Annals of Operations Research

, Volume 154, Issue 1, pp 69–92 | Cite as

Multiple criteria districting problems

The public transportation network pricing system of the Paris region
  • Fernando Tavares-PereiraEmail author
  • José Rui Figueira
  • Vincent Mousseau
  • Bernard Roy


Districting problems are of high importance in many different fields. Multiple criteria models seem a more adequate representation of districting problems in real-world situations. Real-life decision situations are by their very nature multidimensional. This paper deals with the problem of partitioning a territory into “homogeneous” zones. Each zone is composed of a set of elementary territorial units. A district map is formed by partitioning the set of elementary units into connected zones without inclusions. When multiple criteria are considered, the problem of enumerating all the efficient solutions for such a model is known as being NP-hard, which is why we decided to avoid using exact methods to solve large-size instances. In this paper, we propose a new method to approximate the Pareto front based on an evolutionary algorithm with local search. The algorithm presents a new solution representation and the crossover/mutation operators. Its main features are the following: it deals with multiple criteria; it allows to solve large-size instances in a reasonable CPU time and generates high quality solutions. The algorithm was applied to a real-world problem, that of the Paris region public transportation. Results will be used for a discussion about the reform of its current pricing system.


Multiple criteria Districting problems Evolutionary algorithms Local search Combinatorial optimization 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Fernando Tavares-Pereira
    • 1
    • 2
    • 3
    • 4
    Email author
  • José Rui Figueira
    • 3
    • 4
  • Vincent Mousseau
    • 4
  • Bernard Roy
    • 4
  1. 1.Departamento de MatemáticaUniversidade da Beira InteriorCovilhaPortugal
  2. 2.INESC—CoimbraCoimbraPortugal
  3. 3.CEG-IST, Center for Management Studies, Departamento de Engenharia e Gestão, Instituto Superior TécnicoUniversidade Técnica de LisboaPorto SalvoPortugal
  4. 4.LAMSADEUniversité Paris-DauphineParis Cedex 16France

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