# A developed surrogate-based optimization framework combining HDMR-based modeling technique and TLBO algorithm for high-dimensional engineering problems

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## Abstract

The traditional surrogate-based optimization techniques are facing severe challenges for high-dimensional engineering optimization problems. The main challenges are how to overcome metamodeling and optimization difficulties in high-dimensional design space. To solve the above difficulties, a developed surrogate-based optimization framework combining high-dimensional model representation (HDMR)-based modeling technique and teaching-learning-based optimization (TLBO) algorithm is developed. A high-dimensional model can be decomposed into a series of low-dimensional models by HDMR-based modeling technique, which can greatly reduce the difficulty of building high-dimensional model. The TLBO algorithm which has strong optimization ability and non-parameter setting characteristic is introduced to optimize the HDMR-based model to overcome the difficulty of optimization. Several representative functions are selected as examples to verify the developed optimization method for high-dimensional problems. In addition, The developed surrogate-based optimization is applied to solve a typical engineering optimization problem: high-dimensional aerodynamic shape optimization. It can be concluded that the optimization ability of the traditional surrogate-based optimization framework can be improved with assistance of HDMR-based modeling technique and TLBO algorithm for high-dimensional engineering problems.

## Keywords

High-dimensional engineering problems Surrogate model High-dimensional model representation (HDMR) Teaching-learning-based optimization (TLBO) Aerodynamic shape optimization## Notes

### Funding information

“111” project of China (No. B17037), the National Science Fund for Excellent Young Scholars (No. 11622220) supported this work, China Postdoctoral Science Foundation (2018 M643588).

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