A Bilevel Approach to Frequency Optimization in Public Transportation Systems

Authors Agustin Arizti, Antonio Mauttone, Maria E. Urquhart

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Agustin Arizti
  • Universidad de la República, J. Herrera y Reissig 565, Montevideo, Uruguay
Antonio Mauttone
  • Universidad de la República, J. Herrera y Reissig 565, Montevideo, Uruguay
Maria E. Urquhart
  • Universidad de la República, J. Herrera y Reissig 565, Montevideo, Uruguay

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Agustin Arizti, Antonio Mauttone, and Maria E. Urquhart. A Bilevel Approach to Frequency Optimization in Public Transportation Systems. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We consider the problem of frequency optimization in transit systems, whose objective is to determine the time interval between subsequent buses for a set of public transportation lines. We extend an existing single level model by adding a constraint on bus capacities, while maintaining user choice on routes by means of an assignment sub-model. The resulting formulation is bilevel, and is transformed into a mixed integer linear programming formulation (MILP) that can be solved to optimality for small-sized problem instances, using standard MILP techniques. We study different variants of the same formulation to better understand the bilevel nature of the model and its application to real settings.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • transportation
  • public transport capacity
  • transit frequency optimization
  • mixed integer linear programming
  • bilevel programming


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