Designing high performance cooling systems suitable for preserving the service lifetime of nozzle guide vanes of turboshaft engines leads to significant aerodynamic losses. These losses jeopardize the performance of the whole engine. In the same time, a low efficiency cooling system may affect the costs of maintenance repair and overhaul of the engine as component life decreases. Consequently, designing cooling systems of gas turbine vanes is related to a multiobjective design problem. In this paper, it is addressed by investigating the functioning of a blade and optimizing its design by means of an evolutionary algorithm. Systematic 3D CFD simulations are performed to solve the aero-thermal problem. Then, the initial multiobjective problem is solved by aggregating the multiple design objectives into one single relevant and balanced mono-objective function; two different types of mono-objective functions are proposed and compared. This paper also proposes to enhance available knowledge in the literature of cooling systems of gas turbine vanes by simulating the internal cooling system of the vane. From simulations thermal efficiency and aerodynamic losses are compared and their respective influences on the global performances of the whole engine are investigated. Finally, several optimal designs are proposed.