  In many experiments involving conversion of quantum degenerate atomic gases
into molecular dimers via a Feshbach resonance, an external magnetic field is
linearly swept from above the resonance to below resonance. In the adiabatic
limit, the fraction of atoms converted into molecules is independent of the
functional form of the sweep and is predicted to be 100%. However, for
non-adiabatic sweeps through resonance, Landau-Zener theory predicts that a
linear sweep will result in a negligible production of molecules. Here we
employ a genetic algorithm to determine the functional time dependence of the
magnetic field that produces the maximum number of molecules for sweep times
that are comparable to the period of resonant atom-molecule oscillations,
$2\pi\Omega_{Rabi}^{-1}$. The optimal sweep through resonance indicates that
more than 95% of the atoms can be converted into molecules for sweep times as
short as $2\pi\Omega_{Rabi}^{-1}$ while the linear sweep results in a
conversion of only a few percent. We also find that the qualitative form of the
optimal sweep is independent of the strength of the two-body interactions
between atoms and molecules and the width of the resonance.
