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Recent advances in robust optimization: An overview

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  • Gabrel, Virginie
  • Murat, Cécile
  • Thiele, Aurélie

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.

Suggested Citation

  • Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
  • Handle: RePEc:eee:ejores:v:235:y:2014:i:3:p:471-483
    DOI: 10.1016/j.ejor.2013.09.036
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    1. Johannes Hörner & Stefano Lovo, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Econometrica, Econometric Society, vol. 77(2), pages 453-487, March.
    2. Gülpınar, Nalan & Pachamanova, Dessislava & Çanakoğlu, Ethem, 2013. "Robust strategies for facility location under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(1), pages 21-35.
    3. Virginie Gabrel & Cécile Murat & Lei Wu, 2013. "New models for the robust shortest path problem: complexity, resolution and generalization," Annals of Operations Research, Springer, vol. 207(1), pages 97-120, August.
    4. Tao Yao & Supreet Mandala & Byung Chung, 2009. "Evacuation Transportation Planning Under Uncertainty: A Robust Optimization Approach," Networks and Spatial Economics, Springer, vol. 9(2), pages 171-189, June.
    5. Mian Li & Steven Gabriel & Yohan Shim & Shapour Azarm, 2011. "Interval Uncertainty-Based Robust Optimization for Convex and Non-Convex Quadratic Programs with Applications in Network Infrastructure Planning," Networks and Spatial Economics, Springer, vol. 11(1), pages 159-191, March.
    6. Zymler, Steve & Rustem, Berç & Kuhn, Daniel, 2011. "Robust portfolio optimization with derivative insurance guarantees," European Journal of Operational Research, Elsevier, vol. 210(2), pages 410-424, April.
    7. Gorissen, B.L. & Ben-Tal, A. & Blanc, J.P.C. & den Hertog, D., 2012. "A New Method for Deriving Robust and Globalized Robust Solutions of Uncertain Linear Conic Optimization Problems Having General Convex Uncertainty Sets," Discussion Paper 2012-076, Tilburg University, Center for Economic Research.
    8. Ben-Tal, Aharon & Chung, Byung Do & Mandala, Supreet Reddy & Yao, Tao, 2011. "Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1177-1189, September.
    9. Liesiö, Juuso & Mild, Pekka & Salo, Ahti, 2008. "Robust portfolio modeling with incomplete cost information and project interdependencies," European Journal of Operational Research, Elsevier, vol. 190(3), pages 679-695, November.
    10. Nemirovski, Arkadi, 2012. "On safe tractable approximations of chance constraints," European Journal of Operational Research, Elsevier, vol. 219(3), pages 707-718.
    11. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2008. "Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization," Management Science, INFORMS, vol. 54(3), pages 573-585, March.
    12. Werners, Brigitte & Wülfing, Thomas, 2010. "Robust optimization of internal transports at a parcel sorting center operated by Deutsche Post World Net," European Journal of Operational Research, Elsevier, vol. 201(2), pages 419-426, March.
    13. Michel Minoux, 2011. "On 2-stage robust LP with RHS uncertainty: complexity results and applications," Journal of Global Optimization, Springer, vol. 49(3), pages 521-537, March.
    14. J. Lasserre, 2011. "Min-max and robust polynomial optimization," Journal of Global Optimization, Springer, vol. 51(1), pages 1-10, September.
    15. HazIr, Öncü & Haouari, Mohamed & Erel, Erdal, 2010. "Robust scheduling and robustness measures for the discrete time/cost trade-off problem," European Journal of Operational Research, Elsevier, vol. 207(2), pages 633-643, December.
    16. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
    17. Huang, Dashan & Zhu, Shushang & Fabozzi, Frank J. & Fukushima, Masao, 2010. "Portfolio selection under distributional uncertainty: A relative robust CVaR approach," European Journal of Operational Research, Elsevier, vol. 203(1), pages 185-194, May.
    18. Steve Zymler & Daniel Kuhn & Berç Rustem, 2013. "Worst-Case Value at Risk of Nonlinear Portfolios," Management Science, INFORMS, vol. 59(1), pages 172-188, July.
    19. Driouchi, Tarik & Leseure, Michel & Bennett, David, 2009. "A robustness framework for monitoring real options under uncertainty," Omega, Elsevier, vol. 37(3), pages 698-710, June.
    20. Gulpinar, Nalan & Rustem, Berc, 2007. "Worst-case robust decisions for multi-period mean-variance portfolio optimization," European Journal of Operational Research, Elsevier, vol. 183(3), pages 981-1000, December.
    21. Aharon, Ben-Tal & Boaz, Golany & Shimrit, Shtern, 2009. "Robust multi-echelon multi-period inventory control," European Journal of Operational Research, Elsevier, vol. 199(3), pages 922-935, December.
    22. Chung, Byung Do & Yao, Tao & Friesz, Terry L. & Liu, Hongcheng, 2012. "Dynamic congestion pricing with demand uncertainty: A robust optimization approach," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1504-1518.
    23. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    24. Nguyen, Tri-Dung & Lo, Andrew W., 2012. "Robust ranking and portfolio optimization," European Journal of Operational Research, Elsevier, vol. 221(2), pages 407-416.
    25. Isabelle Huault & V. Perret & S. Charreire-Petit, 2007. "Management," Post-Print halshs-00337676, HAL.
    26. Ng, Tsan Sheng & Sun, Yang & Fowler, John, 2010. "Semiconductor lot allocation using robust optimization," European Journal of Operational Research, Elsevier, vol. 205(3), pages 557-570, September.
    27. Marcus Ang & Yun Fong Lim & Melvyn Sim, 2012. "Robust Storage Assignment in Unit-Load Warehouses," Management Science, INFORMS, vol. 58(11), pages 2114-2130, November.
    28. Kai Ye & Panos Parpas & Berç Rustem, 2012. "Robust portfolio optimization: a conic programming approach," Computational Optimization and Applications, Springer, vol. 52(2), pages 463-481, June.
    29. Georgia Perakis & Guillaume Roels, 2010. "Robust Controls for Network Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 12(1), pages 56-76, November.
    30. Schneider, S. & Shabalin, P. & Bichler, M., 2010. "On the robustness of non-linear personalized price combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 206(1), pages 248-259, October.
    31. Laporte, Gilbert & Mesa, Juan A. & Perea, Federico, 2010. "A game theoretic framework for the robust railway transit network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 447-459, May.
    32. Gregory, Christine & Darby-Dowman, Ken & Mitra, Gautam, 2011. "Robust optimization and portfolio selection: The cost of robustness," European Journal of Operational Research, Elsevier, vol. 212(2), pages 417-428, July.
    33. Ben-Tal, A. & den Hertog, D., 2011. "Immunizing Conic Quadratic Optimization Problems Against Implementation Errors," Discussion Paper 2011-060, Tilburg University, Center for Economic Research.
    34. Fertis, Apostolos & Baes, Michel & Lüthi, Hans-Jakob, 2012. "Robust risk management," European Journal of Operational Research, Elsevier, vol. 222(3), pages 663-672.
    35. Akiko Takeda & Shunsuke Taguchi & Tsutomu Tanaka, 2010. "A relaxation algorithm with a probabilistic guarantee for robust deviation optimization," Computational Optimization and Applications, Springer, vol. 47(1), pages 1-31, September.
    36. F. Leibfritz & J. Maruhn, 2009. "A successive SDP-NSDP approach to a robust optimization problem in finance," Computational Optimization and Applications, Springer, vol. 44(3), pages 443-466, December.
    37. Blanquero, R. & Carrizosa, E. & Hendrix, E.M.T., 2011. "Locating a competitive facility in the plane with a robustness criterion," European Journal of Operational Research, Elsevier, vol. 215(1), pages 21-24, November.
    38. Alumur, Sibel A. & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2012. "Hub location under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 46(4), pages 529-543.
    39. Kawas, Ban & Thiele, Aurélie, 2011. "Short sales in Log-robust portfolio management," European Journal of Operational Research, Elsevier, vol. 215(3), pages 651-661, December.
    40. Roy, Bernard, 2010. "Robustness in operational research and decision aiding: A multi-faceted issue," European Journal of Operational Research, Elsevier, vol. 200(3), pages 629-638, February.
    41. Ben-Tal, A. & den Hertog, D. & Vial, J.P., 2012. "Deriving Robust Counterparts of Nonlinear Uncertain Inequalities," Discussion Paper 2012-053, Tilburg University, Center for Economic Research.
    42. Goh, Joel Weiqiang & Lim, Kian Guan & Sim, Melvyn & Zhang, Weina, 2012. "Portfolio value-at-risk optimization for asymmetrically distributed asset returns," European Journal of Operational Research, Elsevier, vol. 221(2), pages 397-406.
    43. Dimitris Bertsimas & Omid Nohadani, 2010. "Robust optimization with simulated annealing," Journal of Global Optimization, Springer, vol. 48(2), pages 323-334, October.
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