Why quality assessment of multiobjective optimizers is difficult

Abstract

Quantitative quality assessment of approximations of the Pareto-optimal set is an important issue in comparing the performance of multi-objective evolutionary algorithms. Most popular are methods that assign each approximation set a vector of real numbers that reflect different aspects of the quality. In this study, we investigate this type of quality assessment from a theoretical point of view. We provide a rigorous analysis of limitations and suggest a mathematical framework on the basis of which existing techniques are classified and discussed.