Journal of Global Optimization

, Volume 21, Issue 4, pp 415–432 | Cite as

A Comparison of Global Optimization Methods for the Design of a High-speed Civil Transport

  • Steven E. Cox
  • Raphael T. Haftka
  • Chuck A. Baker
  • Bernard Grossman
  • William H. Mason
  • Layne T. Watson


The conceptual design of aircraft often entails a large number of nonlinear constraints that result in a nonconvex feasible design space and multiple local optima. The design of the high-speed civil transport (HSCT) is used as an example of a highly complex conceptual design with 26 design variables and 68 constraints. This paper compares three global optimization techniques on the HSCT problem and two test problems containing thousands of local optima and noise: multistart local optimizations using either sequential quadratic programming (SQP) as implemented in the design optimization tools (DOT) program or Snyman's dynamic search method, and a modified form of Jones' DIRECT global optimization algorithm. SQP is a local optimizer, while Snyman's algorithm is capable of moving through shallow local minima. The modified DIRECT algorithm is a global search method based on Lipschitzian optimization that locates small promising regions of design space and then uses a local optimizer to converge to the optimum. DOT and the dynamic search algorithms proved to be superior for finding a single optimum masked by noise of trigonometric form. The modified DIRECT algorithm was found to be better for locating the global optimum of functions with many widely separated true local optima.


Local Optimum Design Space Sequential Quadratic Programming Global Optimization Algorithm Global Optimization Method 
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.


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  1. 1.
    Carlson, H. W. and Miller, D. S. (1974), Numerical Methods for the Design and Analysis of Wings at Supersonic Speeds, NASA TN D-7713, Dec.Google Scholar
  2. 2.
    Carlson, H.W. and Walkley, K.B. (1984), Numerical Methods and a Computer Program for Subsonic and Supersonic Aerodynamic Design and Analysis of Wings with Attainable Thrust Corrections, NASA CR-3808Google Scholar
  3. 3.
    Carter, R., Gablonsky, J.M., Patrick, A., Kelley, C.T. and Eslinger, O.J. (2000), Algorithms for Noisy Problems in Gas Transition Pipeline Optimization, Tech. Rep. CRSC-TR00-10, Centerfor Research in Sci. Computation, North Carolina State University, Raleigh, NCGoogle Scholar
  4. 4.
    Cramer, E.J. (1998), Using Approximate Models for Engineering Design, 7 th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St Louis, Missouri, AIAA Paper-98-4716, Sept.Google Scholar
  5. 5.
    Floudas, C.A. and Pardalos, P.M. (1996), State of the Art in Global Optimization, Kluwer Academic Publishers, Dordrecht, The NetherlandsGoogle Scholar
  6. 6.
    Gablonsky, J. M. (1998), An Implementation of the DIRECT Algorithm, Tech. Rep. CRSCTR98-29, Center for Research in Sci. Computation, North Carolina State Univ., Raleigh, NCGoogle Scholar
  7. 7.
    Haim, D., Giunta, A.A., Holzwarth, M.M., Mason, W.H., Watson, L.T. and Haftka, R.T. (1999), Comparison of optimization software packages for an aircraft multidisciplinary design optimization problem, Design Optimization 1, 9–23.Google Scholar
  8. 8.
    Hopkins, E. J. (1972), Charts for Predicting Turbulent Skin Friction from the Van Driest Method, NASA TN D-6945, Oct.Google Scholar
  9. 9.
    Jones, D.R., Perttunen, C.D. and Stuckman, B.E. (1993), Lipschitzan optimization without the Lipschitz constant, Journal of Optimization Theory and Application 79, 157–181.Google Scholar
  10. 10.
    Knill, D.L., Giunta, A.A., Baker, C.A., Grossman, B., Mason, W.H., Haftka, R.T. and Watson, L.T. (1999), Response surface models combining linear and Euler aerodynamics for supersonic transport design, Journal of Aircraft 36, pp. 75–86.Google Scholar
  11. 11.
    MacMillin, P.E., Golovidov, O.B., Mason, W.H., Grossman, B. and Haftka, R.T. (1997), An MDO Investigation of the Impact of Practical Constraints on an HSCT Configuration, AIAA 35th Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Paper 97–0098, Jan.Google Scholar
  12. 12.
    McGrory, W.D., Slack, D.C., Applebaum, M.P. and Walters, R.W. (1993), GASP Version 2.2 Users Manual, Aerosoft, Inc., Blacksburg, VAGoogle Scholar
  13. 13.
    Nelson, S.A. II, and Papalambros, P.Y. (1998), A Modification to Jones' Global Optimization Algorithm for Fast Local Convergence, 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St Louis, Missouri, AIAA Paper-98-4751, Sept.Google Scholar
  14. 14.
    Snyman, J.A. (1983), An Improved version of the original Leap-Frog dynamic method for unconstrained minimization: LFOP1(b), Appl. Math. Modelling 7, 216–218.Google Scholar
  15. 15.
    Snyman, J.A. (2000), The LFOPC Leap-Frog Algorithm for Constrained Optimization, Computers and Mathmatics with Applications, 40, 1085–1096Google Scholar
  16. 16.
    Vanderplaats Research & Development, Inc. (1995), DOT: Design Optimization Tools, Version 4.20Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Steven E. Cox
    • 1
  • Raphael T. Haftka
    • 1
  • Chuck A. Baker
    • 2
  • Bernard Grossman
    • 2
  • William H. Mason
    • 2
  • Layne T. Watson
    • 3
  1. 1.Department of Aerospace Engineering, Mechanics & Engineering ScienceUniversity of FloridaGainesvilleUSA
  2. 2.Department of Aerospace and Ocean EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  3. 3.Engineous Software, Inc.MorrisvilleUSA

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