Journal ArticleDOI
Solving two-stage robust optimization problems using a column-and-constraint generation method
TLDR
A computational study on a two-stage robust location-transportation problem shows that the column-and-constraint generation algorithm performs an order of magnitude faster than existing Benders-style cutting plane methods.About:
This article is published in Operations Research Letters.The article was published on 2013-09-01. It has received 1010 citations till now. The article focuses on the topics: Robust optimization & Cutting-plane method.read more
Citations
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Integrating Energy Management of Autonomous Smart Grids in Electricity Market Operation
TL;DR: A single-leader multi-follower game is developed, in which every smart grid derives optimal schedules of its own renewable energy resources, storage devices, and responsive demands that are interconnected through a distribution grid using mixed integer linear programming.
Journal ArticleDOI
Adjustable robust optimization through multi-parametric programming
TL;DR: This work proposes a novel method for the derivation of generalized affine decision rules for linear mixed-integer ARO problems through multi-parametric programming, that lead to the exact and global solution of the ARO problem.
Journal ArticleDOI
A tri-level optimization model for power grid defense with the consideration of post-allocated DGs against coordinated cyber-physical attacks
TL;DR: A defensive strategy considering post-allocated Distributed Generators (DGs) is developed, and the traditional Load Redistributed (LR) attack model is reformulated in a discrete form to facilitate the utilization of duality-based method in the tri-level model.
Linearized robust counterparts of two-stage robust optimization problems with applications in operations management
TL;DR: This article discusses an alternative method for deriving conservative approximation models for two-stage robust optimization problems that mainly relies on a linearization scheme emplacing conservative approximations in the middle of the solution.
Journal ArticleDOI
An Optimization‐Based Framework for the Identification of Vulnerabilities in Electric Power Grids Exposed to Natural Hazards
TL;DR: The numerical results demonstrate the effectiveness of the proposed framework for identifying critical locations under multiple hazard events and, thus, for providing a useful tool to help decisionmakers in making more‐informed prehazard preparation decisions.
References
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Journal ArticleDOI
The Price of Robustness
Dimitris Bertsimas,Melvyn Sim +1 more
TL;DR: In this paper, the authors propose an approach that attempts to make this trade-off more attractive by flexibly adjusting the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations.
The price of the robustness
D Bertsimas,M Sim +1 more
TL;DR: An approach is proposed that flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations, and an attractive aspect of this method is that the new robust formulation is also a linear optimization problem, so it naturally extend to discrete optimization problems in a tractable way.
Journal ArticleDOI
Robust Convex Optimization
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: If U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.
Journal ArticleDOI
Generalized Benders decomposition
TL;DR: In this paper, the extremal value of the linear program as a function of the parameterizing vector and the set of values of the parametric vector for which the program is feasible were derived using linear programming duality theory.