Uncertainty quantification methods for evolutionary optimization under uncertainty

In this paper, we discuss the role of uncertainty quantification (UQ) in assisting optimization under uncertainty. UQ plays a significant role in quantifying the robustness of solutions so as to help the optimizer in achieving robust optimum solutions. In this respect, the scientific discipline of UQ addresses various theoretical and practical aspects of uncertainty, which include representations of uncertainty and also efficient computation of the output uncertainty, to name a few. However, the UQ community and the evolutionary computation community rarely interact with each other despite the potential of utilizing the advancement in UQ for research in evolutionary computation. To that end, this paper serves as a short introduction to the science of UQ for the evolutionary computation community. We discuss several aspects of UQ for robust optimization such as aleatory and epistemic uncertainty and objective functions when uncertainties are considered. A tutorial on an aerodynamic design problem is also given to illustrate the use of UQ in a real-world problem.