Nowadays, social networks are one of the most important sources of information available on the Internet, since new users and relationships between them emerge every day in this type of networks. For this reason, it is important to have procedures and mechanisms to obtain, process and analyze the information extracted from them and transform it into useful data. This situation has given rise to new hard combinatorial optimization problems related to social networks, such as influence analysis, sentimental analysis or polarization. All these topics are grouped under the research field of Social Networks Analysis (SNA). In this paper, we focus on one of these topics: the Community Detection Problem (CDP). Specifically, we will deal with a variant of the CDP known as the Overlapping Community Detection Problem (OCDP), in which the same user can be assigned to more than one community simultaneously, which cannot occur in the classical Community Detection Problem. The problem is approached from a heuristic point of view, applying a Greedy Randomized Adaptive Search Procedure (GRASP) combined with a Basic Variable Neighborhood Search (BVNS) algorithm. The proposal is compared with the best method found in the literature, a Density Peaks based algorithm. Synthetic instances are used to evaluate the performance of the proposal. To analyze the quality of the obtained solutions, an evaluation metric that has been adapted from the well-known modularity metric has been used: the overlapping modularity.