  The representation, or encoding, utilized in evolutionary algorithms has a
substantial effect on their performance. Examination of the suitability of
widely used representations for quality diversity optimization (QD) in robotic
domains has yielded inconsistent results regarding the most appropriate
encoding method. Given the domain-dependent nature of QD, additional evidence
from other domains is necessary. This study compares the impact of several
representations, including direct encoding, a dictionary-based representation,
parametric encoding, compositional pattern producing networks, and cellular
automata, on the generation of voxelized meshes in an architecture setting. The
results reveal that some indirect encodings outperform direct encodings and can
generate more diverse solution sets, especially when considering full
phenotypic diversity. The paper introduces a multi-encoding QD approach that
incorporates all evaluated representations in the same archive. Species of
encodings compete on the basis of phenotypic features, leading to an approach
that demonstrates similar performance to the best single-encoding QD approach.
This is noteworthy, as it does not always require the contribution of the
best-performing single encoding.
