The optimization aims to maximize the film cooling performance while minimizing the corresponding aerodynamic penalty. The film cooling performance is assessed using the adiabatic film cooling effectiveness, while the aerodynamic penalty is measured with a mass-averaged total pressure loss coefficient. Two design variables are selected; the coolant to mainstream temperature ratio and total pressure ratio. Two staggered rows of discrete cylindrical film cooling holes on the suction surface of a turbine vane are considered. The effect of varying the coolant flow parameters on the adiabatic film cooling effectiveness and the aerodynamic loss is analyzed using the optimization method and three-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations. The CFD predictions of the adiabatic film cooling effectiveness and aerodynamic performance are assessed and validated against corresponding experimental measurements. The optimal solutions are reproduced in the experimental facility and the Pareto front is substantiated with experimental data. A non-dominated sorting genetic algorithm (NSGA-II) is coupled with an artificial neural network (ANN) to perform a multiple objective optimization of the film coolant flow parameters on the suction surface of a high pressure gas turbine vane. The numerical predictions are employed to construct the artificial neural network that produces low-fidelity predictions of the objectives during the optimization. The Pareto front of optimal solutions is generated by the optimization methodology.