In this work, we consider the problem of Quality-Diversity (QD) optimization with multiple objectives. QD algorithms have been proposed to search for a large collection of both diverse and high-performing solutions instead of a single set of local optima. Thriving for diversity was shown to be useful in many industrial and robotics applications. On the other hand, most real-life problems exhibit several potentially antagonist objectives to be optimized. Hence being able to optimize for multiple objectives with an appropriate technique while thriving for diversity is important to many fields. Here, we propose an extension of the MAP-Elites algorithm in the multi-objective setting: Multi-Objective MAP-Elites (MOME). Namely, it combines the diversity inherited from the MAP-Elites grid algorithm with the strength of multi-objective optimizations by filling each cell with a Pareto Front. As such, it allows to extract diverse solutions in the descriptor space while exploring different compromises between objectives. We evaluate our method on several tasks, from standard optimization problems to robotics simulations. Our experimental evaluation shows the ability of MOME to provide diverse solutions while providing global performances similar to standard multi-objective algorithms.
翻译:在这项工作中,我们考虑到质量-多样性优化的问题,并提出了多重目标。QD算法建议寻找大量多样化和高性能的解决方案,而不是单一的局部选择。在许多工业和机器人应用中,为多样性而奋斗证明是有用的。另一方面,大多数现实生活问题显示出了需要优化的若干潜在敌对目标。因此,能够以适当的技术优化多种目标,同时为多样化而繁荣,对于许多领域都很重要。在这里,我们提议在多目标环境中扩展MAP-Elites算法:多目标式的MAP-Elites(MOME)。也就是说,它将MAP-Elites电网算法遗留下来的多样性与多目标优化的力量结合起来,方法是用Pareto Fron填补每个单元格。因此,它能够在描述空间中找到多种不同的解决方案,同时探索不同目标之间的妥协。我们评估了我们从标准优化问题到机器人模拟的若干任务的方法。我们实验性评估了MOME的模型在提供多种标准性解决方案的同时,提供了类似的全球标准性矩阵的能力。