  We developed a new method PROTES for black-box optimization, which is based
on the probabilistic sampling from a probability density function given in the
low-parametric tensor train format. We tested it on complex multidimensional
arrays and discretized multivariable functions taken, among others, from
real-world applications, including unconstrained binary optimization and
optimal control problems, for which the possible number of elements is up to
$2^{100}$. In numerical experiments, both on analytic model functions and on
complex problems, PROTES outperforms existing popular discrete optimization
methods (Particle Swarm Optimization, Covariance Matrix Adaptation,
Differential Evolution, and others).
