  We learn optimal instance-specific heuristics for the global minimization of
nonconvex quadratically-constrained quadratic programs (QCQPs). Specifically,
we consider partitioning-based mixed-integer programming relaxations for
nonconvex QCQPs and propose the novel problem of $\textit{strong partitioning}$
to optimally partition variable domains $\textit{without}$ sacrificing global
optimality. We design a local optimization method for solving this challenging
max-min strong partitioning problem and replace this expensive benchmark
strategy with a machine learning (ML) approximation for homogeneous families of
QCQPs. We present a detailed computational study on randomly generated families
of QCQPs, including instances of the pooling problem, using the open-source
global solver Alpine. Our numerical experiments demonstrate that strong
partitioning and its ML approximation significantly reduce Alpine's solution
time by factors of $3.5 - 16.5$ and $2 - 4.5$ $\textit{on average}$ and by
maximum factors of $15 - 700$ and $10 - 200$, respectively, over the different
QCQP families.
