Journal ArticleDOI
Uncertainty feature optimization: An implicit paradigm for problems with noisy data
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Optimization problems with noisy data solved using stochastic programming or robust optimization approaches require the explicit characterization of an uncertainty set U that models the nature of the noise.Abstract:
Optimization problems with noisy data solved using stochastic programming or robust optimization approaches require the explicit characterization of an uncertainty set U that models the nature of the noise. Such approaches depend on the modeling of the uncertainty set and suffer from an erroneous estimation of the noise.
In this article, we introduce a framework that considers the uncertain data implicitly. We define the concept of Uncertainty Features (UF), which are problem-specific structural properties of a solution. We show how to formulate an uncertain problem using the Uncertainty Feature Optimization (UFO) framework as a multi-objective problem. We show that stochastic programming and robust optimization are particular cases of the UFO framework. We present computational results for the Multi-Dimensional Knapsack Problem (MDKP) and discuss the application of the framework to the airline scheduling problem. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011 © 2011 Wiley Periodicals, Inc.read more
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Book ChapterDOI
Algorithm engineering in robust optimization
Marc Goerigk,Anita Schöbel +1 more
TL;DR: This paper argues that the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions.
Journal ArticleDOI
Review. Assessing uncertainty and risk in forest planning and decision support systems: review of classical methods and introduction of new approaches
M. Pasalodos-Tato,A. Mäkinen,Jordi Garcia-Gonzalo,José G. Borges,T. Lämås,Ljusk Ola Eriksson +5 more
TL;DR: The study can aid forest managers in the decision making process when designing a forest management plan considering risk and uncertainty, and new approaches are introduced, showing the opportunities that their application present in forest planning.
Journal ArticleDOI
Robust flight schedules through slack re-allocation
TL;DR: In this article, a flight schedule adjustment model that strategically re-allocates existing schedule slack to achieve a more robust schedule is proposed, and the results show that minor schedule adjustments to the original schedule can significantly improve overall schedule performance.
Journal ArticleDOI
Robust optimization: Lessons learned from aircraft routing
TL;DR: This paper develops and presents advanced models that address issues of tractability and solution quality for the large-scale networks which are representative of real-world airline scheduling problems and can be applied to aircraft routing in multiple ways, through varied descriptions of the uncertainty sets.
Combining Robustness and Recovery for Airline Schedules
TL;DR: A general framework to solve problems subject to uncertainty: the Uncertainty Feature Optimization (UFO) framework, which implicitly embeds the uncertainty the problem is prone to, and shows that UFO is a generalization of existing methods relying on explicit uncertainty models that protects against possible errors in its modeling.
References
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BookDOI
Introduction to Stochastic Programming
John R. Birge,Franois Louveaux +1 more
TL;DR: This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability to help students develop an intuition on how to model uncertainty into mathematical problems.
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.
MonographDOI
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
TL;DR: The authors present the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming as well as their numerous applications in engineering.