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.