Wrote my progress report for my midterm exam (23 May.). Courses: “Logic-based methods for optimization” – Study group about how to use logic-based methods to solve mathematical programming models. “Ph.D. course in scientific writing”, University of Aarhus. Summer School: “Donet Summer School – Integer and Combinatorial Optimization”, Utrecht, The Netherlands, June 11 – 12, 2001. Conferences: “IPCO 2001 – Eighth Conference on Integer Programming and Combinatorial Optimization”, Utrecht, The Netherlands, June 13 – 15, 2001. Teaching: Student assistant in “Management Science and Operations Research 4” (Drøk 4 – 1½ classes).

# Research

I have been staying in Camerino, Italy for 3 months where I have visited professor Daniele Pretolani. During my stay, we developed procedures to solve the k’th shortest hyperpath problem and the bi-SBT problem. The k’th shortest hyperpath problem is solved using a new branching rule which divides the hypergraph into subhypergraphs. The bi-SBT problem is solved using different methods which are tested against each other (simple k’th method, two-phases method and k’th diagonal method). During my stay I also found a small error in the definition of a hyperpath which has been used in many papers. I therefore wrote a short note with a new definition (see publications).

I have started a project on bicriterion shortest hyperpaths (bi-SBT) together with my supervisor Kim Allan Andersen. This is a totally new research area, and we have to start from scratch by defining a bicriterion hypergraph and formulating the bi-SBT problem. First, I began studying the bicriterion shortest path problem and the methods to solve it. There are two main approaches, namely node labeling and path/tree. The node labeling approach seems to be hard to transfer to hypergraphs because a hyperpath has a more complex structure than a path, resulting in more complex node labeling procedure. Furthermore, an efficient path satisfies that its subpaths are efficient; this is not always the case for hyperpaths. The path/tree approach seems more adaptable to hypergraphs. Most papers use a k’th shortest path subprocedure to solve the problem. Therefore I first developed methods to solve the k’th shortest hyperpath problem. Conferences: “Probabilistic methods in […]

I started my Ph.D. in august 1999. I first began to study the theory of directed hypergraphs. Hypergraphs have different applications, one of them is that hypergraphs can be used to modelling dynamic networks. More precisely a hypergraph model for random time-dependent shortest paths can be formulated. Hence by finding shortest hyperpaths, we can find the minimum expected/min-max travel time of the dynamic network. Courses: “Logical inference I” – Study group in logic inference concerning how the use of mathematical programming methods can be used in logic inference. “Seminar in Mathematical Programming” by Tage Bai Andersen. Teaching: Student assistant in “Mathematics for economists” (Mat Ø – 2 classes).