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

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