  We had been gradually working towards building a comprehensive quarkonia
suppression formalism to explain all 3 dependencies of quarkonium suppression
obtained from heavy-ion collision experiments. We present here the improved
version of quarkonia suppression framework. It assumes bottomonia produced in
the early stage which dissociates due to color screening, gluonic dissociation,
and collisional damping in addition to the shadowing as an initial state
effect. The QGP medium formed in the collisions is assumed to evolve under
($3+1$)-dimensional relativistic viscous hydrodynamics which is modeled using
ECHO-QGP. This replaces the Bjorken's hydrodynamics which we had used in our
earlier work where we determined the centrality and transverse momentum
dependent suppression. The correlated bottom quark and bottom anti-quark could
recombine in the plasma. A rate equation is employed, whose solution gives the
final number of bottomonium after dissociation and recombination under
$(3+1)$-dimensional expansion of the QGP medium. The Shadowing effect, which is
the dominant Cold Nuclear Matter effect at LHC energies, has now been modified
by employing the most recent parton distribution functions obtained from CT14
global analysis and shadowing factors from EPPS16. Using this improved
formalism we determine the centrality, transverse momentum, and rapidity,
dependencies of bottomonium suppression for $\Upsilon(1S)$, and $\Upsilon(2S)$
at the LHC's energies of $2.76$ TeV and $5.02$ TeV. We find a fairly good
agreement between theoretically calculated survival probability and the
measured nuclear modification factor($R_{AA}$) at the two energies.
