  Quality-Diversity (QD) algorithms evolve behaviourally diverse and
high-performing solutions. To illuminate the elite solutions for a space of
behaviours, QD algorithms require the definition of a suitable behaviour space.
If the behaviour space is high-dimensional, a suitable dimensionality reduction
technique is required to maintain a limited number of behavioural niches. While
current methodologies for automated behaviour spaces focus on changing the
geometry or on unsupervised learning, there remains a need for customising
behavioural diversity to a particular meta-objective specified by the end-user.
In the newly emerging framework of QD Meta-Evolution, or QD-Meta for short, one
evolves a population of QD algorithms, each with different algorithmic and
representational characteristics, to optimise the algorithms and their
resulting archives to a user-defined meta-objective. Despite promising results
compared to traditional QD algorithms, QD-Meta has yet to be compared to
state-of-the-art behaviour space automation methods such as Centroidal Voronoi
Tessellations Multi-dimensional Archive of Phenotypic Elites Algorithm
(CVT-MAP-Elites) and Autonomous Robots Realising their Abilities (AURORA). This
paper performs an empirical study of QD-Meta on function optimisation and
multilegged robot locomotion benchmarks. Results demonstrate that QD-Meta
archives provide improved average performance and faster adaptation to a priori
unknown changes to the environment when compared to CVT-MAP-Elites and AURORA.
A qualitative analysis shows how the resulting archives are tailored to the
meta-objectives provided by the end-user.
