Response surface methodology involves relationships between different variables, specifically experimental inputs as controllable factors, and a response or responses by incorporating uncontrollable factors named nuisance. In order to optimize these response surfaces, we should have accurate response models. A common approach to estimate a response surface is the ordinary least squares (OLS) method. Since OLS is very sensitive to outliers, some robust approaches have been discussed in the literature. Most problems face with more than one response which are mostly correlated, that are called multi-response problem. This paper presents a new approach which takes the benefits of robust multivariate regression to cope with the mentioned difficulties. After estimating accurate response surfaces, optimization phase should be applied in order to have proper combination of variables and optimum solutions. Global criterion method of multi-objective optimization has also been used to reach a compromise solution which improves all response variables simultaneously. Finally, the proposed approach is described analytically by a numerical example.
Accepté le :
DOI : 10.1051/ro/2018016
Mots clés : Multi-response, simultaneous equation systems, multivariate robust regression, global criterion (GC) method
@article{RO_2018__52_4-5_1233_0,
author = {Moslemi, Amir and Seyyed-Esfahani, Mirmehdi},
title = {A novel robust multivariate regression approach to optimize multiple surfaces},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1233--1243},
publisher = {EDP-Sciences},
volume = {52},
number = {4-5},
year = {2018},
doi = {10.1051/ro/2018016},
zbl = {1420.62351},
mrnumber = {3880601},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2018016/}
}
TY - JOUR AU - Moslemi, Amir AU - Seyyed-Esfahani, Mirmehdi TI - A novel robust multivariate regression approach to optimize multiple surfaces JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 1233 EP - 1243 VL - 52 IS - 4-5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2018016/ DO - 10.1051/ro/2018016 LA - en ID - RO_2018__52_4-5_1233_0 ER -
%0 Journal Article %A Moslemi, Amir %A Seyyed-Esfahani, Mirmehdi %T A novel robust multivariate regression approach to optimize multiple surfaces %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 1233-1243 %V 52 %N 4-5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2018016/ %R 10.1051/ro/2018016 %G en %F RO_2018__52_4-5_1233_0
Moslemi, Amir; Seyyed-Esfahani, Mirmehdi. A novel robust multivariate regression approach to optimize multiple surfaces. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 4-5, pp. 1233-1243. doi : 10.1051/ro/2018016. http://www.numdam.org/articles/10.1051/ro/2018016/
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