Real-Time Optimization Meets Bayesian Optimization and Derivative-Free Optimization: A Tale of Modifier Adaptation

TL;DR

This paper introduces a novel modifier-adaptation scheme for real-time optimization that combines Bayesian and derivative-free optimization techniques, effectively handling plant-model mismatch in uncertain processes.

Contribution

It integrates Bayesian and derivative-free optimization with modifier adaptation, using Gaussian processes and trust-region methods to improve real-time process optimization.

Findings

Effective handling of plant-model mismatch demonstrated

Use of Gaussian processes enhances non-parametric modeling

Numerical case studies validate the approach

Abstract

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 areas 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 illustrated on numerical case studies, including a semi-batch photobioreactor optimization problem.