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Top1. Introduction
In the context of manufacturing, a multiple response optimization problem may be stated as determining the setting conditions of input variables (which can include in-process machine variables and raw material compositions) that simultaneously optimize multiple response or quality characteristics. Simultaneous optimization of correlated multiple quality characteristics is generally referred to as ‘multiple response optimization’ (MRO) (Khuri, Ghosh & Rao, 1996; Bera, 2012). In practice, MRO problem typically involves responses that are correlated. In other words, improving or moving towards improved solution, either by statistical experimentation or simulation search strategy, for a particular response can result in sacrificing the best solution of another response. Thus, there always exist trade-off solutions in case of correlated conflicting responses. Determining superior solution quality for a typical MRO problem considering mean and variance of responses is a continual research endeavor.
The conventional graphical approach that can handle multiple response problem is overlaying contour plot (Lind, Goldin, & Hickman, 1960). However, the number of input (independent) variables in this approach is practically limited to two. Harrington (1965) first proposed a desirability function approach to convert a higher dimensional MRO problem into a single objective optimization problem, using suitable desirability scale transformation function. The desirability function approach is still preferred by many researchers to handle MRO problems (e.g. Kim & Lin, 2006, Mukherjee & Ray, 2008; Bera & Mukherjee, 2010; Bera & Mukherjee, 2012; Sikdar & Mukherjee, 2011). However, the conventional desirability function approach (Derringer & Suich, 1980) does not consider inherent variability of the responses (Kim & Lin, 2006) to arrive at optimal or near optimal conditions. Considering equal variance of all responses may lead to an unrealistic pseudo or suboptimal solutions (Lin & Tu, 1995).