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Sequential RBF surrogate-based efficient optimization method for engineering design problems with expensive black-box functions

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Abstract

As a promising technique, surrogate-based design and optimization(SBDO) has been widely used in modern engineering design optimizations. Currently, static surrogate-based optimization methods have been successfully applied to expensive optimization problems. However, due to the low efficiency and poor flexibility, static surrogate-based optimization methods are difficult to efficiently solve practical engineering cases. At the aim of enhancing efficiency, a novel surrogate-based efficient optimization method is developed by using sequential radial basis function(SEO-SRBF). Moreover, augmented Lagrangian multiplier method is adopted to solve the problems involving expensive constraints. In order to study the performance of SEO-SRBF, several numerical benchmark functions and engineering problems are solved by SEO-SRBF and other well-known surrogate-based optimization methods including EGO, MPS, and IARSM. The optimal solutions, number of function evaluations, and algorithm execution time are recorded for comparison. The comparison results demonstrate that SEO-SRBF shows satisfactory performance in both optimization efficiency and global convergence capability. The CPU time required for running SEO-SRBF is dramatically less than that of other algorithms. In the torque arm optimization case using FEA simulation, SEO-SRBF further reduces 21% of the material volume compared with the solution from static-RBF subject to the stress constraint. This study provides the efficient strategy to solve expensive constrained optimization problems.

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Author information

Authors and Affiliations

  1. Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, Beijing, 100081, China

    Lei Peng, Li Liu, Teng Long & Xiaosong Guo

  2. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Lei Peng, Li Liu, Teng Long & Xiaosong Guo

Authors
  1. Lei Peng
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  2. Li Liu
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  3. Teng Long
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  4. Xiaosong Guo
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Corresponding author

Correspondence to Teng Long.

Additional information

Supported by National Natural Science Foundation of China(Grant Nos. 51105040, 11372036), Aeronautical Science Foundation of China(Grant Nos. 2011ZA72003, 2009ZA72002), Excellent Young Scholars Research Fund of Beijing Institute of Technology(Grant No. 2010Y0102), and Foundation Research Fund of Beijing Institute of Technology(Grant No. 20130142008)

PENG Lei, born in 1987, is currently a PhD candidate at School of Aerospace Engineering, Beijing Institute of Technology, Beijing, China. He received his bachelor degree from Beijing Institute of Technology, China, in 2009. His research interests include the theories and application of multidisciplinary design optimization, and flight vehicle conceptual optimization design.

LIU Li, born in 1964, is currently a professor at Beijing Institute of Technology, China. She received her PhD degree from Beihang University, China. Her research interests include flight vehicle conceptual design, flight vehicle engineering structural optimization design, multidisciplinary design optimization, flight vehicle guidance and control.

LONG Teng, born in 1982, is currently an associate professor at Beijing Institute of Technology, China. He received his PhD degree from Beijing Institute of Technology, China, in 2009. His research interests include flight vehicle preliminary design, theories and applications of multidisciplinary design optimization, multiple UVAs cooperative control and decision.

GUO Xiaosong, born in 1989, is currently a master candidate at School of Aerospace Engineering, Beijing Institute of Technology, Beijing, China. His research field is flight vehicle conceptual design.

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Peng, L., Liu, L., Long, T. et al. Sequential RBF surrogate-based efficient optimization method for engineering design problems with expensive black-box functions. Chin. J. Mech. Eng. 27, 1099–1111 (2014). https://doi.org/10.3901/CJME.2014.0820.138

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  • DOI: https://doi.org/10.3901/CJME.2014.0820.138

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