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A nonlinear interval-based optimization method with local-densifying approximation technique

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Abstract

In this paper, a new method is proposed to promote the efficiency and accuracy of nonlinear interval-based programming (NIP) based on approximation models and a local-densifying method. In conventional NIP methods, searching for the response bounds of objective and constraints are required at each iteration step, which forms a nested optimization and leads to extremely low efficiency. In order to reduce the computational cost, approximation models based on radial basis functions (RBF) are used to replace the actual computational models. A local-densifying method is suggested to guarantee the accuracy of the approximation models by reconstructing them with densified samples in iterations. Thus, through a sequence of optimization processes, an optimal result with fine accuracy can be finally achieved. Two numerical examples are used to test the effectiveness of the present method, and it is then applied to a practical engineering problem.

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Acknowledgments

This work is supported by the National Science Fund of China for Distinguished Young Scholars (10725208), the National Science Foundation of China (10802028) and the National 973 Program of China under the Grant No. 2010CB832705.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City, 410082, People’s Republic of China

    Ziheng Zhao, Xu Han, Chao Jiang & Xingxing Zhou

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  1. Ziheng Zhao
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  2. Xu Han
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  3. Chao Jiang
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  4. Xingxing Zhou
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Correspondence to Xu Han.

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Zhao, Z., Han, X., Jiang, C. et al. A nonlinear interval-based optimization method with local-densifying approximation technique. Struct Multidisc Optim 42, 559–573 (2010). https://doi.org/10.1007/s00158-010-0501-2

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  • DOI: https://doi.org/10.1007/s00158-010-0501-2

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