Optimization of Multiple Responses Considering both Model Uncertainty and Regret Effect

Abstract

Loss function approach is effective for multi-response optimization. However, previous loss function approach ignore model uncertainty and decision-makers’ regret effect when determining the optimal input settings. In this paper, an overall loss function is proposed to optimize correlated multiple responses via confidence intervals, and we refer to the idea of worst case strategy used in decision theory to incorporate model uncertainty and decision makers’ regret effect into the loss function. The new loss function is composed of three sub-functions: expect performance, robustness performance, and regret performance, through which model uncertainty and regret effect are quantified. It is found that the traditional loss function will be a special case of the proposed approach if engineers could collect sufficient experimental data to estimate model parameters. An example is employed to illustrate the effectiveness of the proposed approach. The results show that the proposed approach can achieve reliable optimal operating conditions in comparison with those of traditional loss function approach.