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Tropical Neighbourhood Search: A New Heuristic for Periodic Timetabling

Authors Enrico Bortoletto , Niels Lindner , Berenike Masing

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Author Details

Enrico Bortoletto
  • Zuse Institute Berlin, Germany
Niels Lindner
  • Zuse Institute Berlin, Germany
Berenike Masing
  • Zuse Institute Berlin, Germany

Funding

  • Bortoletto, Enrico: Funded within the Research Campus MODAL, funded by the German Federal Ministry of Education and Research (BMBF) (fund number 05M20ZBM).
  • Masing, Berenike: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689).

Cite AsGet BibTex

Enrico Bortoletto, Niels Lindner, and Berenike Masing. Tropical Neighbourhood Search: A New Heuristic for Periodic Timetabling. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/OASIcs.ATMOS.2022.3

Abstract

Periodic timetabling is a central aspect of both the long-term organization and the day-to-day operations of a public transportation system. The Periodic Event Scheduling Problem (PESP), the combinatorial optimization problem that forms the mathematical basis of periodic timetabling, is an extremely hard problem, for which optimal solutions are hardly ever found in practice. The most prominent solving strategies today are based on mixed-integer programming, and there is a concurrent PESP solver employing a wide range of heuristics [Borndörfer et al., 2020]. We present tropical neighborhood search (tns), a novel PESP heuristic. The method is based on the relations between periodic timetabling and tropical geometry [Bortoletto et al., 2022]. We implement tns into the concurrent solver, and test it on instances of the benchmarking library PESPlib. The inclusion of tns turns out to be quite beneficial to the solver: tns is able to escape local optima for the modulo network simplex algorithm, and the overall share of improvement coming from tns is substantial compared to the other methods available in the solver. Finally, we provide better primal bounds for five PESPlib instances.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Mathematics of computing → Combinatorial optimization
  • Mathematics of computing → Network flows
  • Mathematics of computing → Solvers
  • Mathematics of computing → Integer programming
  • Computing methodologies → Concurrent algorithms
Keywords
  • Periodic Timetabling
  • Tropical Geometry
  • Neighborhood Search
  • Mixed-Integer Programming

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References

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