Risk measures in the context of robust and reliability based optimization

Abstract

The base concepts of robust optimization are described and detailed in this chapter. In particular, the approach based on risk measurements is introduced, after a first quick review of the classical deterministic approach. In this context, the use of some special classes of risk measures, used in financial engineering, is reported along with the main advantages and drawbacks related to their mathematical features. The usage of these risk measures will be then illustrated in an example problem of robust aerodynamic design optimization. The focus is also given to advanced techniques for error and confidence interval estimations and how they can be used in the context of robust optimization to improve the overall efficiency and effectiveness of the process.