An Alternative Approach of Dual Response Surface Optimization Based on Penalty Function Method

Abstract

The dual response surface for simultaneously optimizing the mean and variance models as separate functions suffers some deficiencies in handling the tradeoffs between bias and variance components of mean squared error (MSE). In this paper, the accuracy of the predicted response is given a serious attention in the determination of the optimum setting conditions. We consider four different objective functions for the dual response surface optimization approach. The essence of the proposed method is to reduce the influence of variance of the predicted response by minimizing the variability relative to the quality characteristics of interest and at the same time achieving the specific target output. The basic idea is to convert the constraint optimization function into an unconstraint problem by adding the constraint to the original objective function. Numerical examples and simulations study are carried out to compare performance of the proposed method with some existing procedures. Numerical results show that the performance of the proposed method is encouraging and has exhibited clear improvement over the existing approaches.

Entropy-Based Weighting for Multiobjective Optimization: An Application on Vertical Turning

“…Their application, a priori, is possible in various contexts and with different numbers of objective functions. Besides, the proposal is applicable to many studies using stochastic programming where it is necessary to include, at the same time, the mean and variance in the objective function, as in the works developed by [33,44].…”

“…According to [32], an experiment can be defined as a test or a series of tests in which purposeful changes are made to the input variables of a process, aiming thereby to observe how such changes affect the responses. The goal of the experimenter is to determine the optimal settings for the design variables that minimize or maximize the fitted response [33]. Design of Experiments (DOE) is then defined as the process of planning experiments so that appropriate data is collected and then analyzed by statistical methods, leading to valid and objective conclusions.…”

High Breakdown Estimator for Dual Response Optimization in the Presence of Outliers

“…As mentioned earlier, this function does not clearly specify how far the estimated mean response is from the desired target τ. Therefore, in this study, an alternative optimization scheme, which is based on the penalty function method proposed by Baba et al (2015) is employed. The Penalty method is to,…”

“…Amongst all of the methods mentioned, most of the existing methods failed to obtain an estimate of mean response close to the target value with small variation. Therefore, Baba et al (2015) proposed a penalty functionbased approach as another alternative optimization scheme. The Penalty method (PM) is, minimize =…”

Optimization and Decision Making Stages for Analysis of Dual Response Problem: Median-Mad, Nsga-Ii, Topsis

“…Mean and standard deviation statistics of replicates have been preferred to use as dual responses so far in various studies, e.g. [3][4][5][6][7][8][9][10][11][12]. The detailed literature studies can be found in the study of [13].…”