title: ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð² Ð·Ð°Ð´Ð°ÑÐ°Ñ Ð¿ÑÐµÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ-ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Application of machine learning algorithms in the pursuit-evasion problems
Creators: name: ÐÐµÐ¾Ð½ÑÑÐµÐ², Ð ÑÑÐ»Ð°Ð½
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: ÐÐ°ÑÐ¸Ð½Ð½Ð¾Ðµ Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ
Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ Ñ Ð¿Ð¾Ð´ÐºÑÐµÐ¿Ð»ÐµÐ½Ð¸ÐµÐ¼
Ð¿ÑÐµÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ-ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ðµ
Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¼ÐµÑÐ¾Ð´Ñ
ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ
reinforcement learning
pursuit-evasion
analytical methods
numerical methods

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: âÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð² Ð·Ð°Ð´Ð°ÑÐ°Ñ Ð¿ÑÐµÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ-ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ñâ. ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð² Ð·Ð°Ð´Ð°ÑÐ°Ñ Ð¿ÑÐµÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ-ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¸Ñ Ñ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð¼ÐµÑÐ¾Ð´Ð°Ð¼Ð¸ ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ°ÐºÐ¸Ñ Ð·Ð°Ð´Ð°Ñ â Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐ¼Ð¸. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸ÑÑÑ Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ ÑÑÑÑ Ð·Ð°Ð´Ð°Ñ â Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð½Ð°Ð¸ÑÐºÐ¾ÑÐµÐ¹ÑÐµÐ¼ Ð´Ð¾ÑÑÐ¸Ð¶ÐµÐ½Ð¸Ð¸ Ð·Ð°Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð¾ÑÐ´Ð¸Ð½Ð°ÑÑ, ÐºÐ°Ðº ÑÐ°ÑÑÐ½Ð¾Ð³Ð¾ ÑÐ»ÑÑÐ°Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¿ÑÐµÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ, Ð² ÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ ÑÐµÐ»ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð½ÐµÐ¿Ð¾Ð´Ð²Ð¸Ð¶Ð½Ð°Ñ Ð»Ð¸Ð½Ð¸Ñ, ÑÐ¾Ð¹ Ð¶Ðµ Ð·Ð°Ð´Ð°ÑÐ¸, Ð½Ð¾ Ñ Ð´Ð¾Ð¿Ð¾Ð»Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¼ Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐµÐ½Ð¸ÐµÐ¼, Ð¸ Ð·Ð°Ð´Ð°ÑÐ¸ ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ñ Ñ Ð¿ÑÐ¾ÑÑÑÐ¼ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸ÐµÐ¼. Ð ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÐºÐ¶Ðµ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½ Ð½Ð¾Ð²ÑÐ¹ Ð³Ð¸Ð±ÑÐ¸Ð´Ð½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´ Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ. ÐÐ¾Ð½ÐºÑÐµÑÐ½ÑÐ¹ ÑÐ°Ð·Ð´ÐµÐ» Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ, Ð¸Ð· ÐºÐ¾ÑÐ¾ÑÐ¾Ð³Ð¾ Ð±ÑÐ´ÑÑ Ð²Ð·ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼ÑÐµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ â Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ Ñ Ð¿Ð¾Ð´ÐºÑÐµÐ¿Ð»ÐµÐ½Ð¸ÐµÐ¼. ÐÐºÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑÑÑ ÑÐ°Ð¼Ð¾Ð¹ Ð¿Ð¾ ÑÐµÐ±Ðµ Ð°ÐºÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑÑ Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ. Ð¡ ÑÐ¾ÑÑÐ¾Ð¼ Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð¹ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¼Ð°ÑÐ¸Ð½ ÑÑÐ°Ð½Ð¾Ð²ÑÑÑÑ Ð´Ð¾ÑÑÑÐ¿Ð½ÑÐ¼Ð¸ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñ, ÑÑÐ»Ð¾Ð²Ð¸Ñ ÐºÐ¾ÑÐ¾ÑÑÑ Ð»Ð¸Ð±Ð¾ Ð½ÐµÐ²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾, Ð»Ð¸Ð±Ð¾ Ð¾ÑÐµÐ½Ñ ÑÐ»Ð¾Ð¶Ð½Ð¾ Ð°Ð´Ð°Ð¿ÑÐ¸ÑÐ¾Ð²Ð°ÑÑ Ð¿Ð¾Ð´ ÑÐ¶Ðµ Ð¸Ð¼ÐµÑÑÐ¸ÐµÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ. ÐÐ°Ðº Ð¿ÑÐ°Ð²Ð¸Ð»Ð¾, ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¿ÑÐ¸ÐºÐ»Ð°Ð´Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ ÑÐ°ÑÑÐ¾ Ð·Ð°Ð½Ð¸Ð¼Ð°ÐµÑ Ð¼Ð½Ð¾Ð³Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð¸, ÑÐ°ÐºÐ¶Ðµ, ÐºÐ°Ðº Ð¸ Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÑÐ¸. Ð Ð°Ð±Ð¾ÑÐ° ÑÐ²Ð»ÑÐµÑÑÑ Ð°ÐºÑÑÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¸ Ð² ÑÐ¸Ð»Ñ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾ Ð½ÐµÐ±Ð¾Ð»ÑÑÐ¾Ð³Ð¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° ÑÐ°Ð±Ð¾Ñ Ð½Ð° ÑÑÑ ÑÐµÐ¼Ñ Ð½Ð° ÑÑÑÑÐºÐ¾Ð¼ ÑÐ·ÑÐºÐµ, Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ ÑÐ°Ð±Ð¾ÑÐ°Ð¼Ð¸ Ð½Ð° Ð°Ð½Ð³Ð»Ð¸Ð¹ÑÐºÐ¾Ð¼.
description: The theme of the final qualification work: âApplication of machine learning algorithms in the pursuit-evasion problemsâ. This work is devoted to the study of the applicability of machine learning algorithms in pursuit-evasion problems, as well as their comparison with classical methods for solving such problems â analytical and numerical. The study is carried out on the example of two problems â the problem of reaching the given ordinate as soon as possible, as a special case of the pursuit problem, in which the goal is a fixed line, the same problem with additional restriction, and the lady-in-the-lake problem. The new hybrid machine learning algorithm is also presented in this paper. The specific branch of machine learning from which the algorithms used in this work were taken is reinforcement learning. The relevance of this work is determined by the relevance of machine learning itself. As the computational power of machines grows, new methods for solving problems become available. These methods allow us to solve problems which are difficult or even impossible to adapt to existing algorithms. In case of this work, we mean numerical and analytical methods. Usually, numerical methods used in practice often take a lot of time, as well as training a neural network. Analytical solution of real-life problems is often impossible at all. This work is also relevant due to the relatively small amount of works on this topic in Russian, compared with works in English.