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Elephant herding optimization (EHO) has received widespread attention due to its few control parameters and simple operation but still suffers from slow convergence and low solution accuracy. In this paper, an improved algorithm to solve the above shortcomings, called Gaussian perturbation specular reflection learning and golden-sine-mechanism-based EHO (SRGS-EHO), is proposed. First, specular reflection learning is introduced into the algorithm to enhance the diversity and ergodicity of the initial population and improve the convergence speed. Meanwhile, Gaussian perturbation is used to further increase the diversity of the initial population. Second, the golden sine mechanism is introduced to improve the way of updating the position of the patriarch in each clan, which can make the best-positioned individual in each generation move toward the global optimum and enhance the global exploration and local exploitation ability of the algorithm. To evaluate the effectiveness of the proposed algorithm, tests are performed on 23 benchmark functions. In addition, Wilcoxon rank-sum tests and Friedman tests with 5% are invoked to compare it with other eight metaheuristic algorithms. In addition, sensitivity analysis to parameters and experiments of the different modifications are set up. To further validate the effectiveness of the enhanced algorithm, SRGS-EHO is also applied to solve two classic engineering problems with a constrained search space (pressure-vessel design problem and tension-/compression-string design problem). The results show that the algorithm can be applied to solve the problems encountered in real production., Competing Interests: The authors declare that there are no conflicts of interest regarding the publication of this study., (Copyright © 2021 Yuxian Duan et al.)