FEMOEA: a fast and efficient multi-objective evolutionary algorithm. A multi-objective evolutionary algorithm which can be applied to many nonlinear multi-objective optimization problems is proposed. Its aim is to quickly obtain a fixed size Pareto-front approximation. It adapts ideas from different multi-objective evolutionary algorithms, but also incorporates new devices. In particular, the search in the feasible region is carried out on promising areas (hyperspheres) determined by a radius value, which decreases as the optimization procedure evolves. This mechanism helps to maintain a balance between exploration and exploitation of the search space. Additionally, a new local search method which accelerates the convergence of the population towards the Pareto-front, has been incorporated. It is an extension of the local optimizer SASS and improves a given solution along a search direction (no gradient information is used). Finally, a termination criterion has also been proposed, which stops the algorithm if the distances between the Pareto-front approximations provided by the algorithm in three consecutive iterations are smaller than a given tolerance. To know how far two of those sets are from each other, a modification of the well-known Hausdorff distance is proposed. In order to analyze the algorithm performance, it has been compared to the reference algorithms NSGA-II and SPEA2 and the state-of-the-art algorithms MOEA/D and SMS-EMOA. Several quality indicators have been considered, namely, hypervolume, average distance, additive epsilon indicator, spread and spacing. According to the computational tests performed, the new algorithm, named FEMOEA, outperforms the other algorithms.