An Adaptive Multipoint Formulation for Robust Parametric Optimization

François Gallard (), Bijan Mohammadi (), Marc Montagnac () and Matthieu Meaux ()
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François Gallard: Institute of Technology Antoine de Saint Exupéry
Bijan Mohammadi: Mathématiques (IMAG)
Marc Montagnac: Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
Matthieu Meaux: Airbus Group Innovations

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 2, No 14, 693-715

Abstract: Abstract The performance of a system designed for given functioning conditions often seriously degrades, when operated at other conditions. Therefore, a system operating over a continuous range of conditions should be designed over this range. The aerodynamic shape optimization of an aircraft at multiple altitudes, angles of attack and Mach numbers is a typical case in aerospace. This paper links parametric and multipoint optimizations by the sampling of the operating condition ranges. It is demonstrated that this discrete set of operating conditions, used to formulate a composite objective function, must adequately be chosen. An algorithm is proposed to select these conditions, which ensures a minimal computational cost to the robust optimization. Wing aerodynamic multipoint optimizations using a lifting line model and Reynolds-averaged Navier–Stokes equations, derived with a discrete adjoint formulation, are given as examples.

Keywords: Parametric optimization; Multipoint optimization; Gradient-based optimization; Robust optimization; Aerodynamics; Adjoint method; 93B51; 35Q93; 49M37; 49Q10; 90C31 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0595-6

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