The paper introduces a novel hybrid genetic algorithm (GA) called the Genetic K-Means Algorithm (GKA) for finding a globally optimal partition of a given dataset into a specified number of clusters. The GKA combines the strengths of GA and the K-means algorithm, addressing the computational challenges and convergence issues of traditional GA-based clustering methods. The K-means operator, a one-step of the K-means algorithm, is used as a search operator in GKA, replacing the classical K-means algorithm. The authors define a distance-based mutation operator and prove that GKA converges to the global optimum using finite Markov chain theory. Experimental results on two datasets (German town data and British town data) demonstrate that GKA converges to the best-known optimum and outperforms other evolutionary algorithms in terms of speed and accuracy. The paper also compares GKA with other clustering algorithms, showing its superior performance in terms of both convergence and computational efficiency.The paper introduces a novel hybrid genetic algorithm (GA) called the Genetic K-Means Algorithm (GKA) for finding a globally optimal partition of a given dataset into a specified number of clusters. The GKA combines the strengths of GA and the K-means algorithm, addressing the computational challenges and convergence issues of traditional GA-based clustering methods. The K-means operator, a one-step of the K-means algorithm, is used as a search operator in GKA, replacing the classical K-means algorithm. The authors define a distance-based mutation operator and prove that GKA converges to the global optimum using finite Markov chain theory. Experimental results on two datasets (German town data and British town data) demonstrate that GKA converges to the best-known optimum and outperforms other evolutionary algorithms in terms of speed and accuracy. The paper also compares GKA with other clustering algorithms, showing its superior performance in terms of both convergence and computational efficiency.