  We revisit the evolution of the mass-metallicity relation of low- and
high-redshift galaxies by using a sample of local analogs of high-redshift
galaxies. These analogs share the same location of the UV-selected star-forming
galaxies at $z\sim2$ on the [OIII]/H$\beta$ versus [NII]/H$\alpha$ nebular
emission-line diagnostic (or BPT) diagram. Their physical properties closely
resemble those in $z\sim2$ UV-selected star-forming galaxies being
characterized in particular by high ionization parameters ($\log q\approx7.9$)
and high electron densities ($n_e\approx100~\rm{cm}^{-3}$). With the full set
of well-detected rest-frame optical diagnostic lines, we measure the gas-phase
oxygen abundance in the SDSS galaxies and these local analogs using the
empirical relations and the photoionization models. We find that the
metallicity difference between the SDSS galaxies and our local analogs in the
$8.5<log(M_*/M_{\odot})<9.0$ stellar mass bin varies from -0.09 to 0.39 dex,
depending on strong-line metallicity measurement methods. Due to this
discrepancy the evolution of mass-metallicity should be used to compare with
the cosmological simulations with caution. We use the [SII]/H$\alpha$ and
[OI]/H$\alpha$ BPT diagram to reduce the potential AGN and shock contamination
in our local analogs. We find that the AGN/shock influences are negligible on
the metallicity estimation.
