This study describes a unique hybrid optimization technique that combines the Genetic Algorithm (GA), Sine-Cosine Algorithm (SCA), and Nelder-Mead Algorithm (NMA) to effectively solve complex benchmark functions. The aim of this research is to leverage the strengths of each algorithm: GA for robust global search, SCA for enhancing exploration, and NMA for refining local solutions. By integrating these three techniques, the proposed hybrid algorithm addresses the limitations of standalone methods, such as premature convergence in GA and lack of local refinement in SCA. The hybrid GA-SCA-NMA algorithm is tested on a range of well-known six integer programming problems and six benchmark functions, including Sphere, Ellipsoid, Rastrigin, Rosenbrock, Ackley, and Griewank. Performance metrics such as convergence speed, solution accuracy, and robustness are evaluated. The results demonstrate that the hybrid algorithm consistently outperforms the individual algorithms, achieving faster convergence and higher accuracy across all tested functions. Additionally, the hybrid approach effectively balances exploration and exploitation, ensuring comprehensive search space exploration while refining solutions to reach global optima. The uniqueness of this study establishes in its combination of a global search algorithm (GA), a trigonometric-based exploration algorithm (SCA), and a direct search local optimizer (NMA), offering a synergistic approach that improves optimization performance on multimodal, non-separable functions. This research contributes a powerful tool for solving complex optimization problems and opens new avenues for further applications in real-world scenarios and higher-dimensional search spaces.