(300c) Robust Optimization for Problems with Endogenous Uncertainty
Traditionally, the uncertainty set in RO is a constant set, being unaffected by the optimizerâs decisions. In many cases, however, this is not realistic, as oneâs decisions may affect the level and type of risk one is actually exposed to. These cases are referred to as cases of endogenous uncertainty , and they have been investigated thoroughly in the Stochastic Programming literature [4â7]. In contrast, how to best handle endogenous uncertainty has been a more recent endeavor in the field of RO .
In this talk, we review the state-of-the-art in RO for problems with endogenous uncertainty, and we present novel decision-dependent uncertainty sets to model these settings  as well as a computational framework to optimize in light of such sets. We also present extensive computational results from a number of benchmark problems, including multi-stage problems that involve decision-making with recourse [10-11].
 A. Ben-Tal, L. El Ghaoui, and A. Nemirovski, Robust optimization. Princeton University Press, 2009.
 Y. A. Guzman, L. R. Matthews, and C. A. Floudas, âNew A Priori and A Posteriori Probabilistic Bounds for Robust Counterpart Optimization: I. Unknown Probability Distributions,â Comp. Chem. Eng., vol. 84, pp. 568â598, 2016.
 T. W. JonsbrÃ¥ten, R. J. B. Wets, and D. L. Woodruff, âA class of stochastic programs with decision dependent random elements,â Ann. Oper. Res., vol. 82, pp. 83â106, 1998.
 V. Gupta and I. E. Grossmann, âA new decomposition algorithm for multistage stochastic programs with endogenous uncertainties,â Comput. Chem. Eng., vol. 62, pp. 62â79, 2014.
 V. Gupta and I. E. Grossmann, âSolution strategies for multistage stochastic programming with endogenous uncertainties,â Comput. Chem. Eng., vol. 35, no. 11, pp. 2235â2247, 2011.
 S. Solak, J. P. B. Clarke, E. L. Johnson, and E. R. Barnes, âOptimization of R&D project portfolios under endogenous uncertainty,â Eur. J. Oper. Res., vol. 207, no. 1, pp. 420â433, 2010.
 R. M. Apap and I. E. Grossmann, âModels and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties,â Manuscr. Prep., 2015.
 M. Poss, âRobust combinatorial optimization with variable cost uncertainty,â Eur. J. Oper. Res., vol. 237, no. 3, pp. 836â845, 2014.
 N. H. Lappas and C. E. Gounaris, âThe Use of Decision-dependent Uncertainty Sets in Robust Optimization,â Proc. FOCAPO-2017, paper F71, pp. 1â6, 2017.
 D. Bertsimas and A. Georghiou, âDesign of Near Optimal Decision Rules in Multistage Adaptive Mixed-Integer Optimization,â Oper. Res., vol. 63, no. 3, pp. 610â627, 2015.
 N. H. Lappas and C. E. Gounaris, âMulti-stage Adjustable Robust Optimization for Process Scheduling Under Uncertainty,â AIChE J., vol. 62, no. 5, pp. 1646â1667, 2016.