  Gravitational wave astronomy has been firmly established with the detection
of gravitational waves from the merger of ten stellar mass binary black holes
and a neutron star binary. This paper reports on the all-sky search for
gravitational waves from intermediate mass black hole binaries in the first and
second observing runs of the Advanced LIGO and Virgo network. The search uses
three independent algorithms: two based on matched filtering of the data with
waveform templates of gravitational wave signals from compact binaries, and a
third, model-independent algorithm that employs no signal model for the
incoming signal. No intermediate mass black hole binary event was detected in
this search. Consequently, we place upper limits on the merger rate density for
a family of intermediate mass black hole binaries. In particular, we choose
sources with total masses $M=m_1+m_2\in[120,800]$M$_\odot$ and mass ratios $q =
m_2/m_1 \in[0.1,1.0]$. For the first time, this calculation is done using
numerical relativity waveforms (which include higher modes) as models of the
real emitted signal. We place a most stringent upper limit of
$0.20$~Gpc$^{-3}$yr$^{-1}$ (in co-moving units at the 90% confidence level) for
equal-mass binaries with individual masses $m_{1,2}=100$M$_\odot$ and
dimensionless spins $\chi_{1,2}= 0.8$ aligned with the orbital angular momentum
of the binary. This improves by a factor of $\sim 5$ that reported after
Advanced LIGO's first observing run.
