Bayesian Optimization Based on Student’s T Process for Microstrip Antenna Design

Abstract

Bayesian Optimization (BO) is an efficient global optimization algorithm, which is widely used in the field of engineering design. The probabilistic surrogate model and acquisition function are the two keys to the algorithm. Building an efficient probabilistic surrogate model and designing a collection function with excellent exploring capabilities can improve the performance of BO algorithm, allowing it to find the optimal value of the objective function with fewer iterations. Due to the characteristics of small samples and non-parametric derivation of the Gaussian Process (GP), traditional BO algorithms usually use the GP as a surrogate model. Compared with the GP, the Student’s T Process (STP) retains the excellent properties of GP, and has more flexible posterior variance and stronger robustness. In this paper, STP is used as the surrogate model in BO algorithm, the hyperparameters of the model are optimized by STP, and the estimation strategy function (EST) is improved based on the posterior output of the optimized STP, thus realizing the improved BO algorithm based on the STP. To verify the performance of the proposed algorithm, numerical experiments are designed to compare the performances of the traditional BO algorithm, which includes the lower confidence bound function (LCB) and EST as acquisition function respectively and GP as the surrogate model, and the proposed BO algorithm with STP as the surrogate model and LCB, expected improvement function (EI), expected regret minimization function (ERM) as acquisition function respectively. The results show that the proposed algorithm in this paper performs well when finding the global minimum of multimodal functions. Based on the developed algorithm in this paper, the resonant frequency of printed dipole antenna and E-shaped antenna is modeled and optimized, which further confirms the good design ability and design accuracy of the BO algorithm proposed in this paper.