)9783030365929;9783030365912
Hard problems of discrete geometry may be formulated as a global optimization problems, which may be solved by general purpose solvers implementing branch-and-bound (B&B) algorithm. A problem of densest packing of N equal circles in special geometrical object, so called Square Flat Torus, R-2/Z(2), with the induced metric, is considered. It is formulated as mixed-integer problem with linear and nonconvex quadratic constraints. The open-source B&B-solver SCIP and its parallel implementation ParaSCIP have been used to find optimal arrangements for N <= 9. The main result is a confirmation of the conjecture on optimal packing for N = 9 that was published in 2012 by O. Musin and A. Nikitenko.
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