Invited ReviewRecent advances in robust optimization: An overview☆
Introduction
This review focuses on papers indexed on Web of Science as having been published since 2007 (included), belonging to the area of Operations Research and Management Science, and having ‘robust’ and ‘optimization’ in their title. There were 130 such papers when this paper was revised in May 2013. We also identified 45 PhD dissertations from 2007 on with ‘robust’ in their title and belonging to the areas of operations research or management. Among those we chose to focus on the works with a primary focus on management science rather than system design or optimal control, which are broad fields that would deserve a review paper of their own, and papers that could be of interest to a large segment of the robust optimization research community. We also felt it was important to include PhD dissertations to identify these recent graduates as the new generation trained in robust optimization, whether they have remained in academia or joined industry. We have also added not-yet-published preprints identified through the online archive optimization-online.org to capture ongoing research efforts; however, we have not attempted to provide a comprehensive picture of works-in-progress, which may evolve substantially, including in their content, as they make their way through the peer-reviewing process. We have augmented this list by selecting, among the 883 works indexed by Web of Science that had either robustness (for 95 of them) or robust (for 788) in their title and belonged to the Operations Research and Management Science topic area, the ones best completing the coverage of the previously identified papers. While many additional works would have deserved inclusion, we feel that the works selected give an informative and comprehensive view of the state of robust optimization to date in the context of operations research and management science.
Section snippets
Definitions and basics
The term “robust optimization” has come to encompass several approaches to protecting the decision-maker against parameter ambiguity and stochastic uncertainty. At a high level, the manager must determine what it means for him to have a robust solution: is it a solution whose feasibility must be guaranteed for any realization of the uncertain parameters? or whose objective value must be guaranteed? or whose distance to optimality must be guaranteed? The main paradigm relies on worst-case
Applications of robust optimization
We describe below examples to which robust optimization has been applied. While an appealing feature of robust optimization is that it leads to models that can be solved using off-the-shelf software, it is worth pointing the existence of algebraic modeling tools that facilitate the formulation and subsequent analysis of robust optimization problems on the computer such as ROME (Goh & Sim, 2011), AIMMS (Paragon Decision Technologies, 2011) and Yalmip (Löfberg, 2012).
Conclusions
In this paper we have reviewed recent developments in the literature on robust optimization in operations research and management science. The large number of papers published on robustness and robust optimization since 2007 is a testimony to the vitality of this research area both from a theoretical perspective and in terms of practical applications. Key recent developments include: (i) an extensive body of work on robust decision-making under uncertainty with uncertain distributions, i.e.,
Acknowledgments
The authors would like to thank the Associate Editor and three anonymous referees for their insightful comments and suggestions.
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Work supported in part by a one-month Visiting Professor Position at Université Paris-Dauphine, 2012 and 2013.