This paper introduces a novel Parallel Multi-Objective Evolutionary Algorithm (pMOEA) which is based on the island model. The serial algorithm on which this approach is based uses the differential evolution operators as its search engine, and includes two mechanisms for improving its convergence properties (through local dominance and environmental selection based on scalar functions). Two different parallel approaches are presented. The first aims at improving effectiveness (i.e., for better approximating the Pareto front) while the second aims to provide a better efficiency (i.e., by reducing the execution time through the use of small population sizes in each sub-population). To assess the performance of the proposed algorithms, we adopt a set of standard test functions and performance measures taken from the specialized literature. Results are compared with respect to its serial counterpart and with respect to three algorithms representative of the state-of-the-art in the area: NSGA-II, MOEA/D and MOEA/D-DE.