This paper proposes a novel hybrid genetic algorithm (GKA) for clustering, which combines the K-means algorithm with genetic algorithms to find a globally optimal partition of data into a specified number of clusters. Traditional genetic algorithms for clustering often use expensive crossover operators or fitness functions. GKA replaces crossover with the K-means operator, a one-step process of the K-means algorithm, and introduces a distance-based mutation operator to improve convergence. Using finite Markov chain theory, the authors prove that GKA converges to the global optimum with probability one. Simulations show that GKA converges to the best known optimum and outperforms other evolutionary algorithms in terms of speed. The algorithm maintains a population of encoded solutions, applies selection, mutation, and K-means operators, and evolves until a termination condition is met. The K-means operator helps speed up convergence, while the distance-based mutation ensures global convergence. The paper also compares GKA with other clustering algorithms, including K-means, evolutionary strategies, and evolutionary programming, showing that GKA is faster and more effective in finding globally optimal partitions. The complexity of GKA is analyzed, and it is shown to be more efficient than other algorithms. The study concludes that GKA is a promising hybrid algorithm for clustering, combining the simplicity of K-means with the robustness of genetic algorithms.This paper proposes a novel hybrid genetic algorithm (GKA) for clustering, which combines the K-means algorithm with genetic algorithms to find a globally optimal partition of data into a specified number of clusters. Traditional genetic algorithms for clustering often use expensive crossover operators or fitness functions. GKA replaces crossover with the K-means operator, a one-step process of the K-means algorithm, and introduces a distance-based mutation operator to improve convergence. Using finite Markov chain theory, the authors prove that GKA converges to the global optimum with probability one. Simulations show that GKA converges to the best known optimum and outperforms other evolutionary algorithms in terms of speed. The algorithm maintains a population of encoded solutions, applies selection, mutation, and K-means operators, and evolves until a termination condition is met. The K-means operator helps speed up convergence, while the distance-based mutation ensures global convergence. The paper also compares GKA with other clustering algorithms, including K-means, evolutionary strategies, and evolutionary programming, showing that GKA is faster and more effective in finding globally optimal partitions. The complexity of GKA is analyzed, and it is shown to be more efficient than other algorithms. The study concludes that GKA is a promising hybrid algorithm for clustering, combining the simplicity of K-means with the robustness of genetic algorithms.