  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.
