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).

翻译：我们开发了一种新的黑箱优化方法PROTES，该方法基于从低参数张量列格式的概率密度函数中进行概率采样。我们在复杂多维数组和离散化多变量函数上进行了测试，这些函数取自实际应用场景，包括无约束二进制优化和最优控制问题，其中元素的可能数量高达$2^{100}$。在数值实验中，无论是解析模型函数还是复杂问题，PROTES均优于现有的主流离散优化方法（如粒子群优化、协方差矩阵自适应、差分进化等）。