## 1 Introduction  
Antennas are indispensable devices in modern life and are widely used in radio communications, radar, and navigation. With the diversification of antenna applications, some antennas must simultaneously satisfy more than one objective. The structure of the antennas is more complicated than before and designing the antenna has become a challenging problem [1, 2, 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, 8, 9], and artificial neural network (ANN) [10, 11, 12, 13, 14, 15, 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, 8, 9] used the Kriging algorithm to construct surrogate models for the antenna design. This method is a random interpolation method based on the general least-square way, and the prediction accuracy of data with large fluctuations needs further improvement. Artificial neural networks represent structures created by neural nodes capable of establishing a nonlinear relationship between input and output data to predict the input data. This solid nonlinear prediction ability also makes artificial neural network surrogate models widely used in antenna design. Classical artificial neural networks include multi-layer perception (MLP) [10; 11], radial basis function (RBF) [12; 13], and BP neural networks (BPNN) [14; 15; 16]. However, BPNN has the benefits of self-learning capability, time-saving calculation, and strong generalization ability [16], and it has been widely used in many fields. [PERSON] [14] used BPNN to build the state of charge (SOC) estimated model of the electric vehicle battery, and the feedback of BPNN was used to correct the error. And the average error of the estimated model is less than 0.5%. [PERSON] [15] proposed a BPNN steering angle prediction method to obtain the front wheel's steering angle. The results show that the mean square error is less than 0.66, indicating that the method works well. [PERSON] [16] optimized the structure of BPNN because of its redundant connection and a lot of calculations, built the surrogate model based on \(I\)I-BPNN, and improved the efficiency of antenna design. Although BPNN has achieved good results in different areas, there are still some drawbacks. The structural parameters determine its output. Usually, using random parameters will make the neural network unstable, and it is not easy to achieve the global optimum during optimization, resulting in insufficient prediction accuracy [17; 18; 19]. This requires optimizing its parameters, such as adding a dynamic learning rate to the original BP algorithm to correct the deficiency and enhance the prediction performance [20]. However, this gradient-based algorithm has limitations in global search capability [21]. In recent years, the emergence of intelligent bionic algorithms has overcome this limitation. For example, the sparrow search algorithm [22] is a relatively novel intelligent algorithm discovered by [PERSON]. It has the characteristics of less variable parameters, strong stability, simple operation, and strong global searchability. It performs well in optimizing the parameters of BPNN.