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This paper deals with the study of the cooperation between parallel processing and evolutionary computation to obtain efficient procedures for solving multiobjective optimisation problems. We propose a new algorithm called PSFGA (parallel single front genetic algorithm), an elitist evolutionary algorithm for multiobjective problems with a clearing procedure that uses a grid in the objective space for diversity maintaining purposes. Thus, PSFGA is a parallel genetic algorithm with a structured population in the form of a set of islands. The performance analysis of PSFGA has been carried out in a cluster system and experimental results show that our parallel algorithm provides adequate results in both, the quality of the solutions found and the time to obtain them. It has been shown that its sequential version also outperforms other previously proposed sequential procedures for multiobjective optimisation in the cases studied.