Investigation of Initial Data and Optimizer in Real-Time Optimization Performance via Modifier Adaptation with Gaussian Processes

In order to overcome plant-model mismatch in static real-time optimization (RTO) of uncertain processes, modifier adaptation (MA) schemes have gained much relevance recently. It applies first-order corrections to the model cost and constraint functions in order to reach plant optimality upon convergence. However, calculating the corrections relies on gradient information, which is challenging to obtain. A promising approach to overcome this limitation is to build Gaussian processes (GP) regression functions on steady-state data to represent the plant-model mismatch. The present paper investigates how the initial operating points and optimizer choice affect RTO performance under MA with GP regression. An experiment is designed to evaluate the system’s sensitivity and convergence when initialized with random feasible operating points. Results are compared for a deterministic and evolutionary heuristic to solve the model-based optimization sub-problem: Sequential Quadratic Programming (SQP) and Differential Evolution (DE), respectively. For a semi-batch reactor system case study, we illustrate that SQP can fail to find the global optimum in RTO iterations. As a result, the system’s convergence is degraded and becomes sensitive to the initialization phase. On the other hand, DE achieves a consistent convergence profile, thus being indifferent to the initial data points. For a 95% confidence interval, the results show that DE outperforms SQP for this case study.