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I present a brief review of the generalized Brodsky-Lepage-McKenzie (BLM)approaches to fix the scale-dependence of the renormalization group (RG)invariant quantities in QCD. At first, these approaches are based on theexpansions of the coefficients of the perturbative series for the RG-invariantquantities in the products of the coefficients $\beta_i$ of the QCD$\beta$-function, which are evaluated in the MS-like schemes. As a next stepall $\beta_i$-dependent terms are absorbed into the BLM-type scale(s) of thepowers of the QCD couplings. The difference between two existing formulationsof the above mentioned generalizations based on the seBLM approach and thePrinciple of Maximal Conformality (PMC) are clarified in the case of theBjorken polarized deep-inelastic scattering sum rule. Using the conformalsymmetry-based relations for the non-singlet coefficient functions of the AdlerD-function and of Bjorken polarized deep-inelastic scattering sum rules $C^{\rmBjp}_{\rm NS}(a_s)$ the $\beta_i$-dependent structure of the NNLO approximationfor $C^{\rm Bjp}_{\rm NS}(a_s)$ is predicted in QCD with $n_{gl}$-multiplet ofgluino degrees of freedom, which appear in SUSY extension of QCD. Theimportance of performing the analytical calculation of the N$^3$LO additionalcontributions of $n_{gl}$ gluino multiplet to $C^{\rm Bjp}_{\rm NS}(a_s)$ forchecking the presented in the report NNLO prediction and for the studies of thepossibility to determine the discussed $\{\beta\}$-expansion pattern of thissum rule at the $O(a_s^4)$-level is emphasised.

The generalized BLM approach to fix scale-dependence in QCD: the current status of investigations