Computers and Chemical Engineering

TLDR

Real‑time optimization and control integrated with higher‑level scheduling and planning is essential for profitable operation, yet large‑scale optimization models remain difficult for current solvers. The study aims to revisit integrated real‑time optimization formulations by applying efficient large‑scale barrier methods for nonlinear programming and demonstrating their use in dynamic strategies that combine real‑time optimization with model predictive control. The authors employ IPOPT’s large‑scale barrier and sensitivity extensions to solve million‑variable nonlinear programs and compute perturbed solutions, illustrated on a low‑density polyethylene process case study. These advances dramatically reduce online computation times for large nonlinear optimization models.

Abstract

Integration of real-time optimization and control with higher level decision-making (scheduling and planning) is an essential goal for profitable operation in a highly competitive environment. While integrated large-scale optimization models have been formulated for this task, their size and complexity remains a challenge to many available optimization solvers. On the other hand, recent development of powerful, large-scale solvers leads to a reconsideration of these formulations, in particular, through development of efficient large-scale barrier methods for nonlinear programming (NLP). As a result, it is now realistic to solve NLPs on the order of a million variables, for instance, with the IPOPT algorithm. Moreover, the recent NLP sensitivity extension to IPOPT quickly computes approximate solutions of perturbed NLPs. This allows on-line computations to be drastically reduced, even when large nonlinear optimization models are considered. These developments are demonstrated on dynamic real-time optimization strategies that can be used to merge and replace the tasks of (steady-state) real-time optimization and (linear) model predictive control. We consider a recent case study of a low density polyethylene (LDPE) process to illustrate these concepts.