The objective of this paper is to optimize direct drive permanent magnet synchronous generators for offshore direct drive wind turbines in order to reduce the cost of energy. A 6 MW wind turbine design is assumed and parametric electromagnetic and structural generator models are introduced for a surface-mounted magnet generator topology (using magnets with high BHmax) and a flux-concentrating variant (using magnets with lower BHmax). These are optimized using a hybrid genetic algorithm and pattern search process and the results show that the surface-mounted permanent magnet generator produces the lower cost of energy. The choice of objective function is addressed and it is found that a simplified metric incorporating generator cost and losses proxy produces similar designs to a full cost of energy calculation. Further steps to improve the quality of the model include the effect of generator mass on the design and cost of the turbine tower and foundation, which can add (sic)0.4 m to the turbine cost. Further optimizations are carried out to show the impacts of magnetic material costs (doubling this leads to a (sic)1.1/MWh increase in cost of energy) and generator diameter limits (increasing the upper limit from 6 to 8 m leads to a 0.9% drop in cost of energy) have on the choice of optimum independent variables.