###### Abstract  
Metaheuristic algorithms are favored for solving a variety of problems due to their inherent simplicity, ease of implementation, and effective problem-solving capabilities. This study proposes four new hybrid approaches using swarm-based metaheuristic algorithms. Two of these new approaches are HHHOWOA1 and HHHOWOA2, based on the hybridization of Harris Hawks Optimization (HHO) with the Whale Optimization Algorithm (WOA), and the others are HHHOWOA1 PSO and HHHOWOA2 PSO, based on the hybridization of HHHOWOA1 and HHHOWOA2 with particle swarm optimization (PSO). An evaluation of these four innovative approaches is conducted on 23 benchmark functions, and their results are compared to those reported in the literature under equivalent parameter settings. Among the four approaches, HHHOWOA1 and HHHOWOA2 PSO have demonstrated more favorable results. According to the literature, the HHHOWOA1 and HHHOWOA2 PSO approaches achieve the most optimal results, either better or with the same average fitness values in 15 of the 23 functions and in 18 of the 23 functions, respectively. Moreover, the proposed approaches have been applied to three engineering problems, and the optimum values obtained are compared to the literature. Ultimately, the proposed approaches have proven effective in providing competitive solutions for the majority of optimization problems. H 2025 15 135 2024 2025 25 January 2025 26 January 2025 26 January 2  
MHAs have been classified in a variety of ways. In one of these categorizations, MHAs are divided into population-based and single-based groups [13]. The fundamental concept of single-based metaheuristic algorithms, additionally referred to as trajectory algorithms, is that a single solution is created for each iteration. This solution is improved by using the neighborhood technique. Examples of well-known single-based MHAs [13] are Iterated Local Search (ILS) [14], Simulated Annealing (SA) [15], and Guided Local Search (GLS) [16]. In contrast to single-based MHAs, population-based MHAs present a group of solutions during each run. Population-based MHAs may be classified into four types [17]: swarm-based, human-based, evolutionary-based, and physics-based. Swarm-based MHAs, which have an important place in the literature, model the swarm behavior's intelligent features [18] and use the natural world's collective behaviors as their information source (for instance, birds, bees, and ants). The literature examples for the swarm-based category include the Tunicate Swarm Algorithm (TSA) [19], the Artificial Bee Colony (ABC) [20], the Butterfly Optimization Algorithm (BOA) [21], Harris Hawks Optimization (HHO) [17], the Emperor Penguin Optimizer (EPO) [22], particle swarm optimization (PSO) [23], the Optimal Foraging Algorithm (OFA) [24], Grey Wolf Optimization (GWO) [25], the Grasshopper Optimization Algorithm (GOA) [26], the Salp Swarm Algorithm (SSA) [27], the Whale Optimization Algorithm (WOA) [28], and the Crow Search Algorithm (CSA) [29]. Researchers have recommended tactics to increase the performance of their optimization algorithms, such as providing new algorithms, improving existing ones, and combining several approaches [30; 31]. The most well-known methods or hybrid optimization methods are listed below. The Harris Hawks Optimizer (HHO) simulates the situation in which many hawks collaborate to attack their prey from various angles [17]. Hawks have evolved hunting strategies depending on their prey's attempts to flee. The HHO method has been evaluated in a variety of benchmarks and engineering issues, and the findings suggest that it outperforms previous techniques [17]. Nonetheless, HHO has some faults, such as local optimality, premature convergence, and performance loss for high-dimensional problems [32]. The following are some of the publications in the literature that use the HHO algorithm. For multi-level picture thresholding, Leader Harris Hawks Optimization (LHHO) has been developed to increase HHO's exploration capabilities [33].