Research Interests, Application Areas, Education
Main Research Areas
Current Research and Application Challenges
Main Research Areas:
My main research areas are optimization,
discrete mathematics, and operations research. I am
particularly interested in integer programming and the
geometric approach to combinatorial optimization problems
(polyhedral combinatorics, convex geometry, cutting plane
algorithms, branch&cut methods). On the combinatorial side,
graph and matroid theory come into play here. Specific
combinatorial optimization problems I have worked on are
the travelling salesman problem, the max-cut problem,
the stable set problem and perfect graphs, the linear
ordering problem, clustering, routing and scheduling,
online optimization, and various connectivity
and network flow problems.
I have a deep interest in (real)
applications. I have worked with scientists from other
disciplines and, in particular, with engineers and
economists from industry to mathematically model
challenging problems of their domain of expertise.
The theoretical analysis of such models and the
development of efficient algorithms for their
numerical solution are driving forces of my
research. I have contributed to
the following application areas:
- chip design and very large scale integration
- printed circuit board design and production, control of CNC machines
- simulation and optimization of computer manufacturing
- flexible manufacturing, job scheduling
- production planning in the chemical industry
- logistics, planning of public transportation systems
- vehicle routing, duty scheduling
- online dispatching of vehicles, online elevator control
- control of (semi-)automatically guided vehicles
- location planning in the telecommunication industry
- design and dimensioning of telecommunication networks
- design of optical networks
- frequency assignment in cellular phone networks
- spin glasses
- input-output analysis
Current Research and Application Challenges:
Many of the technical and operational problems of the type
mentioned above can nowadays be solved to the satisfaction
of practitioners. My research team at ZIB contributes to the general "tool development" in linear, integer, and mixed-integer programming by constantly improving our ZIB Optimization Suite that contains ZIMPL, a modeling language, SoPLex, an LP code, and SCIP a solver for mixed-integer programs. In general, however, the "real challenges from practice" cannot be solved with "automatic tools"
yet; mathematical effort and expertise is still needed.
My research team keeps contributing to these issues in a wide range of application areas and by developing new solution methods, but
we think that the time seems ripe to address the
following "big issues" with higher intensity:
|1. ||Online and real time optimization problems, particularly
those arising in practice, need to be investigated more
thoroughly. Algorithmic paradigms, mathematical tools and
concepts of performance analysis have to be developed
that satisfy both theory and practice. Oversimplified,
the big questions are: |
- When is an online algorithm "good"?
- What are typical ingredients of "good" online algorithms?
|2. ||Mathematics usually adresses quantitatively specifiable
questions; it has hardly contributed to more general (often
more important) issues such as the design of "good" systems.
Top management is, in general, not too interested in the
optimization of some machine or the like. It wants to
know whether a company is positioned well to meet the
challenges of the future. Here are typical questions of
this kind: |
- Is the public transportation system of a city good?
- Can the railroad system of a country be improved by
- How does one regulate or deregulate energy supply
- Is the supply chain of a company of good quality?
- What is a good telecommunication network?
It is clear that these are problems of high economic
impact. A hard part here is their "mathematical modelling".
For a mathematician, the questions above are very impricisely
stated. Can we mathematicians (in close cooperation with
specialists) come up with methods to formalize and
quantify these questions more precisely and develop methods
to answer them (somehow)?
I like teaching and try to bring current research into
the university class room. For details click here.
I also participate in education programs for PhD students. I was a member of the
European Graduate Program "Combinatorics, Geometry and Computation" that was a joint endeavor
by the Freie Universität, Humboldt-Universität and Technische Umiversität
as well as the Konrad-Zuse-Zentrum für Informationstechnik Berlin together with the Eidgenössische Technische Hochschule Zürich.
This European Graduate Program "CGC" was sponsored by the Deutsche Forschungsgemeinschaft/German Research Foundation (DFG) until the end of 2005.
Now, I am involved in a new Graduate Program "Methods for Discrete Structures" supported by the German Research Foundation (DFG). The newly established Research Training Group offers scholarships for Ph.D. students and one post-doc. The program started on October 1, 2006.
I participated in a DFG funded Graduate Program "MAGSI"with the title "Stochastic Modelling and Quantitative Analysis of Complex Systems in Engineering".
This was a Graduate Program directed to PhD students, in particular in Engineering and Computer Science to which some mathematicians from TU and HU Berlin contributed their modelling experience. This program ended in 2006.
I helped to organize a Ph.D. program in Applied Mathematics in Ecuador
as a joint project between TU Berlin and Escuela Politécnica Nacional (EPN) in Quito (financed by DAAD from 2002-2006).
Furthermore, I am involved in the activities of the Berlin Mathematical School (joint graduate program of three Berlin universities HU, FU, TU and several mathematical institutes).
But I also think that high school
education (at least in Germany) needs some overhaul. I
therefore started a project
"Diskrete Mathematik für die Schule" (sponsored by VolkswagenStiftung) to bring discrete mathematics and
optimization into high school. I do believe that quite a
number of topics in this area can be taught to high
school students. These new topics broaden their knowledge
range (the current focus in Germany is on geometry and
analysis) and show that interesting issues of the
(modern) daily life of an ordinary person (such as
car navigation, mobile phone operation and planning,
cryptography, garbage truck or postman routing, etc.)
can be tackled with mathematics. This may result in
a more friendly perception of mathematics in school
and in the public domain.
I organized several Summer Schools (in Germany, in China) to teach modern methods of discrete optimization, linear and integer programming.