Development and evaluation of hybrid harris hawks optimization algorithms for advanced engineering applications

(multiple disk clutch, gear train), while average runtimes remained below 0.01 s for most hybrids, markedly faster than champion algorithms such as SPS-L-SHADE-EIG (> 1.4 s) and WMA (> 1.8 s). The results highlight that hybridization significantly enhances HHO's robustness, solution accuracy, and adaptability for solving large-scale, nonlinear, and constrained optimization problems in engineering and scientific domains.