Devising methods for planning a multifactorial multilevel experiment with high dimensionality

This paper considers the task of planning a multifactorial multilevel experiment for problems with high dimensionality. Planning an experiment is a combinatorial task. At the same time, the catastrophically rapid growth in the number of possible variants of experiment plans with an increase in the d...

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Autores principales:	Lev Raskin, Oksana Sira
Formato:	article
Lenguaje:	EN RU UK
Publicado:	PC Technology Center 2021
Materias:	planning of multifactorial multilevel experiment problem with high dimensionality decomposition plan exact plan Technology (General) T1-995 Industry HD2321-4730.9
Acceso en línea:	https://doaj.org/article/d19a28bd681346f4bcded55e26211071
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id	oai:doaj.org-article:d19a28bd681346f4bcded55e26211071
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spelling	oai:doaj.org-article:d19a28bd681346f4bcded55e262110712021-11-04T14:06:45ZDevising methods for planning a multifactorial multilevel experiment with high dimensionality1729-37741729-406110.15587/1729-4061.2021.242304https://doaj.org/article/d19a28bd681346f4bcded55e262110712021-10-01T00:00:00Zhttp://journals.uran.ua/eejet/article/view/242304https://doaj.org/toc/1729-3774https://doaj.org/toc/1729-4061This paper considers the task of planning a multifactorial multilevel experiment for problems with high dimensionality. Planning an experiment is a combinatorial task. At the same time, the catastrophically rapid growth in the number of possible variants of experiment plans with an increase in the dimensionality of the problem excludes the possibility of solving it using accurate algorithms. On the other hand, approximate methods of finding the optimal plan have fundamental drawbacks. Of these, the main one is the lack of the capability to assess the proximity of the resulting solution to the optimal one. In these circumstances, searching for methods to obtain an accurate solution to the problem remains a relevant task. Two different approaches to obtaining the optimal plan for a multifactorial multilevel experiment have been considered. The first of these is based on the idea of decomposition. In this case, the initial problem with high dimensionality is reduced to a sequence of problems of smaller dimensionality, solving each of which is possible by using precise algorithms. The decomposition procedure, which is usually implemented empirically, in the considered problem of planning the experiment is solved by employing a strictly formally justified technique. The exact solutions to the problems obtained during the decomposition are combined into the desired solution to the original problem. The second approach directly leads to an accurate solution to the task of planning a multifactorial multilevel experiment for an important special case where the costs of implementing the experiment plan are proportional to the total number of single-level transitions performed by all factors. At the same time, it has been proven that the proposed procedure for forming a route that implements the experiment plan minimizes the total number of one-level changes in the values of factors. Examples of problem solving are givenLev RaskinOksana SiraPC Technology Centerarticleplanning of multifactorial multilevel experimentproblem with high dimensionalitydecomposition planexact planTechnology (General)T1-995IndustryHD2321-4730.9ENRUUKEastern-European Journal of Enterprise Technologies, Vol 5, Iss 4 (113), Pp 64-72 (2021)
institution	DOAJ
collection	DOAJ
language	EN RU UK
topic	planning of multifactorial multilevel experiment problem with high dimensionality decomposition plan exact plan Technology (General) T1-995 Industry HD2321-4730.9
spellingShingle	planning of multifactorial multilevel experiment problem with high dimensionality decomposition plan exact plan Technology (General) T1-995 Industry HD2321-4730.9 Lev Raskin Oksana Sira Devising methods for planning a multifactorial multilevel experiment with high dimensionality
description	This paper considers the task of planning a multifactorial multilevel experiment for problems with high dimensionality. Planning an experiment is a combinatorial task. At the same time, the catastrophically rapid growth in the number of possible variants of experiment plans with an increase in the dimensionality of the problem excludes the possibility of solving it using accurate algorithms. On the other hand, approximate methods of finding the optimal plan have fundamental drawbacks. Of these, the main one is the lack of the capability to assess the proximity of the resulting solution to the optimal one. In these circumstances, searching for methods to obtain an accurate solution to the problem remains a relevant task. Two different approaches to obtaining the optimal plan for a multifactorial multilevel experiment have been considered. The first of these is based on the idea of decomposition. In this case, the initial problem with high dimensionality is reduced to a sequence of problems of smaller dimensionality, solving each of which is possible by using precise algorithms. The decomposition procedure, which is usually implemented empirically, in the considered problem of planning the experiment is solved by employing a strictly formally justified technique. The exact solutions to the problems obtained during the decomposition are combined into the desired solution to the original problem. The second approach directly leads to an accurate solution to the task of planning a multifactorial multilevel experiment for an important special case where the costs of implementing the experiment plan are proportional to the total number of single-level transitions performed by all factors. At the same time, it has been proven that the proposed procedure for forming a route that implements the experiment plan minimizes the total number of one-level changes in the values of factors. Examples of problem solving are given
format	article
author	Lev Raskin Oksana Sira
author_facet	Lev Raskin Oksana Sira
author_sort	Lev Raskin
title	Devising methods for planning a multifactorial multilevel experiment with high dimensionality
title_short	Devising methods for planning a multifactorial multilevel experiment with high dimensionality
title_full	Devising methods for planning a multifactorial multilevel experiment with high dimensionality
title_fullStr	Devising methods for planning a multifactorial multilevel experiment with high dimensionality
title_full_unstemmed	Devising methods for planning a multifactorial multilevel experiment with high dimensionality
title_sort	devising methods for planning a multifactorial multilevel experiment with high dimensionality
publisher	PC Technology Center
publishDate	2021
url	https://doaj.org/article/d19a28bd681346f4bcded55e26211071
work_keys_str_mv	AT levraskin devisingmethodsforplanningamultifactorialmultilevelexperimentwithhighdimensionality AT oksanasira devisingmethodsforplanningamultifactorialmultilevelexperimentwithhighdimensionality
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Devising methods for planning a multifactorial multilevel experiment with high dimensionality

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