다중반응표면 최적화에서 가중평균제곱오차 최소화법을 위한 선호도사후제시법

Abstract

Multi-Response Surface Optimization aims at finding the optimal setting of input variables considering multiple responses simultaneously. The Weighted Mean Squared Error (WMSE) minimization approach, which imposes a different weight on the two components of mean squared error, squared bias and variance, first obtains WMSE for each response and then minimizes all the WMSEs at once. Most of the methods proposed for the WMSE minimization approach to date are classified into the prior preference articulation approach, which requires that a decision maker (DM) provides his/her preference information a priori. However, it is quite difficult for the DM to provide such information in advance, because he/she cannot experience the relationships or conflicts among the responses. To overcome this limitation, this paper proposes a posterior preference articulation method to the WMSE minimization approach. The proposed method first generates all (or most) of the nondominated solutions without the DM's preference information. Then, the DM selects the best one from the set of nondominated solutions a posteriori. Its advantage is that it provides an opportunity for the DM to understand the tradeoffs in the entire set of nondominated solutions and effectively obtains the most preferred solution suitable for his/her preference structure.