title: ÐÐ¾Ð¸ÑÐº ÑÑÐ±Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ ÐºÐ¾Ð¼Ð¼Ð¸Ð²Ð¾ÑÐ¶ÑÑÐ° Ð¿ÑÐ¸ Ð¿Ð¾Ð¼Ð¾ÑÐ¸ Ð°Ð³ÑÐµÐ³Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ½Ð¾Ð³Ð¾ Ð³ÑÐ°ÑÐ°
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Search for suboptimal solution to TSP with graph aggregation
Creators: name: Ð¯ÑÑÑÐµÐ±Ð¾Ð², ÐÐ¸ÐºÐ¸ÑÐ°
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: 2022
Subjects: Ð·Ð°Ð´Ð°ÑÐ° ÐºÐ¾Ð¼Ð¼Ð¸Ð²Ð¾ÑÐ¶ÑÑÐ°
Ð°Ð³ÑÐµÐ³Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð´ÐµÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ¸Ñ
ÑÐ°Ð·Ð±Ð¸ÐµÐ½Ð¸Ðµ Ð³ÑÐ°ÑÐ°
travelling salesman problem
aggregation
decomposition
graph partitioning

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÐ¾Ð¸ÑÐº ÑÑÐ±Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ ÐºÐ¾Ð¼Ð¼Ð¸Ð²Ð¾ÑÐ¶ÑÑÐ° Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð°Ð³ÑÐµÐ³Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ½Ð¾Ð³Ð¾ Ð³ÑÐ°ÑÐ°Â». ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð½Ð¾Ð²Ð¾Ð³Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð´Ð° Ðº Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð½Ð¾Ð¼Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ ÐºÐ¾Ð¼Ð¼Ð¸Ð²Ð¾ÑÐ¶ÐµÑÐ° Ð¿Ð¾ÑÑÐµÐ´ÑÑÐ²Ð¾Ð¼ Ð´ÐµÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ¸Ð¸ Ð¸ Ð°Ð³ÑÐµÐ³Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ½Ð¾Ð³Ð¾ Ð³ÑÐ°ÑÐ°. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ: ÐÐ±Ð·Ð¾Ñ Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÑ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ ÐºÐ¾Ð¼Ð¼Ð¸Ð²Ð¾ÑÐ¶ÐµÑÐ°, Ð¾ÑÐµÐ½ÐºÐ° Ð¸Ñ ÑÐ²Ð¾Ð¹ÑÑÐ². Ð¤Ð¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²ÐºÐ° Ð¾Ð±ÑÐµÐ³Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð´Ð° Ðº ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ ÐºÐ¾Ð¼Ð¼Ð¸Ð²Ð¾ÑÐ¶ÐµÑÐ° Ð¿Ð¾ÑÑÐµÐ´ÑÑÐ²Ð¾Ð¼ Ð´ÐµÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ¸Ð¸ Ð¸ Ð°Ð³ÑÐµÐ³Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ½Ð¾Ð³Ð¾ Ð³ÑÐ°ÑÐ°. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð²ÑÐ±Ð¾ÑÐ° Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð², Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÑÑÐ¸Ñ Ð¿Ð¾Ð´Ð·Ð°Ð´Ð°ÑÐ¸ Ð¼ÐµÑÐ¾Ð´Ð°. Ð¡Ð¸Ð½ÑÐµÐ· ÐºÑÐ¸ÑÐµÑÐ¸ÐµÐ² Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾ÑÑÐ¸ Ð´Ð»Ñ Ð¿Ð¾Ð´Ð·Ð°Ð´Ð°Ñ ÑÐ°Ð·Ð±Ð¸ÐµÐ½Ð¸Ñ Ð¸ Ð°Ð³ÑÐµÐ³Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ ÐºÑÐ¸ÑÐµÑÐ¸ÐµÐ² Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾ÑÑÐ¸ Ð¿Ð¾Ð´Ð·Ð°Ð´Ð°Ñ Ð½Ð° ÐºÐ°ÑÐµÑÑÐ²Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ. ÐÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð½Ð¾Ð²Ð¸Ð·Ð½Ð° Ð²ÑÐ´Ð²Ð¸Ð³Ð°ÐµÐ¼Ð¾Ð³Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð´Ð°, Ð° ÑÐ°ÐºÐ¶Ðµ ÐµÐ³Ð¾ Ð¿ÐµÑÑÐ¿ÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÑ ÐºÐ°Ðº Ð°Ð»ÑÑÐµÑÐ½Ð°ÑÐ¸Ð²Ð° Ð´ÑÑÐ³Ð¸Ð¼ Ð¼ÐµÑÐ¾Ð´Ð°Ð¼ ÑÐµÑÐµÐ½Ð¸Ñ. Ð ÑÐ¸Ð½Ð°Ð»Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ» Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐ¹ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½Ñ, Ð² ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÐºÐ¾ÑÐ¾ÑÐ¾Ð³Ð¾ ÑÐ´ÐµÐ»Ð°Ð½Ñ Ð²ÑÐ²Ð¾Ð´Ñ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾ Ð¿ÑÐ¸Ð³Ð¾Ð´Ð½Ð¾ÑÑÐ¸ ÐºÐ°Ðº Ð¿Ð¾Ð´ÑÐ¾Ð´Ð° Ð² ÑÐµÐ»Ð¾Ð¼, ÑÐ°Ðº Ð¸ ÑÐ¸Ð½ÑÐµÐ·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ ÐºÑÐ¸ÑÐµÑÐ¸ÐµÐ². ÐÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½ ÐºÐ»Ð°ÑÑ Ð·Ð°Ð´Ð°Ñ, Ð´Ð»Ñ ÐºÐ¾ÑÐ¾ÑÑÑ Ð¾Ð½Ð¸ Ð¼Ð¾Ð³ÑÑ Ð´Ð°Ð²Ð°ÑÑ ÑÐµÑÐµÐ½Ð¸Ðµ, Ð±Ð»Ð¸Ð·ÐºÐ¾Ðµ Ðº ÑÐ¾ÑÐ½Ð¾Ð¼Ñ.
description: The subject of this graduate qualification work is âSearch for suboptimal solution to TSP with graph aggregationâ. The work is devoted to a new approach for solving the TSP with graph decomposition and aggregation. The tasks, fulfilled while processing the research: A review of some existing methods for solving the TSP and their property evaluationStating a basic approach for solving the TSP with graph decomposition and aggregation. A research of subproblem parameters impact on the process of solving the problem. Generation of optimal criteria for the graph partitioning and aggregation subproblems. A research of subproblem optimal criteria impact on the quality of solution. The work features novelty of the approach proposed and its perspectives as an alternative to existing methods for solving the TSP. In the end of this work there has been conduct a series of tests. The results of them allowed the author to assess not only the usability of the entire method, but also of the criteria proposed. Finally, a problem class, for which best results can be provided was defined.