  We present a method for simulating the time evolution of one-dimensional
correlated electron-phonon systems which combines the time-evolving block
decimation algorithm with a dynamical optimization of the local basis. This
approach can reduce the computational cost by orders of magnitude when boson
fluctuations are large. The method is demonstrated on the nonequilibrium
Holstein polaron by comparison with exact simulations in a limited functional
space and on the scattering of an electronic wave packet by local phonon modes.
Our study of the scattering problem reveals a rich physics including transient
self-trapping and dissipation.
