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On the influence of robustness measures on shape optimization with stochastic uncertainties. (English) Zbl 1364.74084
Summary: The unavoidable presence of uncertainties poses several difficulties to the numerical treatment of optimization tasks. In this paper, we discuss a general framework attacking the additional computational complexity of the treatment of uncertainties within optimization problems considering the specific application of optimal aerodynamic design. Appropriate measure of robustness and a proper treatment of constraints to reformulate the underlying deterministic problem are investigated. In order to solve the resulting robust optimization problems, we propose an efficient methodology based on a combination of adaptive uncertainty quantification methods and optimization techniques, in particular generalized one-shot ideas. Numerical results investigating the reliability and efficiency of the proposed method as well as the influence of different robustness measures on the resulting optimized shape will be presented.

74P15 Topological methods for optimization problems in solid mechanics
90C90 Applications of mathematical programming
Spinterp; TAU
Full Text: DOI
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