## 1 Introduction
In the literature [23], the sparrow search algorithm (SSA) and particle swarm algorithm (PSO) are used to optimize BPNN, and the experiments show that the model of SSA-BPNN has higher accuracy for the prediction and classification of water sources. In reference [24], tent chaotic map is introduced to improve SSA, which is used to optimize BPNN. After optimization, the number of iterations of the model is reduced by 75%, and the predicted value is more accurate. However, in the late stage of solving complex optimization problems, SSA has a slow convergent speed and reduces the population's diversity, making optimizing the situation challenging. Given the existing problems of SSA, many scholars have conducted in-depth research on it. [PERSON] et al. [25] used a reverse learning method to dispose of the problems of the population and added the firefly algorithm to improve the exploration capability of the algorithm. [PERSON] et al. [26] introduced a greedy algorithm to deal with the shortage of the population and then used the strategies of genetic operators and sine-cosine search to update the population and searchers to augment the robustness of SSA. [PERSON] et al. [27] proposed a variable helical factor strategy and a local iterative search strategy. At the same time, it improved the control of boundary, which improved the problem of low accuracy in the SSA search process and the convergent accuracy. [PERSON] et al. [28] introduced the chaos map to enhance the singleness of the population. They used \"dispersion\" to update the search rules so that the algorithm could reach the ideal target solution faster. Although the above scholars have proposed some improvements to SSA, which have enhanced some of the capabilities of the algorithm, effective strategies are still needed to improve the initialization of the population and convergent accuracy. For the above reasons, this paper proposes a multi-strategy improved sparrow algorithm (MISSA) to improve the shortcomings of BPNN. The optimized BPNN has a stronger ability for prediction. First, the Bernoulli chaotic map draws in the sparrow population to address the lack of abundance of the primitive population. In the meantime, the inertia weight of the finder's position update equation strengthens the capability of search and increases its performance. Finally, the adaptive t- distribution is added. The distribution interferes with the individual, so the algorithm is more active when searching and reaches the ideal target value. The effectiveness of MISSA is verified by comparing MISSA with the particle swarm algorithm (PSO) [29], grey wolf algorithm (GWO) [30], whale optimization algorithm (WOA) [31], and SSA on ten benchmark functions for optimal performance. The improved MISSA-BP surrogate model has better performance than others. Meanwhile, the design case of the microstrip antenna also confirms the practicality and efficiency of the method in the paper. The other parts of this article are as follows. Section 2 describes the problem of designing the multi-objective antenna. Section 3 introduces the sparrow search algorithm and its improved strategies. Section 4 describes the constructed surrogate model based on MISSA-BP and the design method for multi-objective antennas based on this model. Section 5 utilizes the benchmark function to test the performance of the improved sparrow search algorithm and uses a design example of a planar microstrip antenna to verify the availability of the proposed method. Section 6 summarizes the content of this paper.