GGSA: A Grouping Gravitational Search Algorithm for data clustering. Gravitational Search Algorithm (GSA) is a stochastic population-based metaheuristic designed for solving continuous optimization problems. It has a flexible and well-balanced mechanism for enhancing exploration and exploitation abilities. In this paper, we adapt the structure of GSA for solving the data clustering problem, the problem of grouping data into clusters such that the data in each cluster share a high degree of similarity while being very dissimilar to data from other clusters. The proposed algorithm, which is called Grouping GSA (GGSA), differs from the standard GSA in two important aspects. First, a special encoding scheme, called grouping encoding, is used in order to make the relevant structures of clustering problems become parts of solutions. Second, given the encoding, special GSA updating equations suitable for the solutions with grouping encoding are used. The performance of the proposed algorithm is evaluated through several benchmark datasets from the well-known UCI Machine Learning Repository. Its performance is compared with the standard GSA, the Artificial Bee Colony (ABC), the Particle Swarm Optimization (PSO), the Firefly Algorithm (FA), and nine other well-known classical classification techniques from the literature. The simulation results indicate that GGSA can effectively be used for multivariate data clustering.