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The State of Robust Optimization

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Robustness Analysis in Decision Aiding, Optimization, and Analytics

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 241))

Abstract

This survey presents a broad overview of the developments in robust optimization over the past 5 years, i.e., between 2011 and 2015. We highlight the advancement of knowledge both with respect to the theory of robust optimization and application areas. From a theoretical standpoint, we describe novel findings in static and multi-stage decision making, the connection with stochastic optimization, distributional robustness and robust nonlinear optimization. In terms of application areas, we consider inventory and logistics, finance, revenue management and health care. We conclude with guidelines for researchers interested in immunizing their problem against uncertainty.

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References

  1. Alem, D.J., Morabito, R.: Production planning in furniture settings via robust optimization. Comput. Oper. Res. 39 (2), 139–150 (2012)

    Article  Google Scholar 

  2. Alumur, S.A., Nickel, S., Saldanha-da Gama, F.: Hub location under uncertainty. Transp. Res. Part B Methodol. 46 (4), 529–543 (2012).

    Article  Google Scholar 

  3. Alvarez, P.P., Vera, J.R.: Application of robust optimization to the sawmill planning problem. Ann. Oper. Res. 219 (1), 457–475 (2014)

    Article  Google Scholar 

  4. Alvarez-Miranda, E., Ljubic, I., Toth, P.: A note on the Bertsimas & Sim algorithm for robust combinatorial optimization problems. 4OR-A Q. J. Oper. Res. 11 (4), 349–360 (2013)

    Google Scholar 

  5. Ang, M., Lim, Y.F., Sim, M.: Robust storage assignment in unit-load warehouses. Manag. Sci. 58 (11), 2114–2130 (2012)

    Article  Google Scholar 

  6. Aouam, T., Brahimi, N.: Integrated production planning and order acceptance under uncertainty: a robust optimization approach. Eur. J. Oper. Res. 228 (3), 504–515 (2013)

    Article  Google Scholar 

  7. Ashayeri, J., Ma, N., Sotirov, R.: Supply chain downsizing under bankruptcy: a robust optimization approach. Int. J. Prod. Econ. 154, 1–15 (2014)

    Article  Google Scholar 

  8. Bandi, C., Bertsimas, D.: Tractable stochastic analysis in high dimensions via robust optimization. Math. Program. 134 (1, SI), 23–70 (2012)

    Google Scholar 

  9. Bandi, C., Bertsimas, D.: Optimal design for multi-item auctions: a robust optimization approach. Math. Oper. Res. 39 (4), 1012–1038 (2014)

    Article  Google Scholar 

  10. Baron, O., Milner, J., Naseraldin, H.: Facility location: a robust optimization approach. Prod. Oper. Manag. 20 (5), 772–785 (2011)

    Article  Google Scholar 

  11. Bayraksan, G., Love, D.: Data-driven stochastic programming using phi-divergences. INFORMS TutORials on operations research, pp. 1–19 (2015)

    Google Scholar 

  12. Beliakov, G., Kelarev, A.: Global non-smooth optimization in robust multivariate regression. Optim. Methods Softw. 28 (1), 124–138 (2013)

    Article  Google Scholar 

  13. Ben-Tal, A., den Hertog, D.: Immunizing conic quadratic optimization problems against implementation errors. Technical Report. Tilburg University (2011)

    Google Scholar 

  14. Ben-Tal, A., Nemirovski, A.: Robust convex optimization. Math. Oper. Res. 23, 769–805 (1998)

    Article  Google Scholar 

  15. Ben-Tal, A., Nemirovski, A.: Robust solutions of uncertain linear programs. Oper. Res. Lett. 25, 1–13 (1999)

    Article  Google Scholar 

  16. Ben-Tal, A., Nemirovski, A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Program. 88, 411–424 (2000)

    Article  Google Scholar 

  17. Ben-Tal, A., Nemirovski, A.: Selected topics in robust convex optimization. Math. Program. 112, 125–158 (2011)

    Article  Google Scholar 

  18. Ben-Tal, A., El-Ghaoui, L., Nemirovski, A.: Robust optimization. Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2009)

    Book  Google Scholar 

  19. Ben-Tal, A., Bhadra, S., Bhattacharyya, C., Nath, J.S.: Chance constrained uncertain classification via robust optimization. Math. Program. 127 (1, SI), 145–173 (2011)

    Google Scholar 

  20. Ben-Tal, A., Do Chung, B., Mandala, S.R., Yao, T.: Robust optimization for emergency logistics planning: risk mitigation in humanitarian relief supply chains. Transp. Res. B Methodol. 45 (8, SI), 1177–1189 (2011)

    Google Scholar 

  21. Ben-Tal, A., den Hertog, D., De Waegenaere, A., Melenberg, B., Rennen, G.: Robust solutions of optimization problems affected by uncertain probabilities. Manag. Sci. 59 (2), 341–357 (2013)

    Google Scholar 

  22. Ben-Tal, A., den Hertog, D., Vial, J.P.: Deriving robust counterparts of nonlinear uncertain inequalities. Math. Program. 149, 265–299 (2015)

    Article  Google Scholar 

  23. Ben-Tal, A., Hazan, E., Koren, T., Mannor, S.: Oracle-based robust optimization via online learning. Oper. Res. 63 (3), 628–638 (2015)

    Article  Google Scholar 

  24. Bertsimas, D., Goyal, V.: On the approximability of adjustable robust convex optimization under uncertainty. Math. Meth. Oper. Res. 77 (3), 323–343 (2013)

    Article  Google Scholar 

  25. Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52 (1), 35–53 (2004)

    Article  Google Scholar 

  26. Bertsimas, D., Takeda, A.: Optimizing over coherent risk measures and non-convexities: a robust mixed integer optimization approach. Comput. Optim. Appl. 62 (3), 613–639 (2015)

    Article  Google Scholar 

  27. Bertsimas, D., Goyal, V., Sun, X.: A geometric characterization of the power of finite adaptability in multistage stochastic and adaptive optimization. Math. Oper. Res. 36 (1), 24–54 (2011)

    Article  Google Scholar 

  28. Bertsimas, D., Goyal, V., Lu, B.Y.: A tight characterization of the performance of static solutions in two-stage adjustable robust linear optimization. Math. Program. 150 (2), 281–319 (2015)

    Article  Google Scholar 

  29. Cacchiani, V., Toth, P.: Nominal and robust train timetabling problems. Eur. J. Oper. Res. 219 (3), 727–737 (2012)

    Article  Google Scholar 

  30. Cacchiani, V., Caprara, A., Fischetti, M.: A Lagrangian heuristic for robustness, with an application to train timetabling. Transp. Sci. 46 (1), 124–133 (2012)

    Article  Google Scholar 

  31. Caramanis, C., Mannor, S., Xu, H.: Robust optimization in machine learning. In: Optimization in Machine Learning, pp. 369–402 MIT Press, Cambridge, MA (2011)

    Google Scholar 

  32. Carlsson, D., Flisberg, P., Roennqvist, M.: Using robust optimization for distribution and inventory planning for a large pulp producer. Comput. Oper. Res. 44, 214–225 (2014)

    Article  Google Scholar 

  33. Chan, T.C.Y., Misic, V.V.: Adaptive and robust radiation therapy optimization for lung cancer. Eur. J. Oper. Res. 231 (3), 745–756 (2013)

    Article  Google Scholar 

  34. Chan, T.C.Y., Mahmoudzadeh, H., Purdie, T.G.: A robust-CVaR optimization approach with application to breast cancer therapy. Eur. J. Oper. Res. 238 (3), 876–885 (2014)

    Article  Google Scholar 

  35. Charnes, A., Cooper, W.W.: Chance-constrained programming. Manag. Sci. 6 (1), 73–79 (1959)

    Article  Google Scholar 

  36. Chassein, A.B., Goerigk, M.: A new bound for the midpoint solution in minmax regret optimization with an application to the robust shortest path problem. Eur. J. Oper. Res. 244 (3), 739–747 (2015)

    Article  Google Scholar 

  37. Che, A., Feng, J., Chen, H., Chu, C.: Robust optimization for the cyclic hoist scheduling problem. Eur. J. Oper. Res. 240 (3), 627–636 (2015)

    Article  Google Scholar 

  38. Chen, L., He, S., Zhang, S.: Tight bounds for some risk measures, with applications to robust portfolio selection. Oper. Res. 59 (4), 847–865 (2011)

    Article  Google Scholar 

  39. Classen, G., Koster, A.M.C.A., Schmeink, A.: A robust optimisation model and cutting planes for the planning of energy-efficient wireless networks. Comput. Oper. Res. 40 (1), 80–90 (2013)

    Article  Google Scholar 

  40. Delage, E., Iancu, D.: Robust multistage decision-making. INFORMS TutORials, pp. 20–46 (2015)

    Google Scholar 

  41. Doan, X.V., Kruk, S., Wolkowicz, H.: A robust algorithm for semidefinite programming. Optim. Methods Softw. 27 (4–5, SI), 667–693 (2012)

    Google Scholar 

  42. Dupacova, J., Kopa, M.: Robustness in stochastic programs with risk constraints. Ann. Oper. Res. 200 (1), 55–74 (2012)

    Article  Google Scholar 

  43. Duzgun, R., Thiele, A.: Robust binary optimization using a safe tractable approximation. Oper. Res. Lett. 43 (4), 445–449 (2015)

    Article  Google Scholar 

  44. Duzgun, R., Thiele, A.: Robust optimization with multiple ranges: theory and application to pharmaceutical project selection. In: Proceedings of the 14th INFORMS ICS Conference, pp. 103–118 (2015)

    Google Scholar 

  45. El-Ghaoui, L., Lebret, H.: Robust solutions to least-squares problems with uncertain data. SIAM J. Matrix Anal. Appl. 18 (4), 1035–1064 (1997)

    Article  Google Scholar 

  46. El-Ghaoui, L., Oustry, F., Lebret, H.: Robust solutions to uncertain semidefinite programs. SIAM J. Optim. 9 (1), 33–52 (1998)

    Article  Google Scholar 

  47. Fang, J., Gao, Y., Sun, G., Xu, C., Li, Q.: Multiobjective robust design optimization of fatigue life for a truck cab. Reliab. Eng. Syst. Saf. 135, 1–8 (2015)

    Article  Google Scholar 

  48. Fertis, A., Baes, M., Luethi, H.J.: Robust risk management. Eur. J. Oper. Res. 222 (3), 663–672 (2012)

    Article  Google Scholar 

  49. Fliege, J., Werner, R.: Robust multiobjective optimization & applications in portfolio optimization. Eur. J. Oper. Res. 234 (2), 422–433 (2014)

    Article  Google Scholar 

  50. Gabrel, V., Murat, C., Thiele, A.: Recent advances in robust optimization: an overview. Eur. J. Oper. Res. 235 (3), 471–483 (2014)

    Article  Google Scholar 

  51. Gabrel, V., Lacroix, M., Murat, C., Remli, N.: Robust location transportation problems under uncertain demands. Discret. Appl. Math. 164 (1, SI), 100–111 (2014). 1st International Symposium on Combinatorial Optimization (ISCO), Hammamet, TUNISIA, Mar 24–26, 2010

    Google Scholar 

  52. Galli, L.: Combinatorial and robust optimisation models and algorithms for railway applications. 4OR-A Q. J. Oper. Res. 9 (2), 215–218 (2011)

    Google Scholar 

  53. Ghezavati, V., Soltanzadeh, F., Hafezalkotob, A.: Optimization of reliability for a hierarchical facility location problem under disaster relief situations by a chance-constrained programming and robust optimization. Proc. Inst. Mech. Eng. O J Risk Reliab. 229 (6), 542–555 (2015)

    Google Scholar 

  54. Goh, J., Sim, M.: Distributionally robust optimization and its tractable approximations. Oper. Res. 58, 902–917 (2010)

    Article  Google Scholar 

  55. Golias, M., Portal, I., Konur, D., Kaisar, E., Kolomvos, G.: Robust berth scheduling at marine container terminals via hierarchical optimization. Comput. Oper. Res. 41, 412–422 (2014)

    Article  Google Scholar 

  56. Gorissen, B.L., Yanikoglu, I., den Hertog, D.: A practical guide to robust optimization. OMEGA Int. J. Manag. Sci. 53, 124–137 (2015)

    Article  Google Scholar 

  57. Goryashko, A.P., Nemirovski, A.S.: Robust energy cost optimization of water distribution system with uncertain demand. Autom. Remote Control 75 (10), 1754–1769 (2014)

    Article  Google Scholar 

  58. Guelpinar, N., Pachamanova, D., Canakoglu, E.: Robust strategies for facility location under uncertainty. Eur. J. Oper. Res. 225 (1), 21–35 (2013)

    Article  Google Scholar 

  59. Hanasusanto, G., Kuhn, D., Wallace, S., Zymler, S.: Distributional robust multi-item newsvendor problems with multimodal demand distributions. Math. Prog. 152, 1–32 (2015)

    Article  Google Scholar 

  60. Hanasusanto, G., Kuhn, D., Wiesemann, W.: K-adaptability in two-stage robust binary programming. Oper. Res. 63, 877–891 (2015)

    Article  Google Scholar 

  61. Hassanzadeh, F., Nemati, H., Sun, M.: Robust optimization for interactive multiobjective programming with imprecise information applied to R&D project portfolio selection. Eur. J. Oper. Res. 238 (1), 41–53 (2014)

    Article  Google Scholar 

  62. Holte, M., Mannino, C.: The implementor/adversary algorithm for the cyclic and robust scheduling problem in health-care. Eur. J. Oper. Res. 226, 551–559 (2013)

    Article  Google Scholar 

  63. Houska, B., Diehl, M.: Nonlinear robust optimization via sequential convex bilevel programming. Math. Prog. 142 (1–2), 539–577 (2013)

    Article  Google Scholar 

  64. Hu, J., Mehrotra, S.: Robust and stochastically weighted multiobjective optimization models and reformulations. Oper. Res. 60 (4), 936–953 (2012)

    Article  Google Scholar 

  65. Hu, J., Mehrotra, S.: Robust decision making over a set of random targets or risk-averse utilities with an application to portfolio optimization. IIE Trans. 47 (4, SI), 358–372 (2015)

    Google Scholar 

  66. Iancu, D.A., Trichakis, N.: Pareto efficiency in robust optimization. Manag. Sci. 60 (1), 130–147 (2014)

    Article  Google Scholar 

  67. Iancu, D.A., Sharma, M., Sviridenko, M.: Supermodularity and affine policies in dynamic robust optimization. Oper. Res. 61 (4), 941–956 (2013)

    Article  Google Scholar 

  68. Ide, J., Tiedemann, M., Westphal, S., Haiduk, F.: An application of deterministic and robust optimization in the wood cutting industry. 4OR-A Q. J. Oper. Res. 13 (1), 35–57 (2015)

    Google Scholar 

  69. Jeyakumar, V., Li, G.Y.: Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization. Math. Prog. 147 (1–2), 171–206 (2014)

    Article  Google Scholar 

  70. Jeyakumar, V., Li, G., Suthaharan, S.: Support vector machine classifiers with uncertain knowledge sets via robust optimization. Optimization 63 (7), 1099–1116 (2014)

    Article  Google Scholar 

  71. Jiang, H., Netessine, S., Savin, S.: Technical note: Robust newsvendor competition under asymmetric information. Oper. Res. 59, 254–261 (2011)

    Article  Google Scholar 

  72. Jiang, R., Wang, J., Guan, Y.: Robust unit commitment with wind power and pumped storage hydro. IEEE Trans. Power Syst. 27 (2), 800–810 (2012)

    Article  Google Scholar 

  73. Kakouris, I., Rustem, B.: Robust portfolio optimization with copulas. Eur. J. Oper. Res. 235 (1), 28–37 (2014)

    Article  Google Scholar 

  74. Kang, S.C., Brisimi, T.S., Paschalidis, I.C.: Distribution-dependent robust linear optimization with applications to inventory control. Ann. Oper. Res. 231 (1), 229–263 (2015)

    Article  Google Scholar 

  75. Kapsos, M., Christofides, N., Rustem, B.: Worst-case robust omega ratio. Eur. J. Oper. Res. 234, 499–507 (2014)

    Article  Google Scholar 

  76. Kawas, B., Thiele, A.: A log-robust optimization approach to portfolio management. OR Spectr. 33 (1), 207–233 (2011)

    Article  Google Scholar 

  77. Kawas, B., Thiele, A.: Short sales in Log-robust portfolio management. Eur. J. Oper. Res. 215 (3), 651–661 (2011)

    Article  Google Scholar 

  78. Kawas, B., Laumanns, M., Pratsini, E.: A robust optimization approach to enhancing reliability in production planning under non-compliance risks. OR Spectr. 35 (4), 835–865 (2013)

    Article  Google Scholar 

  79. Koebis, E.: On robust optimization relations between scalar robust optimization and unconstrained multicriteria optimization. J. Optim. Theory Appl. 167 (3), 969–984 (2015)

    Article  Google Scholar 

  80. Kuhn, D., Wiesemann, W., Georghiou, A.: Primal and dual linear decision rules in stochastic and robust optimization. Math. Prog. 130 (1), 177–209 (2011)

    Article  Google Scholar 

  81. Lagos, G., Espinoza, D., Moreno, E., Vielma, J.P.: Restricted risk measures and robust optimization. Eur. J. Oper. Res. 241 (3), 771–782 (2015)

    Article  Google Scholar 

  82. Lassiter, K., Khademi, A., Taaffe, K.M.: A robust optimization approach to volunteer management in humanitarian crises. Int. J. Prod. Econ. 163, 97–111 (2015)

    Article  Google Scholar 

  83. Li, M., Gabriel, S.A., Shim, Y., Azarm, S.: Interval uncertainty-based robust optimization for convex and non-convex quadratic programs with applications in network infrastructure planning. Netw. Spat. Econ. 11 (1), 159–191 (2011)

    Article  Google Scholar 

  84. Lima, R.M., Novais, A.Q., Conejo, A.J.: Weekly self-scheduling, forward contracting, and pool involvement for an electricity producer. An adaptive robust optimization approach. Eur. J. Oper. Res. 240 (2), 457–475 (2015)

    Google Scholar 

  85. Long, D.Z., Qi, J.: Distributionally robust discrete optimization with entropic value-at-risk. Oper. Res. Lett. 42 (8), 532–538 (2014)

    Article  Google Scholar 

  86. Maillet, B., Tokpavi, S., Vaucher, B.: Global minimum variance portfolio optimisation under some model risk: a robust regression-based approach. Eur. J. Oper. Res. 244 (1), 289–299 (2015)

    Article  Google Scholar 

  87. Marzban, S., Mahootchi, M., Khamseh, A.A.: Developing a multi-period robust optimization model considering American style options. Ann. Oper. Res. 233 (1), 305–320 (2015)

    Article  Google Scholar 

  88. Meng, F., Qi, J., Zhang, M., Ang, J., Chu, S., Sim, M.: A robust optimization model for managing elective admission in a public hospital. Oper. Res. 63, 1452–1467 (2015)

    Article  Google Scholar 

  89. Minoux, M.: Two-stage robust optimization, state-space representable uncertainty and applications. RAIRO Oper. Res. 48 (4), 455–475 (2014)

    Article  Google Scholar 

  90. Moon, Y., Yao, T.: A robust mean absolute deviation model for portfolio optimization. Comput. Oper. Res. 38 (9), 1251–1258 (2011)

    Article  Google Scholar 

  91. Mulvey, J., Vanderbei, R., Zenios, S.: Robust optimization of large-scale systems. Oper. Res. 43, 264–281 (1995)

    Article  Google Scholar 

  92. Najafi, M., Eshghi, K., Dullaert, W.: A multi-objective robust optimization model for logistics planning in the earthquake response phase. Transp. Res. Part E Log. 49 (1), 217–249 (2013)

    Article  Google Scholar 

  93. Nemirovski, A.: On safe tractable approximations of chance constraints. Eur. J. Oper. Res. 219, 707–718 (2012)

    Article  Google Scholar 

  94. Nguyen, T.D., Lo, A.W.: Robust ranking and portfolio optimization. Eur. J. Oper. Res. 221 (2), 407–416 (2012)

    Article  Google Scholar 

  95. Nha, V.T., Shin, S., Jeong, S.H.: Lexicographical dynamic goal programming approach to a robust design optimization within the pharmaceutical environment. Eur. J. Oper. Res. 229 (2), 505–517 (2013)

    Article  Google Scholar 

  96. Ozmen, A., Weber, G.W., Karimov, A.: A new robust optimization tool applied on financial data. Pac. J. Optim. 9 (3), 535–552 (2013)

    Google Scholar 

  97. Paul, J.A., Wang, X.J.: Robust optimization for United States Department of Agriculture food aid bid allocations. Transp. Res. Part E Log. 82, 129–146 (2015)

    Article  Google Scholar 

  98. Poss, M.: Robust combinatorial optimization with variable budgeted uncertainty. 4OR-A Q. J. Oper. Res. 11 (1), 75–92 (2013)

    Google Scholar 

  99. Qiu, R., Shang, J.: Robust optimisation for risk-averse multi-period inventory decision with partial demand distribution information. Int. J. Prod. Res. 52 (24), 7472–7495 (2014)

    Article  Google Scholar 

  100. Qiu, R., Shang, J., Huang, X.: Robust inventory decision under distribution uncertainty: a CVaR-based optimization approach. Int. J. Prod. Econ. 153, 13–23 (2014)

    Article  Google Scholar 

  101. Remli, N., Rekik, M.: A robust winner determination problem for combinatorial transportation auctions under uncertain shipment volumes. Transp. Res. Part C Emerg. Technol. 35 (SI), 204–217 (2013)

    Google Scholar 

  102. Sauma, E., Traub, F., Vera, J.: A Robust optimization approach to assess the effect of delays in the connection-to-the-grid time of new generation power plants over transmission expansion planning. Ann. Oper. Res. 229 (1), 703–741 (2015)

    Article  Google Scholar 

  103. Schoenlein, M., Makuschewitz, T., Wirth, F., Scholz-Reiter, B.: Measurement and optimization of robust stability of multiclass queueing networks: applications in dynamic supply chains. Eur. J. Oper. Res. 229 (1), 179–189 (2013)

    Article  Google Scholar 

  104. Shapiro, A.: A dynamic programming approach to adjustable robust optimization. Oper. Res. Lett. 39 (2), 83–87 (2011)

    Article  Google Scholar 

  105. Shishebori, D., Babadi, A.Y.: Robust and reliable medical services network design under uncertain environment and system disruptions. Transp. Res. Part E Log. 77, 268–288 (2015)

    Article  Google Scholar 

  106. Sniedovich, M.: Fooled by local robustness. Risk Anal. 32, 1630–1637 (2012)

    Article  Google Scholar 

  107. Soyster, A.L.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21 (5), 1154–1157 (1973)

    Article  Google Scholar 

  108. Sun, H., Gao, Z., Szeto, W.Y., Long, J., Zhao, F.: A distributionally robust joint chance constrained optimization model for the dynamic network design problem under demand uncertainty. Netw. Spat. Econ. 14 (3–4), 409–433 (2014)

    Article  Google Scholar 

  109. Suzuki, S., Kuroiwa, D., Lee, G.M.: Surrogate duality for robust optimization. Eur. J. Oper. Res. 231 (2), 257–262 (2013)

    Article  Google Scholar 

  110. Tajik, N., Tavakkoli-Moghaddam, R., Vahdani, B., Mousavi, S.M.: A robust optimization approach for pollution routing problem with pickup and delivery under uncertainty. J. Manuf. Syst. 33 (2), 277–286 (2014)

    Article  Google Scholar 

  111. Tong, X., Wu, F.: Robust reward-risk ratio optimization with application in allocation of generation asset. Optimization 63 (11), 1761–1779 (2014)

    Article  Google Scholar 

  112. Varas, M., Maturana, S., Pascual, R., Vargas, I., Vera, J.: Scheduling production for a sawmill: a robust optimization approach. Int. J. Prod. Econ. 150, 37–51 (2014)

    Article  Google Scholar 

  113. Wiesemann, W., Kuhn, D., Rustem, B.: Robust Markov decision processes. Math. Oper. Res. 38 (1), 153–183 (2013)

    Article  Google Scholar 

  114. Wiesemann, W., Kuhn, D., Sim, M.: Distributionally robust convex optimization. Oper. Res. 62 (6), 1358–1376 (2014)

    Article  Google Scholar 

  115. Xu, H., Caramanis, C., Mannor, S.: A distributional interpretation of robust optimization. Math. Oper. Res. 37 (1), 95–110 (2012)

    Article  Google Scholar 

  116. Xu, H., Caramanis, C., Sanghavi, S.: Robust PCA via outlier pursuit. IEEE Trans. Inf. Theory 58 (5), 3047–3064 (2012)

    Article  Google Scholar 

  117. Ye, K., Parpas, P., Rustem, B.: Robust portfolio optimization: a conic programming approach. Comput. Optim. Appl. 52 (2), 463–481 (2012)

    Article  Google Scholar 

  118. Zeng, B., Zhao, L.: Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper. Res. Lett. 41 (5), 457–461 (2013)

    Article  Google Scholar 

  119. Zhen, L.: Task assignment under uncertainty: stochastic programming and robust optimisation approaches. Int. J. Prod. Res. 53 (5), 1487–1502 (2015)

    Article  Google Scholar 

  120. Zugno, M., Conejo, A.J.: A robust optimization approach to energy and reserve dispatch in electricity markets. Eur. J. Oper. Res. 247 (2), 659–671 (2015)

    Article  Google Scholar 

  121. Zymler, S., Kuhn, D., Rustem, B.: Distributionally robust joint chance constraints with second-order moment information. Math. Prog. 137 (1–2), 167–198 (2013)

    Article  Google Scholar 

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  1. Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, 18015, USA

    Seçil Sözüer & Aurélie C. Thiele

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  1. School of Production Engineering & Mgmt, Technical University of Crete, Chania, Greece

    Michael Doumpos

  2. School of Production Engineering & Mgmt, Technical University of Crete, Chania, Greece

    Constantin Zopounidis

  3. School of Production Engineering & Mgmt, Technical University of Crete, Chania, Greece

    Evangelos Grigoroudis

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Sözüer, S., Thiele, A.C. (2016). The State of Robust Optimization. In: Doumpos, M., Zopounidis, C., Grigoroudis, E. (eds) Robustness Analysis in Decision Aiding, Optimization, and Analytics. International Series in Operations Research & Management Science, vol 241. Springer, Cham. https://doi.org/10.1007/978-3-319-33121-8_5

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