Optimization algorithms are essential for tackling complicated problems in industries such as engineering and data analysis. Traditional genetic algorithms (GAs) are effective for global exploration across the search space but often lack the precision required for local refinement, which can result in solutions that are close to, but not at, the true optimum. To address this, we proposed the Real-Coded Subdivision with Adaptive Refinement (RCGS-AR) algorithm, which integrates Nelder-Mead (NM) local optimization with a sub-population structure to balance exploration and exploitation. RCGS-AR starts by dividing a real-coded population into four sub-populations that undergo tournament selection, one-point crossover, and Gaussian mutation. The top individuals in each sub-population are further refined using NM, a gradient-free local optimization technique. The sub-populations are then merged with the initial population, and only the fittest individuals are retained to ensure diversity. This process repeats until convergence is achieved. 28 Benchmark testing, including both unimodal, multimodal, and composition functions, shows that RCGS-AR outperforms traditional GAs, offering faster convergence and greater accuracy. Furthermore, RCGS-AR effectively estimates parameters for the Weibull 3-parameter distribution solved by Maximum Likelihood Estimation (MLE), Modified Maximum Likelihood Estimation (MMLE), proving its robustness in both theoretical and practical optimization problems.