Abstract:

To address the issues of uneven population distribution in the initialization phase， susceptibility to the local optimum in complex search space， and insufficient optimization capability in the later exploitation phase of Hippopotamus Optimization （HO） algorithm， an improved HO algorithm based on Latin hypercube sampling， Neural population dynamic optimization with coupled interference and Covariance matrix adaptation （LNC_HO） was proposed. First， in the initialization phase， Latin hypercube sampling was employed to optimize the initial population distribution， thereby enhancing population diversity and global coverage. Second， in the exploration phase， a coupled interference strategy was combined to strengthen the algorithm’s global search capability in high-dimensional space， thereby reducing the risk of falling into the local optimum. Finally， in the exploitation phase， a Covariance Matrix Adaptation Evolution Strategy （CMA-ES） was introduced to adjust the covariance matrix and step-size parameters adaptively， thereby enhancing the algorithm’s dynamic adaptability to search space structures and improving both convergence speed and accuracy in the late-stage local search. Experimental results on twelve multi-type benchmark functions in CEC2017， compared with seven mainstream swarm intelligence algorithms， show that LNC_HO ranks first in terms of optimal fitness value， and achieves an improvement of 42.22% in convergence accuracy and reduces standard deviation by 27.37% compared to the HO algorithm， indicating its superior convergence performance and stability， thereby validating the effectiveness of the improvement strategies. When LNC_HO is applied to the pressure vessel design engineering optimization problem， it achieves a cost reduction of 8.28% compared to the HO algorithm in 30 independent runs， validating its practical value in real-world engineering applications.

Key words: Hippopotamus Optimization (HO) algorithm, Latin hypercube sampling, coupling interference strategy, Covariance Matrix Adaption Evolution Strategy (CMA-ES), swarm intelligence algorithm

摘要：

针对河马优化（HO）算法在初始化阶段种群分布不均、复杂搜索空间中易陷入局部最优和后期开发阶段寻优能力不足的问题，提出基于拉丁超立方采样、神经种群动态优化的耦合干扰与协方差矩阵适应性的改进HO算法（LNC_HO）。首先，在初始化阶段，采用拉丁超立方采样优化初始种群分布，提高种群多样性和全局覆盖范围；其次，在探索阶段，融合耦合干扰策略强化算法在高维空间中的全局搜索能力，降低陷入局部最优的风险；最后，在开发阶段，引入协方差矩阵适应性进化策略（CMA-ES），自适应调整协方差矩阵及步长参数，增强算法对搜索空间结构的动态适应能力，提升迭代后期局部搜索的收敛速度与精度。在CEC2017多类型的12个基准测试函数上，与7种主流群智能算法的对比实验结果表明，LNC_HO的最优适应度值排名最高；相较于HO算法，LNC_HO的收敛精度提升了42.22%，标准差降低了27.37%，表明LNC_HO具有较好的收敛性和稳定性，验证了改进策略的有效性。将LNC_HO应用于压力容器设计工程优化问题，在30次独立运行中相较于HO算法成本降低了8.28%，验证了算法在实际工程问题中的应用价值。

关键词: 河马优化算法, 拉丁超立方采样, 耦合干扰策略, 协方差矩阵适应性进化策略, 群智能算法