Decision-Dependent Robust OPtimization – DDROP

The robust optimization framework allows addressing uncertainty in optimization problems through bounded uncertainty sets, thus avoiding the need of the precise knowledge of probability distributions. Recently, there has been considerable methodological advances in this field under the assumption that the uncertain parameters are independent of the decisions. However, many real-life decision-making problems include some form of interaction between the actions of the decision-maker and the realization of uncertain parameters. These problems have mostly been neglected in the literature despite their theoretical and applied interest, leaving many research questions open.
With the objective of filling this gap, this project proposes the study and solution of robust optimization models formalizing such interactions under a single mathematical framework with decision-dependent uncertainty sets. This encapsulates general models of particular interest in this project, namely, uncertainty reduction and information discovery.
The first models the mitigation of the impact of uncertainty through proactive actions that limit the size of the uncertainty set, while the second models the possibility of exploring some uncertain parameters before the final decision-making stage, typically through investment. These problems are still not well understood in the literature and solution algorithms are lacking.
This project aims to improve the state of the art in terms of the understanding and solution of robust optimization problems with decision-dependent uncertainty sets by studying the complexity and solution algorithms for these problems. We will explore their connections with paradigms such as bilevel programming and adjustable robust optimization and develop solution algorithms based on reformulations, decomposition algorithms and machine learning. Our algorithmic developments will specifically focus on uncertainty reduction, information discovery and related applications.