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Frequency optimization in public transportation systems: Formulation and metaheuristic approach

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  • Martínez, Héctor
  • Mauttone, Antonio
  • Urquhart, María E.

Abstract

We study the transit frequency optimization problem, which aims to determine the time interval between subsequent buses for a set of public transportation lines given by their itineraries, i.e., sequences of stops and street sections. The solution should satisfy a given origin–destination demand and a constraint on the available fleet of buses. We propose a new mixed integer linear programming (MILP) formulation for an already existing model, originally formulated as a nonlinear bilevel one. The proposed formulation is able to solve to optimality real small-sized instances of the problem using MILP techniques. For solving larger instances we propose a metaheuristic which accuracy is estimated by comparing against exact results (when possible). Both exact and approximated approaches are tested by using existing cases, including a real one related to a small-city which public transportation system comprises 13 lines. The magnitude of the improvement of that system obtained by applying the proposed methodologies, is comparable with the improvements reported in the literature, related to other real systems. Also, we investigate the applicability of the metaheuristic to a larger-sized real case, comprising more than 130 lines.

Suggested Citation

  • Martínez, Héctor & Mauttone, Antonio & Urquhart, María E., 2014. "Frequency optimization in public transportation systems: Formulation and metaheuristic approach," European Journal of Operational Research, Elsevier, vol. 236(1), pages 27-36.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:27-36
    DOI: 10.1016/j.ejor.2013.11.007
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    6. Ren, Hualing & Song, Yingjie & Long, Jiancheng & Si, Bingfeng, 2021. "A new transit assignment model based on line and node strategies," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 121-142.
    7. Benjamin Otto, 2019. "Aggregation techniques for frequency assignment in public transportation," Public Transport, Springer, vol. 11(1), pages 51-87, June.
    8. Daraio, Cinzia & Diana, Marco & Di Costa, Flavia & Leporelli, Claudio & Matteucci, Giorgio & Nastasi, Alberto, 2016. "Efficiency and effectiveness in the urban public transport sector: A critical review with directions for future research," European Journal of Operational Research, Elsevier, vol. 248(1), pages 1-20.
    9. Ibarra-Rojas, O.J. & Delgado, F. & Giesen, R. & Muñoz, J.C., 2015. "Planning, operation, and control of bus transport systems: A literature review," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 38-75.
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    11. Sánchez-Martínez, Gabriel E. & Koutsopoulos, Haris N. & Wilson, Nigel H.M., 2016. "Optimal allocation of vehicles to bus routes using automatically collected data and simulation modelling," Research in Transportation Economics, Elsevier, vol. 59(C), pages 268-276.

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