Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets

Hota, Ashish R.; Cherukuri, Ashish; Lygeros, John

doi:10.23919/acc.2019.8814677

Cited by 59 publications

(49 citation statements)

References 37 publications

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“…Recently, data-driven chance constraints over Wasserstein balls were exactly reformulated as mixed-integer conic constraints [145,146]. Leveraging the strong duality result [147], distributionally robust chance constrained programs with Wasserstein ambiguity set were studied for linear constraints with both right and left hand uncertainty [148], as well as for general nonlinear constraints [149].…”

Section: Data-driven Chance Constrained Programmentioning

confidence: 99%

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Ning

You

2019

Computers & Chemical Engineering

255

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This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learningbased data-driven multistage optimization with a learning-while-optimizing scheme is presented.

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Section: Data-driven Chance Constrained Programmentioning

confidence: 99%

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Ning

You

2019

Computers & Chemical Engineering

255

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“…With the definition and property of CVaR, a sufficient condition for (17) can be expressed by [30]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \underset{P \in {scriptM}_{i}^{ε}}{truesup} {CVaR}_{1 - α}^{P} (L (ξ_{normalΣ}, P_{normalΣ}^{normalr})) \leq 0 \end{matrix}

where

{CVaR}_{1 - α}^{P} ()(, L false(ξ_{Σ}, P_{Σ}^{r} false))

can be calculated by solving the following problem over

γ

[31]:

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \underset{γ \in R}{trueinf} α^{- 1} {double-struckE}_{P} {(][, L ()(, ξ_{Σ}, P_{Σ}^{r}) + γ)}_{+} - γ \end{matrix}

where

false(\cdot false)_{+} = truemax falsefalse{\cdot, 0 falsefalse}

. With a collection of given samples, the expectation operator

E_{P}

can be approximated.…”

Section: Solution Strategymentioning

confidence: 99%

“…With a collection of given samples, the expectation operator

E_{P}

can be approximated. Further, employing Lemma V.8 in [30], a sufficient condition of CVaR constraint (18) is:

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ ε H_{normalL} + \underset{γ \in R}{trueinf} \frac{1}{K} \sum_{k = 1}^{K} {(][, L ()(, {\hat{ξ}}_{Σ}^{k}, P_{Σ}^{normalr, k}) + γ)}_{+} - γ α \leq 0 \end{matrix}

where

H_{L}

is the measurement of Lipschitz continuity. In addition, we claim the loss function

L ()(, ξ_{Σ}, P_{Σ}^{r})

satisfies the boundedness, convexity, and Lipschitz continuity assumptions required by Lemma V.8.…”

Section: Solution Strategymentioning

confidence: 99%

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Sizing energy storage to reduce renewable power curtailment considering network power flows: a distributionally robust optimisation approach

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Wei

Chen

et al. 2020

IET Renewable Power Generation

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“…As (16) is chance-constrained programming, it can be reformulated as the following CVaR constraint [26] to limit the frequency and severity of constraint violations…”

Section: ) Capacity Limitation Of Chargers Msbs and Transformersmentioning

confidence: 99%

Data‐driven robust planning of electric vehicle charging infrastructure for urban residential car parks

Yan

Zhao

et al. 2020

IET gener. transm. distrib.

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The number of electric vehicles (EVs) is expected to grow significantly, which calls for effective planning of charging infrastructures. While the planning of the charging infrastructure relies on an accurate charging demands, the behaviours of EVs charging are not always predictable and can be sensitive to many uncertain future environmental factors. Considering such uncertainties, this study aims to robustly and optimally determine the chargers and main switch board (MSB) capacities without violating queuing time constraints and load flow constraints. The non-parametric estimations of charging demands are derived with data-driven charging behaviour analysis considering diverse social factors, including travelling patterns, queuing, and changes of charging facilities. Then, the impacts of the EV integration are modeled by a stochastic load flow program. The samples of the stochastic load flow stipulate the conditional value-at-risk constraints for the planning of chargers and MSBs, which consider the probabilities and scenarios in a box of ambiguity with bounds. Afterwards, by limiting the frequency and severity of constraints violation, the total investment cost is minimized with a distributionally robust optimisation program. Simulation based on a real-world residential community in Singapore is carried out to testify the effectiveness of the proposed method.

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Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets

Cited by 59 publications

References 37 publications

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Sizing energy storage to reduce renewable power curtailment considering network power flows: a distributionally robust optimisation approach

Data‐driven robust planning of electric vehicle charging infrastructure for urban residential car parks

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