Allocating of people in multiple projects is an important issue considering the efficiency of groups from the point of view of social interaction. In this paper, based on previous works, the Multiple Team Formation Problem (MTFP) based on sociometric techniques is formulated as an optimization problem taking into account the social interaction among team members. To solve the resulting optimization problem we propose a Genetic Algorithm due to the NP-hard nature of the problem. The social cohesion is an important issue that directly impacts the productivity of the work environment. So, maintaining an appropriate level of cohesion keeps a group together, which will bring positive impacts on the results of a project. The aim of the proposal is to ensure the best possible effectiveness from the point of view of social interaction. In this way, the presented algorithm serves as a decision-making tool for managers to build teams of people in multiple projects. In order to analyze the performance of the proposed method, computational experiments with benchmarks were performed and compared with the exhaustive method. The results are promising and show that the algorithm generally obtains near-optimal results within a short computational time.