Abstract: It is empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. We here show that the convergence rate of all comparison-based multiobjective algorithms, for the Hausdorff distance, is not much better than the convergence rate of the random search, unless the number of objectives is very moderate, in a framework in which the stronger assumptions are (i) that the objectives are conflicting (ii) that lower bounding the computational cost by the number of comparisons is a good model. Our conclusions are (i) the relevance of the number of conflicting objectives (ii) the relevance of criteria based on comparisons with random-search for multi-objective optimization (iii) the very-hardness of more than 3- objectives optimization (iv) some hints about cross-over operators.