Safe approximations of ambiguous chance constraints using historical data

I. Yanikoglu, D. den Hertog

Research output: Contribution to journalArticleScientificpeer-review

Abstract

This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant, especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach.
Original languageEnglish
Pages (from-to)666-681
JournalINFORMS Journal on Computing
Volume25
Issue number4
Early online date27 Nov 2012
DOIs
Publication statusPublished - 2013

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Statistics
Approximation
Chance constraints
Uncertainty
Robust optimization
Goodness of fit
Guarantee

Cite this

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title = "Safe approximations of ambiguous chance constraints using historical data",
abstract = "This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant, especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach.",
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Safe approximations of ambiguous chance constraints using historical data. / Yanikoglu, I.; den Hertog, D.

In: INFORMS Journal on Computing, Vol. 25, No. 4, 2013, p. 666-681.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Yanikoglu, I.

AU - den Hertog, D.

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AB - This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant, especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach.

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