## 1 Introduction  
The ever-increasing demands of modern wireless communications, including 4G/5G, wireless sensor networks, and Internet of Things (IoT), require antenna designs to handle multiple objectives, e.g., wideband or multi-band, high gain or efficiency, compact size, etc. In this circumstance, automated antenna optimization based on multi-objective evolutionary algorithms (MOEAs), such as genetic algorithm (GA) [1], particle swarm optimization (PSO) [2], and multi-objective optimization algorithm based on decomposition (MOEA/D) [3], provide a new path for antenna designers because of their strong capabilities of simultaneously handling multiple design objectives and optimizing multiple design parameters. However, the direct application of MOEAs to antenna optimizations may be computationally intensive in the multi-parameter antenna designs since a large number of full-wave EM simulations are usually involved in the optimization process [4]. Fortunately, the recently developed surrogate-based optimization techniques [5; 6; 7; 8; 9; 10; 11; 12] have proven to be more computationally efficient compared with conventional EM-driven simulations. Compared with traditional EM-driven approaches, surrogate-based optimization techniques construct a mathematical mapping between the antenna dimensions and antenna performance, thereby greatly reducing EM simulations and the computational cost. Different surrogate models are proposed for antenna optimizations, such as Kriging [5; 6], Gaussian Process (GP) [7; 8], and artificial neural networks (ANNs) [9; 10; 11; 12]. The Kriging method used in References [5; 6] is essentially an interpolation method with poor generalization and the prediction accuracy depends mostly on the initial sampling, which may cause the model to either stop prematurely or search too locally [13]. The GP method used in [7; 8] is developed from the Kriging model, assuming that the objective function is a sample of a Gaussian stochastic process [14]. However, GP model inherits the shortcomings from Kriging model and may lose efficiency in high-dimensional design space. ANNs [9; 10; 11; 12] are flexible mathematical structures which are capable of identifying complex nonlinear relationships between input and output data sets. Generally, backward propagation neural networks (BPNNs) [9; 10] and radial basis function neural networks (RBFNNs) [11; 12] are two kinds of typical models among ANNs. Compared to BPNNs, RBFNNs converge much faster as they have both a supervised and unsupervised component to their learning [12; 15]. Additionally, RBFNNs automatically adjust the number of processing elements in the hidden layer until the defined accuracy is reached instead of empirically choosing hidden elements in BPNNs [15]. Therefore, RBFNNs are applied to construct antenna surrogate model for performance prediction in this paper. RBFNNs, motivated by the locally tuned responses in biologic neurons, have been extensively used for prediction [16; 17] and classification [18] due to its strong nonlinear approximation and good generalization ability [19]. It has been proved that RBFNNs can map the input-output relationship in any continuous function to a desired degree of precision, as long as the RBF neurons are provided adequately [20]. [PERSON] et al. [11] proposed an RBFNN model to predict the optimum geometrical dimensions of both the patch and feeding microstrip line for resonating an antenna at a specific frequency. [PERSON] et al. [12] estimated the directivity of uniform linear arrays composing of collinear and parallel short dipoles through RBFNNs. Although the above work greatly reduced the computational cost of antenna or antenna array designs, they simply apply conventional RBFNNs to antenna optimization without considering the selection of RBFNNs parameters (e.g., centers, widths, connection weights, and thresholds). An RBFNN with inappropriate parameters is likely to weaken the accuracy and effectiveness of the network.