Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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A Posterior Preference Articulation Method to the Weighted Mean Squared Error Minimization Approach in Multi-Response Surface Optimization

다중반응표면 최적화에서 가중평균제곱오차 최소화법을 위한 선호도사후제시법

  • Jeong, In-Jun (Department of Business Administration, Daegu University)
  • Received : 2015.07.08
  • Accepted : 2015.10.08
  • Published : 2015.10.31
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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.

다중반응표면 최적화는 다수의 반응변수(품질특성치)를 동시에 고려하여 최적의 입력변수 조건을 찾는 반응표면분석의 세부 분야이다. 가중평균제곱오차(Weighted Mean Squared Error, WMSE) 최소화법은 평균제곱오차의 두 구성 요소인 제곱편차와 분산에 가중치를 부여한 WMSE를 활용하는데, 반응변수별로 WMSE를 구하여 이들을 종합적으로 최소화한다. 지금까지 WMSE 최소화법과 관련하여 개발된 기법은 대부분 의사결정자의 선호도 정보를 문제풀이 이전에 결정할 것을 요구하는 선호도사전제시법에 해당된다. 그러나 현실적으로 의사결정자가 자신의 선호도 정보를 사전에 정확히 제공하는 것은 매우 어렵다. 본 논문에서는 이러한 한계점을 개선하기 위하여 WMSE 최소화를 위한 선호도사후제시법을 제안한다. 제안된 방법은 의사결정자의 선호도 정보 없이 다수의 비지배적해를 생성한 후, 의사결정자가 생성된 비지배해 중 최고선호해를 선택하는 단계로 진행된다. 제안된 방법은 의사결정자로 하여금 전체 해집합의 트레이드오프 관계를 보다 폭넓은 시각으로 이해한 후 선호도 정보를 제시할 수 있도록 함으로써, 의사결정자의 선호도에 부합하는 최고선호해를 효과적으로 도출할 수 있다.

Keywords

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