(216g) Recent Advances in Pyros: The Pyomo Solver for Two-Stage Nonconvex Robust Optimization

Two-stage robust optimization (RO) is a particularly useful framework for obtaining robust designs of chemical process and energy systems. Optimization models for process and energy systems are often subject to parametric uncertainty, which may arise from the use of empirical correlations as property models, temporal variability in feedstock, or economic stochasticity [1, 2]. Since any changes in the prevailing values of these uncertain parameters may significantly affect the model outputs, deterministic optimization may yield system designs which are suboptimal or infeasible under off-nominal scenarios. Moreover, the design of a plant should account for any built-in controllability that will allow the operator to adjust plant response during operation. In such contexts, two-stage RO is an appropriate framework for design [1, 3].

The recently developed two-stage RO solver PyROS [4] is designed to obtain robust solutions to process models. A typical process design model features nonconvexities, design and recourse degrees of freedom, and a large prevalence of equality constraints which constitute the “simulation part” of the model. The equality constraints are often highly complex, to the extent that they cannot, in general, be reformulated out of the model [1]. Based on a generalization [1] of the robust cutting set algorithm of [5], PyROS is the first two-stage RO solver that systematically handles the equality constraints without reformulation requirements [6].

PyROS is designed for ease of use, and implemented for models written in Pyomo [7], a widely used, open-source algebraic modeling language. Successful invocation of PyROS requires only a deterministic model, a partitioning of the model’s degrees of freedom variables into design (first-stage) and recourse (second-stage) variables, an uncertainty set, and access to subordinate local and global nonlinear programming optimizers. The underlying solution methodology uses polynomial decision rules to approximate the adjustability of the second-stage variables with respect to the uncertain parameters [1, 6]; the desired degree of the decision rules can optionally be specified.

In this work, we present recent algorithmic and implementation advances of PyROS, and a benchmarking study which demonstrates the utility of PyROS for two-stage RO problems. Our advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the initializations of the subproblems used by the underlying cutting set algorithm, and extensions of the uncertainty set interfaces. Our benchmarking study is performed on a library of over 8,500 instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. Overall, our results highlight the effectiveness of PyROS for obtaining robust solutions to process models with uncertain equality constraints.

References

[1] Isenberg NM, Akula P, Eslick JC, Bhattacharyya D, Miller DC, Gounaris CE. A generalized cutting‐set approach for nonlinear robust optimization in process systems engineering. AIChE Journal. 2021 May;67(5):e17175.

[2] Morgan JC, Bhattacharyya D, Tong C, Miller DC. Uncertainty quantification of property models: Methodology and its application to CO2‐loaded aqueous MEA solutions. AIChE Journal. 2015 Jun;61(6):1822-39.

[3] Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A. Adjustable robust solutions of uncertain linear programs. Mathematical programming. 2004 Mar;99(2):351-76.

[4] Isenberg, NM, Sherman, JA, Siirola, JD, & Gounaris, CE. PyROS Solver. Pyomo Documentation. 2023. https://pyomo.readthedocs.io/en/stable/contributed_packages/pyros.html

[5] Mutapcic A, Boyd S. Cutting-set methods for robust convex optimization with pessimizing oracles. Optimization Methods & Software. 2009 Jun 1;24(3):381-406.

[6] Isenberg, NM, Sherman, JA, Siirola, JD, & Gounaris, CE. PyROS: The Pyomo Robust Optimization Solver. Forthcoming. 2023.

[7] Bynum ML, Hackebeil GA, Hart WE, Laird CD, Nicholson BL, Siirola JD, Watson JP, Woodruff DL. Pyomo-optimization modeling in python. Berlin/Heidelberg, Germany: Springer; 2021 Mar 30.