Informs Annual Meeting 2017

TD82

INFORMS Houston – 2017

2 - Stochastic Dynamic Programming using Optimal Quantizers Anna Timonina-Farkas, Postdoctoral Researcher, EPFL, RAO, Rue Saint-Laurent 33, Lausanne, Switzerland, anna.farkas@epfl.ch Multi-stage stochastic optimization is a well-known quantitative tool for decision- making under uncertainty. Theoretical solution of stochastic programs can be found explicitly only in very exceptional cases due to the problems complexity. Therefore, the necessity of numerical solution arises. In this work, we deal with numerical approximation methods for the solution of multi-stage optimization problems, which enhance both accuracy and efficiency of the solution. We preserve accuracy of the estimation by the use of optimal distribution discretization techniques on scenario trees, as well as we enhance efficiency of numerical algorithms by the combination with the dynamic programming. 3 - On the Optimality of Affine Policies for Budget of Uncertainty Sets Omar El Housni, oe2148@columbia.edu, Vineet Goiyal The performance of affine policies for two-stage adjustable robust optimization problem under a budget of uncertainty set. This important class of uncertainty sets provide the flexibility to adjust the level of conservatism in terms of probabilistic bounds on constraint violations. The two-stage adjustable robust optimization problem is hard to approximate within a factor better than $\Omega(\log n)$ even for budget of uncertainty sets where $n$ is the number of decision variables. We show affine policies provide the best possible approximation of $O(\log n)$ for budget of uncertainty sets. We discuss performance of affine when the uncertainty set is given by intersection of budget constraints. 382B Recent Advances in Risk Averse Optimization Sponsored: Optimization, Optimization Under Uncertainty Sponsored Session Chair: Gabor Rudolf, Koc University, Koc University, Istanbul, 34450, Turkey, grudolf@ku.edu.tr 1 - Optimization with Incomplete Information About Risk Measures Jonathan Yu-Meng Li, Telfer School of Management, University of Ottawa, 55 Laurier Avenue East, Ottawa, ON, K1N 6N5, Canada, jonathan.li@telfer.uottawa.ca, Erick Delage New risk theories have been developed recently that formalize measures that reasonably capture ones’ risk preferences. The problem, however, of applying these theories is that in reality only limited information about ones’ risk preferences is available. In this talk, we present a unified framework, preference robust optimization, that allows one to apply principles established by the latest risk theory to measure risk even when the preference information is incomplete and to generate solutions that are robust in terms of one’s true risk preferences. Our main result is to show that most optimization problems under uncertainty can be tractably solved even with incomplete preference information. 2 - Acceptability Pricing of Contingent Claims under Model Ambiguity using Stochastic Optimization Optimal bid and ask prices for contingent claims can be found by mathematical optimization. The traditional strategies find the optimal prices under the constraint that all risks are shifted to the resp. counterparty. We weaken this assumption by introducing risk (acceptability) functionals in the stochastic optimization framework. Moreover, we consider the associated ambiguity problem, where we replace the single probability model by a nonparametric set of models. We show that weakening the acceptability constraint leads to a shrinking bid-ask spread while considering model ambiguity makes it even larger. We discuss algorithmic solution methods and present some illustrative examples. 3 - A Decomposition Algorithm for ASD Risk Measure for Stochastic Programs with 0-1 Variables Saravanan Venkatachalam, Wayne State University, 4815 Fourth St., Detroit, MI, 48377, United States, saravanan.v@wayne.edu, Lewis Ntaimo Due to the lack of block-angular structure, stochastic programs with ASD risk measure pose computational challenges. In this talk, we propose a decomposition algorithm to ASD risk-measure and computational results are presented for a supply chain application. Martin Glanzer, PhD Student, University of Vienna, Oskar-Morgenstern-Platz 1, Vienna, 1090, Austria, martin.glanzer@univie.ac.at, Georg Ch. Pflug TD82

4 - Optimization with Stochastic Preferences Based on a General Class of Scalarization Functions Gabor Rudolf, Koc University, Koc University, Istanbul, 34450, Turkey, grudolf@ku.edu.tr, Nilay Noyan We consider problems where a decision leads to multiple uncertain outcomes, and decision makers’ preferences are incorporated via risk measures or via dominance constraints. Scalarization functions are a common tool to combine multiple outcomes. While the stochastic multi-objective literature largely relies on linear scalarization, a variety of other functions are used in deterministic settings. We incorporate a general class of scalarizations into multi-criteria decision models with stochastic preference constraints, and develop a theoretical background along with tractable solution methods. 382C Optimization, Robust Contributed Session Chair: Shunichi Ohmori, Waseda University, Tokyo, Japan, ohmori0406@gmail.com 1 - A Robust Optimization Approach in Dynamic Pricing with Online Demand Learning Maryam Zokaeinikoo, Graduate Research Assistant, Pennsylvania State University, Department of Industrial and Manufacturing Engineering, 364 Leonhard Building, University Park, State College, PA, 16802, United States, mzz30@psu.edu, Janis Terpenny, Tao Yao, Xue Wang We consider dynamic pricing problem in revenue management where the goal is to maximize revenue from multiple products with limited inventory over a finite time horizon. The demand function is unknown and should be learned from the sales data. We can formulate this problem as a multi-armed bandit problem to address the challenge of exploration-exploitation tradeoff. Through exploration, the retailer attempts to learn the demand at different prices and set a price that maximizes revenue over the remainder of the selling season (exploitation). We use robust optimization in this problem and show that the regret bound achieves near optimal performance compared to an oracle that knows all the parameters. 2 - Many-objective Evolutionary Approach to Scenario-based Optimization Problems Hayrullah Mert Sahinkoc, Bogazici University, Istanbul, Turkey, hmertsahinkoc@gmail.com, Umit Bilge We propose to approach optimization problems under scenario-based uncertainty by transforming them into multi-objective optimization problems where each scenario is considered as a separate objective. Solving the multi-objective counterpart provides optimal solutions with respect to different robust performance measures in a Pareto optimal set. To overcome the challenges posed by more than three scenarios, we resort to an emerging research area called many-objective optimization. The proposed many-objective evolutionary algorithm strategically combines several features and yields promising results on scenario-based 0-1 Knapsack problem compared to a set of existing algorithms. 3 - Optimization Problem for the Most Robust Preference Jian Hu, Assistant Professor, University of Michigan-Dearborn, 4901 Evergreen Rd., Dept. of IMSE,, Dearborn, MI, 48128, United States, jianhu@umich.edu We propose an optimal model with most robust preference. This problem is to seek a valid option most robustly preferable to benchmark. We develop an approximation approach based on Bernstein polynomials, and a cut-generation algorithm to solve the approximation problem. A financial portfolio investment problem has been used to illustrate the effectiveness of this model. 4 - A Heuristic Method for Stochastic Optimization TD83

Shunichi Ohmori, Assistant Professor, Waseda University, Room 0903A, Okubo 3-4-1, Shinjuku, Tokyo, Japan, ohmori0406@gmail.com

We studied stochastic non-convex optimization problem. We proposed an analysis framework using stochastic dynamical system and analyze stability of algorithm. By doing so, we can adjust the balance between diversification and convergence.

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