  Quality-Diversity (QD) algorithms have recently gained traction as
optimisation methods due to their effectiveness at escaping local optima and
capability of generating wide-ranging and high-performing solutions. Recently,
Multi-Objective MAP-Elites (MOME) extended the QD paradigm to the
multi-objective setting by maintaining a Pareto front in each cell of a
map-elites grid. MOME achieved a global performance that competed with NSGA-II
and SPEA2, two well-established Multi-Objective Evolutionary Algorithms (MOEA),
while also acquiring a diverse repertoire of solutions. However, MOME is
limited by non-directed genetic search mechanisms which struggle in
high-dimensional search spaces. In this work, we present Multi-Objective
MAP-Elites with Policy-Gradient Assistance and Crowding-based Exploration
(MOME-PGX): a new QD algorithm that extends MOME to improve its data efficiency
and performance. MOME-PGX uses gradient-based optimisation to efficiently drive
solutions towards higher performance. It also introduces crowding-based
mechanisms to create an improved exploration strategy and to encourage
uniformity across Pareto fronts. We evaluate MOME-PGX in four simulated robot
locomotion tasks and demonstrate that it converges faster and to a higher
performance than all other baselines. We show that MOME-PGX is between 4.3 and
42 times more data-efficient than MOME and doubles the performance of MOME,
NSGA-II and SPEA2 in challenging environments.
