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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 ( 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 case of combined polarizations, we reveal a design with a normalized band-gap size exceeding 60%.