## 1 Introduction  
In recent years, the effectiveness of metaheuristics in addressing complex challenges, especially those involving intricate combinatorial problems, has been established. This utility is evidenced across various fields, such as mechanical engineering [1], logistics [2], civil engineering [3, 4], and operations research [5], among others. The pursuit of more efficient metaheuristic algorithms continues to be an important area of research. This is particularly true as optimization problems, especially combinatorial or mixed types, grow in complexity with the addition of new variables and constraints. Additionally, the non-free lunch theorem [6] emphasizes that no single optimization technique can consistently outperform all others across every possible problem space. A promising direction for the advancement of metaheuristic algorithms is seen in the strategic integration of various techniques. The method of hybridization, which involves the integration of various metaheuristic algorithms to improve performance, stands as a notable strategy in the realm of metaheuristic combinations. An example of this approach is the development of an algorithm that utilizes the hybridization of two metaheuristics for addressing the feature selection issue, as discussed in [7]. This study introduced the application of feature selection for IoT Intrusion Detection, evaluating the efficiency of the proposed hybrid algorithm by comparing its outcomes with those obtained from the original methodologies. The enhanced performance of the hybrid algorithm was evident in both the quality of solutions and the acceleration of convergence times. Additionally, ref. [8] presented another persuasive instance where the challenge of extending the lifespan of wireless sensor networks through cluster generation techniques was explored. Here, a hybrid model was proposed by the authors, merging the particle swarm optimization algorithm with the Sea Lion technique for the purpose of cluster identification. When compared to traditional algorithms like the genetic algorithm and particle swarm optimization, this hybridized approach demonstrated a superior performance, surpassing these methods by more than 11% in solution quality. Exploring the integration of additional operators into metaheuristics has emerged as a significant field of study. The enhancement of algorithmic performance through various strategies, including the use of initialization operators, local search mechanisms, and binarization processes, has gained attention in scholarly work for its effectiveness in boosting algorithmic outcomes. The strategic employment of initialization operators is pivotal in defining the search space boundaries, thereby enabling more effective exploration that may yield superior outcomes. Local search mechanisms are essential in circumventing local optima and guiding the search process towards more promising areas by iteratively refining potential solutions. Moreover, the application of binarization processes facilitates the transformation of continuous problems into their discrete counterparts, expanding the metaheuristic algorithms' range of applicability to include a wider variety of problem types. Consequently, these additional operators are lauded for their instrumental role in enhancing the flexibility and overall performance of metaheuristic approaches. In this context, an exploration of these aspects has been delved into by some works. For instance, an in-depth examination of the influence of various solution initialization methods on the effectiveness of a hybrid algorithm, tailored for the set union knapsack problem, was conducted in the research outlined in [9]. An unequivocal connection between the initialization strategy and the algorithm's performance was conclusively established by this study, with the supremacy of the weighted method being persistently marked. Notably, both self-sufficiency and remarkable competitiveness were reflected in the study's outcomes when benchmarked against other established metaheuristic methodologies.