How entropy-theorems can show that approximating high-dim Pareto-fronts is too hard.
In: PPSN-BTP 2006, 2006, Reykjavik.
It is empirically established that multiobjective evolutionary algorithms do not scale well with the nu
mber of conflicting objectives. We here show that the convergence rate of any comparison-based multi-obj
ective 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 assumpti
on is that the objectives have conflicts. Our conclusions are (i) the relevance of the number of conflic
ting objectives (ii) the relevance of random-search-based criterions (iii) the very-hardness of more tha
n 3-objectives optimization (iv) some hints about new cross-over operators.