Kriging模型及代理优化算法研究进展

代理模型方法由于能显著提高工程优化设计问题的效率，在航空航天及其他领域得到了广泛重视，并逐渐发展成为一类优化算法，本文称其为代理优化（SBO）算法。在现有的代理模型方法中，如多项式响应面、径向基函数、神经网络、支持向量回归、多变量插值/回归、多项式混沌展开等，源于地质统计学的Kriging模型具有代表性，是一种非常具有应用潜力的代理模型方法。以飞行器设计领域的优化问题为背景，介绍了Kriging代理模型及应用于优化设计的理论和算法的最新研究进展。首先，概述了Kriging模型的基本理论和算法，并讨论了影响Kriging模型鲁棒性和效率的几个关键性问题。其次，回顾了Kriging模型理论和算法研究的3个最新研究进展，包括梯度增强型Kriging、CoKriging和分层Kriging模型。而后，分析提炼了基于Kriging模型的代理优化算法的优化机制和优化框架，给出了“优化加点准则”和“子优化”的概念，并介绍了目前常用的几种优化加点准则及其相应子优化问题的求解与约束处理；同时，还介绍了最新提出的局部EI加点准则以及代理优化的终止条件。最后，介绍了代理优化在标准测试函数算例验证、飞行器气动与多学科优化设计典型算例确认方面的研究进展，并对当前存在的一些关键科学问题以及未来研究方向进行了讨论。

Kriging surrogate model and its application to design optimization:A review of recent progress

Over the past two decades, surrogate modeling has received much attention from the researchers in the area of aerospace science and engineering due to its capability of greatly improving the efficiency of design optimization when high-fidelity numerical analysis is employed. Design optimization via surrogate models is intensively researched and eventually leads to a new type of optimization algorithm which is called surrogate-based optimization (SBO). Among the available surrogate models, such as polynomial response surface model, radial-basis functions, artificial neutral network, support-vector regression, multivariate interpolation or regression, and polynomial chaos expansion, Kriging model is the most representative surrogate model which has great potential in engineering design and optimization. In the context of aircraft design, this paper reviews the theory, algorithm and recent progress for researches on the Kriging surrogate model. First, the fundamental theory and algorithm of Kriging model are briefly reviewed and the experience about how to improve the robustness and efficiency is presented. Second, three major breakthroughs of Kriging model in recent years are reviewed, including gradient-enhanced Kriging, CoKriging and hierarchical Kriging. Third, the optimization mechanism and framework of surrogate-based optimization using Kriging model are discussed. In the meanwhile, the concept of infill-sampling criterion and sub optimization is presented. Five infill-sampling criteria as well as the dedicated constraint handling methods are described. Furthermore, the newly developed local EI (expected improvement) method and termination criteria for SBO are introduced. Fourth, a number of test cases including benchmark optimization problems as well as aerodynamic and multidisciplinary design optimization problems are given to demonstrate the excellent performance and great potential of the surrogate-based optimization using Kriging model. At last, the key challenges as well as future directions about the theory, algorithm and applications are discussed.