  Here, through a systematic methodology and the use of high performance
computing, we calculate the optimum shape for a wave energy converter under the
action of incident waves of (i) monochromatic unidirectional, (ii)
monochromatic directional, (iii) polychromatic unidirectional and (iv)
polychromatic directional (with both directional symmetry and asymmetry). As a
benchmark for our study, without loss of generality, we consider a submerged
planar pressure differential wave energy converter, and use Genetic Algorithm
to search through a wide range of shapes. A new parametric description of
absorber shape based on Fourier decomposition of geometrical shapes is
introduced, and for each shape hydrodynamic coefficients are calculated,
optimum power take-o? parameters are obtained, and overall efficiency is
determined. We show that an optimum geometry of the absorber plate can absorb a
significantly higher energy (in some cases a few times higher) when compared to
a circular shape of the same area. Specifically, for a unidirectional incident
wave, the optimum shape, as expected, is obtained to be the most elongated
shape. For directional incident waves, a butterfly-shape is the optimum
geometry whose details depend on not only the amplitude and direction of
incident wave components, but also the relative phases of those components. For
the latter effect, we find an optimally averaged profile through a statistical
analysis. Keywords: Wave energy conversion, Shape optimization
