Informs Annual Meeting 2017

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INFORMS Houston – 2017

4 - Robust Defense Strategy for Gas-electric Systems Against Malicious Attacks Feng Qiu, Argonne National Laboratory, Lemont, IL, United States, fqiu@anl.gov, Cheng Wang, Jianhui Wang This talk proposes a methodology to identify and protect vulnerable components of connected gas and electric infrastructures from malicious attacks, and to guarantee a resilient operation by deploying valid corrective actions, while accounting for the interdependency of gas pipeline network and power transmission network. The proposed mathematical formulation gives rise to to a tri-level optimization problem. Case studies on two test systems demonstrate the effectiveness and efficiency of the proposed methodology.

quantitative relationships between the distributionally robust model and the corresponding risk-neutral and classical robust optimization models. Our study can guide decision makers to choose an appropriate level of robustness.

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382B Optimization in the Presence of Network Uncertainties Sponsored: Optimization, Optimization Under Uncertainty Sponsored Session Chair: Anna Timonina-Farkas, EPFL, RAO, Anna.farkas@epfl.ch 1 - Distributionally Robust Location-routing Problem Dimitri Papadimitriou, Nokia Bell Labs, In Distributionally Robust Optimization (DRO), model data is represented as random variable over a family of probability distributions. The motivation of using this technique for the solving location-routing problems stems from the ambiguity characterizing the probability distribution of demands in space (origin) and size driving location and allocation-dependent routing decisions. For this propose, we propose a data-driven DRO model which produces decisions that are robust with respect to the ambiguity set of all demand distributions that satisfy prescribed statistical hypothesis tests. 2 - Optimizing Crashing Decisions in Project Management Problem with Disruptions Haoxiang Yang, Northwestern University, 2145 Sheridan Road, Room C151, Evanston, IL, 60208, United States, haoxiangyang2019@u.northwestern.edu, David Morton We consider the problem of crashing a PERT network to accelerate project completion under a small number of disruptions. When a disruption occurs, the duration of an activity, which has not started, can change. The magnitude of that change, and the timing of the disruption, can both be random. We formulate this problem as a stochastic mixed integer program (SMIP). We propose a branch-and- bound algorithm to solve the SMIP and evaluate the computational performance of our approach. 3 - Information Theoretic Learning in MDPs with Hierarchical Parametric Uncertainty in Transition Probabilities Peeyush Kumar, B14, Industrian and Systems Engineering, MEB, University of Washington Seattle, Seattle, WA, 98195-2650, United States, agaron@uw.edu, Archis Ghate This research extends the recent work on Information Directed Policy Sampling (IDPS) to hierarchical MDPs. IDPS provides a way for decision maker to simultaneously balance the effect of exploration and exploitation. We consider MDPs where uncertainty in transition probabilities comes from two levels. The top level uncertainty corresponds to the decision-maker’s uncertainty about the system model. The bottom-level uncertainty is rooted in the decision-maker’s knowledge about the model parameters. This research extends IDPS to hierarchical MDPs and provides analytical performance bounds as well as numerical analysis on Response Guided Dosing. 4 - Robust PageRank: Stationary Distribution on a Growing Network Structure Anna Timonina-Farkas, EPFL, RAO, Rue Saint-Laurent 33, Lausanne, Switzerland, anna.farkas@epfl.ch PageRank is a challenging and important network ranking algorithm, which plays a crucial role in information technologies and numerical analysis due to its huge dimension and wide range of possible applications. Recently, a robust formulation of the PageRank model has been proposed for the case, when links in the network structure may vary influencing the transportation matrix defined by the network structure. In this work, we make a further step forward, allowing the network to vary not only in links, but also in the number of nodes. We propose a new robust formulation of the PageRank problem for uncertain networks with fixed growth rate. Rue du Charme 24, Brussels, 1190, Belgium, dimitri.papadimitriou@nokia-bell-labs.com

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382A Distributionally Robust Stochastic Programming Sponsored: Optimization, Optimization Under Uncertainty Sponsored Session Chair: Hamed Rahimian, Ohio State University, Columbus, OH, 43210, United States, rahimian.1@osu.edu 1 - Wasserstein Distributional Robustness and Regularization in Statistical Learning Rui Gao, Georgia Institute of Technology, Atlanta, GA, 30332, United States, rgao32@gatech.edu, Xi Chen, Anton J.Kleywegt A central question in statistical learning is to design algorithms that generalize to new data. We tackle this problem by formulating a Wassestein distributionally robust stochastic optimization (DRSO), and establish its connection with gradient- norm regularization. Such connection has several important implications. (i) It provides new interpretations for problems involving regularization, including many machine learning problems and discrete choice models. (ii) It enables a new way to derive generalization error bounds for statistical learning problems using tools from DRSO. (iii) It suggests a systematic approach to regularize problems in deep learning (e.g. training of GANs). 2 - Decomposition Algorithms for Distributionally Robust Optimization using Wasserstein Metric Sanjay Mehrotra, Northwestern University, Dept of I.E./ M.S.C246 Tech Inst, 2145 Sheridan Road, Evanston, IL, 60208- 3119, United States, mehrotra@iems.northwestern.edu, Fenqiao Luo We study distributionally robust optimization (DRO) problems where the ambiguity set is defined using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-infinite programs. We give a central cutting-surface method for the convex objective, assuming that we have a separation oracle. We used a distributionally robust generalization of the logistic regression model (DRLR) to test our algorithm. Numerical experiments on the DRLR models show that the number of oracle calls are typically $20\sim 50$ to achieve 5-digit precision. The solution found by the model is generally better in its ability to predict with a smaller standard error. 3 - Data-driven Distributionally Robust Chance-constrained Programming with Wasserstein Metric Ran Ji, Assistant Professor, George Mason University, 4400 University Dr. MS.4A6, Fairfax, VA, 22031, United States, rji2@gmu.edu, Miguel A.Lejeune We investigate a class of distributionally robust chance-constrained (DRCC) optimization problems with Wasserstein metric. We develop a reformulation and algorithmic framework to solve the problem. We formulate a series of new DRCC models for portfolio optimization problems, including some widely used reward- risk ratios in finance. The computational study shows the applicability and scalability of the proposed framework. 4 - Distributionally Robust Newsvendor Problems with Variation Distance Hamed Rahimian, The Ohio State University, 1971 Neil Avenue, 210 Baker Systems Building, Columbus, OH, 43210, United States, rahimian.1@osu.edu, Guzin Bayraksan, Tito Homem-de-Mello We use distributionally robust stochastic optimization to model a general class of newsvendor problems. We form the ambiguity set by all demand distributions that their variation distances are bounded by a level of robustness-from a nominal distribution. For this problem: (1) we derive closed-form expressions of the optimal solution as a function of the level of robustness, (2) we determine the regions of demand that are critical to the optimal cost, and (3) we establish

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