Robust Bi-objective Shortest Path Problem in Real Road Networks

  • Christian CintranoEmail author
  • Francisco Chicano
  • Enrique Alba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10268)


Road journeys are one of our most frequent daily tasks. Despite we need them, these trips have some associated costs: time, money, pollution, etc. One of the usual ways of modeling the road network is as a graph. The shortest path problem consists in finding the path in a graph that minimizes a certain cost function. However, in real world applications, more than one objective must be optimized simultaneously (e.g. time and pollution) and the data used in the optimization is not precise: it contains errors. In this paper we propose a new mathematical model for the robust bi-objective shortest path problem. In addition, some empirical studies are included to illustrate the utility of our formulation.


Robustness Traffic road network Bi-objective shortest path Multi-objective optimization 



This research was partially funded by the University of Málaga, Andalucía Tech, and the Spanish Ministry of Economy and Competitiveness and FEDER (grant TIN2014-57341-R).


  1. 1.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)CrossRefGoogle Scholar
  3. 3.
    Cintrano, C., Stolfi, D.H., Toutouh, J., Chicano, F., Alba, E.: CTPATH: a real world system to enable green transportation by optimizing environmentaly friendly routing paths. In: Alba, E., Chicano, F., Luque, G. (eds.) Smart-CT 2016. LNCS, vol. 9704, pp. 63–75. Springer, Cham (2016). doi: 10.1007/978-3-319-39595-1_7 Google Scholar
  4. 4.
    Hansen, P.: Bicriterion path problems. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making Theory and Application. LNE, vol. 177, pp. 109–127. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  5. 5.
    Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton (2009)CrossRefzbMATHGoogle Scholar
  6. 6.
    Ide, J., Schöbel, A.: Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts. OR Spectrum 38(1), 235–271 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Duque, D., Lozano, L., Medaglia, A.L.: An exact method for the biobjective shortest path problem for large-scale road networks. Eur. J. Oper. Res. 242(3), 788–797 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Cheng, J., Lisser, A., Letournel, M.: Distributionally robust stochastic shortest path problem. Electr. Notes Discrete Math. 36, 511–518 (2010)CrossRefGoogle Scholar
  9. 9.
    Hasuike, T.: Robust shortest path problem based on a confidence interval in fuzzy bicriteria decision making. Inf. Sci. 221, 520–533 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Pascoal, M.M., Resende, M.: The minmax regret robust shortest path problem in a finite multi-scenario model. Appl. Math. Comput. 241, 88–111 (2014)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Ehrgott, M., Ide, J., Schöbel, A.: Minmax robustness for multi-objective optimization problems. Eur. J. Oper. Res. (1), 17–31Google Scholar
  12. 12.
    Kuhn, K., Raith, A., Schmidt, M., Schöbel, A.: Bi-objective robust optimisation. Eur. J. Oper. Res. 252(2), 418–431 (2016)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Christian Cintrano
    • 1
    Email author
  • Francisco Chicano
    • 1
  • Enrique Alba
    • 1
  1. 1.Departamento de Lenguajes y Ciencias de la ComputaciónUniversidad de MálagaMálagaSpain

Personalised recommendations