944 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 72, NO. 1, JANUARY 2024
Communication
Hybrid Method of Artificial Neural Network and Simulated Annealing
Algorithm for Optimizing Wideband Patch Antennas
Yejun He , Jinhua Huang, Wenting Li , Long Zhang , Sai-Wai Wong , and Zhi Ning Chen
Abstract— In order to design the wideband patch antenna, a hybrid
method based on the artificial neural network (ANN) and the simulated
annealing (SA) algorithm is proposed in this communication. The ANN
is employed to describe the nonlinear relationship between the geometric
parameters and the S-parameters of the antenna. The ANN is trained by
the dataset obtained from the high-frequency structure simulator (HFSS).
More importantly, the dataset is divided into three groups according to
their own characteristics so that the ANN can be trained faster and better.
The SA is employed to broaden the bandwidth of the patch antenna with
the required center frequency. Then three wideband patch antennas with
different center frequencies are designed to demonstrate the feasibility of
the proposed method. Several slots are added to the patch to achieve the
wide bandwidth. The results prove that the proposed method can obtain
the wideband patch antenna quickly and efficiently.
Index Terms— Artificial neural network (ANN), simulated annealing
(SA) algorithm, wideband antenna.
I. INTRODUCTION
With the rapid development of the information technology, spec-
trum resources are increasingly becoming scarce. As an important
part of the communication system, wideband antennas are becoming
more and more demanding [1]. In general, the design of the wideband
antenna is more time-consuming than that of the narrowband antenna.
To speed up the design, many methods such as using parametric
study [2], applying various optimization algorithms [3], [4], and
employing the artificial neural network (ANN) [5], [6] have been
proposed.
As a powerful method, the ANN can learn the complex nonlinear
relationship between the input and output after being trained by the
dataset. It has contributed greatly to modeling microwave filters [7],
power amplifiers [8], [9], transistors [10], and antenna designs [11],
[12], [13], [14]. The ANN can greatly accelerate the speed of antenna
optimization. Therefore, the antenna design based on the ANN has
received more and more attention.
Manuscript received 8 April 2023; revised 17 September 2023; accepted
10 October 2023. Date of publication 14 November 2023; date of current
version 9 February 2024. This work was supported in part by the National Key
Research and Development Program of China under Grant 2023YFE0107900;
in part by the National Natural Science Foundation of China under
Grant 62101341 and Grant 62071306; and in part by the Shenzhen Sci-
ence and Technology Program under Grant 20200810131855001, Grant
JCYJ20200109113601723, Grant JSGG20210420091805014, and Grant
JSGG20210802154203011. (Corresponding author: Wenting Li.)
Yejun He, Jinhua Huang, Wenting Li, Long Zhang, and Sai-Wai
Wong are with the State Key Laboratory of Radio Frequency Heteroge-
neous Integration, Sino-British Antennas and Propagation Joint Laboratory,
Guangdong Engineering Research Center of Base Station Antennas, Shenzhen
Key Laboratory of Antennas and Propagation, College of Electronics
and Information Engineering, Shenzhen University, Shenzhen 518060,
China (e-mail: heyejun@126.com; 1493107204@qq.com; w.li@szu.edu.cn;
long.zhang@szu.edu.cn; wsw@szu.edu.cn).
Zhi Ning Chen is with the Department of Electrical and Computer
Engineering, National University of Singapore, Singapore 117583 (e-mail:
eleczn@nus.edu.sg).
Color versions of one or more figures in this communication are available
at https://doi.org/10.1109/TAP.2023.3331249.
Digital Object Identifier 10.1109/TAP.2023.3331249
The ANN can predict the electromagnetic (EM) responses of the
antenna accurately after it is well trained [15], [16]. In [17], a method
with the ANN for array synthesis is proposed, where two serial ANNs
are employed. One ANN is used as an encoder and the other is used
as a decoder to realize the synthesis of the beam pattern for the linear
array. Xiao et al. [18] utilize the combination of the ANN and the data
classification technology to improve the performance of the antenna.
In addition to the above applications, the inverse problems of the
antenna design could also be solved by the ANN [19], [20]. The EM
responses of the antenna are fed into the ANN, and the geometric
parameters could be output by the ANN. In [21], an ANN inverse
model is established, in which the EM field intensity is the input,
while the output is the radius of the loop antenna. A multibranch
ANN is proposed to improve the performance of antenna arrays
in [22]. The dataset is divided into different groups by judging the
monotonicity of the data for solving the nonuniqueness problem, and
each group is employed to train each branch.
In this communication, a hybrid method applying the combination
of the ANN and the simulated annealing (SA) algorithm to design
a wideband patch antenna is proposed. The dataset is employed to
train the ANN which is obtained from the high-frequency structure
simulator (HFSS). The input of the ANN is geometric parameters
while the output is S-parameters. A trained ANN can describe the
relationship between the geometric parameters and the EM responses
of the antenna. Additionally, the ANN is called by the SA algorithm
to calculate the cost function. Compared to the traditional optimiza-
tion algorithm, the proposed method does not need to call the EM
simulation repeatedly. As a result, it can speed up the design of the
antenna, which requires only a small amount of human resources and
can reduce the workload of the designer greatly. More importantly, the
characteristic of the dataset is analyzed, and the dataset is separated
into three subsets to train the ANN. In this way, the ANN can be
trained better and faster. The bandwidth and center frequency of
the antennas are optimized simultaneously. Three wideband patch
antennas with different center frequencies are designed to verify the
validity of the proposed method.
The communication is arranged as follows. The proposed method
is introduced in detail in Section II. In Section III, the configuration
of the antenna, the basic theory of the ANN, and the SA algorithm
in the proposed method are introduced. In Section IV, the simulated
and measured results of the three wideband patch antennas are given.
Section V concludes the communication.
II. PROPOSED HYBRID METHOD
A. Artificial Neural Network
As a mathematical model for information processing, the ANN is
inspired by a biological neural network. Although the ANN requires
a large number of parameters and takes too long to learn, it has many
advantages at the same time, for example, it can fully approximate
complex nonlinear relations, has the ability of associative memory,
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