This proposed algorithm provides a promising direction for improving the performance of nature-inspired optimization algorithms. In this approach, the Genetic Algorithm is used to address the limitations of the Mountain Gazelle Optimizer, which may suffer from premature convergence and a lack of exploitation in certain scenarios. By combining both algorithms, the hybrid approach often finds more accurate solutions to complex optimization problems. We conducted tests on benchmark functions, and the results show that the hybrid GAME algorithm outperforms the standalone GO and GA in terms of convergence speed, solution accuracy, and robustness.