Data-driven Prediction of Relevant Scenarios for Robust Combinatorial Optimization

Optimization under uncertainty is an important research field especially due to its relevance in practical applications from operations research. In the real world many parameters of an optimization problem can be uncertain, e.g. the demands, returns or traffic situations or any other parameters which are not precisely known due to measurement or rounding errors. It was shown that hedging against possible perturbations in the problem parameters is essential, since already small perturbations can lead to a large violation of the constraints [BTEGN09]. Driven by the seminal works [Soy73, KY96, BTN98, BTN99, BS04] robust optimization evolved to be one of the most popular approaches to tackle uncertainty in optimization problems by finding solutions which are worst-case optimal and feasible for all parameters of a pre-defined uncertainty set; see [BBC11, BK18, GMT14] for a literature overview. Later the classical robust optimization approach was extended to the two-stage robust optimization approach (also called adaptive robust optimization) in [BTGGN04] which has been extensively studied from then on; see e.g.