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Distributionally Robust Facility Location Problem under Decision-dependent Stochastic Demand [article]

Beste Basciftci, Shabbir Ahmed, Siqian Shen
2020 arXiv   pre-print
We conduct an extensive computational study, in which we compare our model with the existing (decision-independent) stochastic and robust models.  ...  Then, we propose a decision-dependent distributionally robust optimization model, and develop its exact mixed-integer linear programming reformulation.  ...  Our studies indicate superior performance of the proposed approach, which results in consistently higher profit and less unmet demand, compared to existing stochastic programming and distributionally robust  ... 
arXiv:1912.05577v2 fatcat:fkgf26g2lnf7fiop22l4ch2zre

Probabilistic Optimization Techniques in Smart Power System

Muhammad Riaz, Sadiq Ahmad, Irshad Hussain, Muhammad Naeem, Lucian Mihet-Popa
2022 Energies  
The computational complexity of stochastic programming and the conservativeness of robust optimization are both reduced by distributionally robust optimization.Chance constrained algorithms help in solving  ...  Such problems could be effectively solved using a probabilistic optimization strategy. It is further divided into stochastic, robust, distributionally robust, and chance-constrained optimizations.  ...  Distributionally Robust Optimization Distributionally robust optimization, also known as min-max stochastic programming, reduces the computational complexity of stochastic programming and conservative  ... 
doi:10.3390/en15030825 fatcat:sq23ggirbjcv7iiomfeqddghbm

A Decomposition Method for Distributionally-Robust Two-stage Stochastic Mixed-integer Cone Programs [article]

Fengqiao Luo, Sanjay Mehrotra
2019 arXiv   pre-print
We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex cone programs, and its important special case of distributionally-robust two-stage stochastic  ...  Computational results suggest that solution time requirement does not increase significantly when considering distributional robust counterparts to the stochastic programming models.  ...  Table 4 Numerical results for solving instances with 1000 scenarios and the total variation distance set to be 0.1.  ... 
arXiv:1911.08713v1 fatcat:bwnczzskrvhnnbk2qiourqnbwi

Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming

Chao Ning, Fengqi You
2019 Computers and Chemical 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  ...  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.  ...  Data-driven stochastic program and distributionally robust optimization The literature review of data-driven stochastic program, also known as distributionally robust optimization (DRO), is presented in  ... 
doi:10.1016/j.compchemeng.2019.03.034 fatcat:75rchq2egvdsfefuw6tvakodau

Distributionally Robust Optimization: A Review [article]

Hamed Rahimian, Sanjay Mehrotra
2019 arXiv   pre-print
A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities.  ...  This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization.  ...  They propose easy-to-check conditions to identify the effective and ineffective scenarios for the case that the distributional ambiguity is modeled via the total variation distance. Rahimian et al.  ... 
arXiv:1908.05659v1 fatcat:cliwiafz4vffvj2j3b67uix5nm

Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations

Peyman Mohajerin Esfahani, Daniel Kuhn
2017 Mathematical programming  
In this paper we demonstrate that, under mild assumptions, the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs-in many interesting  ...  We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset.  ...  We thank Soroosh Shafieezadeh Abadeh for helping us with the numerical experiments. The authors are grateful to Ruiwei Jiang and Nathan Kallus for their valuable and instructive comments.  ... 
doi:10.1007/s10107-017-1172-1 fatcat:3ajvciiiu5c4jnhmyomr7watjm

Wasserstein Distributionally Robust Look-Ahead Economic Dispatch [article]

Bala Kameshwar Poolla, Ashish R. Hota, Saverio Bolognani, Duncan S. Callaway, Ashish Cherukuri
2020 arXiv   pre-print
The first one is a tractable convex program in which the uncertain constraints are defined via the distributionally robust conditional-value-at-risk.  ...  The second one is a scalable robust optimization program that yields an approximate distributionally robust chance-constrained LAED.  ...  Furthermore, chance-constrained programs, and hence distributionally robust chance-constrained programs (DRCCPs) are in general non-convex.  ... 
arXiv:2003.04874v2 fatcat:nqqnw62tlvgchpe36rotn3yzlq

Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance [article]

Hamed Rahimian and Guzin Bayraksan and Tito Homem-de-Mello
2021 arXiv   pre-print
We then propose easy-to-check conditions to identify the effectiveness of scenario paths in the multistage setting when the distributional ambiguity is modeled via the total variation distance.  ...  We study multistage distributionally robust optimization (DRO) to hedge against ambiguity in quantifying the underlying uncertainty of a problem.  ...  , our choice to work with the total variation distance has other benefits.  ... 
arXiv:2109.06791v1 fatcat:6ybxdtyiy5a5zbwqzv2dvaqiua

A Two-stage Distributionally Robust Optimization Model for Wind Farms and Storage Units Jointly Operated Power Systems

Panpan Li, Liangyun Song, Jixian Qu, Yuehui Huang, Xiaoyun Wu, Xi Lu, Shiwei Xia
2021 IEEE Access  
To explore the benefit of energy storage for countering high-level wind power fluctuations, a two-stage distributionally robust optimization model is proposed for wind farms and storage units (SUs) jointly  ...  Finally, the influence of confidence level of confidence sets and SU capacities on system total cost is analyzed, and the effectiveness of the proposed model is also validated by the case studies.  ...  However as the DRO model with distance-based ambiguity set is usually a threelevel programming problem, it is usually intractable to be directly solved.  ... 
doi:10.1109/access.2021.3101569 fatcat:o54urbherfe47mavilwavhjfqa

Uncertainty in Unit Commitment in Power Systems: A Review of Models, Methods, and Applications

Ying-Yi Hong, Gerard Francesco D. G. Apolinario
2021 Energies  
Various methods have been developed to model the uncertainties of these parameters, such as stochastic programming, probabilistic methods, chance-constrained programming (CCP), robust optimization, risk-based  ...  Uncertainty management in a UCP has been of great interest to both operators and researchers.  ...  and demand variations are defined and incorporated into the proposed model together with the PEM scenarios.  ... 
doi:10.3390/en14206658 fatcat:7y6v7oofbzho7clkn5uyybzdq4

A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization

Sanjay Mehrotra, Dávid Papp
2014 SIAM Journal on Optimization  
Our primary motivation for the higher level of generality is to solve distributionally robust optimization problems with moment uncertainty.  ...  in which the uncertainty set consists of probability distributions with given bounds on their moments.  ...  Therefore, solving (15) for m = ∞ amounts to solving a stochastic programming problem with a continuous scenario set. (Recall Theorem 7.)  ... 
doi:10.1137/130925013 fatcat:w7dfwlwotnf6hpqfsefmz6o4fm

Data Driven Robust Energy and Reserve Dispatch Based on a Nonparametric Dirichlet Process Gaussian Mixture Model

Li Dai, Dahai You, Xianggen Yin
2020 Energies  
The simulation results demonstrated that the proposed optimization method was less conservative than traditional data driven robust optimization methods and distributionally robust optimization methods  ...  To avoid such conservative results from traditional robust optimization methods, in this paper a novel data driven optimization method based on the nonparametric Dirichlet process Gaussian mixture model  ...  Compared to stochastic optimization, a robust optimization tends to produce conservative solutions because it only optimizes the worst case scenario in the uncertainty set [6] .  ... 
doi:10.3390/en13184642 fatcat:rrktgptozfaazcrzrhzgb74c5a

Efficient Methods for Several Classes of Ambiguous Stochastic Programming Problems Under Mean-MAD Information

Krzysztof Postek
2016 Social Science Research Network  
Moreover, as found in many applications, the model may contain integer variables in some or all stages.  ...  Our approach is straightforward to implement using of-the-shelf software as illustrated in our numerical experiments.  ...  Solution methods for continuous stochastic programming models with exponentially many scenarios In Sections 2 and 3 we have shown how to reduce a distributionally robust optimization problem to an SP problem  ... 
doi:10.2139/ssrn.2845229 fatcat:xxaxklhesvg7jpty6ke33hxzou

A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization [article]

Sanjay Mehrotra, David Papp
2014 arXiv   pre-print
We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum, and stochastic programming at  ...  Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent  ...  Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DOE-SP0011568.  ... 
arXiv:1306.3437v3 fatcat:7ixpsr25unfejbtvn3fk63slwu

A distributionally robust optimization approach for two-stage facility location problems

Arash Gourtani, Tri-Dung Nguyen, Huifu Xu
2020 EURO Journal on Computational Optimization  
We formulate the optimal decision problem as a twostage stochastic mixed integer programming problem: an optimal selection of facility locations in the first stage and an optimal decision on the operation  ...  We then develop two numerical schemes for solving the distributionally robust facility location problem: a semi-infinite programming approach which exploits moments of certain reference random variables  ...  In Sect. 2, we formally describe the deterministic model, a two-stage stochastic model and a distributionally robust formulation of the stochastic model. 2.  ... 
doi:10.1007/s13675-020-00121-0 fatcat:nwnz27ly4jfgjcxecgoa5n67uy
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