  The construction of a Supersymmetric Grand Unified Model based on the
Pati-Salam gauge group is briefly reviewed and the low energy consequences of
the derived asymptotic Yukawa quasi-unification conditions are examined. In the
framework of the resulting Constrained Minimal Supersymmetric Standard Model,
the cosmological relic density of the bino-like LSP is calculated and the
results are explicitly compared with {\tt micrOMEGAs}. In addition to the Cold
Dark Matter constraint, restrictions on the parameter space, arising from the
Higgs boson masses, the SUSY corrections to $b$-quark mass, the muon anomalous
magnetic moment and the inclusive decay $b\to s\gamma$ are, also, investigated.
For $\mu>0$, a wide and natural range of parameters is allowed. On the
contrary, the $\mu<0$ case not only is disfavored from the present experimental
data on the muon anomalous magnetic moment, but also, it can be excluded from
the combination of the Cold Dark Matter and BR($b\to s \gamma$) requirements.
