Real-time optimization meets Bayesian optimization and derivative-free optimization: A tale of modifier adaptation

This paper investigates a new class of modifier-adaptation schemes to overcome plant-model mismatch in real-time optimization of uncertain processes. The main contribution lies in the integration of concepts from the fields of Bayesian optimization and derivative-free optimization. The proposed schemes embed a physical model and rely on trust-region ideas to minimize risk during the exploration, while employing Gaussian process regression to capture the plant-model mismatch in a non-parametric way and drive the exploration by means of acquisition functions. The benefits of using an acquisition function, knowing the process noise level, or specifying a nominal process model are analyzed on numerical case studies, including a semi-batch photobioreactor optimization problem with a dozen decision variables.