title: ÐÐ¾Ð¸ÑÐº ÑÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ½Ð¾Ð³Ð¾ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ
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: The search for static transport equilibrium
Creators: name: ÐÑÑÑÑÐ½Ð½Ð°Ñ, Ð®Ð»Ð¸Ñ
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: 2024
Subjects: ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ½Ð¾Ðµ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ðµ
ÑÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ½Ð¾Ðµ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ðµ
Ð¼ÐµÑÐ¾Ð´ Ð¤ÑÐ°Ð½Ðº-ÐÑÐ»ÑÑÐ°
Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ CFW
Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ BFW
Ð³ÑÐ°ÑÑ
Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ
transport equilibrium
static transport equilibrium
Frank-Wolfe method
CFW algorithm
BFW algorithm
graphs
optimization

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¼ Ð´Ð¸Ð¿Ð»Ð¾Ð¼Ð½Ð¾Ð¼ Ð¿ÑÐ¾ÐµÐºÑÐµ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð° ÑÐ°Ð±Ð¾ÑÐ° Ð¼ÐµÑÐ¾Ð´Ð° Ð¤ÑÐ°Ð½ÐºÐ°-ÐÑÐ»ÑÑÐ° Ð¸ ÐµÐ³Ð¾ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¹ CFW Ð¸ BFW Ð½Ð° Ð½ÐµÑÐºÐ¾Ð»ÑÐºÐ¸Ñ Ð¿ÑÐ¸Ð¼ÐµÑÐ°Ñ ÑÐµÐ°Ð»ÑÐ½ÑÑ ÑÐ»Ð¸ÑÐ½Ð¾-Ð´Ð¾ÑÐ¾Ð¶Ð½ÑÑ ÑÐµÑÐµÐ¹. ÐÑÐ¾Ð¼Ðµ ÑÐ¾Ð³Ð¾, Ð´Ð°Ð½Ñ Ð¾Ð±ÑÐ¸Ðµ Ð¿Ð¾Ð½ÑÑÐ¸Ñ, Ð¸Ð·Ð»Ð¾Ð¶ÐµÐ½ Ð¿ÑÐ¾ÑÐµÑÑ Ð¿ÐµÑÐµÑÐ¾Ð´Ð° Ð¾Ñ Ð¾Ð±ÑÐµÐ¹ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ñ Ðº Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐµ, Ð¿Ð¾Ð´ÑÐ¾Ð±Ð½Ð¾ Ð¾Ð¿Ð¸ÑÐ°Ð½Ñ Ð¿ÑÐ¸Ð¼ÐµÑÑ Ð¸ Ð´Ð°Ð½Ð½ÑÐµ, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¿Ð¾Ð´Ð°ÑÑÑÑ Ð½Ð° Ð²ÑÐ¾Ð´ Ð¼ÐµÑÐ¾Ð´Ð°Ð¼. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½ Ð°Ð½Ð°Ð»Ð¸Ð· Ð½ÐµÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸, Ð¸Ð·Ð»Ð¾Ð¶ÐµÐ½Ð½Ð¾Ð¹ Ð² Ð¸ÑÑÐ¾ÑÐ½Ð¸ÐºÐ°Ñ.Â  ÐÑÐ°ÑÐ°ÐºÑÐµÑÐ¸Ð·Ð¾Ð²Ð°Ð½Ð¾ ÑÐ¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ðµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ðµ Ð¸Ð·ÑÑÐ°ÐµÐ¼Ð¾Ð¹ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ñ, ÐµÐµ Ð°ÐºÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ. ÐÑÐ¾Ð¿Ð¸ÑÐ°Ð½Ð° ÑÑÑÑÐºÑÑÑÐ° Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð²ÑÑÐµÑÐ¿Ð¾Ð¼ÑÐ½ÑÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¤ÑÐ°Ð½ÐºÐ°-ÐÑÐ»ÑÑÐ° Ð¸ ÐµÐ³Ð¾ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¹ CFW Ð¸ BFW, Ð¾Ð¿Ð¸ÑÐ°Ð½Ñ Ð¸Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ¸Ñ. ÐÐ°Ð½Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð². ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ñ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐµÐ¹ Ð´Ð¾ÑÑÐ¸Ð³Ð½ÑÑÐ¾Ð¹ ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¾Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° Ð¸ÑÐµÑÐ°ÑÐ¸Ð¹ Ð¸ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð¾Ñ ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸, Ð¿Ð¾ Ð½Ð¸Ð¼ ÑÐ´ÐµÐ»Ð°Ð½Ñ Ð²ÑÐ²Ð¾Ð´Ñ. Ð Ð°Ð±Ð¾ÑÐ° Ð²ÑÑÐµÑÐ¿Ð¾Ð¼ÑÐ½ÑÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð², Ð¿ÑÐ¾Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð°Ñ Ð½Ð° Ð½Ð¾Ð²Ð¾Ð¼ Ð¿ÑÐ¸Ð¼ÐµÑÐµ, ÑÑÐ°Ð»Ð° Ð±Ð¾Ð»ÐµÐµ Ð¿Ð¾Ð½ÑÑÐ½Ð°, Ð°ÐºÑÑÐ°Ð»ÑÐ½Ð° Ð¸ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð° Ð´Ð»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÐµÐ¹ Ð¸ ÑÐ¿ÐµÑÐ¸Ð°Ð»Ð¸ÑÑÐ¾Ð² Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ°.
description: In this topic, the work of the Frank-Wolfe method and its modifications of CFW and BFW is considered on several examples of real road networks. In addition, general concepts are given, the process of transition from a general problem to an optimization problem is described, examples and data that are submitted to the input methods are described in detail. The analysis of some information presented in the sources has been carried out.Â  The current state of the problem under study and its relevance are characterized. The structure of the algorithms of the above-mentioned Frank-Wolfe methods and its modifications CFW and BFW is prescribed, their differences are described. The results of the methods are given. Graphs of the dependencies of the achieved accuracy on the number of iterations and time on accuracy are constructed, conclusions are drawn from them. The work of the above-mentioned methods, analyzed using a new example, has become more understandable, relevant and effective for researchers and specialists in the field of transport.