  We study general non-supersymmetric heterotic string models, including
so-called interpolating models, $d$-dimensionally compactified with the
arbitrary number of freely acting $\mathbb{Z}_{2}$ twisted directions. Taking
the limits of the compactified radii to zero and infinity (the endpoint
limits), we show some examples of the various interpolation patterns in the
$d=2$ (8-dimensional) case. In the region where supersymmetry is asymptotically
restored, we derive the formula for the one-loop cosmological constant of
$(10-d)$ dimensional non-supersymmetric heterotic string models with general
$\mathbb{Z}_{2}$ twists, which does not depend on all the other endpoints and
find out the points in the moduli space where the cosmological constant is
exponentially suppressed. The moduli stability of the cosmological constant is
also analyzed.
