Invited Review
Recent advances in robust optimization: An overview

https://doi.org/10.1016/j.ejor.2013.09.036Get rights and content

Highlights

  • Overview of papers on robust optimization published since 2007.

  • Give an informative and comprehensive view of the robust optimization domain.

  • Vitality of this research area with theoretical and practical studies.

Abstract

This paper provides an overview of developments in robust optimization since 2007. It seeks to give a representative picture of the research topics most explored in recent years, highlight common themes in the investigations of independent research teams and highlight the contributions of rising as well as established researchers both to the theory of robust optimization and its practice. With respect to the theory of robust optimization, this paper reviews recent results on the cases without and with recourse, i.e., the static and dynamic settings, as well as the connection with stochastic optimization and risk theory, the concept of distributionally robust optimization, and findings in robust nonlinear optimization. With respect to the practice of robust optimization, we consider a broad spectrum of applications, in particular inventory and logistics, finance, revenue management, but also queueing networks, machine learning, energy systems and the public good. Key developments in the period from 2007 to present include: (i) an extensive body of work on robust decision-making under uncertainty with uncertain distributions, i.e., “robustifying” stochastic optimization, (ii) a greater connection with decision sciences by linking uncertainty sets to risk theory, (iii) further results on nonlinear optimization and sequential decision-making and (iv) besides more work on established families of examples such as robust inventory and revenue management, the addition to the robust optimization literature of new application areas, especially energy systems and the public good.

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.

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