Combined electrical and structural models of five types of permanent magnet linear electrical machines suitable for direct-drive power take-off on wave energy applications are presented. Electromagnetic models were developed using polynomial approximation to finite element analysis results. The structural models are based on simple beam theory, other classical techniques, and automated finite element analysis formulations. The machine models have been integrated with a time-domain model of a wave energy converter based on a heaving buoy. They have then been optimised using a genetic algorithm approach, using a score based primarily on the amortised cost per unit of energy production. The optimised designs have then been used for a comparison of the economic performance of the generator types.