Response surface methodology with prediction uncertainty : a multi-objective optimisation approach

In the field of response surface methodology (RSM), the prediction uncertainty of the empirical model needs to be considered for effective process optimisation. Current methods combine the prediction mean and uncertainty through certain weighting strategies, either explicitly or implicitly, to form a single objective function for optimisation. This paper proposes to address this problem under the multi-objective optimisation framework. Overall, the method iterates through initial experimental design, empirical modelling and model-based optimisation to allocate promising experiments for the next iteration. Specifically, the Gaussian process regression is adopted as the empirical model due to its demonstrated prediction accuracy and reliable quantification of prediction uncertainty in the literature. The non-dominated sorting genetic algorithm II (NSGA-II) is used to search for Pareto points that are further clustered to give experimental points to be conducted in the next iteration. The application study, on the optimisation of a catalytic epoxidation process, demonstrates that the proposed method is a powerful tool to aid the development of chemical and potentially other processes