volume | PIER Journals

Abstract

The design of ultra-wideband (UWB) band-notched antennas is highly sensitive to geometric dimensions. Consequently, traditional metaheuristic algorithms incur prohibitive computational costs from massive full-wave electromagnetic (EM) simulations. An efficient co-design framework, termed the Surrogate-Assisted Nutcracker Optimization Algorithm with Gaussian Process (SANOA-GP), is proposed. By leveraging a GP surrogate for epistemic uncertainty quantification with a lower confidence bound (LCB) prescreening strategy, SANOA-GP balances exploration and exploitation, overcoming high-dimensional multimodal traps. Moreover, intelligent early stopping is achieved through a performance-driven dual-termination criterion with a progressive reward mechanism. Sobol global sensitivity analysis is incorporated to quantitatively evaluate geometric influences, enhancing black-box interpretability and verifying the independent tunability of the dual notches. Measurement results confirm that the optimized antenna achieves precise and deep notches (S₁₁ > -5 dB) at the 5G N79 and X-band frequencies. Remarkably, SANOA-GP converges with an average of only 69.3 full-wave EM simulations. Compared to surrogate-free algorithms, it reduces computational time by over 50%, while still ensuring high optimization accuracy and physical reliability. The proposed framework offers an efficient and reliable paradigm for the automated design of complex radio frequency (RF) and microwave components.

1. Sakkila, L., C. Tatkeu, A. Rivenq, J. Zaidouni, and M. Bocquet, "UWB radar detection theory," 2020 10th International Symposium on Signal, Image, Video and Communications (ISIVC), 1-5, Saint-Etienne, France, 2021.
doi:10.1109/ISIVC49222.2021.9487541

2. Wang, Xun, Shuning Zhang, Si Chen, Linsheng Hou, and Lingzhi Zhu, "An antijamming method based on multichannel singular spectrum analysis and affinity propagation for UWB ranging sensors," IEEE Sensors Journal, Vol. 23, No. 11, 11869-11878, Jun. 2023.
doi:10.1109/jsen.2023.3266231 Google Scholar

3. Yadav, Rohit and Leeladhar Malviya, "UWB antenna and MIMO antennas with bandwidth, band-notched, and isolation properties for high-speed data rate wireless communication: A review," International Journal of RF and Microwave Computer-Aided Engineering, Vol. 30, No. 2, e22033, 2020.
doi:10.1002/mmce.22033 Google Scholar

4. Singh, Chandraveer, Chetna Sharma, and Ashok Kumar, "Miniaturized ultra-wideband microstrip antenna with triple band-notched characteristics at WiMAX/WLAN/X-band for medical applications," Physica Scripta, Vol. 100, No. 5, 055523, 2025.
doi:10.1088/1402-4896/adc6d0 Google Scholar

5. Pasumarthi, Srinivasa Rao, K. Vasu Babu, Jagabathuni Kavitha, and Uppala Jayaram, "High performance triple band-notched UWB monopole antenna for mitigation of narrowband interference," Physica Scripta, Vol. 100, No. 7, 075567, Jul. 2025.
doi:10.1088/1402-4896/aded4d Google Scholar

6. Bouchachi, Islem, Abdelmalek Reddaf, Mounir Boudjerda, Khaled Alhassoon, Badreddine Babes, Fahad N. Alsunaydih, Enas Ali, Mohammad Alsharef, and Fahd Alsaleem, "Design and performances improvement of an UWB antenna with DGS structure using a Grey Wolf Optimization algorithm," Heliyon, Vol. 10, No. 5, e26337, Mar. 2024.
doi:10.1016/j.heliyon.2024.e26337 Google Scholar

7. Li, Yingsong, Wenxing Li, and Raj Mittra, "A compact CPW-fed circular slot antenna with reconfigurable dual band-notch characteristics for UWB communication applications," Microwave and Optical Technology Letters, Vol. 56, No. 2, 465-468, Feb. 2014.
doi:10.1002/mop.28087 Google Scholar

8. Koziel, Slawomir and Anna Pietrenko-Dabrowska, "Global EM-driven optimization of multi-band antennas using knowledge-based inverse response-feature surrogates," Knowledge-Based Systems, Vol. 227, 107189, Sep. 2021.
doi:10.1016/j.knosys.2021.107189 Google Scholar

9. Storn, Rainer and Kenneth Price, "Differential evolution --- A simple and efficient heuristic for global optimization over continuous spaces," Journal of Global Optimization, Vol. 11, No. 4, 341-359, Dec. 1997.
doi:10.1023/a:1008202821328 Google Scholar

10. Wang, Zilai, Naibo Zhang, Jianming Huang, Yansong Cui, Weizheng Ren, Haozhe Hou, Jiayu Zhao, and Kaile Yu, "Design of multi-sense antenna with coupled lines based on cryptogenic particle swarm optimization," IEEE Antennas and Wireless Propagation Letters, Vol. 24, No. 11, 3946-3950, Nov. 2025.
doi:10.1109/lawp.2025.3582751 Google Scholar

11. Güneş, F., S. Demirel, and S. Nesil, "A novel design approach to X-band Minkowski reflectarray antennas using the full-wave EM simulation-based complete neural model with a hybrid GA-NM algorithm," Radioengineering, Vol. 23, No. 1, 144-153, 2014. Google Scholar

12. Dong, Jian, Yingjuan Li, and Meng Wang, "Fast multi-objective antenna optimization based on RBF neural network surrogate model optimized by improved PSO algorithm," Applied Sciences, Vol. 9, No. 13, 2589, 2019.
doi:10.3390/app9132589 Google Scholar

13. Sendrea, Ricardo E., Constantinos L. Zekios, and Stavros V. Georgakopoulos, "A review of multi-fidelity learning approaches for electromagnetic problems," Electronics, Vol. 14, No. 1, 89, 2025.
doi:10.3390/electronics14010089 Google Scholar

14. Rahman, MuhibUr, Dong-Sik Ko, and Jung-Dong Park, "A compact multiple notched ultra-wide band antenna with an analysis of the CSRR-TO-CSRR coupling for portable UWB applications," Sensors, Vol. 17, No. 10, 2174, 2017.
doi:10.3390/s17102174 Google Scholar

15. Yang, Wendong, Shengzhuo Liu, and Jianyi Yang, "An optimized surrogate model and algorithm with rapid multi-parameter processing capability for antenna design," Measurement, Vol. 241, 115719, Feb. 2025.
doi:10.1016/j.measurement.2024.115719 Google Scholar

16. Gao, Jing, Yubo Tian, and Xuezhi Chen, "Antenna optimization based on co-training algorithm of Gaussian process and support vector machine," IEEE Access, Vol. 8, 211380-211390, 2020.
doi:10.1109/access.2020.3039269 Google Scholar

17. Abdel-Basset, Mohamed, Reda Mohamed, Mohammed Jameel, and Mohamed Abouhawwash, "Nutcracker optimizer: A novel nature-inspired metaheuristic algorithm for global optimization and engineering design problems," Knowledge-Based Systems, Vol. 262, 110248, Feb. 2023.
doi:10.1016/j.knosys.2022.110248 Google Scholar

18. Manfredi, Paolo, "Probabilistic uncertainty propagation using gaussian process surrogates," International Journal for Uncertainty Quantification, Vol. 14, No. 6, 71-104, 2024.
doi:10.1615/int.j.uncertaintyquantification.2024052162 Google Scholar

19. Jones, Donald R., Matthias Schonlau, and William J. Welch, "Efficient global optimization of expensive black-box functions," Journal of Global Optimization, Vol. 13, No. 4, 455-492, Dec. 1998.
doi:10.1023/a:1008306431147 Google Scholar

20. Koziel, Slawomir and Anna Pietrenko-Dabrowska, "Efficient simulation-based global antenna optimization using characteristic point method and nature-inspired metaheuristics," IEEE Transactions on Antennas and Propagation, Vol. 72, No. 4, 3706-3717, Apr. 2024.
doi:10.1109/tap.2024.3370296 Google Scholar

21. Zhang, F. and L. J. O’Donnell, "Support vector regression," Machine Learning: Methods and Applications to Brain Disorders, 123-140, Cambridge, MA, USA, 2020.

22. Breiman, Leo, "Random forests," Machine Learning, Vol. 45, No. 1, 5-32, Oct. 2001.
doi:10.1023/a:1010933404324 Google Scholar

23. Mirjalili, Seyedali and Andrew Lewis, "The whale optimization algorithm," Advances in Engineering Software, Vol. 95, 51-67, May 2016.
doi:10.1016/j.advengsoft.2016.01.008 Google Scholar

24. Mirjalili, Seyedali, Seyed Mohammad Mirjalili, and Andrew Lewis, "Grey Wolf Optimizer," Advances in Engineering Software, Vol. 69, 46-61, Mar. 2014.
doi:10.1016/j.advengsoft.2013.12.007 Google Scholar

25. Harrison, Kyle Robert, Andries P. Engelbrecht, and Beatrice M. Ombuki-Berman, "Self-adaptive particle swarm optimization: A review and analysis of convergence," Swarm Intelligence, Vol. 12, No. 3, 187-226, 2018.
doi:10.1007/s11721-017-0150-9 Google Scholar

26. Wang, Jun, Wen-Chuan Wang, Xiao-Xue Hu, Lin Qiu, and Hong-Fei Zang, "Black-winged kite algorithm: A nature-inspired meta-heuristic for solving benchmark functions and engineering problems," Artificial Intelligence Review, Vol. 57, No. 4, 98, 2024.
doi:10.1007/s10462-024-10723-4 Google Scholar

27. Su, Hang, Dong Zhao, Ali Asghar Heidari, Lei Liu, Xiaoqin Zhang, Majdi Mafarja, and Huiling Chen, "RIME: A physics-based optimization," Neurocomputing, Vol. 532, 183-214, 2023.
doi:10.1016/j.neucom.2023.02.010 Google Scholar

Dr. Huawei Zhuang

Mr. Zijian Zhang

Dr. Fei Wang

Dr. Haonan Tian

Dr. Xiaoyang Liu

Dr. Fanmin Kong