Cut generation for optimization problems with multivariate risk constraints

Küçükyavuz, Simge; Noyan, Nilay

doi:10.1007/s10107-015-0953-7

Cited by 15 publications

(31 citation statements)

References 19 publications

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“…Observe that in the multivariate CVaR-constrained problems studied in Noyan and Rudolf (2013) and Küçükyavuz and Noyan (2015), given a random benchmark vector Y, the cut generation problems are given by min c∈C CVaR(c G(z * )) − CVaR(c Y) (we will revisit this cut generation problem in Section 3). Due to the similar structure, we can use the formulations and enhancements given in Noyan and Rudolf (2013) and Küçükyavuz and Noyan (2015) to formulate the cut generation problem (CutGen − Robust) as a mixedinteger program.…”

Section: Solution Methodsmentioning

confidence: 99%

“…Due to the similar structure, we can use the formulations and enhancements given in Noyan and Rudolf (2013) and Küçükyavuz and Noyan (2015) to formulate the cut generation problem (CutGen − Robust) as a mixedinteger program. Let X = G(z * ) with the realizations x 1 , .…”

Section: Solution Methodsmentioning

confidence: 99%

“…However, the big-M type constraints may lead to weak LP relaxation bounds and computational difficulties. In order to deal with these difficulties, Küçükyavuz and Noyan (2015) propose an improved model based on a new representation of VaR α .…”

Section: Solution Methodsmentioning

confidence: 99%

“…For this cut generation problem, Küçükyavuz and Noyan (2015) introduce a MIP formulation based on the VaR representation of CVaR (see (14)), which is given by…”

Section: Finite Convergencementioning

confidence: 99%

“…These finite representation results allow them to develop finitely convergent delayed cut generation algorithms, where each cut is obtained by solving a mixed-integer programming (MIP) problem. Since solving these MIP formulations is the main computational bottleneck, Küçükyavuz and Noyan (2015) develop computationally effective solution methods for the cut generation problems arising in both types of optimization models.…”

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confidence: 99%

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Robust multicriteria risk-averse stochastic programming models

2017

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In this paper, we study risk-averse models for multicriteria optimization problems under uncertainty. We use a weighted sum-based scalarization and take a robust approach by considering a set of scalarization vectors to address the ambiguity and inconsistency in the relative weights of each criterion. We model the risk aversion of the decision makers via the concept of multivariate conditional value-at-risk (CVaR). First, we introduce a model that optimizes the worst-case multivariate CVaR, and develop a finitely convergent delayed cut generation algorithm for finite probability spaces. We also show that this model can be reformulated as a compact linear program under certain assumptions. In addition, for the cut generation problem, which is in general a mixed-integer program, we give a stronger formulation for the equiprobable case. Next, we observe that similar polyhedral enhancements are also useful for a related class of multivariate CVaR-constrained optimization problems that has attracted attention recently. In our computational study, we use a budget allocation application to compare the decisions from our proposed maximin type risk-averse model with those from its risk-neutral version and the multivariate CVaR-constrained model. Finally, we illustrate the effectiveness of the proposed solution methods for both classes of models.

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Section: Solution Methodsmentioning

confidence: 99%

Section: Solution Methodsmentioning

confidence: 99%

Section: Solution Methodsmentioning

confidence: 99%

“…For this cut generation problem, Küçükyavuz and Noyan (2015) introduce a MIP formulation based on the VaR representation of CVaR (see (14)), which is given by…”

Section: Finite Convergencementioning

confidence: 99%

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confidence: 99%

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Robust multicriteria risk-averse stochastic programming models

2017

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A polyhedral study on chance constrained program with random right-hand side

2016

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Two-stage stochastic programming under multivariate risk constraints with an application to humanitarian relief network design

2019

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In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure that the associated random outcome vector of interest is preferable to a specified benchmark with respect to the multivariate polyhedral conditional value-at-risk (CVaR) or a multivariate stochastic order relation. In this case, the classical decomposition methods cannot be used directly due to the complicating multivariate stochastic benchmarking constraints. We propose an exact unified decomposition framework for solving these two classes of optimization problems and show its finite convergence. We apply the proposed approach to a stochastic network design problem in a pre-disaster humanitarian logistics context and conduct a computational study concerning the threat of hurricanes in the Southeastern part of the United States. Our numerical results on these large-scale problems show that our proposed algorithm is computationally scalable.

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Cut generation for optimization problems with multivariate risk constraints

Cited by 15 publications

References 19 publications

Robust multicriteria risk-averse stochastic programming models

Robust multicriteria risk-averse stochastic programming models

A polyhedral study on chance constrained program with random right-hand side

Two-stage stochastic programming under multivariate risk constraints with an application to humanitarian relief network design

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