  We discuss generalizations of the BLM optimization procedure for
renormalization group invariant quantities. In this respect, we discuss in
detail the features and construction of the $\{\beta\}$--expansion
representation instead of the standard perturbative series with regards to the
Adler $D$-function and Bjorken polarized sum rules obtained in order of ${\cal
O}(\alpha_s^4)$. Based on the $\{\beta\}$--expansion we analyse different
schemes of optimization, including the corrected Principle of Maximal
Conformality, numerically illustrating their results. We suggest our scheme for
the series optimization and apply it to both the above quantities.
