MRSO: Balancing Exploration and Exploitation through Modified Rat Swarm Optimization for Global Optimization  
[PERSON]  
1 Department of Computer Science, College of Science, Charmo University, Charmohanal 46023, Iraq; [EMAIL_ADDRESS] (H.S.A. ); [EMAIL_ADDRESS] (S.S.)  
[PERSON]  
1 Department of Computer Science, College of Science, Charmo University, Charmohanal 46023, Iraq; [EMAIL_ADDRESS] (H.S.A. ); [EMAIL_ADDRESS] (S.S.)  
[PERSON]  
1 Department of Computer Science, College of Science, Charmo University, Charmohanal 46023, Iraq; [EMAIL_ADDRESS] (H.S.A. ); [EMAIL_ADDRESS] (S.S.)  
[PERSON]  
2 Department of Information Technology, Technical College of Informatics, Sulaimani Polytechnic University, Sulaymaniyah P.O. Box 70-236, Iraq; [EMAIL_ADDRESS] (Computer Science and Engineering Department, University of Kurdistan Hewler, Erbil 44001, Iraq; carativecomnons.org/licenses/py/4.0/). [PERSON]  
3 Computer Science and Engineering Department, University of Kurdistan Hewler, Erbil 44001, Iraq; carativecomnons.org/licenses/py/4.0/).3.  
and development. However, traditional optimization algorithms have a limited application scope as optimization challenges continue to grow. To tackle this, researchers have started exploring new methods, with metaheuristic algorithms emerging as an effective solution. Metaheuristics are advanced algorithms based on heuristic principles, designed to solve a wide range of complex optimization problems [3; 4]. As a result, metaheuristic algorithms have become very useful tools that combine evolutionary principles, natural selection, and inheritance with ideas from natural events and how people and animals behave. Their adaptability and robustness make them highly effective in addressing diverse real-world optimization challenges. Consequently, the adoption of nature-inspired algorithms has become widespread in engineering and scientific research, underscoring their vital role in contemporary optimization tasks [5; 6]. A crucial attribute of metaheuristic algorithms is their ability to balance exploration and exploitation within the search space. Exploitation involves local searches to refine solutions, while exploration encompasses global searches to discover new optima across the entire search landscape. This dual capability ensures a comprehensive exploration of potential solutions, offering a robust population of feasible options. Metaheuristics are versatile and simple to implement, often inspired by natural phenomena, and have successfully addressed practical problems across various fields. Their general-purpose nature means they require minimal structural changes when applied to different themes, though their reliance on random initial solutions often results in approximate rather than exact outcomes. Metaheuristic algorithms are particularly valuable for solving complex real-world problems characterized by numerous local optima and a global optimum that would be computationally infeasible to pinpoint precisely. This is exemplified by the set-covering problem, a significant optimization challenge in computer theory and operations research. Here, the objective is to minimize the cost of covering a set of elements with subsets, and this has applications in route planning, resource allocation, and decision-making. The inherent flexibility and ease of implementation of metaheuristics, combined with their gradient-free problem-solving approach, make them indispensable in efficiently obtaining optimal solutions for such intricate problems [2; 7]. The Rat Swarm Optimizer (RSO) is one of the recent metaheuristic algorithms inspired by the natural behaviors of rats, particularly their chasing and attacking strategies [8]. This algorithm has demonstrated success in solving various real-world constrained engineering design problems and performs effectively across diverse search spaces [9; 10]. The RSO has demonstrated effectiveness in solving optimization problems; however, the RSO faces several limitations that hinder its performance in complex optimization tasks.