Complex optimization problems are prevalent across various domains, often requiring sophisticated algorithms that balance exploration and exploitation. Standard deterministic methods risk converging to local optima, while metaheuristic algorithms, though better at global search, can be computationally expensive and may lack final precision. This paper investigates the performance benefits of a hybrid optimization strategy by comparing the standard Artificial Bee Colony (ABC) metaheuristic algorithm against a hybrid approach that combines ABC with the deterministic Nelder-Mead (NM) algorithm. The comparison is conducted using the well-known Rastrigin and Rosenbrock benchmark functions in several dimensions. The hybrid method utilizes ABC for initial search space exploration, followed by NM for local refinement, initiated at different stages of the ABC run. Results demonstrate that for the Rastrigin function, the hybrid approach can achieve comparable solution quality to the full ABC run but with significantly fewer fitness function calls, enhancing computational efficiency. For the Rosenbrock function, the hybrid method consistently produced superior results, overcoming the precision limitations of ABC alone. The study concludes that combining the global search capabilities of ABC with the local refinement strength of NM yields a hybrid algorithm that can offer both faster execution and improved solution accuracy compared to the standalone ABC method.