Variable-fidelity optimization: Efficiency and robustness

Author: Marduel Xavier   Tribes Christophe   Trépanier Jean-Yves  

Publisher: Springer Publishing Company

ISSN: 1389-4420

Source: Optimization and Engineering, Vol.7, Iss.4, 2006-12, pp. : 479-500

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

This paper deals with variable-fidelity optimization, a technique in which the advantages of high- and low-fidelity models are used in an optimization process. The high-fidelity model provides solution accuracy while the low-fidelity model reduces the computational cost.An outline of the theory of the Approximation Management Framework (AMF) proposed by Alexandrov (1996) and Lewis (1996) is given. The AMF algorithm provides the mathematical robustness required for variable-fidelity optimization.This paper introduces a subproblem formulation adapted to a modular implementation of the AMF. Also, we propose two types of second-order corrections (additive and multiplicative) which serve to build the approximation of the high-fidelity model based on the low-fidelity one.Results for a transonic airfoil shape optimization problem are presented. Application of a variable-fidelity algorithm leads to a threefold savings in high-fidelity solver calls, compared to a direct optimization using the high-fidelity solver only. However, premature stops of the algorithm are observed in some cases.A study of the influence of the numerical noise of solvers on robustness deficiency is presented. The study shows that numerical noise artificially introduced into an analytical function causes premature stops of the AMF. Numerical noise observed with our CFD solvers is therefore strongly suspected to be the cause of the robustness problems encountered.