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

Harris Hawk Optimizer (HHO) is a recent revolutionary algorithm developed in the literature that simulates the cooperative hunting behaviour of Parabuteo Unicinctus. Despite its simplicity, the standard HHO often suffers from slow convergence, limited exploitation capacity and performance degradation on high-dimensional and constrained problems. This study aims to develop seven novel Harris Hawk Optimizer (HHO) variants, HHO-ADAP, HHO-CHAOS, HHO-Elite, HHO-GA, HHO-Inertia, HHO-PSO, and HHO-ULTRA, that integrate adaptive mechanisms, chaotic dynamics, elite preservation, and cross-algorithmic hybridization to improve the balance between exploration and exploitation. The proposed methods were rigorously tested on the CEC 2014 benchmark suite for dimensions 10, 30, 50, and 100, as well as ten constrained engineering design problems, and results are compared against state-of-the-art optimizers CMA-ES, L-SHADE, LSHADE-cnEpSin, SPS-L-SHADE-EIG, EBOwithCMAR, WMA, and OWMA. Quantitative results demonstrate that the hybrids consistently outperform the baseline HHO and classical optimizers. HHO-PSO and HHO-Elite achieved up to 35% faster convergence and reached solution values as small as 10⁻²¹⁶, compared with much weaker values (10⁻⁴²-10⁻⁴⁷) for classical baselines. On multimodal and fixed-dimension functions, HHO-Elite, HHO-CHAOS, and HHO-ADAP effectively delayed stagnation and preserved diversity, avoiding premature convergence. For engineering problems, the hybrids produced near-optimal designs: pressure vessel (≈5885.2), spring (≈0.01267), welded beam (≈1.7257), gear train (= 0), and Belleville spring (≈1.9795). Variance was as low as 10⁻¹⁶ (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.