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- Title
Constraint aggregation for large number of constraints in wing surrogate-based optimization.
- Authors
Zhang, Ke-Shi; Han, Zhong-Hua; Gao, Zhong-Jian; Wang, Yuan
- Abstract
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 parameter ρ can 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.
- Subjects
STRUCTURAL optimization; AIRPLANE wing design; AEROFOIL design &; construction; MATHEMATICAL optimization; MATHEMATICAL functions; HESSIAN matrices
- Publication
Structural & Multidisciplinary Optimization, 2019, Vol 59, Issue 2, p421
- ISSN
1615-147X
- Publication type
Article
- DOI
10.1007/s00158-018-2074-4