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Home Enrico Bortoletto Defends His Dissertation At The FU Berlin

Enrico Bortoletto defends his dissertation at the FU Berlin

2025/07/16

Enrico Bortoletto successfully defended his dissertation “Geometric Advances and Infrastructure Awareness in Periodic Timetabling” at the Institute of Mathematics at Freie Universität Berlin on July 14, 2025. He introduced two novel geometric perspectives on the periodic event scheduling problem, that was hitherto studied in terms of periodic tensions. In the periodic timetabling space, the set of feasible solutions turns out to be a collection of polytropes, i.e., tropical polytopes that are also polytopes in the Euclidean sense. These polytropes have a neighborhood structure that arises from flips in periodic tensions, and that in turn gives rise to a new tropical neighborhood search algorithm. This method effectively complements existing methods and fueled the discovery of new best solutions to five of the twenty-two instances of the PESPLIB, a collection notoriously difficult benchmark testset for periodic timetabling. In the cycle offset space, the fractional solutions produce a cographic zonotope feature a fine tiling, in which the maximal tiles correspond in a duality relation with the feasible timetables. Furthermore, the volume of the cographic zonotope equals the number of spanning trees, and a scaled version provides a lower bound for the width of a cycle basis, two result that are interesting in their own right. Cycles are also the key to deal with constraints on the occupation of infrastructure elements that ensure, e.g., that at any time only one train is scheduled to be at any platform; these inability to deal with such constraints has been a major problem in practical applications, in particular, in the timetabling for construction sites. By a canonical extension of the standard periodic timetabling  formulation, such constraints can now be dealt with efficiently, as the thesis demonstrates at the example of scenarios at the S-Bahn Berlin. The research was funded in part by the Berlin Mathematics Excellence Center Math+, and in part by the MobilityLab of the BMBF Research Campus MODAL. 

The photo shows (from left to right) Philine Schiewe (Aalto University, external committee member), Christian Haase (committee member), Enrico Bortoletto, Ralf Borndörfer (promoter and committee head), and Ansgar Freyer (postdoc committee member).

Congratulations! 

 

Enrico Bortoletto defends his dissertation at the FU Berlin