A method was developed to perform shape optimization of a tidal stream turbine hydrofoil using a multi-objective genetic algorithm. A bezier curve parameterized the reference hydrofoil profile NACA 63815. Shape optimization of this hydrofoil maximized its lift-to-drag ratio and minimized its pressure coefficient, thereby increasing the turbines power output power and improving its cavitation characteristics. The Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) was employed to perform the shape optimization. A comparative study of two- and three-dimensional optimizations was carried out. The effect of varying the angle of attack on the quality of optimized results was also studied. Predictions based on two-dimensional panel method results were also studied. Predictions based on a two-dimensional panel method and on a computational fluid dynamics code were compared to experimental measurements.