Research made public.

Our research in the areas of operations research, mathematics, and computer science regularly appears in peer-reviewed scientific journals. Of course we also participate in international conferences and workshops. All our results are also freely available as preprints.

319
Talks
61
Preprints
126
Publications

Integer Programming and Combinatorial Optimization

Buch-Cover: A. Schrijver, Theory of Linear and Integer Programming
Schrijver's book cover inspired our chair's logo

We love discreteness.

We model optimization problems with highly expressive variables that lead to strong relaxations. In particular, we develop algorithms that exploit the structure of integer programs to solve them more efficiently. This often results in column generation/branch-and-price (CGBP) or other decomposition strategies. Our chair belongs to the leading international research groups in this field. A flagship project is the generic solver GCG which automatically performs Dantzig-Wolfe decompositions and applies CGBP.

Machine Learning meets Optimization

Statistik aus unserem Paper Bergner et al. (2015)
Statistics from Bergner et al. (2015)

Data-Based Algorithm Improvements.

The intersection of machine learning and optimization is a highly topical field of research. In machine learning also appear discrete optimization problems that are still rarely modeled via integer programs and solved to optimality. Inversely, machine learning approaches can help to enhance the understanding of optimization algorithms and provide new intuition for theoretic aspects. Our research focuses primarily on the latter of these two areas.

Prescriptive Analytics

A Puzzle
Optimization is the missing piece!

From Data to Optimal Decision Making.

All our practice projects are simultaneously projects of mathematical research. This is primarily due to the fact that we look for challenges that are still without or with only insufficient solutions. Nearly always new decision models must be developed and algorithms must either partially be adapted to the special structure of the application or be drafted completely from scratch. The practical tasks often result in more general theoretic questions whose answers in turn provide new findings for practice.

Research Fields of our Associates

Macht was mit Wahlkreisen

Sebastian Goderbauer: does weird stuff with voting districts

Michael Bastubbe: a decent decom-poser

Software

Implementing Our Research.

Part of our research is performing computational experiments. To evaluate our ideas and algorithms, they need to be implemented. We often make the developed software available to the public.

Data

Benchmarks, Instances, Generators

We publish the data and instances upon which our research results are based. This allows the scientific community to compare to our methods and to comprehend and reproduce our results. We maintain libraries of benchmark instances for selected applications.

Our Partners