Developing Efficient Random Flight Searches in Bounded Domains

  • Thomas A. WettergrenEmail author
Part of the STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health book series (STEAM)


We develop a new method for computing the parameters defining an efficient random flight for searchers that are constrained to search in a bounded domain. Using concepts from observations of animal foraging behavior, we define a random search plan that provides an optimally efficient search in terms of coverage relative to the constraints of random motion in the bounded domain. In contrast to the previous studies, our method directly accounts for the change to the behavior that occurs for bounded flights. In addition, we show how to modify the resulting random flight parameters to account for the effects of multiple searchers in the same region. Numerical simulations are performed to illustrate the effectiveness of this random search strategy.


  1. 1.
    M. Andersson. On optimal predator search. Theor. Popul. Biol. 19(1), 58–86 (1981)MathSciNetCrossRefGoogle Scholar
  2. 2.
    B.W. Andrews, K.M. Passino, T.A. Waite, Foraging theory for autonomous vehicle decision-making system design. J. Intell. Robot. Syst. 49, 39–65 (2007)CrossRefGoogle Scholar
  3. 3.
    B.W. Andrews, K.M. Passino, T.A. Waite, Social foraging theory for robust multiagent system design. IEEE Trans. Autom. Sci. Eng. 4(1), 79–86 (2007)CrossRefGoogle Scholar
  4. 4.
    F. Bartumeus, J. Catalan, U.L. Fulco, M.L. Lyra, G.M. Viswanathan, Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies. Phys. Rev. Lett. 88(9), Article number 097901 (2002)Google Scholar
  5. 5.
    D. Boyer, O. Miramontes, H. Larralde, Lévy-like behaviour in deterministic models of intelligent agents exploring heterogeneous environments. J. Phys. A: Math. Theor. 42, Article number 434015 (2009)CrossRefGoogle Scholar
  6. 6.
    N. Chernov, Entropy, Lyapunov exponents, and mean free path for billiards. J. Stat. Phys. 88(1–2), 1–29 (1997)MathSciNetCrossRefGoogle Scholar
  7. 7.
    N.E. Humphries, N. Quieroz, J.R.M. Dyer, N.G. Pade, M.K. Musyl, K.M. Schaefer, D.W. Fuller, J.M. Brunnschweiler, T.K. Doyle, J.D.R. Houghton, G.C. Hays, C.S. Jones, L.R. Noble, V.J. Wearmouth, E.J. Southall, D.W. Sims, Environmental context explains Lévy and Brownian movement patterns of marine predators. Nature 465, 1066–1069 (2010)CrossRefGoogle Scholar
  8. 8.
    B.O. Koopman, Search and Screening: General Principles with Historical Applications (Pergamon Press, New York, 1980)zbMATHGoogle Scholar
  9. 9.
    P.W. Kuchel, R.J. Vaughan, Average lengths of chords in a square. Math. Mag. 54(5), 261–269 (1981)MathSciNetCrossRefGoogle Scholar
  10. 10.
    M. Mangel, C. Clark, Search theory in natural resource modeling. Nat. Resour. Model. 1, 1–54 (1986)MathSciNetCrossRefGoogle Scholar
  11. 11.
    V.V. Palyulin, A.V. Chechkin, R. Metzler, Lévy flights do not always optimize random blind search for sparse targets. Proc. Natl. Acad. Sci. 111(8), 2931–2936 (2014)CrossRefGoogle Scholar
  12. 12.
    E.P. Raposo, S.V. Buldyrev, M.G.E. da Luz, G.M. Viswanathan, H.E. Stanley, Lévy flights and random searches. J. Phys. A: Math. Theor. 42, Article number 434003 (2009)MathSciNetCrossRefGoogle Scholar
  13. 13.
    G.D. Ruxton, Increasing search rate over time may cause a slower than expected increase in prey encounter rate with increasing prey density. Biol. Lett. 1, 133–135 (2005)CrossRefGoogle Scholar
  14. 14.
    M.C. Santos, E.P. Raposo, G.M. Viswanathan, M.G.E. da Luz, Optimal random searches of revisitable targets: crossover from superdiffusive to ballistic random walks. Europhys. Lett. 67(5), 734–740 (2004)CrossRefGoogle Scholar
  15. 15.
    J.M. Smith, G.R. Price, The logic of animal conflict. Nature 246, 15–18 (1973)CrossRefGoogle Scholar
  16. 16.
    D.W. Stephens, J.R. Krebs, Foraging Theory (Princeton University Press, Princeton, 1986)Google Scholar
  17. 17.
    J.M.J. Travis, S.C.F. Palmer, Spatial processes can determine the relationship between prey encounter rate and prey density. Biol. Lett. 1, 136–138 (2005)CrossRefGoogle Scholar
  18. 18.
    G.M. Viswanathan, V. Afanasyev, S.V. Buldyrev, E.J. Murphy, P.A. Prince, H.E. Stanley, Lévy flight search patterns of wandering albatrosses. Nature 381, 413–415 (1996)CrossRefGoogle Scholar
  19. 19.
    G.M. Viswanathan, S.V. Buldyrev, S. Havlin, M.G.E. da Luz, E.P. Raposo, H.E. Stanley, Optimizing the success of random searches. Nature 401, 911–914 (1999)CrossRefGoogle Scholar
  20. 20.
    G.M. Viswanathan, V. Afanasyev, S.V. Buldyrev, S. Havlin, M.G.E. da Luz, E.P. Raposo, H.E. Stanley, Lévy flights in random searches. Phys. A 282, 1–12 (2000)CrossRefGoogle Scholar
  21. 21.
    T.A. Wettergren, C.M. Traweek, The search benefits of autonomous mobility in distributed sensor networks. Int. J. Distrib. Sens. Netw. 8(2) (2012). Article ID 797040CrossRefGoogle Scholar
  22. 22.
    K. Zhao, R. Jurdak, J. Liu, D. Westcott, B. Kusy, H. Parry, P. Sommer, A. McKeown, Optimal Lévy-flight foraging in a finite landscape. J. R. Soc. Interface 12, Article number 20141158 (2015)CrossRefGoogle Scholar

Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2018

Authors and Affiliations

  1. 1.Naval Undersea Warfare CenterNewportUSA

Personalised recommendations