  Motivated by recent results using shaken optical lattices to perform atom
interferometry, we explore splitting of an atom cloud trapped in a
phase-modulated ("shaken") optical lattice. Using a simple analytic model we
are able to show that we can obtain the simplest case of $\pm2\hbar
k_\mathrm{L}$ splitting via single-frequency shaking. This is confirmed both
via simulation and experiment. Furthermore, we are able to split with a
relative phase $\theta$ between the two split arms of $0$ or $\pi$ depending on
our shaking frequency. Addressing higher-order splitting, we determine that
$\pm6\hbar k_\mathrm{L}$ splitting is sufficient to be able to accelerate the
atoms in counter-propagating lattices. Finally, we show that we can use a
genetic algorithm to optimize $\pm4\hbar k_\mathrm{L}$ and $\pm6\hbar
k_\mathrm{L}$ splitting to within $\approx0.1\%$ by restricting our
optimization to the resonance frequencies corresponding to single- and
two-photon transitions between Bloch bands.
