This study forms part of research into the optimization of the shape of a wave energy collector to improve energy extraction using genetic algorithms. The wave energy collector geometry uses a parametric description based upon bi-cubic B-spline surfaces, generated from a relatively small number of control points to reduce the dimensionality of the search space. The collector shapes that are optimized have either one or two planes of symmetry. An elementary cost function is used to determine the performance of each candidate solution. The collectors move in two degrees of freedom (surge-and-pitch), and are optimally tuned to absorb the greatest power from a number of incident regular waves, the results being weighted according to a generalized occurrence distribution. High velocities and large collector volumes are penalized. A benchmark collector shape, against which the optimized shapes are compared, is identified. The overall optimization strategy entails performing repeated runs of the algorithm for a fixed number of generations, then restarting the optimization with the run that produces the best result. An appraisal of the results is made, looking at the performance of all the shapes assessed as well as those deemed the best.