Abstract
Pareto compliance is a critical property of quality indicators (QIs) focused on measuring convergence to the Pareto front. This property allows a QI not to contradict the order imposed by the Pareto dominance relation. Hence, Pareto-compliant QIs are remarkable when comparing approximation sets of multi-objective evolutionary algorithms (MOEAs) since they do not produce misleading conclusions. However, the practical effect of Pareto-compliant QIs as the backbone of MOEAs' survival mechanisms is not entirely understood. In this paper, we study the practical effect of IGD++ (which is a combination of IGD+ and the hypervolume indicator), IGD+, and IGD, which are Pareto-compliant, weakly Pareto-compliant, and not Pareto-compliant QIs, respectively. To this aim, we analyze the convergence and diversity properties of steady-state MOEAs based on the previously mentioned QIs throughout the whole evolutionary process. Our experimental results showed that, in general, the practical effect of a Pareto-compliant QI in a selection mechanism is not very significant concerning weaker QIs, taking into account the whole evolutionary process.
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