  We consider two-dimensional phononic crystals formed from silicon and voids,
and present optimized unit cell designs for (1) out-of-plane, (2) in-plane and
(3) combined out-of-plane and in-plane elastic wave propagation. To feasibly
search through an excessively large design space (10e40 possible realizations)
we develop a specialized genetic algorithm and utilize it in conjunction with
the reduced Bloch mode expansion method for fast band structure calculations.
Focusing on high symmetry plain-strain square lattices, we report unit cell
designs exhibiting record values of normalized band-gap size for all three
categories. For the combined polarizations case, we reveal a design with a
normalized band-gap size exceeding 60%.
