, Volume 11, Issue 3, pp 275–294 | Cite as

Bicriteria path problem minimizing the cost and minimizing the number of labels

  • Marta Pascoal
  • M. Eugénia Captivo
  • João Clímaco
  • Ana Laranjeira
Research paper


We address a bicriterion path problem where each arc is assigned with a cost value and a label (such as a color). The first criterion intends to minimize the total cost of the path (the summation of its arc costs), while the second intends to get the solution with a minimal number of different labels. Since these criteria, in general, are conflicting criteria we develop an algorithm to generate the set of non-dominated paths. Computational experiments are presented and results are discussed.


Minimal cost Minimal number of labels Bicriteria Shortest path 

Mathematics Subject Classification (2000)

05C85 90C27 90C29 



This work was partially supported by the FCT Portuguese Foundation of Science and Technology (Fundação para a Ciência e a Tecnologia) under projects PEst-C/EEI/UI0308/2011, PEst-OE/MAT/UI0152 and PTDC/EEA-TEL/101884/2008. The authors deeply acknowledge the INESC-Coimbra research group on urban transportation, led by João Coutinho Rodrigues, for providing data about the metropolitan area of Coimbra.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Marta Pascoal
    • 1
    • 2
  • M. Eugénia Captivo
    • 3
  • João Clímaco
    • 2
    • 4
  • Ana Laranjeira
    • 1
  1. 1.Departamento de Matemática da FCTUCCoimbraPortugal
  2. 2.Instituto de Engenharia de Sistemas e Computadores—CoimbraCoimbraPortugal
  3. 3.Centro de Investigação Operacional, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal
  4. 4.Faculdade de EconomiaUniversidade de CoimbraCoimbraPortugal

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