The robust pooling problem

Wiebe, Johannes; Cecı́lio, Inês; Misener, Ruth

doi:10.1016/b978-0-12-818634-3.50152-1

Cited by 2 publications

(4 citation statements)

References 27 publications

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“…While any of the problem's parameters could be considered uncertain, we focus on the interesting case of uncertain component inlet concentrations, which occur on the left-hand side of the problems quality constraint in combination with bilinear terms in the decision variables. This work extends a previous conference paper 42 which developed robust reformulations for the pooling problem:…”

Section: ■ Introductionsupporting

confidence: 65%

“…While any of the problem’s parameters could be considered uncertain, we focus on the interesting case of uncertain component inlet concentrations, which occur on the left-hand side of the problems quality constraint in combination with bilinear terms in the decision variables. This work extends a previous conference paper which developed robust reformulations for the pooling problem: In addition to the duality-based robust reformulations from Wiebe et al, we apply robust cutting planes to the nonconvex pooling problem and develop a termination tolerance-based strategy for their integration with global optimization. We develop a simple but practical, safety factor inspired approach as a benchmark and as a computationally effective, conservative approximation to the robust problem. We assess and compare the suitability of these techniques in the context of global optimization and analyze their computational efficiency for several commonly used uncertainty set geometries (box, ellipsoidal, and polyhedral sets). We show how the optimal solution to the pooling problem is affected by varying degrees of uncertainty in the source component concentrations. …”

Section: Introductionmentioning

confidence: 73%

“…• In addition to the duality-based robust reformulations from Wiebe et al 42 , we apply robust cutting planes to the non-convex pooling problem and develop a termination tolerance-based strategy for their integration with global optimization.…”

Section: June 19 2019mentioning

confidence: 99%

“…• In addition to the duality-based robust reformulations from Wiebe et al, 42 we apply robust cutting planes to the nonconvex pooling problem and develop a termination tolerance-based strategy for their integration with global optimization. • We develop a simple but practical, safety factor inspired approach as a benchmark and as a computationally effective, conservative approximation to the robust problem.…”

Section: ■ Introductionmentioning

confidence: 99%

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Robust Optimization for the Pooling Problem

Wiebe

Cecı́lio

Misener

2019

Ind. Eng. Chem. Res.

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The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of parametric uncertainty. This paper applies two robust optimization approaches, reformulation and cutting planes, to the non-linear, non-convex pooling problem. Most applications of robust optimization have been either convex or mixed-integer linear problems. We explore the suitability of robust optimization in the context of global optimization problems which are concave in the uncertain parameters by considering the pooling problem with uncertain inlet concentrations. We compare the computational efficiency of reformulation and cutting plane approaches for three commonly-used uncertainty set geometries on 14 pooling problem instances and demonstrate how accounting for uncertainty changes the optimal solution.

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Section: ■ Introductionsupporting

confidence: 65%

Section: Introductionmentioning

confidence: 73%

Section: June 19 2019mentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust Optimization for the Pooling Problem

Wiebe

Cecı́lio

Misener

2019

Ind. Eng. Chem. Res.

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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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The robust pooling problem

Cited by 2 publications

References 27 publications

Robust Optimization for the Pooling Problem

Robust Optimization for the Pooling Problem

ROmodel: modeling robust optimization problems in Pyomo

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