A Correlation Analysis of Set Quality Indicator Values in Multiobjective Optimization
Résumé
A large spectrum of quality indicators have been proposed so far to assess the performance of discrete Pareto set approximations in multiobjective optimization. Such indicators assign a real-value to any approximation set that reflects a given aspect of its quality. This is an important issue in multiobjective optimization, not only to compare the performance and assets of different approximate algorithms, but also to improve their internal selection mechanisms. However, identifying fine-grained theoretical properties between different classes of indicators is generally out of reach due to the high complexity of the approximation set structures. In this paper, we adopt a statistical analysis to experimentally investigate by how much a subset of state-of-the-art quality indicators agree with each other for a wide range of Pareto set approximations from well-known two-and three-objective benchmark continuous test functions. More particularly, we measure the correlation between the ranking of low-, medium-, and high-quality limited-size approximation sets with respect to inverted generational distance, epsilon, R-metric and hypervolume indicator values. Since none of them obtains the exact same ranking of approximation sets, we show that they actually emphasize different facets of approximation quality. Moreover, our statistical analysis allows us to quantify the degree of compliance between these quality indicators.
Origine : Fichiers produits par l'(les) auteur(s)