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Robust Airfoil Design in the Context of Multi-objective Optimization

Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS,volume 48)


We apply the concept of robustness to multi-objective optimization for finding robust Pareto optimal solutions. The multi-objective optimization and robustness problem is solved by using the \(\varepsilon \)-constraint method combined with the non-intrusive polynomial chaos approach for uncertainty quantification. The resulting single-objective optimization problems are solved with a deterministic method using algorithmic differentiation for the needed derivatives. The proposed method is applied to an aerodynamic shape optimization problem for minimizing drag and maximizing lift in a steady Euler flow. We consider aleatory uncertainties in flight conditions and in the geometry separately to find robust solutions. In the case of geometrical uncertainties we apply a Karhunen-Loeve expansion to approximate the random field and make use of a dimension-adaptive quadrature based on sparse grid methods for the numerical integration in random space.


  • Airfoil
  • Robust Pareto-optimal Solutions
  • Sparse Grid
  • Aerodynamic Shape Optimization Problems
  • Single Objective Optimization Problem

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  • DOI: 10.1007/978-3-319-89988-6_23
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We would like to thank our colleague Tim Albring from TU Kaiserslautern for assistance with SU2, and Claudia Schillings from University of Warwick for providing the code and the support for the dimension-adaptive quadrature.

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Correspondence to Lisa Kusch .

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Kusch, L., Gauger, N.R. (2019). Robust Airfoil Design in the Context of Multi-objective Optimization. In: Minisci, E., Vasile, M., Periaux, J., Gauger, N., Giannakoglou, K., Quagliarella, D. (eds) Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Computational Methods in Applied Sciences, vol 48. Springer, Cham.

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