Summary: An algebraic algorithm is developed for computation of invariants (`generalized Casimir operators’) of general Lie algebras over the real or complex number field. Its main tools are Cartan’s method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. Unlike the first application of the algorithm in the authors’ previous paper [J. Phys. A, Math. Gen. 39, No. 20, 5749--5762 (2006; Zbl 1106.17040
), math-ph/0602046], which deals with low-dimensional Lie algebras, here the effectiveness of the algorithm is demonstrated by its application to computation of invariants of solvable Lie algebras of general dimension $n < \infty$ restricted only by a required structure of the nilradical. Specifically, invariants are calculated here for families of real/complex solvable Lie algebras. These families contain, with only a few exceptions, all the solvable Lie algebras of specific dimensions, for whom the invariants are found in the literature.