Correlation between diversity and hypervolume in evolutionary multiobjective optimization

This paper reports a study of the influence of diversity in the convergence dynamics of Multiobjective Evolutionary Algorithms (MOEAs) towards the Pareto Front (PF). By varying mutation and crossover parameters, several scenarios of exploration and exploitation are considered, in which each of them is analysed in order to assess the role of diversity levels on the evolution of high quality sets of non-dominated solutions, in terms of the Hypervolume indicator. For this task, the application of the NSGA2 algorithm for approximating the PF in five ZDT benchmark problems is considered. The results not only indicate that there are significant statistical correlations between several diversity metrics and the observed maximum Hypervolume levels on the evolved populations, but also suggest that there are predictable temporal patterns of correlation when the evolutionary process is portrayed generation wise.