The traditional multi-objective efficient global optimization (EGO) algorithms have been hybridized and adapted to solving the expensive aerodynamic shape optimization problems based on high-fidelity numerical simulations. Although the traditional EGO algorithms are highly efficient in solving some of the optimization problems with very complex landscape, it is not preferred to solve most of the aerodynamic shape optimization problems with relatively low-degree multi-modal design spaces. A new infill criterion encouraging more local exploitation has been proposed by hybridizing two traditional multi-objective expected improvements (EIs), namely, statistical multi-objective EI and expected hypervolume improvement, in order to improve their robustness and efficiency in aerodynamic shape optimization. Different analytical test problems and aerodynamic shape optimization problems have been investigated. In comparison with traditional multi-objective EI algorithms and a standard evolutionary multi-objective optimization algorithm, the proposed method is shown to be more robust and efficient in the tests due to its hybrid characteristics, easier handling of sub-optimization problems, and enhanced exploitation capability.

传统的多目标高效全局优化 (EGO) 算法已经混合并适用于解决基于高保真数值模拟的昂贵的空气动力学形状优化问题。虽然传统的 EGO 算法在解决一些非常复杂的景观优化问题方面效率很高，但对于解决大多数具有相对低阶多模态设计空间的气动形状优化问题来说，并不是首选。通过混合两种传统的多目标预期改进 (EI)，即统计多目标 EI 和预期超体积改进，提出了一种鼓励更多局部开发的新填充标准，以提高它们在空气动力学形状优化中的鲁棒性和效率。已经研究了不同的分析测试问题和空气动力学形状优化问题。与传统的多目标EI算法和标准的进化多目标优化算法相比，所提出的方法由于其混合特性、更容易处理子优化问题和增强的开发能力，在测试中表现出更强的鲁棒性和效率。能力。