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 set approximating the complete Pareto-front. It adapts ideas from different multi-objective optimization evolutionary algorithms, but also incorporates new devices. In particular, the search in the space 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 optimal 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 criteria has also been proposed, which stops the algorithm if during three consecutive iterations the changes experimented in the candidate Pareto-front are negligible (in terms of the objective function values). To know how far two 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 Keywords Nonlinear multi-objective optimization · evolutionary algorithm · quality indicators · computational study 1 Introduction