This paper presents a new approach for optimization under uncertainty in the presence of probabilistic, interval, and mixed uncertainties, avoiding the need to specify probability distributions on uncertain parameters when such information is not readily available. Existing approaches for optimization under these types of uncertainty mostly rely on treating combinations of statistical moments as separate objectives, but this can give rise to stochastically dominated designs. Here, horsetail matching is extended for use with these types of uncertainties to overcome some of the limitations of existing approaches. The formulation delivers a single, differentiable metric as the objective function for optimization. It is demonstrated on algebraic test problems, the design of a wing using a low-fidelity coupled aerostructural code, and the aerodynamic shape optimization of a wing using computational fluid dynamics analysis.This work was funded by the Engineering and Physical Sciences Research Council, grant number EP/L504920/1. The third author acknowledges support of the U.S. Air Force Office of Scientic Research Multidisciplinary Research Program of the University Research Initiative on managing multiple information sources of multiphysics systems, program manager Jean-Luc Cambier, award number FA9550-15-1-0038
