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

Abstract

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.

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Acknowledgments

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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Correspondence to Marta Pascoal.

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Pascoal, M., Captivo, M.E., Clímaco, J. et al. Bicriteria path problem minimizing the cost and minimizing the number of labels. 4OR-Q J Oper Res 11, 275–294 (2013). https://doi.org/10.1007/s10288-013-0229-0

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Keywords

  • Minimal cost
  • Minimal number of labels
  • Bicriteria
  • Shortest path

Mathematics Subject Classification (2000)

  • 05C85
  • 90C27
  • 90C29