Optimization with variable-fidelity models applied to wing design

TLDR

This work introduces the Approximation Management Framework (AMF), an optimization approach that maximizes the use of cheaper, lower‑fidelity models while strategically employing higher‑fidelity simulations to guide the algorithm. AMF is implemented in three variants using nonlinear programming, applied to 3D wing and 2D airfoil optimizations, where Euler analyses on meshes of varying refinement supply the variable‑fidelity models. The framework converges globally to the high‑fidelity solution and achieves roughly three‑fold and two‑fold reductions in high‑fidelity evaluations for the 3D wing and 2D airfoil cases, respectively.

Abstract

This work discusses an approach, the Approximation Management Framework (AMF), for solving optimization problems that involve computationally expensive simulations. AMF aims to maximize the use of lower-fidelity, cheaper models in iterative procedures with occasional, but systematic, recourse to higher-fidelity, more expensive models for monitoring the progress of the algorithm. The method is globally convergent to a solution of the original, high-fidelity problem. Three versions of AMF, based on three nonlinear programming algorithms, are demonstrated on a 3D aerodynamic wing optimization problem and a 2D airfoil optimization problem. In both cases Euler analysis solved on meshes of various refinement provides a suite of variable-fidelity models. Preliminary results indicate threefold savings in terms of high-fidelity analyses in case of the 3D problem and twofold savings for the 2D problem.