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

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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A Weighted Mean Squared Error Approach Based on the Tchebycheff Metric in Multiresponse Optimization

Tchebycheff Metric 기반 가중평균제곱오차 최소화법을 활용한 다중반응표면 최적화

  • Jeong, In-Jun (Department of Business Administration, Daegu University)
  • Received : 2014.08.20
  • Accepted : 2015.01.08
  • Published : 2015.01.31
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Abstract

Multiresponse optimization (MRO) seeks to find the setting of input variables, which optimizes the multiple responses simultaneously. The approach of weighted mean squared error (WMSE) minimization for MRO imposes a different weight on the squared bias and variance, which are the two components of the mean squared error (MSE). To date, a weighted sum-based method has been proposed for WMSE minimization. On the other hand, this method has a limitation in that it cannot find the most preferred solution located in a nonconvex region in objective function space. This paper proposes a Tchebycheff metric-based method to overcome the limitations of the weighted sum-based method.

다중반응표면 최적화는 다수의 반응변수(품질특성치)를 최적화하는 입력변수의 조건을 찾는 것을 목적으로 한다. 다중반응표면 최적화를 위해 제안된 가중평균제곱오차(Weighted Mean Squared Error, WMSE) 최소화법은 평균제곱오차의 구성요소인 제곱편차와 분산에 서로 다른 가중치를 부여하는 방법이다. 지금까지 WMSE 최소화법과 관련하여, 개별 반응변수의 WMSE를 구성한 후 이들의 가중합을 최소화하는 가중합 기반 WMSE 최소화법이 제안되었다. 그러나 가중합 기반법은 목적함수 공간에서 볼록하지 않은 구간이 있고 이 구간에서 가장 선호되는 해가 존재할 경우 이 해를 찾아내지 못한다는 한계를 지니고 있다. 본 논문에서는 기존의 가중합 기반법의 한계점을 극복하기 위하여 Tchebycheff Metric 기반 WMSE 최소화법을 제안하고자 한다.

Keywords

References

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