Towards Exploratory Quality Diversity Landscape Analysis

TL;DR

This work investigates whether Exploratory Landscape Analysis (ELA) features can characterize Quality Diversity (QD) problems to enable automated algorithm selection. It conducts a large-scale empirical study across three domains and multiple QD settings, comparing LHS sampling with CVT-MAP-Elites variants and varying variation operators, behaviour functions, archive sizes, and genotypic dimensions, while extracting pflacco ELA features. The results show that QD configurations influence ELA features differently from random sampling, with operator choice, behaviour function, archive size, and dimensionality all shaping the feature landscape; some features exhibit strong differences while others remain stable, and several high-cost features are time-intensive. These findings suggest potential for ELA-guided QD automation, while highlighting computational trade-offs and pointing to directions for more efficient feature design and broader domain coverage in future work.

Abstract

This work is a preliminary study on using Exploratory Landscape Analysis (ELA) for Quality Diversity (QD) problems. We seek to understand whether ELA features can potentially be used to characterise QD problems paving the way for automating QD algorithm selection. Our results demonstrate that ELA features are affected by QD optimisation differently than random sampling, and more specifically, by the choice of variation operator, behaviour function, archive size and problem dimensionality.

Figures (6)

• Figure 1: Gaussian mutation operator and IsoLineDD in comparison with LHS with $10000$ archive size on the Robot Arm Repertoire domain with $16$ dimensions. The plots show the median and the interquartile range ($Q_1$ and $Q_3$) over $30$ experimental runs, with mostly notable differences. The x-axis, represents the total number of evaluations, whilst the vertical dashed line marks the $10000$ evaluations, matching the $10000$ evaluations of LHS.
• Figure 2: Gaussian mutation operator and IsoLineDD in comparison with LHS with $10000$ archive cells on the Robot Arm Repertoire domain with $32$ dimensions. The plots show the median and the interquartile range ($Q_1$ and $Q_3$) over $30$ experimental runs, with mostly notable differences. The x-axis, represents the total number of evaluations, whilst the vertical dashed line marks the $10000$ evaluations, matching the $10000$ evaluations of LHS.
• Figure 3: IsoLineDD in comparison with LHS on the Rastrigin function with all the different behaviour functions with $10000$ archive size and $32$ dimensions. The plots show the median and the interquartile range ($Q_1$ and $Q_3$) over $30$ experimental runs, with mostly notable differences. The x-axis, represents the total number of evaluations, whilst the vertical dashed line marks the $10000$ evaluations, matching the $10000$ evaluations of LHS.
• Figure 4: IsoLineDD in comparison with LHS on the Sphere function with all the different behaviour functions $\mathbf{b^i}$ with $10000$ archive size and $32$ dimensions. The plots show the median and the interquartile range ($Q_1$ and $Q_3$) over $30$ experimental runs, with mostly notable differences. The x-axis, represents the total number of evaluations, whilst the vertical dashed line marks the $10000$ evaluations, matching the $10000$ evaluations of LHS.
• Figure 5: IsoLineDD on the Robot Arm Repertoire with $32$ dimensions on different archive sizes. The plots show the state of the features at $10k$ evaluations on different archive sizes (notice the different colours), and how it changes at $1M$ evaluations. The box plots are groups based on theses two evaluation milestones. Some features could not be calculated for $100$ archive size; low sample count.