This research presents a novel hybrid approach, which combines the White Shark Optimizer (WSO) metaheuristic algorithm with chaotic maps integrated into the binarization process. Inspired by the predatory behavior of white sharks, WSO has shown great potential to navigate complex search spaces for optimization tasks. On the other hand, chaotic maps are nonlinear dynamical systems that generate pseudo-random sequences, allowing for better solution diversification and avoiding local optima. By hybridizing WSO and chaotic maps through adaptive binarization rules, the complementary strengths of both approaches are leveraged to obtain high-quality solutions. We have solved the Set Covering Problem (SCP), a well-known NP-hard combinatorial optimization challenge with real-world applications in several domains, and experimental results indicate that LOG and TENT chaotic maps are better after statistical testing. This hybrid approach could have practical applications in telecommunication network optimization, transportation route planning, and resource-constrained allocation.