Scalability of population-based search heuristics for many-objective optimization

Beginning with Talagrand [16]'s seminal work, isoperimetric inequalities have been used extensively in analysing randomized algorithms. We develop similar inequalities and apply them to analysing population-based randomized search heuristics for multiobjective optimization in ℝn space. We demonstrate the utility of the framework in explaining an empirical observation so far not explained analytically: the curse of dimensionality, for many-objective problems. The framework makes use of the black-box model now popular in EC research.