Quality diversity (QD) algorithms have shown to provide sets of high quality solutions for challenging problems in robotics, games, and combinatorial optimisation. So far, theoretical foundational explaining their good behaviour in practice lack far behind their practical success. We contribute to the theoretical understanding of these algorithms and study the behaviour of QD algorithms for a classical planning problem seeking several solutions. We study the all-pairs-shortest-paths (APSP) problem which gives a natural formulation of the behavioural space based on all pairs of nodes of the given input graph that can be used by Map-Elites QD algorithms. Our results show that Map-Elites QD algorithms are able to compute a shortest path for each pair of nodes efficiently in parallel. Furthermore, we examine parent selection techniques for crossover that exhibit significant speed ups compared to the standard QD approach.

翻译：质量多样性（QD）算法已被证明能为机器人学、游戏和组合优化中的挑战性问题提供高质量解集。迄今为止，解释其良好实践表现的理论基础远落后于其实际成功。我们致力于增进对这些算法的理论理解，并研究QD算法在寻求多个解的经典规划问题中的行为。我们研究了全节点对最短路径（APSP）问题，该问题基于给定输入图中所有节点对提供了行为空间的自然形式化描述，可被Map-Elites QD算法使用。我们的研究结果表明，Map-Elites QD算法能够高效并行计算每对节点的最短路径。此外，我们研究了交叉操作的父代选择技术，相比标准QD方法展现出显著的加速效果。