  We consider a generalization of the standard Metropolis algorithm
acceptance/rejection decision rule and numerically explore its properties using
auxiliary field quantum Monte Carlo. The generalization involves a free
parameter which, given a criterion for proposing attempted moves, can be used
to tune the average acceptance rate in a particular way. Such tuning can also
potentially change Monte Carlo autocorrelation times, and the combination of
the changing acceptance rate and autocorrelation times raises the possibility
of more efficient simulations. We explore these issues using primarily
massively parallel quantum Monte Carlo runs of the ``test case''
two-dimensional Hubbard model, and discuss results and applications.
