Constraint aggregation for large number of constraints in wing surrogate-based optimization
Constraint aggregation for large number of constraints in wing surrogate-based optimization
复制标题
基于机翼代理的优化中大量约束的约束聚合
DOI：
10.1007/s00158-018-2074-4
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发表时间：
2018-09
影响因子：
3.9
通讯作者：
Wang Yuan
中科院分区：
文献类型：
--
作者：
Zhang Ke-Shi;Han Zhong-Hua;Gao Zhong-Jian;Wang Yuan
将大量约束聚合为一个或几个约束的方法已成功地应用于基于梯度局部优化的机翼结构设计。然而，在聚集约束的局部曲率变得非常大从而可能产生病态Hessian矩阵的情况下，可能会出现数值困难。本文的目的是在无梯度优化的框架内测试不同的约束聚集方法，该优化利用评估成本低的代理模型来寻找全局最优解。研究了三种约束集结方法：最大约束法、常参数Kreisselmeier-Steinhauser(KS)函数和自适应KS函数。我们还探索了在整个结构和子领域内聚合约束的方法。以某运输机机翼为例进行了结构优化和气动结构优化，结果表明：(1)固定参数ρ较大的KS函数可以得到比自适应方法更好的优化结果，因为主动约束被更准确地逼近；(2)将约束集中在子域内而不是全部集中在一起可以提高聚集约束的精度，从而有助于找到更好的设计方案。最后，从目前的测试案例中得出结论，基于机翼代理优化的大规模约束处理最有效的方法是在子域内聚集约束，并且具有相对较大的常量参数。
The method of aggregating a large number of constraints into one or few constraints has been successfully applied to wing structural design using gradient-based local optimization. However, numerical difficulties may occur in the case that the local curvatures of the aggregated constraint become extremely large and then ill-conditioned Hessian matrix may be yielded. This paper aims to test different methods of constraint aggregation within the framework of a gradient-free optimization, which makes use of cheap-to-evaluate surrogate models to find the global optimum. Three constraint aggregation approaches are investigated: the maximum constraint approach, the constant parameter Kreisselmeier-Steinhauser (KS) function, and the adaptive KS function. We also explore methods of aggregating constraints over the entire structure and within sub-domains. Examples of structural optimization and aero-structural optimization for a transport aircraft wing are employed and the results show that (1) the KS function with a larger constant parameterρcan lead to better optimization results than the adaptive method, as the active constraints are approximated more accurately; (2) lumping the constraints within sub-domains instead of all together can improve the accuracy of the aggregated constraint and therefore helps find a better design. Finally, it is concluded from current test cases that the most efficient way of handling large-scale constraints for wing surrogate-based optimization is to aggregate constraints within sub-domains and with a relatively large constant parameter.
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影响因子：
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作者：
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通讯作者：
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