  Let $f$ be a semi-weighted-homogeneous polynomial having an isolated
singularity at 0. Let $\alpha_{f,k}$ be the spectral numbers of $f$ at 0. By
Malgrange and Varchenko there are non-negative integers $r_k$ such that the
$\alpha_{f,k}-r_k$ are the roots up to sign of the local Bernstein-Sato
polynomial $b_f(s)$ divided by $s+1$. However, it is quite difficult to
determine these shifts $r_k$ explicitly on the parameter space of
$\mu$-constant deformation of a weighted homogeneous polynomial. Assuming the
latter is nearly Brieskorn-Pham type, we can obtain a very simple algorithm to
determine these shifts, which can be realized by using Singular (or even C)
without employing Gr\"obner bases. This implies a refinement of classical work
of M. Kato and P. Cassou-Nogu\`es in two variable cases, showing that the
stratification of the parameter space can be controlled by using the (partial)
additive semigroup structure of the weights of parameters. As a corollary we
get for instance a sufficient condition for all the shiftable roots of $b_f(s)$
to be shifted. We can also produce examples where the minimal root of $b_f(s)$
is quite distant from the others as well as examples of semi-homogeneous
polynomials with roots of $b_f(s)$ nonconsecutive.
