How entropy-theorems can show that approximating high-dim Pareto-fronts is too hard
Olivier Teytaud · HAL (Le Centre pour la Communication Scientifique Directe) · 2006
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 any comparison-based multi-objective algorithm, 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 assumption is that the objectives have conflicts. Our conclusions are (i) the relevance of the number of conflicting objectives (ii) the relevance of random-search-based criterions (iii) the very-hardness of more than 3- objectives optimization (iv) some hints about new cross-over operators.