  Simulations at physical quark masses are affected by the critical slowing
down of the solvers. Multigrid preconditioning has proved to deal effectively
with this problem. Multigrid accelerated simulations at the physical value of
the pion mass are being performed to generate $N_f = 2$ and $N_f = 2 + 1 + 1$
gauge ensembles using twisted mass fermions. The adaptive aggregation-based
domain decomposition multigrid solver, referred to as DD-$\alpha$AMG method, is
employed for these simulations. Our simulation strategy consists of an hybrid
approach of different solvers, involving the Conjugate Gradient (CG),
multi-mass-shift CG and DD-$\alpha$AMG solvers. We present an analysis of the
multigrid performance during the simulations discussing the stability of the
method. This significant speeds up the Hybrid Monte Carlo simulation by more
than a factor $4$ at physical pion mass compared to the usage of the CG solver.
