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 HHHOWOA1PSO and HHHOWOA2PSO, 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 HHHOWOA2PSO have demonstrated more favorable results. According to the literature, the HHHOWOA1 and HHHOWOA2PSO 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.