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Uwe Gotzes

Dr. Uwe Gotzes

Former member of the Workgroup Optimierung und algorithmische diskrete Mathematik

Currently, I work in the system support department at Open Grid Europe GmbH. Most of the time, my colleagues and I work on a project connected to MODAL GasLab.




Book cover: Evaluating Gas Network Capacities
EURO Award 2016: Certificate

Although my contribution to the book is tiny, I'd like to mention it, because I was involved in the related project FORNE (Forschungskooperation Netzoptimierung/Research cooperation network optimization) for several years.

2009 – Dissertation available:

Book cover dissertation Uwe Gotzes

Two-stage stochastic programming models are considered as attractive tools for making optimal decisions under uncertainty. Traditionally, optimality is formalized by applying statistical parameters such as the expectation or the conditional value at risk to the distributions of objective values.

Uwe Gotzes analyzes an approach to account for risk aversion in two-stage models based upon partial orders on the set of real random variables. These stochastic orders enable the incorporation of the characteristics of whole distributions into the decision process. The profit or cost distributions must pass a benchmark test with a given acceptable distribution. Thus, additional objectives can be optimized. For this new class of stochastic optimization problems, results on structure and stability are proven and a tailored algorithm to tackle large problem instances is developed. The implications of the modelling background and numerical results from the application of the proposed algorithm are demonstrated with case studies from energy trading.


Jahr der Mathematik - Logo




Bundesliga optimization problem.

The German football league - An optimization problem?

In 2012 or so a colleague motivated me to develop optimization models related to football. This section presents the results of my work. The following tables and graphs contain the information which ranking each team of the german Bundesliga can at most reach until the end of the season ("MAX"-column/green graph) and which ranking each team will definitely reach ("MIN"-column/red graph). The "NOW"-column and the grey graph contain the current position of the respective team. The results are obtained by a set of integer programs that I solve using scip. The optimization models incorporate the fact that when teams play against each other at most one team can win, i.e. can gain three points from the match. See model description below. Usually I update the data on mondays or tuesdays. In the middle and at the end of the season, it becomes exciting. Then the red and the green graph form a narrowing corridor. "Final position" in the graphs refers to round robin and double round robin, thus there is a jump in the red and the green graph after the winter break. No responsibility is taken for the correctness of this information. Angaben ohne Gewähr.

The results for season 2016/2017 can be downloaded here (Bundesliga) and here (Second Bundesliga).

Bundesliga (the German football league)

Second Bundesliga

Theory: The Optimization models behind


vbc2dot.rb is a Ruby-script that generates a .dot-file from scip's vbc-file output. Then the program dot is applied to the dot-file to generate a visualization of scip's branch-and-bound tree.

In scip (>= 5.0.1), set visual/vbcfilename=vbcfilename and visual/dispsols=TRUE. After you have solved a problem, you can run ruby vbc2dot.rb vbcfilename [options], what will generate a visualization of the branch-and-bound tree of the problem. The tool is still under development, but I think it generates reasonable results. You will need to have ruby and graphviz installed on your system. Alternatively you could use webgraphviz. This is a sample output of vbc2dot (full tree evolution). Another sample output of vbc2dot (final tree only) based upon the problem air04.mps from miplib.

>ruby vbc2dot.rb -h yields:

Usage: vbc2dot.rb vbcfilename [options]

-r, --rankdir=dirabbr "TB", "LR", "BT", "RL", corresponding to directed graphs drawn from top to bottom, from left to right, from bottom to top, and from right to left, respectively.
-o, --output=filename Name of generated filenames. Postfixes are chosen automatically, default filename is vbcfilename.
-l, --legend Generate a legend in the output files.
-d, --delay=float Wait float seconds until next ps-file is generated (movielike ps observation possible).
-f, --frequency=int Generate output according to frequency.
-t, --probtype=minormax Use option if vbcfile does not contain any information on primal bounds.

Jeep problem revisited.

U. Gotzes, C. Gotzes, The jeep problem – Zimpl files.


Any comments on any of the topics of this page are welcome. Please do not hesitate to contact me.

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