  Parent selection in evolutionary algorithms for multi-objective optimisation
is usually performed by dominance mechanisms or indicator functions that prefer
non-dominated points. We propose to refine the parent selection on evolutionary
multi-objective optimisation with diversity-based metrics. The aim is to focus
on individuals with a high diversity contribution located in poorly explored
areas of the search space, so the chances of creating new non-dominated
individuals are better than in highly populated areas. We show by means of
rigorous runtime analysis that the use of diversity-based parent selection
mechanisms in the Simple Evolutionary Multi-objective Optimiser (SEMO) and
Global SEMO for the well known bi-objective functions ${\rm O{\small
NE}M{\small IN}M{\small AX}}$ and ${\rm LOTZ}$ can significantly improve their
performance. Our theoretical results are accompanied by experimental studies
that show a correspondence between theory and empirical results and motivate
further theoretical investigations in terms of stagnation. We show that
stagnation might occur when favouring individuals with a high diversity
contribution in the parent selection step and provide a discussion on which
scheme to use for more complex problems based on our theoretical and
experimental results.

Neural and Evolutionary Computing