  We perform Monte Carlo investigations of the 4d ${\cal N}=1$ supersymmetric
Yang-Mills (SYM) theory on the lattice with dynamical gluinos in the adjoint
representation of the SU(2) gauge group. Our aim is to determine the mass
spectrum of the low-lying bound states which is expected to be organised in
supermultiplets in the infinite volume continuum limit. For this purpose we
perform simulations on large lattices, up to an extension $L/r_0 \simeq 6$
where $r_0 \simeq 0.5 \rm fm$ is the Sommer scale parameter. We apply improved
lattice actions: tree-level improved Symanzik (tlSym) gauge action and in the
later runs a Stout-smeared Wilson fermion action. The gauge configuration
samples are prepared by the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC)
update algorithm.
