C.: Robust Design Optimization

Within the robust design optimization, the statistical variability of the design parameter is considered. The most general method for solving optimization problems under uncertainties is the well established Monte Carlo simulation method. However, the major shortcoming of this approach is its vast need of computational resources (the number of solver runs required), and these cannot be presumed in general situations. This paper reviews theories and methodologies that have been developed to solve optimization problems under uncertainties. In the first part the paper gives an overview over the state of the art in stochastic optimization methods such as robust design and reliability-based design optimization. In addition, new adaptive response surface techniques as well as evolutionary algorithm in combination with first order reliability methods in robust design optimization and reliability-based optimization are developed. A numerical example from structural analysis under static and dynamic loading conditions shows the applicability of these concepts. The probabilistic and structural analysis tasks are performed with the optiSLang and SLang software packages