  Results of a numerical simulation concerning the low-lying spectrum of
four-dimensional N=1 SU(2) Supersymmetric Yang-Mills (SYM) theory on the
lattice with light dynamical gluinos are reported. We use the tree-level
Symanzik improved gauge action and Wilson fermions with stout smearing of the
gauge links in the Wilson-Dirac operator. The configurations are produced with
the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithm. We performed
simulations on lattices up to a size of 24^3x48 at \beta=1.6. Using QCD units
with the Sommer scale being set to r_0=0.5 fm, the lattice spacing is about
a~0.09 fm, and the spatial extent of the lattice corresponds to 2.1 fm to
control finite size effects. At the lightest simulated gluino mass our results
indicate a mass for the lightest gluino-glue bound state, which is considerably
heavier than the values obtained for its possible superpartners. Whether
supermultiplets are formed remains to be studied in upcoming simulations.
