Gravity inversion is a classical tool in applied geophysics that corresponds, both, to a linear (density unknown) or nonlinear (geometry unknown) inverse problem depending on the model parameters. Inversion of basement relief of sedimentary basins is an important application among the nonlinear techniques. A common way to approach this problem consists in discretizing the basin using polygons (or other geometries), and iteratively solving the nonlinear inverse problem by local optimization. Nevertheless, this kind of approach is highly dependent of the prior information that is used and lacks from a correct solution appraisal (nonlinear uncertainty analysis). In this paper, we present the application of a full family Particle Swarm Optimizers (PSO) to the 20 gravity inversion and model appraisal (uncertainty assessment) of basement relief in sedimentary basins. The application of these algorithms to synthetic and real cases (a gravimetric profile from Atacama Desert in north Chile) shows that it is possible to perform a fast inversion and uncertainty assessment of the gravimetric model using a sampling while optimizing procedure. Besides, the parameters of these exploratory PSO optimizers are automatically tuned and selected based on stability criteria. We also show that the result is robust to the presence of noise in data. The fact that these algorithms do not require large computational resources makes them very attractive to solve this kind of gravity inversion problems. (C) 2015 Elsevier B.V. All rights reserved.