Genetic Algorithms and Game Theory for High Lift Multi-Airfoil Design Problems in Aerodynamics

  • Wang Jiangfeng
  • J. Periaux
Conference paper
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 78)


This paper presents a multi-objective evolutionary optimization method combining Genetic Algorithms (GAs) and Game Theory (GT) for high lift multi-airfoil systems in Aerospace Engineering. GAs are IT based evolutionary methods introduced by J.H. Holland for mimicking natural adaptation systems in the computer. Due to large dimension global optimization problems and the increasing importance of low cost distributed parallel environments it is a natural idea to replace a global optimization by decentralized local sub-optimizations using GT which introduces the notion of games associated to an optimization problem. This GT/GAs combined optimization method is developed in this paper and used for reconstruction and optimization problems applied to high lift multi-airfoil design. Numerical results obtained with this new approach are compared favorably with single global GAs’ ones and illustrate the promising robustness and efficient parallel properties of coupled GAs with different game scenarios for future advanced multidisciplinary aerospace technologies.


Nash Equilibrium Lift Coefficient Reconstruction Problem Nash Game High Lift 
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]
    Holland J.H. Adaptation in Natural and Artificial System. University of Michigan Press, Ann Arbor, 1975Google Scholar
  2. [2]
    Nash J.F. Non-cooperative Games. Annals of Mathematics, 54, 289, 1951MathSciNetCrossRefGoogle Scholar
  3. [3]
    Periaux J. Calcul des parametres de couche limite suivant la ligne de glissement en laminaire et turbulent. Technical report, note AP 4173, 1970Google Scholar
  4. [4]
    Courty J.C. Problemes de confluence sillage couche limite a l’aide d’un modele elabore de turbulence. In 13eme colloque d’Aerodynamiquee Appliquee, Ecole Centrale de Lyon, 1976Google Scholar
  5. [5]
    Caupenne P. Calcul des Decollements par Methodes de Singularites. In 13eme colloque d’Aerodynamiquee Appliquee, Ecole Centrale de Lyon, 1976Google Scholar
  6. [6]
    Mantel B., Periaux J., Sefrioui M., Stoufflet B., Desideri J-A., Lanteri S., and Marco N. Evolutionary Computational Methods for Complex Design in Aerodynamics. AIAA 98–0222, 1998Google Scholar
  7. [7]
    Mitchel M. An Introduction to Genetic Algorithms. Mit press, 1997Google Scholar
  8. [8]
    Goldberg D.E. Genetic Algorithms in search, optimization, and Machine Learning. Addison-Wesley, Reading, Mass, 1989Google Scholar
  9. [9]
    Mckinsey J.C.C, Introduction to the Theory of Games. RAND Series, 1952Google Scholar
  10. [10]
    Michalewicz Z. Genetic Algorithms + Data Structure = Evolutionary Programs. Artificial intelligence. Springer-Verlag, New York, 1992Google Scholar
  11. [11]
    Lewontin R.C. Evolution and the Theory of Games. Theoretical Biology, 1: 382–403, 1961CrossRefGoogle Scholar
  12. [12]
    In Industrial Design and Control Applications using Genetic Algorithms and Evolutionary Strategies (INGENET). INGENET Data Base, T52.5, test case 2nd workshop in Capoua, Italy. January 2000Google Scholar
  13. [13]
    HQ Chen, J.Periaux and A. Ecer, Domain Decomposition Methods using Gas and game Theory for the parallel solution of CFD problems, Proceedings of ParCFD2000, Trondheim, Eds, A. Ecer, J.Periaux and N. Satofuka, Elsevier, to appearGoogle Scholar
  14. [14]
    J.Maynard Smith, E. Szathmary, The origins of life, From the Birth of Life to the origins of language, Oxford University Press, 1999Google Scholar
  15. [15]
    Periaux.J., Sefrioui M., and Mantel B. ErroGen97, chapter GA Multiple Objective Optimization Strategies for Electromagnetic Backscattering. John Wiley, Trieste, 1997Google Scholar
  16. [16]
    Eyi S., Chand K.K., and Lee K.D. Multi-Element High-lift Design Using the Navier-Stokes Equations. ln 27th AJAA Fluid Dynamics Conference. AIAA 96–1943, New Orleans, LA. 1996Google Scholar
  17. [17]
    J.F. Wang, Distributed Design Optimisation using GAs and Game Theory and related applications to high lift CFD problems in Aerodynamics, These 3eme cycle Univ. Paris 6, in preparationGoogle Scholar
  18. [18]
    M. Ridley, Mendel’s demon: Gene Justice and the Complexity of Life, Weidenfeld & Nicolson, London, 2000Google Scholar
  19. [19]
    Van Damme E., Stability and Perfection of Nash Equilibria. Spring-Verlag, Second edition, 1991zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Wang Jiangfeng
    • 1
    • 2
  • J. Periaux
    • 2
  1. 1.Institute of AerodynamicsNUAANanjingP.R.China
  2. 2.Pole Scientifique Dassault-Aviation/UPMCSt CloudFrance

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