A generalized cutting‐set approach for nonlinear robust optimization in process systems engineering

Abstract

We propose a novel computational framework for the robust optimization of highly nonlinear, non‐convex models that possess uncertainty in their parameter data. The proposed method is a generalization of the robust cutting‐set algorithm that can handle models containing irremovable equality constraints, as is often the case with models in the process systems engineering domain. Additionally, we accommodate general forms of decision rules to facilitate recourse in second‐stage (control) variables. In particular, we compare and contrast the use of various types of decision rules, including quadratic ones, which we show in certain examples to be able to decrease the overall price of robustness. Our proposed approach is demonstrated on three process flow sheet models, including a relatively complex model for amine‐based CO2 capture. We thus verify that the generalization of the robust cutting‐set algorithm allows for the facile identification of robust feasible designs for process systems of practical relevance.

The IDAES process modeling framework and model library—Flexibility for process simulation and optimization

“…[ 38 ] The IDAES‐CMF has also been applied to a range of other problem types, such as conceptual design and process intensification [ 39 ] and dynamic real‐time optimization and control, [ 40 ] and non‐linear robust optimization. [ 41 ]…”

Two-Stage Robust Quadratic Optimization with Equalities and its Application to Optimal Power Flow

“…This paper focuses on such cases by replacing the non-linear functions defining the equalities by their piece-wise affine approximations that would reflect the original functions as closely as needed. Recently, some progress has been made in that direction such as the work presented in Ardestani-Jaafari and Delage 2016, Aßmann et al 2018, and Isenberg et al 2021.…”

“…The results in this paper are distinct from Molzahn and Roald 2018 since in the latter work a robust solution is obtained by iteratively tightening the inequality constraints. In Isenberg et al 2021, the authors also tackle general nonlinear optimization problems but use an alternative formulation of ARO problems and thus a distinct solution strategy. Our approach is close in spirit to the approach in Roald and Andersson 2018.…”