A novel approach for non-normal multi-response optimisation problems

Various creative multi-response optimisation approaches have been developed in the literature. Most of these researches are based on the normality assumption of the response distribution. However, this assumption does not necessarily hold in some real cases, such as non-normal multiple responses. Also, the reproducibility of optimisation results does not hold in some practical applications due to the variability of predicted responses associated with model uncertainty. In this paper, a novel approach is proposed to address the issues for non-normal multi-response optimisation. The proposed method not only identifies significant effects for each response by incorporating factorial effect principles into the framework of the Bayesian generalised linear models (GLMs) but also takes into account the model uncertainty and the variability of predicted responses by using the Bayesian sampling technique and Pareto optimal strategy. Furthermore, the optimal parameter settings are found by using grey incidence analysis (GIA). Besides, two examples are used to illustrate the effectiveness of the proposed method. The results show that the proposed method not only effectively identify significant factors but also find more satisfactory parameter settings when the reliability and reproducibility of optimisation results are considered simultaneously.