  We combine a general formulation of microswimmmer equations of motion with a
numerical bead-shell model to calculate the hydrodynamic interactions with the
fluid, from which the swimming speed, power and efficiency are extracted. From
this framework, a generalized Scallop Theorem emerges. The applicability to
arbitrary shapes allows for the optimization of the efficiency with respect to
the swimmer geometry. We apply this scheme to `three-body swimmers' of various
shapes and find that the efficiency is characterized by the single body
friction coefficient in the long-arm regime, while in the short-arm regime the
minimal approachable distance becomes the determining factor. Next, we apply
this scheme to a biologically inspired swimmer that propels itself using a
rotating helical flagellum. Interestingly, we find two distinct optimal shapes,
one of which is fundamentally different from the shapes observed in nature
(e.g. bacteria).
