Finding Risk-Averse Shortest Path with Time-Dependent Stochastic Costs

  • Dajian Li
  • Paul Weng
  • Orkun Karabasoglu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10053)


In this paper, we tackle the problem of risk-averse route planning in a transportation network with time-dependent and stochastic costs. To solve this problem, we propose an adaptation of the A* algorithm that accommodates any risk measure or decision criterion that is monotonic with first-order stochastic dominance. We also present a case study of our algorithm on the Manhattan, NYC, transportation network.


Route planning Shortest path Risk-averse decision-making Conditional Value-at-Risk Time-dependent stochastic costs 


  1. 1.
    Artzner, P., Delbaen, F., Eber, J., Heath, D.: Coherent measures of risk. Mathe. Finan. 9(3), 203–228 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bast, H., Delling, D., Goldberg, A., Müller-Hannemann, M., Pajor, T., Sanders, P., Wagner, D., Werneck, R.: Route planning in transportation networks (2015). arXiv:1504.05140v1
  3. 3.
    Bäuerle, N., Müller, A.: Stochastic orders and risk measures: Consistency and bounds. Math. Econ. 38, 132–148 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bellman, R.: On a routing problem. Q. Appl. Math. 16, 87–90 (1958)zbMATHGoogle Scholar
  5. 5.
    Bertsekas, D., Tsitsiklis, J.: An analysis of stochastic shortest paths problems. Math. Oper. Res. 16, 580–595 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chen, B.Y., Lam, W.H.K., Sumalee, A., Li, Q., Tam, M.L.: Reliable shortest path problems in stochastic time-dependent networks. J. Intell. Transp. Syst. 18(2), 177–189 (2014)CrossRefGoogle Scholar
  7. 7.
    Delling, D., Sanders, P., Schultes, D., Wagner, D.: Engineering route planning algorithms. In: Lerner, J., Wagner, D., Zweig, K.A. (eds.) Algorithmics of Large and Complex Networks. LNCS, vol. 5515, pp. 117–139. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-02094-0_7 CrossRefGoogle Scholar
  8. 8.
    Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dreyfus, S.: An appraisal of some shortest-path algorithms. Oper. Res. 17(3), 395–412 (1969)CrossRefzbMATHGoogle Scholar
  10. 10.
    Embrechts, P., Kluppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance. Springer, Berlin (1997)CrossRefzbMATHGoogle Scholar
  11. 11.
    Ford, L.J.: Network flow theory. Technical report, Rand Corporation (1956)Google Scholar
  12. 12.
    Frank, H.: Shortest paths in probabilistic graphs. Oper. Res. 17(4), 583–599 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Fu, L., Rilett, L.: Expected shortest paths in dynamic and stochastic traffic networks. Transp. Res. Part B: Methodol. 32(7), 499–516 (1998)CrossRefGoogle Scholar
  14. 14.
    Gavriel, C., Hanasusanto, G., Kuhn, D.: Risk-averse shortest path problems. In: IEEE 51st Annual Conference on Decision and Control, pp. 2533–2538 (2012)Google Scholar
  15. 15.
    Goldberg, A., Harrelson, C.: Computing the shortest path: A* meets graph theory. In: SODA, pp. 156–165 (2005)Google Scholar
  16. 16.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Cybern. 4(2), 100–107 (1968)CrossRefGoogle Scholar
  17. 17.
    Jorion, P.: Value-at-Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill, New York (2006)Google Scholar
  18. 18.
    Kaufman, D., Smith, R.: Fastest paths in time-dependent networks for intelligent vehicle-highway systems application. J. Intell. Transp. Syst. 1(1), 1–11 (1993)Google Scholar
  19. 19.
    Moore, E.F.: The shortest path through a maze. In: Proceedings of the International Symposium on the Theory of Switching, pp. 285–292 (1959)Google Scholar
  20. 20.
    von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)zbMATHGoogle Scholar
  21. 21.
    Nie, Y., Wu, X.: Shortest path problem considering on-time arrival probability. Transp. Res. Part B: Methodol. 43(6), 597–613 (2009)CrossRefGoogle Scholar
  22. 22.
    Ogryczak, W., Ruszczynski, A.: From stochastic dominance to mean-risk models: semideviations as risk measures. Eur. J. Oper. Res. 116, 33–50 (1999)CrossRefzbMATHGoogle Scholar
  23. 23.
    Orda, A., Rom, R.: Shortest-path and minimum delay algorithms in networks with time-dependent edge-length. J. ACM 37(3), 607–625 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Parmentier, A., Meunier, F.: Stochastic shortest paths and risk measures. In: arXiv preprint (2014)Google Scholar
  25. 25.
    Peyer, S., RautenBach, D., Vygen, J.: A generalization of Dijkstra’s shortest path algorithm with applications to VLSI routing. J. Discret. Algorithms 7(4), 377–390 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Puterman, M.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Hoboken (1994)CrossRefzbMATHGoogle Scholar
  27. 27.
    Quiggin, J.: Generalized Expected Utility Theory: The Rank-dependent Model. Kluwer Academic Publishers, Berlin (1993)CrossRefzbMATHGoogle Scholar
  28. 28.
    Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Prentice-Hall, Upper Saddle River (2003)zbMATHGoogle Scholar
  29. 29.
    Savage, L.: The Foundations of Statistics. Wiley, Hoboken (1954)zbMATHGoogle Scholar
  30. 30.
    Shaked, M., Shanthikumar, J.: Stochastic Orders and Their Applications. Academic Press, New York (1994)zbMATHGoogle Scholar
  31. 31.
    Sigal, C., Pritsker, A., Solberg, J.: The stochastic shortest route problem. Oper. Res. 28, 1122–1129 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Yaari, M.: The dual theory of choice under risk. Econometrica 55, 95–115 (1987)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.School of Electronics and Information Technology, SYSU-CMU Joint Institute of EngineeringSun Yat-sen UniversityGuangzhouChina
  3. 3.SYSU-CMU Shunde Joint Research InstituteShundeChina

Personalised recommendations