  In this paper, we introduce the notion of standard homogeneous
$(\alpha_1,\alpha_2)$-metrics, as a natural non-Riemannian deformation for the
normal homogeneous Riemannian metrics. We prove that with respect to the given
bi-invariant inner product and orthogonal decompositions for $\mathfrak{g}$, if
there exists one generic standard g.o. $(\alpha_1,\alpha_2)$-metric, then all
other standard homogeneous $(\alpha_1,\alpha_2)$-metrics are also g.o.. For
standard homogeneous $(\alpha_1,\alpha_2)$-metrics associated with a triple of
compact connected Lie groups, we can refine our theorem and get some simple
algebraic equations as the criterion for the g.o. property. As the application
of this criterion, we discuss standard g.o. $(\alpha_1,\alpha_2)$-metric from
H. Tamaru's classication work, and find some new examples of non-Riemannian
g.o. Finsler spaces which are not weakly symmetric. On the other hand, we also
prove that all standard g.o. $(\alpha_1,\alpha_2)$-metrics on the three Wallach
spaces, $W^6=SU(3)/T^2$, $W^{12}=Sp(3)/Sp(1)^3$ and $W^{24}=F_4/Spin(8)$, must
be the normal homogeneous Riemannian metrics.
