13,141 research outputs found
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
K-Adaptability in Two-Stage Distributionally Robust Binary Programming
We propose to approximate two-stage distributionally robust programs with binary recourse decisions by their associated K-adaptability problems, which pre-select K candidate secondstage policies here-and-now and implement the best of these policies once the uncertain parameters have been observed. We analyze the approximation quality and the computational complexity of the K-adaptability problem, and we derive explicit mixed-integer linear programming reformulations. We also provide efficient procedures for bounding the probabilities with which each of the K second-stage policies is selected
Data-Driven Robust Optimization
The last decade witnessed an explosion in the availability of data for
operations research applications. Motivated by this growing availability, we
propose a novel schema for utilizing data to design uncertainty sets for robust
optimization using statistical hypothesis tests. The approach is flexible and
widely applicable, and robust optimization problems built from our new sets are
computationally tractable, both theoretically and practically. Furthermore,
optimal solutions to these problems enjoy a strong, finite-sample probabilistic
guarantee. \edit{We describe concrete procedures for choosing an appropriate
set for a given application and applying our approach to multiple uncertain
constraints. Computational evidence in portfolio management and queuing confirm
that our data-driven sets significantly outperform traditional robust
optimization techniques whenever data is available.Comment: 38 pages, 15 page appendix, 7 figures. This version updated as of
Oct. 201
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