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Математическая модель робастной оптимизации параметров высокоскоростной лезвийной обработки древесных материалов на базе экспериментальных данных

Математическая модель робастной оптимизации параметров высокоскоростной лезвийной обработки древесных материалов на базе экспериментальных данных

Abstract

Данная статья посвящена возможности учета неопределенностей в моделях оптимизации. В реальных задачах оптимизации данные обычно неточны, в результате точно неизвестно, когда решение найдено. При традиционном подходе доли процентов неопределенности данных просто игнорируются, и проблема решается так, как если бы номинальные данные были идентичны фактическим данным. Однако эксперименты показывают, что уже довольно небольшие возмущения неопределенных данных могут привести к тому, что номинальное (т.е. соответствующее номинальным данным) оптимальное решение в значительной степени неосуществимо и, следовательно, практически бессмысленно. Например, в 13 из 90 задач линейного программирования из библиотеки NETLIB 0,01 % случайных возмущений неопределенных данных приводят к более чем 50 % нарушениям правых частей некоторых ограничений, оцениваемых при номинальных оптимальных решениях. Таким образом, в приложениях существует реальная потребность в методологии, которая дает робастные (т.е. надежные) решения, обладающие защитой против неопределенности исходных данных. This article is devoted to the possibility of accounting for uncertainties in optimization models. Since data is usually inaccurate in real-world optimization problems, as a result, it is not known exactly when the solution was found. In the traditional approach, fractions of a percentage of data uncertainty are simply ignored and the problem is solved as if the nominal data were identical to the actual data. However, experiments show that even rather small perturbations of uncertain data can lead to the fact that the nominal (i.e., corresponding to nominal data) optimal solution is largely unrealizable and, therefore, practically meaningless. For example, in 13 out of 90 linear programming problems from the NETLIB library, 0.01 % of random perturbations of undefined data lead to more than 50 % violations of the right-hand sides of some constraints estimated for nominal optimal solutions. Thus, in applications, there is a real need for a methodology that provides robust (i.e. reliable) solutions that are defense against uncertainty in the underlying data.

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Keywords

ЛЕЗВИЙНАЯ ОБРАБОТКА ДРЕВЕСНЫХ МАТЕРИАЛОВ, ДЕРЕВООБРАБАТЫВАЮЩАЯ ПРОМЫШЛЕННОСТЬ, ДРЕВЕСНЫЕ МАТЕРИАЛЫ

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green