Optimization under Uncertainty

Typically, input data for an optimization problem is fraught with uncertainties, especially when input fluctuates, when it is derived from measurements or forecast from historically observed data. Stochastic optimization stands as a traditional modeling and solution approach in this context, but it usually requires knowledge of the probability distribution of uncertain parameters. However, as these are often unknown themselves, there is intensive research at the intersection of stochastic and robust optimization. Robust optimization has established itself in uncertainty optimization over the past decades and is under intensive investigation. Robust optimization determines solutions that remain feasible as long as input data fall within pre-defined, “typical” uncertainties and in addition yield best guaranteed objective values. Whereas it is known that under appropriate modelling assumptions, (mixed-integer) linear and combinatorial optimization problems allow the derivation of algorithmically tractable robust counterparts, the resulting exponentially large or even semi-infinite robust problem formulations are often already NP-hard in restricted settings.

Natural research questions arise regarding the necessary size and geometry of uncertainty sets and a suitable choice of optimization models that allow for practically efficient solution methods. The goal is to obtain algorithmically tractable robust optimization models and corresponding algorithms, for example, through reformulations, decomposition, or approximation approaches so that practically efficient methodologies can be derived. In our research, we develop novel structural insights and resulting algorithms for combinatorial, (mixed-integer) linear and nonlinear robust optimization. We also investigate new approaches for distributionally robust optimization problems, in particular when iteratively new data or information can be integrated over time.

MINOA: Mixed-Integer Non-Linear Optimisation: Algorithms and Applications

MINOA will train a new generation of scientists in the rather young but fast growing field of mixed-integer nonlinear optimisation applications and algorithms, by enhancing research-related and transferable competences and exposure to the non-academic sector. Through self-organizing training events, the young researchers take responsibility at an early stage of their career. The settings provided by the hosting institutions empower the ESRs to become independent and creative researchers, which increases their employability. Mobility and internationality is provided through secondments within our international consortium that includes institutions from 6 European countries. Furthermore, network-wide events take place regularly.
Details

Participants: Frauke Liers, Martin Schmidt, Dennis Adelhütte