## 6 Conclusions  
In this article, a multi-fidelity/multi-objective EGO combined with kriging and RBF was proposed based on the hybrid surrogate model to solve the multi-objective optimization problems and was applied to solve the multi-objective airfoil design problem. The proposed method constructed a hybrid surrogate model based on an RBF that predicts a global model and an ordinary kriging method that predicts the local variance. EHVI was used as an index to find additional samples for the optimization process. For multi-fidelity optimization, the global model was constructed using a dataset evaluated by a low-fidelity function, and the local variance was estimated using a dataset evaluated by a high-fidelity function. To examine the proposed multi-fidelity/multi-objective EGO, two-/three-objective test problems were solved, and the results of the proposed multi-fidelity/multi-objective EGO were compared with those of the single-fidelity/multi-objective EGO. The results for the test functions showed that the proposed multi-fidelity/multi-objective EGO achieves faster convergence than the single-fidelity/multi-objective EGO. Moreover, the results showed that the proposed multi-fidelity/multi-objective EGO has greater diversity of the non-dominated solutions than the single-fidelity/multi-objective EGO. In addition, the results showed that the proposed multi-fidelity/multi-objective EGO has fewer global errors. Thus, the proposed multi-fidelity/multi-objective EGO can be widely applied to real-world problems. Further, the proposed multi-fidelity/multi-objective EGO was applied to an aerodynamic airfoil shape optimization problem with two objectives: minimize \(\mathrm{C_{d}}\) at cruising speed and maximize the thickness around the trialing edge. To evaluate the aerodynamic performance, XFOIL was used to construct a low-fidelity/low-cost dataset, and a Navier-Stokes solver was used to construct a high-fidelity/high-cost dataset. The results of the proposed multi-fidelity/multi-objective EGO were compared with those of the single-fidelity/multi-objective EGO. The optimization results showed that the proposed multi-fidelity/multi-objective EGO achieves greater diversity of the non-dominated solutions than the single-fidelity/multi-objective EGO. In addition, the cross-validation results showed that the proposed multi-fidelity/multi-objective EGO has fewer global errors. Finally, the proposed multi-fidelity/multi-objective EGO was applied to an aerodynamic airfoil shape optimization problem with three objectives: minimize \(\mathrm{C_{d}}\) at cruising speed, maximize the thickness around the trialing edge and maximize \(\mathrm{C_{l}}\) in the landing condition. The results showed that the proposed multi-fidelity/multi-objective EGO achieves greater diversity of the non-dominated solutions than the single-fidelity/multi-objective EGO. In addition, the error between the exact value and the predicted value of the hybrid surrogate model was smaller than that of the single-fidelity model. These results  
Figure 18: Comparison of design geometries of three-objective airfoil shape optimization problem: (**a**) multi-fidelity approach; (**b**) single-fidelity approach. suggest that the multi-fidelity/multi-objective EGO is suitable for real-world multi-objective design problems. In this study, we limited the optimization to two/three objectives for simple aerodynamic design problems. In the future, we expect that our algorithm will be used to solve more complicated design problems, and we will investigate the effects of the application of multi-fidelity data in advanced kriging methods such as universal kriging and anisotropy kriging. The author would like to express deep appreciation and to special thanks to the studies funded by the Asian Human Resources Fund (AHRF) from the Tokyo Metropolitan Government to the Tokyo Metropolitan University (TMU). Although [PERSON] developed the algorithm/performed the experiment/analysis of the data and wrote the paper; [PERSON] performed analysis of data and wrote the paper.