Citation: Wang, Z.; Qin, J.; Hu, Z.;
He, J.; Tang, D. Multi-Objective
Antenna Design Based on BP Neural
Network Surrogate Model Optimized
by Improved Sparrow Search
Algorithm. Appl. Sci. 2022, 12, 12543.
https://doi.org/10.3390/app122412543
Academic Editors: Phivos Mylonas,
Katia Lida Kermanidis and
Manolis Maragoudakis
Received: 26 October 2022
Accepted: 5 December 2022
Published: 7 December 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Multi-Objective Antenna Design Based on BP Neural Network
Surrogate Model Optimized by Improved Sparrow
Search Algorithm
Zhongxin Wang , Jian Qin * , Zijiang Hu, Jian He and Dong Tang
School of Electronic and Communication Engineering, Guangzhou University, Guangzhou 510006, China
* Correspondence: gzu_jian@gzhu.edu.cn
Abstract:
To solve the time-consuming, laborious, and inefficient problems of traditional methods
using classical optimization algorithms combined with electromagnetic simulation software to design
antennas, an efficient design method of the multi-objective antenna is proposed based on the multi-
strategy improved sparrow search algorithm (MISSA) to optimize a BP neural network. Three
strategies, namely Bernoulli chaotic mapping, inertial weights, and t-distribution, are introduced into
the sparrow search algorithm to improve its convergent speed and accuracy. Using the Bernoulli
chaotic map to process the population of sparrows to enhance its population richness, the weight
is introduced into the updated position of the sparrow to improve its search ability. The adaptive
t-distribution is used to interfere and mutate some individual sparrows to make the algorithm reach
the optimal solution more quickly. The initial parameters of the BP neural network were optimized
using the improved sparrow search algorithm to obtain the optimized MISSA-BP antenna surrogate
model. This model is combined with multi-objective particle swarm optimization (MOPSO) to solve
the design problem of the multi-objective antenna and verified by a triple-frequency antenna. The
simulated results show that this method can predict the performance of the antennas more accurately
and can also design the multi-objective antenna that meets the requirements. The practicality of the
method is further verified by producing a real antenna.
Keywords:
antenna design; surrogate model; improved sparrow search algorithm; multi-objective
antenna; prediction of performance
1. Introduction
Antennas are indispensable devices in modern life and are widely used in radio com-
munications, radar, and navigation. With the diversification of antenna applications, some
antennas must simultaneously satisfy more than one objective. The structure of the anten-
nas is more complicated than before and designing the antenna has become a challenging
problem [
1
–
3
]. Currently, the traditional design process of antenna optimization usually
requires applying electromagnetic simulation software, which can accurately evaluate the
antenna’s performance, such as return loss and gain. The accuracy of the electromagnetic
simulation is high. However, it has some problems, such as extensive calculations and
time-consuming [4].
To address the defects of traditional methods, some scholars have begun to study
new methods of antenna design. That is to use the surrogate model to replace standard
simulation software. This method builds a nonlinear relationship between the size and
performance of the antenna, making the antenna design more efficient and less complicated.
The surrogate models commonly used in antenna design include support vector regression
(SVR) [
5
,
6
], kriging model (KM) [
7
–
9
], and artificial neural network (ANN) [
10
–
16
], etc.
Literature [
5
,
6
] constructed a surrogate model based on support vector regression (SVR).
However, when experimental data are small, it will lead to inaccurate modeling and some
errors in predicting antenna performance. Literature [
7
–
9
] used the Kriging algorithm to
Appl. Sci. 2022, 12, 12543. https://doi.org/10.3390/app122412543 https://www.mdpi.com/journal/applsci
