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A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction.

ABSTRACT: Probabilistic guarantees on constraint satisfaction for robust counterpart optimization are studied in this paper. The robust counterpart optimization formulations studied are derived from box, ellipsoidal, polyhedral, "interval+ellipsoidal" and "interval+polyhedral" uncertainty sets (Li, Z., Ding, R., and Floudas, C.A., A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear and Robust Mixed Integer Linear Optimization, Ind. Eng. Chem. Res, 2011, 50, 10567). For those robust counterpart optimization formulations, their corresponding probability bounds on constraint satisfaction are derived for different types of uncertainty characteristic (i.e., bounded or unbounded uncertainty, with or without detailed probability distribution information). The findings of this work extend the results in the literature and provide greater flexibility for robust optimization practitioners in choosing tighter probability bounds so as to find less conservative robust solutions. Extensive numerical studies are performed to compare the tightness of the different probability bounds and the conservatism of different robust counterpart optimization formulations. Guiding rules for the selection of robust counterpart optimization models and for the determination of the size of the uncertainty set are discussed. Applications in production planning and process scheduling problems are presented.

SUBMITTER: Li Z

PROVIDER: S-EPMC3544168 | biostudies-literature | 2012

REPOSITORIES: biostudies-literature

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A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction.

Li Zukui Z Floudas Christodoulos A CA

Industrial & engineering chemistry research 20120416 19

Probabilistic guarantees on constraint satisfaction for robust counterpart optimization are studied in this paper. The robust counterpart optimization formulations studied are derived from box, ellipsoidal, polyhedral, "interval+ellipsoidal" and "interval+polyhedral" uncertainty sets (Li, Z., Ding, R., and Floudas, C.A., A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear and Robust Mixed Integer Linear Optimization, Ind. Eng. Chem. Res, 2011, 5 ...[more]

PMID: 23329868

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Project description:BACKGROUND: An important step in strain optimization is to identify reactions whose activities should be modified to achieve the desired cellular objective. Preferably, these reactions are identified systematically, as the number of possible combinations of reaction modifications could be very large. Over the last several years, a number of computational methods have been described for identifying combinations of reaction modifications. However, none of these methods explicitly address uncertainties in implementing the reaction activity modifications. In this work, we model the uncertainties as probability distributions in the flux carrying capacities of reactions. Based on this model, we develop an optimization method that identifies reactions for flux capacity modifications to predict outcomes with high statistical likelihood. RESULTS: We compare three optimization methods that select an intervention set comprising up- or down-regulation of reaction flux capacity: CCOpt (Chance constrained optimization), DetOpt (Deterministic optimization), and MCOpt (Monte Carlo-based optimization). We evaluate the methods using a Monte Carlo simulation-based method, MCEval (Monte Carlo Evaluations). We present two case studies analyzing a CHO cell and an adipocyte model. The flux capacity distributions required for our methods were estimated from maximal reaction velocities or elementary mode analysis. The intervention set selected by CCOpt consistently outperforms the intervention set selected by DetOpt in terms of tolerance to flux capacity variations. MCEval shows that the optimal flux predicted based on the CCOpt intervention set is more likely to be obtained, in a probabilistic sense, than the flux predicted by DetOpt. The intervention sets identified by CCOpt and MCOpt were similar; however, the exhaustive sampling required by MCOpt incurred significantly greater computational cost. CONCLUSIONS: Maximizing tolerance to variable engineering outcomes (in modifying enzyme activities) can identify intervention sets that statistically improve the desired cellular objective.

Dataset Information

A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction.

Publications

A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction.

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