Exploiting the Trade-off between Convergence and Diversity Indicators

Recently, it has been stressed that multi-objective evolutionary algorithms (MOEAs) should produce Pareto front approximations with good diversity regardless of the Pareto front geometry. In this light, the use of selection mechanisms based on multiple quality indicators (QIs) is a promising approach due to the exploitation of their strengths. In this paper, we propose to exploit the trade-off between the $\mathrm{I}\mathrm{G}\mathrm{D}^{+}$ and the Riesz s energy indicators, which assess convergence and diversity of a Pareto front approximation, respectively. Since the preferences of both indicators are regularly in conflict due to their different measure scope, it is possible to design a selection mechanism that exploits such trade-off, aiming to generate Pareto front approximations with a good degree of convergence and diversity simultaneously. Our proposed density estimator is embedded in a steady-state MOEA, denoted as PFI-EMOA, which is compared with several state-of-the-art MOEAs. Our experimental results based on the WFG and $\mathrm{W}\mathrm{F}\mathrm{G}^{-1}$ test problems show that PFIEMOA outperforms several state-of-the-art MOEAs, providing outcomes having good convergence and diversity. Additionally, the performance of PFI-EMOA does not depend on the Pareto front shape.