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다중반응표면 최적화를 위한 단변량 손실함수법: 대화식 절차 기반의 가중치 결정

A Univariate Loss Function Approach to Multiple Response Surface Optimization: An Interactive Procedure-Based Weight Determination

정인준
한국지식경영학회 (The Knowledge Management Society of Korea)|2020.03|지식경영연구 (Knowledge Management Research)|제21권 제1호|pp. 27-40|DOI 10.15813/kmr.2020.21.1.002

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키워드

Multi-response surface optimizationUnivariate loss function approachMean square errorWeighted tchebycheff methodWeight determinationInteractive procedure
주제분류경영학

초록

Response surface methodology (RSM) empirically studies the relationship between a response variable and input variables in the product or process development phase. The ultimate goal of RSM is to find an optimal condition of the input variables that optimizes (maximizes or minimizes) the response variable. RSM can be seen as a knowledge management tool in terms of creating and utilizing data, information, and knowledge about a product production and service operations. In the field of product or process development, most real-world problems often involve a simultaneous consideration of multiple response variables. This is called a multiple response surface (MRS) problem. Various approaches have been proposed for MRS optimization, which can be classified into loss function approach, priority-based approach, desirability function approach, process capability approach, and probability-based approach. In particular, the loss function approach is divided into univariate and multivariate approaches at large. This paper focuses on the univariate approach. The univariate approach first obtains the mean square error (MSE) for individual response variables. Then, it aggregates the MSE’s into a single objective function. It is common to employ the weighted sum or the Tchebycheff metric for aggregation. Finally, it finds an optimal condition of the input variables that minimizes the objective function. When aggregating, the relative weights on the MSE’s should be taken into account. However, there are few studies on how to determine the weights systematically. In this study, we propose an interactive procedure to determine the weights through considering a decision maker’s preference. The proposed method is illustrated by the ‘colloidal gas aphrons’ problem, which is a typical MRS problem. We also discuss the extension of the proposed method to the weighted MSE (WMSE).

Abstract

Response surface methodology (RSM) empirically studies the relationship between a response variable and input variables in the product or process development phase. The ultimate goal of RSM is to find an optimal condition of the input variables that optimizes (maximizes or minimizes) the response variable. RSM can be seen as a knowledge management tool in terms of creating and utilizing data, information, and knowledge about a product production and service operations. In the field of product or process development, most real-world problems often involve a simultaneous consideration of multiple response variables. This is called a multiple response surface (MRS) problem. Various approaches have been proposed for MRS optimization, which can be classified into loss function approach, priority-based approach, desirability function approach, process capability approach, and probability-based approach. In particular, the loss function approach is divided into univariate and multivariate approaches at large. This paper focuses on the univariate approach. The univariate approach first obtains the mean square error (MSE) for individual response variables. Then, it aggregates the MSE’s into a single objective function. It is common to employ the weighted sum or the Tchebycheff metric for aggregation. Finally, it finds an optimal condition of the input variables that minimizes the objective function. When aggregating, the relative weights on the MSE’s should be taken into account. However, there are few studies on how to determine the weights systematically. In this study, we propose an interactive procedure to determine the weights through considering a decision maker’s preference. The proposed method is illustrated by the ‘colloidal gas aphrons’ problem, which is a typical MRS problem. We also discuss the extension of the proposed method to the weighted MSE (WMSE).

참고문헌 (39)

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다중반응표면최적화를 위한 공정능력함수법에서 최소치최대화 기준의 활용에 관한 연구정인준한국지식경영학회 · 지식경영연구2019 · 제20권 제3호쌍대반응표면최적화를 위한 사후선호도반영법: TOPSIS를 활용한 최고선호해 선택정인준한국지식경영학회 · 지식경영연구2018 · 제19권 제2호대화식 절차를 활용한 공정능력지수 기반 다중반응표면 최적화정인준한국품질경영학회 · 품질경영학회지2017 · 제45권 제2호쌍대반응표면최적화를 위한 가중평균제곱오차 최소화법: 공정능력지수 기반의 가중치 결정정인준한국품질경영학회 · 품질경영학회지2014 · 제42권 제4호Multiresponse Optimization: A Literature Review and Research Opportunities정인준한국품질경영학회 · 품질경영학회지2011 · 제39권 제3호쌍대반응표면최적화를 위한 반복적 선호도사후제시법정인준한국품질경영학회 · 품질경영학회지2012 · 제40권 제4호

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