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Appl. Sci. 2017, 7(12), 1318; doi:10.3390/app7121318

Multi-Fidelity Multi-Objective Efficient Global Optimization Applied to Airfoil Design Problems

Department of Aerospace Engineering, Graduate School of System Design, Tokyo Metropolitan University, Hino-shi, Tokyo 191-0065, Japan
These authors contributed equally to this work.
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Received: 30 October 2017 / Revised: 29 November 2017 / Accepted: 15 December 2017 / Published: 18 December 2017
(This article belongs to the Special Issue Soft Computing Techniques in Structural Engineering and Materials)
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Abstract

In this study, efficient global optimization (EGO) with a multi-fidelity hybrid surrogate model for multi-objective optimization is proposed to solve multi-objective real-world design problems. In the proposed approach, a design exploration is carried out assisted by surrogate models, which are constructed by adding a local deviation estimated by the kriging method and a global model approximated by a radial basis function. An expected hypervolume improvement is then computed on the basis of the model uncertainty to determine additional samples that could improve the model accuracy. In the investigation, the proposed approach is applied to two-objective and three-objective optimization test functions. Then, it is applied to aerodynamic airfoil design optimization with two objective functions, namely minimization of aerodynamic drag and maximization of airfoil thickness at the trailing edge. Finally, the proposed method is applied to aerodynamic airfoil design optimization with three objective functions, namely minimization of aerodynamic drag at cruising speed, maximization of airfoil thickness at the trialing edge and maximization of lift at low speed assuming a landing attitude. XFOILis used to investigate the low-fidelity aerodynamic force, and a Reynolds-averaged Navier–Stokes simulation is applied for high-fidelity aerodynamics in conjunction with a high-cost approach. For comparison, multi-objective optimization is carried out using a kriging model only with a high-fidelity solver (single fidelity). The design results indicate that the non-dominated solutions of the proposed method achieve greater data diversity than the optimal solutions of the kriging method. Moreover, the proposed method gives a smaller error than the kriging method. View Full-Text
Keywords: multi-fidelity optimization; efficient global optimization; multi-objective optimization; airfoil design multi-fidelity optimization; efficient global optimization; multi-objective optimization; airfoil design
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Ariyarit, A.; Kanazaki, M. Multi-Fidelity Multi-Objective Efficient Global Optimization Applied to Airfoil Design Problems. Appl. Sci. 2017, 7, 1318.

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