Study of preference relations in many-objective optimization

Abstract

This paper presents a quantitative analysis of different preference relations proposed to deal with problems with a high number of objectives. Since the relations stress different subsets of the Pareto front, we based the comparison on the Tchebycheff distance of the approximation set to the "knee" of the Pareto front. Additionally, the convergence induced by the preference relations is studied by analyzing the generational distance observed at each generation of the search. The results show that some preference relations contribute to converge quickly to the Pareto front, but they promote the generation of solutions far from the knee region. Moreover, even if a preference relation generates solutions near the knee, there exists a trade-off between convergence and the extension of