  We propose the generalized uncertainty principle (GUP) with an additional
term of quadratic momentum motivated by string theory and black hole physics as
a quantum mechanical framework for the minimal length uncertainty at the Planck
scale. We demonstrate that the GUP parameter, $\beta_0$, could be best
constrained by the the gravitational waves observations; GW170817 event. Also,
we suggest another proposal based on the modified dispersion relations (MDRs)
in order to calculate the difference between the group velocity of gravitons
and that of photons. We conclude that the upper bound reads $\beta_0 \simeq
10^{60}$. Utilizing features of the UV/IR correspondence and the obvious
similarities between GUP (including non-gravitating and gravitating impacts on
Heisenberg uncertainty principle) and the discrepancy between the theoretical
and the observed cosmological constant $\Lambda$ (apparently manifesting
gravitational influences on the vacuum energy density), known as {\it
catastrophe of non-gravitating vacuum}, we suggest a possible solution for this
long-standing physical problem, $\Lambda \simeq 10^{-47}~$GeV$^4/\hbar^3 c^3$.
