Quality Diversity optimization using the IsoLineDD operator: forward and backward directions are equally important

Abstract

Quality Diversity (QD) optimization aims at returning a diverse collection of high quality solutions in a single run. Prior work indicated that the optimized collection concentrates in a subspace of the genotype space called the Elite Hypervolume. This suggested that if the Elite Hypervolume is convex, perturbing a solution (elite) towards the direction of another elite would create a solution inside the subspace. To accelerate QD optimization, the IsoLineDD operator was proposed which perturbs a solution along the line that connects it with another elite, both in the forward and the backward direction (i.e., towards and away from another elite), with equal probability. In this work, we hypothesize that the backward direction is mostly useful for exploration, at the beginning of QD optimization, rather than exploitation. To validate our hypothesis, we create a dynamic IsoLineDD operator that modifies its probability of creating solutions in the forward and backward directions, respectively. Our experiments and analysis in the robotic arm repertoire and Rastrigin problems invalidate this hypothesis by demonstrating that the forward and backward directions of vanilla IsoLineDD equally contribute to the optimization of the collection.