A Polynomial-Chaos based Algorithm for Robust optimization in the presence of Bayesian Uncertainty

The paper presents a computationally efficient approach for solving a robust optimization problem in the presence of parametric uncertainties, where the uncertainty description is obtained using the Bayes' Theorem. The approach is based on Polynomial Chaos Expansions (PCE) that are used to propagate the uncertainty into the objective function for each function evaluation, resulting in significant reduction in the computational time when compared to Monte Carlo sampling. A fed-batch process for penicillin production is used as a case study to illustrate the strength of the methodology both in terms of computational efficiency as well as in terms of accuracy when compared to results obtained with more simplistic (e.g. normal) representations of parametric uncertainty.