Adaptive approximation algorithms for real-time optimization of industrial process management systems

Abstract

The problem of real-time optimization (RTO) of industrial processes requires finding a compromise between the following factors: high fidelity of the underlying process dynamics, model uncertainty, and computational constraints. This paper presents the Adaptive Approximation Algorithm for Real-Time Optimization (AAA-RTO), which involves a self-updating approximation space as part of a minimax robust optimization methodology. The adaptive approximation scheme continuously updates the approximation order depending on the approximation error and provides a balance between the model accuracy and computation requirements. Projected saddle-point iteration is utilized for simultaneous optimization of process decision variables and the worst-case scenario realization. It is theoretically proved that the proposed algorithm ensures a uniform upper bound for the approximation error and, correspondingly, for the minimax value error, thus providing a connection between approximation quality and robust optimization performance. Convergence of the proposed iterative procedure to a saddle point is proved under certain convexity, smoothness, compactness, and step-size conditions. A benchmark example of industrial process optimization shows that the AAA-RTO method outperforms the fixed-order approximation and gradient-based minimax robust optimization procedures with respect to the speed of convergence, approximation error, and robustness. Furthermore, the AAA-RTO method allows saving up to 44% of CPU time.