  New research has highlighted a shortfall in the Standard Model (SM) because
it predicts neutrinos to have zero mass. However, recent experiments on
neutrino oscillation have revealed that the majority of neutrino parameters
indeed indicate their significant mass. In response, scientists are
increasingly incorporating discrete symmetries alongside continuous ones for
better justification of observed patterns of neutrino mixing. In this study, we
have examined a model within $A_4\times Z_3\times Z_{10}$ symmetry to estimate
the neutrino masses using particle swarm optimization technique for both mass
hierarchy of neutrino. This model employed a hybrid seesaw mechanism, a
combination of seesaw mechanism of type-I and type-II, to establish the
effective Majorana neutrino mass matrix. After calculating the mass eigenvalues
and lepton mixing matrix upto second order perturbation theory in this
framework, this study seeks to investigate the scalar potential for vacuum
expectation values (VEVs), optimize the parameters, $U_{PMNS}$ matrix, neutrino
masses: $|{m_{1}^{\prime}}^N|=0.0292794-0.0435082\ eV$,
$|{m_{2}^{\prime}}^N|=1.78893\times 10^{-18}-0.0293509\ eV$,
$|{m_{3}^{\prime}}^N|=0.0307414-0.0471467\ eV$,
$|{m_{1}^{\prime}}^I|=0.00982013-0.0453623\ eV$,
$|{m_{2}^{\prime}}^I_|=0.0379702-0.0471197\ eV$, and
$|{m_{3}^{\prime}}^I|=0.0122063-0.027544\ eV$, effective neutrino mass
parameters: $\langle {m_{ee}} \rangle^N=(0.170-3.93)\times10^{-2}\ eV$,
$\langle {m_{\beta}} \rangle^N=(0.471-1.39)\times10^{-2}\ eV$, $\langle
{m_{ee}} \rangle^I=(1.85-4.55)\times10^{-2}\ eV$ and $\langle {m_{\beta}}
\rangle^I=(2.26-4.56)\times10^{-2}\ eV$, are predicted for both mass hierarchy
through particle swarm optimization (PSO), showing strong agreement with recent
experimental findings.
