An Adaptive Multi-Elite Hippopotamus Algorithm for High-Dimensional Optimization and its Wasserstein Distance Penalty Mechanism

High-dimensional optimization is widely employed in fields such as aerospace, mechanical engineering, and automatic control. However, because of the vast search space and the complexity of objective functions, conventional swarm intelligence algorithms often become trapped in local optima and struggle to maintain population diversity. To address these challenges, this paper introduces an Adaptive Multi-Elite Hippopotamus Algorithm (AWEHO), building upon the Hippopotamus Optimization framework and incorporating a dynamic penalty mechanism based on the Wasserstein distance. This mechanism is designed to curb premature convergence and enhance global exploration. In each iteration, multiple elite individuals are selected and subjected to dynamic perturbations, while a globally sampled reference set is constructed. If the Wasserstein distance between the current population and the reference set falls below an adaptive threshold, a penalty term is enforced to preserve necessary search diversity. Numerical experiments on various high-dimensional benchmark functions show that AWEHO achieves superior performance in convergence speed, solution accuracy, and stability compared to several established swarm intelligence algorithms, indicating promising potential for engineering applications.