Bridging the gap between theory and practice can be challenging. Although mathematical models can often capture the key features to describe natural or human-made complex systems, their precision relies on the accuracy of the chosen model parameters. Unfortunately, these parameters itself are prone to errors such as measurement errors in the influx of material into a reactor or fluctuations in renewable energy production due to weather effects. Moreover, they might also originate from ill-behavior, e.g., because the data inserted into the model was corrupted by a cyberattack.
It is therefore of critical importance that input data is assessed with great care and if doubts about its accuracy remain, the optimization model is aware and resilient against potential inaccuracies. To aid in this undertaking, we contribute with two main research directions.
Data-Driven Optimization
On the one hand, we aim to utilize modern Data Science tools, such as (un-)supervised learning, particularly via neural networks, to gather data-driven information about the features in question. Subsequently, we incorporate the data-driven information to enhance classical optimization models. This often allows to capture features, that are out of reach with classical modeling techniques, but comes at the price that the obtained information may be uncertain and has to be critically assessed. This assessment can be done either within the discipline of optimization, e.g. by robustification or interdisciplinary, by experimental verification. Applications include image recognition or efficient power system operation.
Robust Optimization
On the other hand, we aim to capture uncertainties of parameters within existing deterministic models and incorporate information about their distribution. There are two main research questions within this direction:
- How can we take decisions that are robust against detrimental scenarios?
- How can we adjust effectively to a specific set of scenarios?
Game-theoretically, both questions can be seen as two players playing each other, where in question one the decision maker has the first move and in question two a potential adversarial player moves first. This structure is present in a variety of fields, and therefore has applications in discrete geometry, chemical engineering, electrical engineering or logistics – to name a few.
