Further Use of Heuristic Methods

  • Val Lowndes
  • Stuart Berry
  • Chris Parkes
  • Ovidiu BagdasarEmail author
  • Nicolae Popovici
Part of the Simulation Foundations, Methods and Applications book series (SFMA)


The next section shows not only how a heuristic approach can be employed to solve hard problems but also how an investigation of the mathematical model can lead to a simpler solution technique.


Travel Time Journey Time Traffic Flow Equilibrium Problem Road Segment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Fisk C (1980) Some developments in equilibrium traffic assignment. Transp Res Part B Methodol 14(3):243–256MathSciNetCrossRefGoogle Scholar
  2. 2.
    Horowitz J (1984) The stability of stochastic equilibrium in a two link transportation network. Transp Res Part B Methodol 18(1):13–28Google Scholar
  3. 3.
    Hartman J (2009) Special issue on transport infrastructure: a route choice experiment with an efficient toll, networks and spatial economics. Accessible at:
  4. 4.
    Roughgarden T (2005) Selfish routing and the price of anarchy. MIT Press, LondonzbMATHGoogle Scholar
  5. 5.
    Youn H, Jeong H, Gastner M (2009) The price of anarchy in transportation networks: efficiency and optimality control. Phys Rev Lett 101 (19 Sept 2009)Google Scholar
  6. 6.
    Skinner, Carlin (2013) The price of anarchy. SignificanceGoogle Scholar
  7. 7.
    Braess D, Nagurney A, Wakolbinger (2005) On a paradox of transport planning (a translation of the 1968 article). Transp Sci 39(4):446–450Google Scholar
  8. 8.
    Steinberg R, Zangwill W (1983) The prevalence of Braess’ paradox. Transp Sci 17(3):301–318Google Scholar
  9. 9.
    Dafermos SC, Nagurney A (1984) On some traffic equilibrium theory paradoxes Transp Res Ser B 18(2):101–110Google Scholar
  10. 10.
    Catoni S, Pallottino S (1991) Traffic equilibrium paradoxes. Transp Sci 25(3):240–244CrossRefzbMATHGoogle Scholar
  11. 11.
    Pas E, Principio S (1997) Braess’ paradox: some new insights. Transp Res B 31(3):265–276CrossRefGoogle Scholar
  12. 12.
    Abrams R, Hagstrom J (2006) Improving traffic flows at no cost. In: Lawphongpanich S, Hearn D, Smith M (eds) Mathematical and computational models for congestion changing. Springer, New YorkGoogle Scholar
  13. 13.
    Mogoridge M (1997) The self-defeating nature of urban road capacity policy. Transp Policy 4(1):5–23Google Scholar
  14. 14.
    Arnott R, Small K (1994) The economics of traffic congestion. Am Sci 82:446–455Google Scholar
  15. 15.
    Stanley RP (2012) Enumerative combinatorics, vol 1 (2nd ed.). Cambridge Studies in Advanced Mathematics, 49, Cambridge University Press, CambridgeGoogle Scholar
  16. 16.
    The On-Line Encyclopedia of Integer Sequences (2011) OEIS Foundation Inc
  17. 17.
    Bellman R (1957) Dynamic programming. Princeton University Press, PrincetonzbMATHGoogle Scholar
  18. 18.
    Bazaraa MS, Sherali HD & Shetti CM (2006) Non linear programming. Wiley, New YorkGoogle Scholar
  19. 19.
    Rockafellar RT (1970) Convex analysis. Princeton Mathematical Series 28, Princeton University Press, PrincetonGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Val Lowndes
    • 1
  • Stuart Berry
    • 2
  • Chris Parkes
    • 2
  • Ovidiu Bagdasar
    • 2
    Email author
  • Nicolae Popovici
    • 3
  1. 1.University of DerbyDerbyUK
  2. 2.College of Engineering and TechnologyUniversity of DerbyDerbyUK
  3. 3.Babes-Bolyai UniversityCluj-NapocaRomania

Personalised recommendations