Bayesian Optimization Based on Student’s T Process for Microstrip Antenna Design

Authors

  • Qing Li Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212003, China
  • Fei Meng School of Information and Communication Engineering, Guangzhou Maritime University, Guangzhou 510725, China
  • Yubo Tian School of Information and Communication Engineering, Guangzhou Maritime University, Guangzhou 510725, China
  • Xiaoyan Wang Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212003, China

DOI:

https://doi.org/10.13052/2022.ACES.J.370804

Keywords:

acquisition function, Antenna optimization, Bayesian Optimization, Gaussian process, Student’s T process

Abstract

Bayesian Optimization (BO) is an efficient global optimization algorithm, which is widely used in the field of engineering design. The probabilistic surrogate model and acquisition function are the two keys to the algorithm. Building an efficient probabilistic surrogate model and designing a collection function with excellent exploring capabilities can improve the performance of BO algorithm, allowing it to find the optimal value of the objective function with fewer iterations. Due to the characteristics of small samples and non-parametric derivation of the Gaussian Process (GP), traditional BO algorithms usually use the GP as a surrogate model. Compared with the GP, the Student’s T Process (STP) retains the excellent properties of GP, and has more flexible posterior variance and stronger robustness. In this paper, STP is used as the surrogate model in BO algorithm, the hyperparameters of the model are optimized by STP, and the estimation strategy function (EST) is improved based on the posterior output of the optimized STP, thus realizing the improved BO algorithm based on the STP. To verify the performance of the proposed algorithm, numerical experiments are designed to compare the performances of the traditional BO algorithm, which includes the lower confidence bound function (LCB) and EST as acquisition function respectively and GP as the surrogate model, and the proposed BO algorithm with STP as the surrogate model and LCB, expected improvement function (EI), expected regret minimization function (ERM) as acquisition function respectively. The results show that the proposed algorithm in this paper performs well when finding the global minimum of multimodal functions. Based on the developed algorithm in this paper, the resonant frequency of printed dipole antenna and E-shaped antenna is modeled and optimized, which further confirms the good design ability and design accuracy of the BO algorithm proposed in this paper.

Downloads

Download data is not yet available.

Author Biographies

Qing Li, Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Qing Li was Born in Anqing, Anhui Province, China, studying in Jiangsu University of science and technology, master’s degree, research direction: intelligent optimization algorithm, intelligent electromagnetic optimization.

Fei Meng, School of Information and Communication Engineering, Guangzhou Maritime University, Guangzhou 510725, China

Fei Meng was born in Shenyang, Liaoning Province, China, in 1977. She is currently with the School of Information and Communication Engineering, Guangzhou Maritime University, Guangzhou, China. She has authored and coauthored 10 Journal papers. Her research interest is surrogates and their applications.

Yubo Tian, School of Information and Communication Engineering, Guangzhou Maritime University, Guangzhou 510725, China

Yubo Tian was born in Tieling, Liaoning Province, China, in 1971. He received the Ph.D. degree in radio physics from the De-partment of Electronic Science and Engineering, Nanjing University, Nanjing, China. He has been a visiting scholar at the University of California Los Angeles in 2009 and the Griffith University in 2015, respectively. From 1997 to 2004, he was with the Department of Information Engineering, Shenyang University, Shenyang, China. From 2005 to 2020, he was with the School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang, China, where he was a full professor and vice Dean from 2011. He is currently with the School of Information and Communication Engineering, Guangzhou Maritime University, Guangzhou, China. Dr. Tian has authored and coauthored more than 100 Journal papers and 3 books. He also holds more than 20 filed/granted China patents. His current research interest is Machine Learning methods and their applications in electronics and electromagnetics.

Xiaoyan Wang, Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Xiaoyan Wang studying in Jiangsu University of science and technology, master’s degree, research direction: intelligent optimization algorithm, intelligent electromagnetic optimization.

References

L. Acerbi and W. J. Ma, “Practical Bayesian optimization for model fitting with Bayesian adaptive direct search,” Advances in Neural Information Processing Systems, vol. 30, 2017.

V. Nguyen, S. Schulze, and M. Osborne, “Bayesian optimization for iterative learning,” Advances in Neural Information Processing Systems, vol. 33, pp. 9361-9371, 2020.

M. Wistuba and J. Grabocka, “Few-shot bayesian optimization with deep kernel surrogates,” arXiv preprint arXiv:2101.07667, 2021.

D. Yenicelik, “Parameter Optimization using high-dimensional Bayesian Optimization,” arXiv preprint arXiv:2010.03955, 2020.

J. Mockus, V. Tiesis, and A. Zilinskas, “The application of Bayesian methods for seeking the extremum,” Towards Global Optimization, vol. 2, no. 117-129, p. 2, 1978.

L. Breiman, “Random forests,” Machine Learning, vol. 45, no. 1, pp. 5-32, 2001.

J. Snoek, O. Rippel, K. Swersky, R. Kiros, N. Satish, N. Sundaram, M. Patwary, M. Prabhat, and R. Adams, “Scalable bayesian optimization using deep neural networks,” International Conference on Machine Learning, pp. 2171-2180,2015.

S. R. Chowdhury and A. Gopalan, “No-regret algorithms for multi-task bayesian optimization,” International Conference on Artificial Intelligence and Statistics, pp. 1873-1881, 2021.

D. Ginsbourger, R. L. Riche, and L. Carraro, “Kriging is well-suited to parallelize optimization,” Computational Intelligence in Expensive Optimization Problems, pp. 131-162, 2010.

Z. Feng, Q. Zhang, Q. Zhang, Q. Tang, T. Yang, and Y. Ma, “A multiobjective optimization based framework to balance the global exploration and local exploitation in expensive optimization,” Journal of Global Optimization, vol. 61, no. 4, pp. 677-694, 2015.

S. Han, Y. Tian, W. Ding, and P. Li, “Resonant frequency modeling of microstrip antenna based on deep kernel learning,” IEEE Access, vol. 9, pp. 39067-39076, 2021.

T. Zhang, Y. Tian, X. Chen, and J. Gao, “Antenna Resonant Frequency Modeling based on AdaBoost Gaussian Process Ensemble,” Applied Computational Electromagnetics Society (ACES) Journal, pp. 1485-1492, 2020.

A. O’Hagan, “On outlier rejection phenomena in Bayes inference,” Journal of the Royal Statistical Society: Series B (Methodological), vol. 41, no. 3, pp. 358-367, 1979.

A. Shah, A. Wilson, and Z. Ghahramani, “Student-T processes as alternatives to Gaussian processes,” Artificial Intelligence and Statistics, pp. 877-885, 2014.

A. Solin and S. Särkkä, “State space methods for efficient inference in Student-t process regression,” Artificial Intelligence and Statistics, pp. 885-893, 2015.

Q. Tang, L. Niu, Y. Wang, T. Dai, W. An, J. Cai, and S.-T. Xia, “Student-T process regression with Student-T likelihood,” IJCAI, pp. 2822-2828, 2017.

Z. Chen, B. Wang, and A. N. Gorban, “Multivariate Gaussian and Student-T process regression for multi-output prediction,” Neural Computing and Applications, vol. 32, no. 8, pp. 3005-3028,2020.

W. Wang, Q. Yu, and M. Fasli, “Altering Gaussian process to Student-T process for maximum distribution construction,” International Journal of Systems Science, vol. 52, no. 4, pp. 727-755, 2021.

L. Kang, R.-S. Chen, N. Xiong, Y.-C. Chen, Y.-X. Hu, and C.-M. Chen, “Selecting hyper-parameters of Gaussian process regression based on non-inertial particle swarm optimization in Internet of Things,” IEEE Access, vol. 7, pp. 59504-59513, 2019.

Z. Le, L. Zhong, Z. Jianqiang, and R. Xiongwei, “Improved Gaussian process model based on artificial bee colony algorithm optimization,” Journal of National University of Defense Science and Technology, p. 7, 2014.

A. Shah, A. G. Wilson, and Z. Ghahramani, “Bayesian optimization using Student-T processes,” NIPS Workshop on Bayesian Optimization, 2013.

B. D. Tracey and D. Wolpert, “Upgrading from Gaussian processes to Student’s T processes,” 2018 AIAA Non-Deterministic Approaches Conference, p. 1659, 2018.

C. Clare, G. Hawe, and S. McClean, “Expected regret minimization for bayesian optimization with Student’s-T processes,” Artificial Intelligence and Pattern Recognition, pp. 8-12, 2020.

W. Ding, Y. Tian, P. Li, H. Yuan, and R. Li, “Antenna optimization based on master-apprentice broad learning system,” International Journal of Machine Learning and Cybernetics, vol. 13, no. 2, pp. 461-470, 2022.

J. Gao, Y. Tian, X. Zheng, and X. Chen, “Resonant frequency modeling of microwave antennas using Gaussian process based on semisupervised learning,” Complexity, vol. 2020, 2020.

H. M. Torun, M. Swaminathan, A. K. Davis, and M. L. F. Bellaredj, “A global Bayesian optimization algorithm and its application to integrated system design,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 26, no. 4, pp. 792-802, 2018.

Z. Wang, B. Zhou, and S. Jegelka, “Optimization as estimation with Gaussian processes in bandit settings,” Artificial Intelligence and Statistics, pp. 1022-1031, 2016.

C. E. Rasmussen, “Gaussian processes in machine learning,” Summer School on Machine Learning, pp. 63-71, 2003.

W. P. du Plessis and J. P. Jacobs, “Improved Gaussian Process Modelling of On-Axis and Off-Axis Monostatic RCS Magnitude Responses of Shoulder-Launched Missiles,” Applied Computational Electromagnetics Society (ACES) Journal, pp. 1750-1756, 2019.

J. Vanhatalo, P. Jylänki, and A. Vehtari, “Gaussian process regression with Student-t likelihood,” Advances in Neural Information Processing Systems, vol. 22, 2009.

Q. T. Y. Wang and S.-T. Xia, “Student-T process regression with dependent Student-t noise,” ECAI 2016: 22nd European Conference on Artificial Intelligence, 29 August-2 September 2016, The Hague, The Netherlands-Including Prestigious Applications of Artificial Intelligence (PAIS 2016), vol. 285, p. 82, 2016.

S. Greenhill, S. Rana, S. Gupta, P. Vellanki, and S. Venkatesh, “Bayesian optimization for adaptive experimental design: A review,” IEEE Access, vol. 8, pp. 13937-13948, 2020.

A. M. Beigi and A. Maroosi, “Parameter identification for solar cells and module using a hybrid firefly and pattern search algorithms,” Solar Energy, vol. 171, pp. 435-446, 2018.

D. Calandriello, L. Carratino, A. Lazaric, M. Valko, and L. Rosasco, “Gaussian process optimization with adaptive sketching: Scalable and no regret,” Conference on Learning Theory, pp. 533-557, 2019.

L. A. Martín and E. C. Garrido-Merchán, “Many Objective Bayesian Optimization,” arXiv preprint arXiv:2107.04126, 2021.

L. Tani and C. Veelken, “Comparison of Bayesian and particle swarm algorithms for hyperparameter optimisation in machine learning applications in high energy physics,” arXiv preprint arXiv:2201.06809, 2022.

J. M. Hernández-Lobato, M. W. Hoffman, and Z. Ghahramani, “Predictive entropy search for efficient global optimization of black-box functions,” Advances in Neural Information Processing Systems, vol. 27, 2014.

I. Bogunovic and A. Krause, “Misspecified gaussian process bandit optimization,” Advances in Neural Information Processing Systems, vol. 34, 2021.

V. Nguyen and M. A. Osborne, “Knowing the what but not the where in Bayesian optimization,” International Conference on Machine Learning, pp. 7317-7326, 2020.

W.-T. Ding, F. Meng, Y.-B. Tian, and H.-N. Yuan, “Antenna optimization based on auto-context broad learning system,” International Journal of Antennas and Propagation, vol. 2022, 2022.

W. Tian, D. Wu, Q. Chao, Z. Chen, and Y. Wang, “Application of genetic algorithm in M×

N reconfigurable antenna array based on RF MEMS switches,” Modern Physics Letters B, vol. 32, no. 30, p. 1850365, 2018.

D. Ustun, A. Toktas, and A. Akdagli, “Deep neural network–based soft computing the resonant frequency of E–shaped patch antennas,” AEU-International Journal of Electronics and Communications, vol. 102, pp. 54-61, 2019.

Downloads

Published

2023-01-02

How to Cite

[1]
Q. . Li, F. . Meng, Y. . Tian, and X. . Wang, “Bayesian Optimization Based on Student’s T Process for Microstrip Antenna Design”, ACES Journal, vol. 37, no. 08, pp. 856–866, Jan. 2023.