Hierarchical opposition-driven hippopotamus optimization for engineering and fog computing applications
Mingdong Han, Jiangxia Deng, Lingyan Fan · Results in Engineering · 2025
The efficient optimization of complex, high-dimensional systems is a persistent challenge in engineering, particularly in dynamic distributed environments like fog computing. Existing metaheuristics often struggle with premature convergence and an inability to adaptively balance exploration and exploitation. To address these limitations, this paper proposes a multi-strategy enhanced Hippopotamus Optimization algorithm, termed Hippopotamus-based Composite Hierarchical Optimization (HCHO). The framework integrates three core strategies: 1) composite low-discrepancy initialization for superior population diversity, 2) hierarchical opposition-based learning to prevent stagnation, and 3) flexible adaptive wave control for dynamic search behavior tuning. Comprehensive tests on the CEC 2019 and CEC 2022 benchmarks show that HCHO surpasses ten recent algorithms, improving accuracy by 84% and convergence speed by 39.8%, both statistically significant. Two engineering applications confirm the practical utility of HCHO: classical mechanical design problems and a large-scale fog computing load-balancing scenario. In fog computing, HCHO demonstrated superior scalability and efficiency compared to the original HO. For a scenario with 200 tasks and 20 servers, it achieved a 90.27% reduction in maximum server load and a 90.51% decrease in total delay. Under a more challenging load of 1000 tasks and 100 servers, HCHO still attained substantial improvements, reducing the maximum load and total delay by 35.78% and 44.07%, respectively. These results affirm HCHO as a robust and scalable optimization tool, offering both methodological advances and tangible benefits for real-world engineering systems.