The aim of this paper is to show the influence of genetic operators such as crossover and mutation on the performance of a genetic algorithm (GA). The GA is applied to the multi-objective permutation flowshop problem. To achieve our goal an experimental study of a set of crossover and mutation operators is presented. A measure related to the dominance relations of different non-dominated sets, generated by different algorithms, is proposed so as to decide which algorithm is the best. The main conclusion is that there is a crossover operator having the best average performance on a very specific set of instances, and under a very specific criterion. Explaining the reason why a given operator is better than others remains an open problem.