This paper aims to optimize film coolant flow parameters on the suction surface of a high-pressure gas turbine blade in order to obtain an optimum compromise between a high film cooling effectiveness and a low aerodynamic loss. An optimization algorithm coupled with three-dimensional Reynolds-averaged Navier Stokes (RANS) analysis is used to determine the optimum film cooling configuration. The VKI blade with two staggered rows of axially oriented, conically flared, film cooling holes on its suction surface is considered. Two design variables are selected; the coolant to mainstream temperature ratio and total pressure ratio. The effect of varying these coolant flow parameters on the film cooling effectiveness and the aerodynamic loss is analyzed using an optimization method and three dimensional steady CFD simulations. The optimization process involves a genetic algorithm and a response surface approximation of the artificial neural network type to provide low-fidelity predictions of the objective function. The CFD simulations are performed using the commercial software CFX. The numerical predictions of the aerodynamics and wall heat transfer are validated against experimental data. The optimization objective consists of maximizing the spatially averaged film cooling effectiveness and minimizing the aerodynamic penalty produced by film cooling. The results of this optimization are reported in terms of the aerodynamic loss and adiabatic cooling effectiveness.