Informs Annual Meeting Phoenix 2018

INFORMS Phoenix – 2018

PLENARY

Monday, 10:00AM - 10:50AM

4 - On a Class of Chance-constrained Nonlinear Programming Problems Belleh Fontem, University of Mary Washington, Fredericksburg, VA, United States, Jeremiah Smith We consider the non-convex problem of minimizing a linear deterministic cost objective subject to a probabilistic requirement on a nonlinear multivariate stochastic expression attaining, or exceeding a given threshold. The stochastic expression represents the output of a noisy system featuring the product of mutually-uncorrelated, uniform random parameters each raised to a linear function of one of the decision vector’s constituent variables. We prove a connection to (i) the probability measure on the superposition of a finite collection of uncorrelated exponential random variables, and (ii) an entropy-like affine function. Numerical experiments shed light on several model properties. Optimization under Multistage Uncertainty Sponsored: Optimization/Optimization Under Uncertainty Sponsored Session Chair: Beste Basciftci, Georgia Institute of Technology, Atlanta, GA, 30332, United States 1 - Matheuristic Algorithms for Multistage Location-assignment Problems under Uncertainty Araceli Garin, Ph. Dr., University of the Basque Country, Bilbao (Bizkaia), 48015, Spain, Laureano Fernando Escudero, Celeste Pizarro, Aitziber Unzueta We present two matheuristic procedures to build good feasible solutions (frequently, the optimal one) by considering the solutions of relaxed problems of large-sized instances of the multi-period stochastic pure 0-1 location-assignment problem. Additionally, for both procedures, a lazy heuristic scheme, based on scenario clustering, is considered for obtaining a feasible solution as an upper bound of the solution value of the full problem. Then, the same framework provides for the two procedures lower and upper bounds on the solution value. A broad computational experience is reported for 14 instances, up to 15 facilities, 75 customers, 6 periods, over 260 scenarios in the scenario tree. 2 - On the Value of Multistage Stochastic Facility Location with (or without) Risk Aversion Xian Yu, University of Michigan, Shabbir Ahmed, Siqian Shen We consider facility location over a finite time horizon with uncertain demand. Comparing to a two-stage approach, we formulate a multistage stochastic integer program using scenario tree, to dynamically locate facilities at each period. We examine an expectation-based risk-neutral model and a risk-averse variant based on coherent risk measure. We show that the gaps between optimal objective values of the two multistage models and their two-stage counterparts are bounded from below, and the bound with risk aversion is at least as large as the risk-neutral bound. We also develop algorithms using SDDiP for solving both multistage models and demonstrate the computational efficiency. 3 - Adaptive Two-stage Stochastic Programming Beste Basciftci, Georgia Institute of Technology, H. Milton Stewart School, 755 Ferst Drive NW, Atlanta, GA, 30332, United States, Shabbir Ahmed, Nagi Gebraeel In this study, we propose a novel adaptive stochastic programming approach, in which the best time to realize the uncertainty is a decision variable. Our approach can be considered as an approximation to multi-stage stochastic programming where the decision maker is not allowed to revise the decisions in each stage due to the problem restrictions. We provide theoretical bounds on the performance of the proposed approach compared to two-stage and multi-stage programs. We also propose algorithms for efficiently solving the resulting optimization model. In order to illustrate our results, we study various cases demonstrating the advantages of the adaptive two-stage approach. n MB02 North Bldg 121B

n Plenary West Bldg 301AB Plenary: Learning in Games (Philip McCord Morse Lecture) Plenary Session Chair: Margaret L. Brandeau, Stanford University, Management Science and Engineering, 475 Via Ortega, Stanford, CA, 94305-4026, United States 1 - Learning in Games Eva Tardos, Cornell University, Ithaca, NY, United States Selfish behavior can often lead to suboptimal outcome for all participants, a phenomenon illustrated by many classical examples in game theory. Over the last decade we developed good understanding on how to quantify the impact of strategic user behavior on the overall performance in many games (including traffic routing as well as online auctions). In this talk we will focus on games where players use a form of learning that helps them adapt to the environment, and consider two closely related questions: What are broad classes of learning behaviors that guarantee high social welfare in games, and are these results robust to situations when game or the population of players is dynamically changing. n MB01 North Bldg 121A Chance Constrained Optimization Sponsored: Optimization/Optimization Under Uncertainty Sponsored Session Chair: Bismark Singh, Sandia National Laboratories, Albuquerque, NM, 87185, United States 1 - Approximating Two-Stage Chance-Constrained Programs with Classical Probability Bounds Bismark Singh, Sandia National Laboratories, P.O. Box 5800, MS 1326, Albuquerque, NM, 87185, United States, Jean-Paul Watson We consider a joint-chance constraint (JCC) as a union of events, and approximate this union using bounds from classical probability theory. When these bounds are used in an optimization model constrained by the JCC, we obtain corresponding upper and lower bounds on the optimal objective function value. We investigate the strength of these bounds under two different sampling schemes, and observe that a larger correlation between the uncertainties results Monday, 11:00AM - 12:30PM Yankai Cao, University of Wisconsin-Madison, 2011 Engineering Hall, 1415 Engineering Drive, Madison, WI, 53706, United States, Victor M. Zavala We propose a sigmoidal approximation for the value-at-risk and we use this approximation to tackle nonlinear programs with chance constraints. We prove that the approximation is conservative and that the level of conservatism can be made arbitrarily small for limiting parameter values. We establish explicit connections between SigVaR and other approximations reported in the literature. A key benefit of SigVaR is that one can establish an explicit connection with the conditional value at risk approximation and exploit this connection to obtain initial guesses for the approximation parameters. We present small- and large- scale numerical studies to illustrate the developments. 3 - Chance Constrained Optimization Based Solar Microgrid Design and Dispatch for Radial Distribution Networks Hossein Dashti, University of Arizona, Tucson, AZ, United States, Jianqiang Cheng, Pavlo A. Krokhmal We propose a two-stage model for optimal placement and planning of distribution generation (DG) and energy storage system units. We incorporate time series modeling to characterize the solar irradiance uncertainty. Design (location and sizing of DGs) and dispatch decisions (how much to generate and store) are made such that electricity demand is met reliably and cost effectively. We employ chance constraints to control the real load shedding within a predefined probability. We combine sample average approximation (SAA) and linearization techniques to solve the problem. Finally, we conduct an out-of-sample simulation on a case study in Arizona to assess the effectiveness of our approach. in a more computationally challenging optimization model. 2 - A Sigmoidal Approximation for Chance Constrained Nonlinear Programs

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