Data clustering helps one discern the structure of and simplify the complexity of massive quantities of data. It is a common technique for statistical data analysis and is used in many fields, including machine learning, data mining, pattern recognition, image analysis, and bioinformatics. The well-known K-means algorithm, which has been successfully applied to many practical clustering problems, suffers from several drawbacks due to its choice of initializations. However, its performance depends on the initial state of centroids and may trap in local optima. The gravitational search algorithm (GSA) is one effective method for find optimal solution. The GSA-KM algorithm helps the k means algorithm to escape from local optima and also increases the convergence speed of the GSA algorithm. A hybrid technique based on combining the K-means algorithm, Gravitational Search algorithm, Nelder–Mead simplex search, and particle swarm optimization, called KM–GSA-NM–PSO, is proposed. The KM-GSA–NM–PSO searches for cluster centers of an arbitrary data set as does the K-means algorithm, but it can effectively and efficiently find the global optima. The new KM–GSA-NM–PSO algorithm is tested on UCI repository data sets, and its performance is compared with those of K means and KM-GSA clustering algorithms. Enhancement can be made to this algorithm such as image segmentation and university time tabling.