Advertisement

Computational Optimization and Applications

, Volume 21, Issue 3, pp 311–323 | Cite as

Using DIRECT to Solve an Aircraft Routing Problem

  • M.C. Bartholomew-Biggs
  • S.C. Parkhurst
  • S.P. Wilson
Article

Abstract

In this paper we discuss a global optimization problem arising in the calculation of aircraft flight paths. Since gradient information for this problem may not be readily available, a direct-search algorithm (DIRECT), proposed by Jones et al., Journal of Optimization Theory and Applications, vol. 79, pp. 157–181, 1993, appears to be a promising solution technique. We describe some numerical experience in which DIRECT is used in several different ways to solve a sample problem.

global optimization direct search methods route planning 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K.S. Al-Sultan and M.A. Al-Fawzan, “A tabu search Hooke and Jeeves algorithm for unconstrained optimization,” in European Journal of OR, vol. 103, pp. 198–208, 1997.Google Scholar
  2. 2.
    C.A. Baker, L.T. Watson, S.E. Cox, B. Grossman, R.T. Hafka, and W.H. Mason, “Study of a global design space exploration method for aerospace vehicles,” in 5th NASA High Performance Computing and Communicationa Computational Aerosciences Workshop, NASA, Mountain View, 2000.Google Scholar
  3. 3.
    C.A. Baker, L.T. Watson, B. Grossman, R.T. Hafka, and W.H. Mason, “Parallel global aircraft configuration design space exploration,” in Proceedings of the High Performance Computing Symposium 2000, A. Tentner (Ed.), Society for Computer Simulation International: San Diego, 2000, pp. 101–106.Google Scholar
  4. 4.
    C.A. Baker, L.T. Watson, B. Grossman, W.H. Mason, and R.T. Hafka, “Parallel global aircraft configuration design space exploration,” in Int. J. Comput. Res., to appear.Google Scholar
  5. 5.
    R. Chelouah and P. Siarry, “Tabu search applied to global optimization,” European Journal of OR, vol. 123, pp. 256–270, 2000.Google Scholar
  6. 6.
    S.E. Cox, R.T. Hafka, C.A. Baker, B. Grossman, W.H. Mason, and L.T.Watson, “Global optimization of a high speed civil transport configuration,” in 3rd World Congress of Structural and Multidisciplinary Optimization, Buffalo, 1999.Google Scholar
  7. 7.
    S.E. Cox, R.T. Hafka, C.A. Baker, B. Grossman, W.H. Mason, and L.T. Watson, “Global multi-disciplinary optimization of a high speed civil transport,” J. Global Optim, to appear.Google Scholar
  8. 8.
    J.M. Gablonsky, “An implementation of the DIRECT algorithm,” Technical Report CRSC-TR98-29, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, 1998.Google Scholar
  9. 9.
    C. Hewitt and S.A. Broatch, “A tactical navigation and routeing system for low-level flight,” Technical Report, GEC-Marconi Avionics, Rochester, Kent, UK, AGARD, Italy, 1992.Google Scholar
  10. 10.
    C. Hewitt and P. Martin, “Advanced mission management,” Technical Report, GEC-Marconi Avionics, Rochester, Kent, UK, IEE—FITEC, 1998.Google Scholar
  11. 11.
    D.R. Jones, C.D. Perttunen, and B.E. Stuckman, “Lipschitzian optimization without the Lipschitz constant,” Journal of Optimization Theory and Applications, vol. 79, pp. 157–181, 1993.Google Scholar
  12. 12.
    L.T. Watson and C.A. Baker, “A fully distributed parallel global search algorithm,” in 10th SIAM Conference on Parallel Processing for Scientific Computing, SIAM, Philadelphia, 2001.Google Scholar
  13. 13.
    L.T. Watson and C.A. Baker, “A fully distributed parallel global search algorithm,” Engrg. Comput, to appear.Google Scholar
  14. 14.
    S.P. Wilson, S.C. Parkhurst, and M.C. Bartholomew-Biggs, “The aircraft routing problem,” Technical Report 331, Numerical Optimisation Centre, University of Hertfordshire, Dec. 2000.Google Scholar
  15. 15.
    M.A. Wolfe, “Interval mathematics, algebraic equations and optimization,” J. Computational and Applied Mathematics, vol. 124, pp. 263–280, 2000.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M.C. Bartholomew-Biggs
    • 1
  • S.C. Parkhurst
    • 1
  • S.P. Wilson
    • 1
  1. 1.Numerical Optimisation CentreUniversity of HertfordshireHatfieldUK

Personalised recommendations