Discrete Gene Crossover Accelerates Solution Discovery in Quality-Diversity Algorithms

TL;DR

This work proposes a mutation operator which augments variation-based operators with discrete, gene-level crossover, enabling rapid recombination of elite genetic material, and demonstrates improvements in QD score, coverage, and max fitness.

Abstract

Quality-Diversity (QD) algorithms aim to discover diverse, high-performing solutions across behavioral niches. However, QD search often stagnates as incremental variation operators struggle to propagate building blocks across large populations. Existing mutation operators rely on gradual variation to solutions, limiting their ability to efficiently explore regions of the search space distant from parent solutions or to spread beneficial genetic material through the population. We propose a mutation operator which augments variation-based operators with discrete, gene-level crossover, enabling rapid recombination of elite genetic material. This crossover mechanism mirrors the biological principle of meiosis and facilitates both the direct transfer of genetic material and the exploration of novel genotype configurations beyond the existing elite hypervolume. We evaluate operators on three locomotion environments, demonstrating improvements in QD score, coverage, and max fitness, with particularly strong performance in later stages of optimization once building blocks have been established in the archive. These results show that the addition of a discrete crossover mutation provides a complementary exploration mechanism that sustains quality-diversity growth beyond the performance demonstrated by existing operators.

Figures (6)

• Figure 1: A 2D illustration of the baseline and proposed operators. Parents are shown in black with the order randomly selected for each sample. Offspring are shown in red. (A) Isotropic Gaussian mutation ( Iso). (B) Iso Cross, demonstrating exploration through recombination. (C) Iso+ LineDD, demonstrating directional variation between parents. (D) Iso Line Cross, demonstrating both directional variation between parents and exploration through recombination.
• Figure 2: QD Score, Coverage, and Max Fitness for Iso, Iso Cross, Iso+ LineDD, and Iso Line Cross. Each experiment is replicated 20 times with random seeds. The solid line is the median and the shaded region represents the interquartile range.
• Figure 3: 500 generation rolling average of offspring added (left) and the QD score added per offspring (right) for each operator and environment. We see similar levels of offspring added for all operators, with QD score added notably higher for the Iso Line Cross operator than Iso+ Line DD across all generations.
• Figure 4: Box plots showing the distribution of results for each of the operators on the QD metrics (see Section \ref{['sec: envs+metrics']}). The black line within the box represents the median, the box the interquartile range, the whiskers 1.5$x$ IQR, and the white circle outliers beyond this range.
• Figure 5: HalfCheetah Uni archive at the end of training for all operators.