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.

中文翻译：

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高斯扰动镜面反射学习和基于黄金正弦机制的全局优化问题的大象群优化

大象放牧优化（EHO）由于其控制参数少、操作简单而受到广泛关注，但仍存在收敛速度慢和求解精度低的问题。在本文中，提出了一种解决上述缺点的改进算法，称为高斯微扰镜面反射学习和基于黄金正弦机制的 EHO（SRGS-EHO）。首先，在算法中引入镜面反射学习，增强初始种群的多样性和遍历性，提高收敛速度。同时，利用高斯扰动进一步增加初始种群的多样性。二是引入金正弦机制，改进各氏族族长位置更新方式，可以使每一代中处于最佳位置的个体向全局最优移动，增强算法的全局探索和局部开发能力。为了评估所提出算法的有效性，对 23 个基准函数进行了测试。此外，还调用了 Wilcoxon 秩和检验和 5% 的 Friedman 检验，将其与其他八种元启发式算法进行了比较。此外，还建立了对不同修改的参数和实验的敏感性分析。为了进一步验证增强算法的有效性，还应用 SRGS-EHO 来解决两个具有约束搜索空间的经典工程问题（压力容器设计问题和张力/压缩弦设计问题）。