  Multi-wavelength simultaneous observations are essential to the constraints
on the origin of fast radio bursts (FRBs). However, it is a significant
observational challenge due to the nature of FRBs as transients with a radio
millisecond duration, which occur randomly in the sky regardless of time and
position. Here, we report the search for short-time fast optical bursts in the
GWAC archived data associated with FRB 20181130B, which were detected by the
Five Hundred Meter Spherical Radio Telescope (FAST) and recently reported. No
new credible sources were detected in all single GWAC images with an exposure
time of 10 s, including image with coverage of the expected arrival time in
optical wavelength by taking the high dispersion measurements into account. Our
results provide a limiting magnitude of 15.43$\pm0.04$ mag in R band,
corresponding to a flux density of 1.66 Jy or 8.35 mag in AB system by assuming
that the duration of the optical band is similar to that of the radio band of
about 10 ms. This limiting magnitude makes the spectral index of $\alpha<0.367$
from optical to radio wavelength. The possible existence of longer duration
optical emission was also investigated with an upper limits of 0.33 Jy (10.10
mag), 1.74 mJy (15.80 mag) and 0.16 mJy (18.39 mag) for the duration of 50 ms,
10 s and 6060 s, respectively. This undetected scenario could be partially
attributed to the shallow detection capability, as well as the high inferred
distance of FRB 20181130B and the low fluence in radio wavelength. The future
detectability of optical flashes associated with nearby and bright FRBs are
also discussed in this paper.
