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Constrained mixed-integer Gaussian mixture Bayesian optimization and its applications in designing fractal and auxetic metamaterials

  • Anh Tran
  • Minh Tran
  • Yan Wang
Research Paper
  • 70 Downloads

Abstract

Bayesian optimization (BO) is a global optimization method that has the potential for design optimization. However, in classical BO algorithm, the variables are considered as continuous. In real-world engineering problems, both continuous and discrete variables are present. In this work, an efficient approach to incorporate discrete variables to BO is proposed. In the proposed constrained mixed-integer BO method, the sample set is decomposed into smaller clusters during sequential sampling, where each cluster corresponds to a unique ordered set of discrete variables, and a Gaussian process regression (GP) metamodel is constructed for each cluster. The model prediction is formed as the Gaussian mixture model, where the weights are computed based on the pair-wise Wasserstein distance between clusters and gradually converge to an independent GP as the optimization process advances. The definition of neighborhood can be flexibly and manually defined to account for independence between clusters, such as in the case of categorical variables. Theoretical results are provided in concert with two numerical and engineering examples, and two examples for metamaterial developments, including one fractal and one auxetic metamaterials, where the effective properties depend on both the geometry and the bulk material properties.

Keywords

Bayesian optimization Gaussian process Constrained Mixed-integer Metamaterials 

Notes

Acknowledgments

Authors thank Prof. Hongyuan Zha (Georgia Tech) for numerous helpful conversations about Bayesian optimization. The authors are grateful to two anonymous reviewers for their constructive feedback.

Funding information

The research was supported in part by the National Science Foundation under grant number CMMI-1306996. Also, this research was supported in part through research cyberinfrastructure resources and services provided by the Partnership for an Advanced Computing Environment (PACE) at the Georgia Institute of Technology, Atlanta, GA, USA.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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