A novel robust multivariate regression approach to optimize multiple surfaces

¹ Department of Industrial Engineering, West Tehran Branch, Islamic Azad University, Tehran, Iran.
² Department of Industrial Engineering and Management Systems, Amirkabir University of Technology, Tehran, Iran.

^* Corresponding author: msesfahani@aut.ac.ir

Received: 8 December 2016
Accepted: 23 February 2018

Abstract

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.