Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers
Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers
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DOI：
10.2514/1.45331
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发表时间：
2010-05-01
期刊：
影响因子：
2.5
通讯作者：
Sagaut, P.
中科院分区：
文献类型：
--
作者：
Laurenceau, J.;Meaux, M.;Sagaut, P.
本文用高保真度求解器研究气动外形优化问题。由于求解reynolds -average Navier-Stokes方程所需的计算成本，尽管有大量的设计变量，但必须使用很少的目标函数评估来提高形状的性能。在我们的框架中，参考算法是一个准牛顿梯度优化器。伴随方法计算函数相对于设计变量的灵敏度，以便宜地建立目标函数的梯度。通常，当形状变化时，空气动力学函数会显示出许多局部最优，而一个更全局的优化器有望是有益的。因此，建立并描述了一个基于克里格的优化器。它使用原始的采样细化过程，通过使用函数最小化和误差最小化之间的平衡，每次迭代增加三个点。为了有效地将该算法应用于高维问题，重复使用相同的采样过程，形成基于cokriging（梯度增强模型）的优化器。比较研究，然后描述了两个拖曳最小化问题取决于6和45个设计变量。本研究使用了一套原始的性能标准，从改进、成本、勘探和开发等方面描述了每个优化器的优缺点。
This paper deals with aerodynamic shape optimization using a high-fidelity solver. Because of the computational cost needed to solve the Reynolds-averaged Navier-Stokes equations, the performance of the shape must be improved using very few objective function evaluations, despite the high number of design variables. In our framework, the reference algorithm is a quasi-Newton gradient optimizer. An adjoint method inexpensively computes the sensitivities of the functions, with respect to design variables, to build the gradient of the objective function. As usual, aerodynamic functions show numerous local optima when the shape varies, and a more global optimizer is expected to be beneficial. Consequently, a kriging-based optimizer is set up and described. It uses an original sampling refinement process that adds up to three points per iteration by using a balancing between function minimization and error minimization. To efficiently apply this algorithm to high-dimensional problems, the same sampling process is reused to form a cokriging (gradient-enhanced model) based optimizer. A comparative study is then described on two drag-minimization problems depending on 6 and 45 design variables. This study was conducted using an original set of performance criteria, characterizing the strength and weakness of each optimizer in terms of improvement, cost, exploration, and exploitation.