Combinatorial optimization problems, characterized by their inherent complexity and exponential search spaces, present significant challenges in achieving optimal solutions. Metaheuristic algorithms have emerged as versatile tools to address these challenges, with advancements incorporating hybrid approaches such as chaotic maps to enhance their stochastic behavior. This study investigates the application of the Fox Optimizer (FOX) to the Set Covering Problem (SCP), an NP-hard problem with extensive practical relevance. By implementing standard and chaotic binary configurations of FOX and comparing them with Particle Swarm Optimization (PSO) and Grey Wolf Optimizer (GWO), this research evaluates the impact of binarization rules and chaotic maps on algorithmic performance. Experimental results demonstrate that elitist configurations combined with chaotic maps consistently achieve high-quality solutions, offering accelerated convergence and enhanced exploration capabilities. Additionally, execution time analysis highlights the computational efficiency of chaotic configurations, emphasizing their suitability for large-scale problems. This work underscores the importance of aligning algorithmic strategies with problem characteristics and opens avenues for future exploration of chaotic maps and adaptive methodologies in combinatorial optimization.