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Robustness Measures for Multi-objective Robust Design

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Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS,volume 55)


A significant step to engineering design is to take into account uncertainties and to develop optimal designs that are robust with respect to perturbations. Furthermore, when multiple optimization objectives are involved it is important to define suitable descriptions for robustness. We introduce robustness measures for robust design with multiple objectives that are suitable for considering the effect of uncertainties in objective space. A direct formulation and a two-phase formulation based on expected losses in objective space are presented for finding robust optimal solutions. We apply both formulations to the robust design of an airfoil. Fluid mechanical quantities are optimized under the consideration of aleatory uncertainties. The uncertainties are propagated with the help of the non-intrusive polynomial chaos approach. The resulting multi-objective optimization problem is solved with a constraint-based approach, that combines adjoint-based optimization methods and evolutionary methods evaluated on surrogate models.


  • Multi-objective optimization
  • Robust design
  • Aerodynamic shape optimization

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  • DOI: 10.1007/978-3-030-57422-2_12
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We would like to thank Lionel Mathelin from LIMSI-CNRS for the joint development of the two-phase approach for multi-objective robust design.

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Correspondence to Lisa Kusch .

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Kusch, L., Gauger, N.R. (2021). Robustness Measures for Multi-objective Robust Design. In: Gaspar-Cunha, A., Periaux, J., Giannakoglou, K.C., Gauger, N.R., Quagliarella, D., Greiner, D. (eds) Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Computational Methods in Applied Sciences, vol 55. Springer, Cham.

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