Optimization Using Multiple Dominance Criteria for Aerospace Design Under Uncertainty

In optimization under uncertainty for aerospace design, statistical moments of the quantity of interest are often treated as separate objectives and are traded off in a multi-objective optimization formulation. However, in many design problems, the tradeoff between statistical moments can be large, and the Pareto front representing this tradeoff can include designs with undesirable behavior, such as being robust but being guaranteed to give a worse performance than another design. When a simulation of a system is computationally expensive, obtaining the full Pareto front is unfeasible, and so spending optimization time obtaining such undesirable designs wastes time that could be spent obtaining more desirable alternatives. As a remedy, an optimization formulation is proposed that can use multiple dominance criteria to avoid generating potentially inferior designs. Various orders of stochastic dominance are considered as criteria to use alongside statistical moment-based Pareto dominance, and it is illustrated how this gives rise to improved designs using a limited computational budget in an acoustic horn design problem and a transonic airfoil design problem.