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We propose the generalized uncertainty principle (GUP) with an additionalterm of quadratic momentum motivated by string theory and black hole physics asa quantum mechanical framework for the minimal length uncertainty at the Planckscale. We demonstrate that the GUP parameter, $\beta_0$, could be bestconstrained 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 gravitonsand that of photons. We conclude that the upper bound reads $\beta_0 \simeq10^{60}$. Utilizing features of the UV/IR correspondence and the obvioussimilarities between GUP (including non-gravitating and gravitating impacts onHeisenberg uncertainty principle) and the discrepancy between the theoreticaland the observed cosmological constant $\Lambda$ (apparently manifestinggravitational influences on the vacuum energy density), known as {\itcatastrophe of non-gravitating vacuum}, we suggest a possible solution for thislong-standing physical problem, $\Lambda \simeq 10^{-47}~$GeV$^4/\hbar^3 c^3$.

A Possible Solution of the Cosmological Constant Problem based on Minimal Length Uncertainty and GW170817 and PLANCK Observations