  We utilize genetic algorithms to find optimal dynamical decoupling (DD)
sequences for a single-qubit system subjected to a general decoherence model
under a variety of control pulse conditions. We focus on the case of sequences
with equal pulse-intervals and perform the optimization with respect to pulse
type and order. In this manner we obtain robust DD sequences, first in the
limit of ideal pulses, then when including pulse imperfections such as finite
pulse duration and qubit rotation (flip-angle) errors. Although our
optimization is numerical, we identify a deterministic structure underlies the
top-performing sequences. We use this structure to devise DD sequences which
outperform previously designed concatenated DD (CDD) and quadratic DD (QDD)
sequences in the presence of pulse errors. We explain our findings using
time-dependent perturbation theory and provide a detailed scaling analysis of
the optimal sequences.
