Modular Harris Hawks optimization with trend-guided differential evolution and Gaussian exploration for global optimization and engineering design

This paper presents DEHHO, a modular and lightweight variant of Harris Hawks Optimization (HHO), engineered to mitigate the stagnation and directional instability often encountered in high-dimensional and structurally complex optimization tasks. The proposed framework integrates two synergistic, phase-specific strategies: a Gaussian-based stochastic perturbation mechanism designed to maintain fine-grained diversity during exploration, and a Trend-Guided Differential Evolution (DE) update incorporating a momentum vector to enforce directional stability for intensified exploitation. A dynamic balancing scheme coordinates these components, ensuring a smooth transition between search phases without incurring excessive computational overhead. Extensive empirical validation on the CEC 2017 and CEC 2020 benchmark suites (up to 100 dimensions) demonstrates that DEHHO statistically outperforms 10 state-of-the-art peer algorithms-comprising 5 advanced HHO variants and 5 mainstream metaheuristics-in terms of convergence accuracy, robustness, and scalability. Furthermore, rigorous ablation studies confirm the individual efficacy and structural complementarity of the proposed mechanisms, establishing DEHHO as a reliable solver for complex numerical and engineering design problems.