Variable-fidelity optimization: efficiency and robustness. (English) Zbl 1179.76074
Summary: 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 N. M. Alexandrov [in: 6th AIAA/NASA/USA/ISSMO symposium on multidisciplinary analysis and optimization, AIAA 1996-4102, Bellevue, WA (1996)] and R. M. Lewis [in: 6th AIAA/NASA/USA/ISSMO symposium on multidisciplinary analysis and optimization, AIAA 1996-4101, Bellevue, WA (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.
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.
MSC:
| 76N25 | Flow control and optimization for compressible fluids and gas dynamics |
| 76H05 | Transonic flows |
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