  We compare exponential-type integrators for the numerical time-propagation of
the equations of motion arising in the multi-configuration time-dependent
Hartree-Fock method for the approximation of the high-dimensional
multi-particle Schr{\"o}dinger equation. We find that among the most widely
used integrators like Runge-Kutta, exponential splitting, exponential
Runge-Kutta, exponential multistep and Lawson methods, exponential Lawson
multistep methods with one predictor/corrector step provide optimal stability
and accuracy at the least computational cost, taking into account that the
evaluation of the nonlocal potential terms is by far the computationally most
expensive part of such a calculation. Moreover, the predictor step provides an
estimator for the time-stepping error at no additional cost, which enables
adaptive time-stepping to reliably control the accuracy of a computation.
