title: ÐÐ¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ ÑÐ°Ð·Ð½Ð¾ÑÑÐ½Ð¾Ð¹ ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸ Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñ Ð´Ð²ÑÑ ÑÑÐ¾Ð²Ð½ÐµÐ²Ð¾Ð¹ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸
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: Modification of the difference evolution for solving bilevel optimization problems
Creators: name: ÐÐ³Ð°Ð»Ð°ÐºÐ¾Ð², ÐÐ°Ð½Ð¸Ð¸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: 2024
Subjects: Ð·Ð°Ð´Ð°ÑÐ° Ð´Ð²ÑÑ ÑÑÐ¾Ð²Ð½ÐµÐ²Ð¾Ð¹ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸
Ð¼ÐµÑÐ¾Ð´ Ð¿Ð°ÑÐ°Ð»Ð»ÐµÐ»ÑÐ½Ð¾Ð¹ ÑÐ°Ð·Ð½Ð¾ÑÑÐ½Ð¾Ð¹ ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸
Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼
ÑÐ°Ð·Ð½Ð¾ÑÑÐ½Ð°Ñ ÑÐ²Ð¾Ð»ÑÑÐ¸Ñ
bilevel optimization problem
differential evolution entirely parallel method
algorithm
differential evolution

description: Ð¦ÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð¿Ð°ÑÐ°Ð»Ð»ÐµÐ»ÑÐ½Ð¾Ð¹ ÑÐ°Ð·Ð½Ð¾ÑÑÐ½Ð¾Ð¹ ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸ (DEEP) Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð´Ð²ÑÑÑÑÐ¾Ð²Ð½ÐµÐ²Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸. Ð ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ð¸ Ñ ÑÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¸ Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸: 1. ÐÐ´Ð°Ð¿ÑÐ¸ÑÐ¾Ð²Ð°ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÑÐ°Ð·Ð½Ð¾ÑÑÐ½Ð¾Ð¹ ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸ (DEEP) Ð´Ð»Ñ ÑÐµÐºÑÑÑÐ¸Ð²Ð½Ð¾Ð³Ð¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð½Ð° Ð´Ð²ÑÑ ÑÑÐ¾Ð²Ð½ÑÑ Ð²Ð»Ð¾Ð¶ÐµÐ½Ð½Ð¾ÑÑÐ¸. 2. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐ°ÑÑ ÑÑÐµÐ¼Ñ ÐºÐ¾Ð´Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð»Ð°Ð½Ð° ÑÐµÑÐµÐ½Ð¸Ñ Ð¾ÑÐºÑÑÑÐ¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¼Ð°ÑÑÑÑÑÐ¸Ð·Ð°ÑÐ¸Ð¸ ÑÑÐ°Ð½ÑÐ¿Ð¾ÑÑÐ½ÑÑ ÑÑÐµÐ´ÑÑÐ² Ð´Ð»Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° DEEP. 3. ÐÑÐ¾Ð²ÐµÑÑÐ¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐµ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÑ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð². Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ» ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ Ð¸ Ð°Ð¿ÑÐ¾Ð±Ð¸ÑÐ¾Ð²Ð°Ð½ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð´Ð²ÑÑÑÑÐ¾Ð²Ð½ÐµÐ²Ð¾Ð¹ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸, Ð±ÑÐ»Ð° Ð¿ÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð° ÐµÐ³Ð¾ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÑ. ÐÑÐ»Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° Ð½Ð¾Ð²Ð°Ñ ÐºÐ¾Ð´Ð¸ÑÑÑÑÐ°Ñ ÑÑÐµÐ¼Ð°. ÐÑÐ»Ð¸ ÑÐ´ÐµÐ»Ð°Ð½Ñ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÑÑÐ¸Ðµ Ð²ÑÐ²Ð¾Ð´Ñ. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð¿ÑÐ¸ ÑÐµÑÐµÐ½Ð¸Ð¸ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð·Ð°Ð´Ð°Ñ Ð¼Ð½Ð¾Ð³Ð¾ÑÑÐ¾Ð²Ð½ÐµÐ²Ð¾Ð¹ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸.
description: The aim of the work is to modify the Differential Evolution Entirely Parallel method (DEEP) to solve a bilevel optimization problem. In accordance with the purpose of the work, the following tasks were set: 1. Adapt the difference evolution algorithm (DEEP) for recursive use at two levels of nesting. 2. To develop a coding scheme for solving the open problem of vehicle routing for using the DEEP algorithm. 3. Conduct numerical experiments and analyze the results obtained. As a result of the work, an algorithm for solving the bilevel optimization problem was developed and tested, and its effectiveness was demonstrated. A new coding scheme has been developed. The relevant conclusions were drawn. The results of this study can be used to solve practical problems of multilevel optimization.