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

翻译：我们提出了一种新的方法PROTES，用于多维数组和离散化多变量函数的优化，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上进行了测试，这些数组来自现实世界应用，包括无约束二元优化和最优控制问题，其中可能元素数量高达 $2^{100}$ 个。在数值实验中，无论是针对解析模型函数还是复杂问题，我们的算法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）。此外，我们在所有数值应用中使用了相同的超参数集合。