  In this work, we pave the way to calculate the productions of $\omega$ and
$K^0_{\rm S}$ mesons at large $p_T$ in p+p and A+A collisions at the RHIC and
the LHC. The $\omega$ meson fragmentation functions (FFs) in vacuum at
next-to-leading order (NLO) are obtained by evolving NLO DGLAP evolution
equations with rescaled $\omega$ FFs at initial scale $Q_0^2=1.5$ GeV$^2$ from
a broken SU(3) model, and the $K^0_{\rm S}$ FFs in vacuum are taken from AKK08
parametrization directly. Within the framework of the NLO pQCD improved parton
model, we make good descriptions of the experimental data on $\omega$ and
$K^0_{\rm S}$ in p+p both at the RHIC and the LHC. With the higher-twist
approach to take into account the jet quenching effect by medium modified FFs,
the nuclear modification factors for $\omega$ meson and $K^0_{\rm S}$ meson at
the RHIC and the LHC are presented with different sets of jet transport
coefficient $\hat{q}_0$. Then we make a global extraction of $\hat{q}_0$ at the
RHIC and the LHC by confronting our model calculations with all available data
on 6 identified mesons: $\pi^0$, $\eta$, $\rho^0$, $\phi$, $\omega$, and
$K^0_{\rm S}$. The minimum value of the total $\chi^2/d.o.f$ for productions of
these mesons gives the best value of $\hat{q}_0=0.5\rm GeV^2/fm$ for Au+Au
collisions with $\sqrt{s_{\rm NN}}=200$ GeV at the RHIC, and $\hat{q}_0=1.2\rm
GeV^2/fm$ for Pb+Pb collisions with $\sqrt{s_{\rm NN}}=2.76$ TeV at the LHC
respectively, with the QGP spacetime evolution given by an event-by-event
viscous hydrodynamics model IEBE-VISHNU. With these global extracted values of
$\hat{q}_0$, the nuclear modification factors of $\pi^0$, $\eta$, $\rho^0$,
$\phi$, $\omega$, and $K^0_{\rm S}$ in A+A collisions are presented, and
predictions of yield ratios such as $\omega/\pi^0$ and $K^0_{\rm S}/\pi^0$ at
large $p_T$ in heavy-ion collisions at the RHIC and the LHC are provided.
