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In this paper, we investigate the use of multiple kernel functions for assisting single-objective Kriging-based efficient global optimization (EGO). The primary objective is to improve the robustness of EGO in terms of the choice of kernel function for solving a variety of black-box optimization problems in engineering design. Specifically, three widely used kernel functions are studied, that is, Gaussian, Matérn-3/2, and Matérn-5/2 function. We investigate both model selection and ensemble techniques based on Akaike information criterion (AIC) and cross-validation error on a set of synthetic (noiseless and noisy) and non-algebraic (aerodynamic and parameter tuning) optimization problems; in addition, the use of cross-validation-based local (i.e., pointwise) ensemble is also studied. Since all the constituent surrogate models in the ensemble scheme are Kriging models, it is possible to perform EGO since the Kriging uncertainty structure is still preserved. Through analyses of empirical experiments, it is revealed that the ensemble techniques improve the robustness and performance of EGO. It is also revealed that the use of Matérn-kernels yields better results than those of the Gaussian kernel when EGO with a single kernel is considered. Furthermore, we observe that model selection methods do not yield any substantial improvement over single kernel EGO. When averaged across all types of problem (i.e., noise level, dimensionality, and synthetic/non-algebraic), the local ensemble technique achieves the best performance. [ABSTRACT FROM AUTHOR]

This paper describes the optimal flight of a discus. Two objective functions are considered. One is the flight distance, and the other is robustness. Robustness is defined as insensitivity to deviations from the local optimal release conditions. The aim of the optimization is to maximize both flight distance and robustness. There are ten control and design variables, which include variables concerned with the skill of the thrower and with the design of the equipment. It was found that there is a trade-off between flight distance and robustness. It was also found that lower drag is preferable in the first half of flight, and greater lift and drag are preferable in the latter half of flight for the world record throw of 77 m. In order to do this, the initial angle between the velocity vector and the discus planform should be negative at the launch, even if the initial lift acts vertically downward. The attitude of the discus should be inclined at launch. The discus rolls with time during the flight, so that the discus planform becomes almost in the horizontal plane in the latter half of the flight. Lower mass is good for achieving longer flight distance, but conversely, mass should be slightly greater for robustness. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes optimization of the size and launch conditions of a discus. The objective function for optimization is the flight distance. Longer flight distance is better. Fourteen design variables are considered. Eight of the fourteen are concerned with the skill of the thrower. They determine the launch conditions, which are controlled by the thrower when he or she throws. The other six variables are concerned with the design of the equipment. These are the dimensions of the discus (width, thickness, radius of the metal rim and diameter of the flat center area on each side), the moment of inertia on the axis of symmetry and finally the mass of the discus. The dependences of size and the angle of attack on the aerodynamic data are estimated by using CFD (computational fluid dynamics) technique. Typical CFD results, including the effect of stalling, were confirmed by comparing the results with experimental data. As a result, the longest flight distance that could be achieved was 79 meters. In order to do this, the initial yaw rate on the axis of symmetry should be maximized. The mass should be the smallest. The moment of inertia on the axis of symmetry, the diameter of the flat center area and the width should be designed to be large. The air inflow to the discus should arrive from the upper side at the very beginning of the flight. [Copyright &y& Elsevier]

Multi-objective optimization in aerodynamics plays an important role in revealing trade-offs between conflicting objectives in order to discover important knowledge and insight for better future design. Of interest here is the use of Kriging surrogate models incorporated into a sequential Bayesian optimization (BO) strategy. In this paper, we studied four variants of multi-objective BO (MOBO) techniques that are based on expected improvement (EI), that is, Euclidean-based EI (EEI), expected hypervolume improvement (EHVI), ParEGO, and expected inverted penalty boundary intersection improvement (EIPBII) to understand their capabilities on handling multi-objective aerodynamic optimization problems. Numerical tests were performed on a set consisting of six generalized Schaffer problems (GSP), five low-fidelity, and one high-fidelity airfoil design problems. Results suggest that EHVI is the only method which consistently performed well on artificial and aerodynamic problems. EEI yields the worst performance and is not suitable to deal with various problem complexities. ParEGO, although it performs modestly on GSP, surprisingly works well on the low- and high-fidelity problems. On the other hand, EIPBII encounters the opposite case, where it is one of the best performer on GSP but yields modest performance on the aerodynamic problems. In light of the results, we suggest that EHVI is a highly potential MOBO method to be applied for multi-objective aerodynamic design optimization. [ABSTRACT FROM AUTHOR]