A method of steepest ascent for multiresponse surface optimization using a desirability function method

Abstract

Multiresponse problems are common in product or process development. Aconventional approach for optimizing multiple responses is to use a responsesurface methodology (RSM), and this approach is called multiresponse surfaceoptimization (MRSO). In RSM, the method of steepest ascent is widely usedfor searching for an optimum region where a response is improved. In MRSO,it is difficult to directly apply the method of steepest ascent because MRSOincludes several responses to be considered. This paper suggests a new methodof steepest ascent for MRSO, which accounts for tradeoffs between multipleresponses. It provides several candidate paths of steepest ascent and allows adecision maker to select the most preferred path. This generation and selectionprocedure is helpful to better understand the tradeoffs between the multipleresponses, and ultimately, it moves the experimental region to a good regionwhere a satisfactory compromise solution exists. A hypothetical example isemployed for illustrating the proposed procedure. The results of this case studyshow that the proposed method searches the region containing an optimumwhere a satisfactory compromise solution exists.