Due to the recent developments of the engine industry, turbine internal channel cooling is a need. In fact, in order to supply more power efficiently, the fluid temperature at turbine inlet approaches to 2000 K when common turbine materials cannot resist temperature values higher than 1500 K. The crucial point is that the engine cycle efficiency and thrust highly depend on the turbine inlet temperature and, so, such a thermal problem needs to be overcome by cooling. Coolant air of the internal channel cooling systems is mostly taken from valuable compressor bleed that makes it to circulate through the serpentine internal passages. The coolant air flow is commonly fully turbulent, incompressible and with 3D characteristics because of the complex shape of the cooling passage. Considering this latter aspect, the pressure drop also plays a relevant role because, in order to minimize the cooling mass flow, it needs to be reduced. In this study, rib cross-section shape optimization of a ribbed internal cooling channel is conducted to assess the trade-off between two conflicting objectives: heat transfer performance and pressure drop. For this purpose, a novel mesh morphing based optimization tool is developed which uses radial basis functions (RBF) for morphing and meta-model assisted evolutionary algorithms (EA) for optimization. Experimental tests characterized by Reynolds number of 20000 are performed to validate such an optimization tool. The local Nusselt number is calculated using hydraulic diameter of channel and air thermal conductivity corresponding to bulk temperature. The cooling effectiveness of the channel is quantified using the ratio of the Nusselt number of the ribbed case to the Nusselt number of the smooth case. With the gained optimized geometry, the heat transfer shows better results than initial case with a pressure loss improvement of 8%.