Distributionally robust chance-constrained programs with right-hand side uncertainty under Wasserstein ambiguity

Ho-Nguyen, Nam; Kılınç-Karzan, Fatma; Küçükyavuz, Simge; Lee, Dabeen

doi:10.1007/s10107-020-01605-y

Cited by 28 publications

(20 citation statements)

References 31 publications

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“…In the case of RHS uncertainty, this connection between (SAA) and (DR-CCP) has been first observed and explored in our previous work [12]. It turns out that this relation is instrumental in improving the MIP formulation of (DR-CCP) with LHS uncertainty given in (8) as well.…”

Section: Connection With the Nominal Chance Constraintmentioning

confidence: 67%

“…We then exploit this connection between (DR-CCP) and SAA to address the (easier) case of RHS uncertainty. Our proposed approach in [12] provides stronger formulations and valid inequalities for (DR-CCP), which are instrumental in solving instances that are an order of magnitude larger than those in the literature, from 100s of scenarios to 1000s of scenarios. In this paper, we further explore this connection between (DR-CCP) and SAA to address the more difficult case of LHS uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Strong Formulations for Distributionally Robust Chance-Constrained Programs with Left-Hand Side Uncertainty under Wasserstein Ambiguity

Ho-Nguyen

Kılınç-Karzan²,

Küçükyavuz

et al. 2020

Preprint

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Distributionally robust chance-constrained programs (DR-CCP) over Wasserstein ambiguity sets exhibit attractive out-of-sample performance and admit big-M -based mixed-integer programming (MIP) reformulations with conic constraints. However, the resulting formulations often suffer from scalability issues as sample size increases. To address this shortcoming, we derive stronger formulations that scale well with respect to the sample size. Our focus is on ambiguity sets under the so-called left-hand side (LHS) uncertainty, where the uncertain parameters affect the coefficients of the decision variables in the linear inequalities defining the safety sets.The interaction between the uncertain parameters and the variable coefficients in the safety set definition causes challenges in strengthening the original big-M formulations. By exploiting the connection between nominal chance-constrained programs and DR-CCP, we obtain strong formulations with significant enhancements. In particular, through this connection, we derive a linear number of valid inequalities, which can be immediately added to the formulations to obtain improved formulations in the original space of variables. In addition, we suggest a quantile-based strengthening procedure that allows us to reduce the big-M coefficients drastically. Furthermore, based on this procedure, we propose an exponential class of inequalities that can be separated efficiently within a branch-and-cut framework. The quantile-based strengthening procedure can be expensive. Therefore, for the special case of covering and packing type problems, we identify an efficient scheme to carry out this procedure.We demonstrate the computational efficacy of our proposed formulations on two classes of problems, namely stochastic portfolio optimization and resource planning.

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Section: Connection With the Nominal Chance Constraintmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Strong Formulations for Distributionally Robust Chance-Constrained Programs with Left-Hand Side Uncertainty under Wasserstein Ambiguity

Ho-Nguyen

Kılınç-Karzan²,

Küçükyavuz

et al. 2020

Preprint

Self Cite

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“…Distributionally robust optimization (DRO) problems have long been studied in robust optimization community for ordinary optimization problems in which the objective function and the constraint functions are explicitly formulated (in contrast to expensive black-box functions as we consider in this study) [Scarf, 1958, Rahimian andMehrotra, 2019]. DRCC problem with explicitly formulated objective and constraint functions were also studied in [Xie, 2021, Ho-Nguyen et al, 2021, and they were applied to practical problems called power flow optimization [Xie andAhmed, 2017, Fang et al, 2019]. On the other hand, the study of DRO problems for black-box functions with high evaluation cost has only recently started.…”

Section: Related Workmentioning

confidence: 99%

Bayesian Optimization for Distributionally Robust Chance-constrained Problem

Yu¹,

Takeno²,

Karasuyama³

et al. 2022

Preprint

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In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account the uncertainty of the environmental variables. Chance-constrained (CC) problem, the problem of maximizing the expected value under a certain level of constraint satisfaction probability, is one of the practically important problems in the presence of environmental variables. In this study, we consider distributionally robust CC (DRCC) problem and propose a novel DRCC Bayesian optimization method for the case where the distribution of the environmental variables cannot be precisely specified. We show that the proposed method can find an arbitrary accurate solution with high probability in a finite number of trials, and confirm the usefulness of the proposed method through numerical experiments.

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“…In particular, by exploiting the right-hand-side (RHS) uncertainty, we drive an MILP reformulation based on the conditional value-at-risk (CVaR) interpretation for DR chance constraints pointed out by Xie (2019), Chen et al (2018). Recently, based on the CVaR (primal) interpretation, Ho- Nguyen et al (2021) provide an MILP reformulations for joint DRCC programs with RHS uncertainty. Different from their work, our results are derived from the dual perspective of CVaR.…”

Section: Summary Of Main Contributionsmentioning

confidence: 99%

Building Load Control using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

Zhang

Dong

2021

Preprint

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Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. However, the time-varying PV generation is not perfectly known when the system operator decides the HVAC control schedules. To consider the unknown uncertain PV generation, in this paper, we formulate a distributionally robust chance-constrained (DRCC) building load control problem under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the DRCC problem under the Wasserstein ambiguity set, we utilize the righthand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known MILP reformulations with big-M constants. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained variant to achieve a trade-off between the operational risk and costs. We derive MILP reformulations under the Wasserstein ambiguity set and second-order conic programming (SOCP) reformulations under the moment-based set. Using real-world data, we conduct computational studies to demonstrate the efficiency of the solution approaches and the effectiveness of the solutions.

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Distributionally robust chance-constrained programs with right-hand side uncertainty under Wasserstein ambiguity

Cited by 28 publications

References 31 publications

Strong Formulations for Distributionally Robust Chance-Constrained Programs with Left-Hand Side Uncertainty under Wasserstein Ambiguity

Strong Formulations for Distributionally Robust Chance-Constrained Programs with Left-Hand Side Uncertainty under Wasserstein Ambiguity

Bayesian Optimization for Distributionally Robust Chance-constrained Problem

Building Load Control using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

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