実世界問題の効率的解決に向けた多点並列追加サンプリング多目的Multi-Fidelity設計法の開発と翼型最適化問題への適用

抄録

In this study, a multi-fidelity approach was developed based on the efficient global optimization (EGO) and integrated with multi-additional sampling. The developed approach was more efficient than the conventional multi-fidelity approach when applied to design problems. The effectiveness of the proposed approach was demonstrated by solving two test problems (a test problem in Van Valedhuizen’s test suite and a test problem with a convex Pareto front) before applying the approach to real-world problems. As a demonstration of solving real-world problem, we solved two objective airfoil design problems for a small unmanned airplane. The objective functions were the drag coefficient (for flight efficiency) and the thickness at the 75% chord position (for structural strength and manufacturability). The results of the test problems revealed that the proposed approach obtained more non-dominant solutions near the theoretical Pareto front than those obtained by the Original optimization approach at the same iteration number of EGO loop; this is because the proposed approach obtained more additional samples than the Original optimization approach (multi-objective multi-fidelity EGO without multi-additional sampling) per additional sampling loop. A comparison of the accuracies of surrogate models based on the proposed approach and the Original optimization approach using leave-one-out cross validation suggested that, depending on the optimization problem, one of the two approaches can yield greater accuracy. The airfoil design results, as well as the test problems, revealed that the proposed approach can obtain several better solutions than those obtained by the Original optimization approach when the number of iterations of additional sampling was the same between both approaches. The hypervolume in the proposed approach also increases more rapidly than that in the Original optimization approach.