  The article demonstrates rather general approach to problems of discrete
geometry: treat them as global optimization problems to be solved by one of
general purpose solver implementing branch-and-bound algorithm (B&B). This
approach may be used for various types of problems, i.e. Tammes problems,
Thomson problems, search of minimal potential energy of micro-clusters, etc.
Here we consider a problem of densest packing of equal circles in special
geometrical object, so called square flat torus $\mathbb{R}^2/\mathbb{Z}^2$
with the induced metric. It is formulated as Mixed-Integer Nonlinear Problem
with linear and non-convex quadratic constraints.
  The open-source B&B-solver SCIP, http://scip.zib.de, and its parallel
implementation ParaSCIP, http://ug.zib.de, had been used in computing
experiments to find "very good" approximations of optimal arrangements. 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. To do that, ParaSCIP took
about 2000 CPU*hours (16 hours x 128 CPUs) of cluster HPC4/HPC5, National
Research Centre "Kurchatov Institute", http://ckp.nrcki.ru
