Robust Optimization for the Pooling Problem

Wiebe, Johannes; Cecı́lio, Inês; Misener, Ruth

doi:10.1021/acs.iecr.9b01772

Cited by 14 publications

(4 citation statements)

References 72 publications

(167 reference statements)

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“…An exception is the the non-linear, nonconvex pooling problem with an ellipsoidal set. For this instance, the cutting plane solver achieves significantly better results, which is in line with previous work on robust pooling problems [27].…”

Section: Resultssupporting

confidence: 89%

ROmodel: modeling robust optimization problems in Pyomo

Wiebe

Misener

2021

Optim Eng

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This paper introduces ROmodel, an open source Python package extending the modeling capabilities of the algebraic modeling language Pyomo to robust optimization problems. ROmodel helps practitioners transition from deterministic to robust optimization through modeling objects which allow formulating robust models in close analogy to their mathematical formulation. ROmodel contains a library of commonly used uncertainty sets which can be generated using their matrix representations, but it also allows users to define custom uncertainty sets using Pyomo constraints. ROmodel supports adjustable variables via linear decision rules. The resulting models can be solved using ROmodels solvers which implement both the robust reformulation and cutting plane approach. ROmodel is a platform to implement and compare custom uncertainty sets and reformulations. We demonstrate ROmodel’s capabilities by applying it to six case studies. We implement custom uncertainty sets based on (warped) Gaussian processes to show how ROmodel can integrate data-driven models with optimization.

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Section: Resultssupporting

confidence: 89%

ROmodel: modeling robust optimization problems in Pyomo

Wiebe

Misener

2021

Optim Eng

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“…To address this, Bertsimas et al 24 proposed a local search algorithm for identifying robust feasible solutions to uncertain optimization problems with non‐convex inequality constraints. Additionally, there have been recent advances in the development of novel methods and applications of RO methods to nonlinear process systems engineering models, including general nonlinear programming robust counterpart formulations, 25 robust counterparts with local linearization of nonlinear uncertain constraints and a novel sampling algorithm, 26 application to the pooling problem utilizing a cutting‐plane solution algorithm, 27 application to water treatment network operation, 28 robust counterpart derivation for the synthesis of fuel refineries under cost uncertainty, 29 and design and operation of process systems with resilience to disruptive events, 30 to name but a few.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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“…In this work, they used nonconvex Benders decomposition to solve the nonconvex MINLP. More recently, Wiebe et al 30 presented a comparison study of reformulation and cutting plane-based robust optimization methods for the pooling problem.…”

Section: Introductionmentioning

confidence: 99%

Two-Stage Robust Optimization of Water Treatment Network Design and Operations under Uncertainty

Kammammettu

2019

Ind. Eng. Chem. Res.

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This paper presents a study of two-stage adaptive nonlinear robust optimization in dealing with uncertainty in the optimal design and operation of water treatment systems. This work aims to obtain (i) a robust process design and (ii) robust operational policies for the water treatment network, which are easily applicable for any realization of uncertainty that the problem has been modeled to handle. The approach uses a two-stage nonlinear robust optimization technique, which is based on the linearization around the nominal value of the uncertainty. The intractable adaptive robust optimization model is transformed into its tractable robust counterpart by applying the linear decision rule over the control variables. To handle the issue of concentration target violation caused by an inaccurate linear approximation model, a modified optimization model with additional constraints on the extreme points of the uncertainty set is further presented. The performance and advantages of the approach are then analyzed and contrasted on two case studies, a small water treatment model and a larger SAGD water treatment network.

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Robust Optimization for the Pooling Problem

Cited by 14 publications

References 72 publications

ROmodel: modeling robust optimization problems in Pyomo

ROmodel: modeling robust optimization problems in Pyomo

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

Two-Stage Robust Optimization of Water Treatment Network Design and Operations under Uncertainty

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