This article presents a geometric optimization study to maximize the total heat transfer rate between an array of discrete pin fins and the surrounding serpentine cooling flow. The fins are installed on the tip cap underside of a high-pressure turbine blade (HPTB) model. The study has three parts. In the first, the numerical model is validated against experimental data obtained with liquid crystal thermography. In the second part, the heat and fluid flow performance of the pin fin assembly is simulated numerically, using RANS turbulence models in the range 25,000 < Re < 100,000 and Pr ∼ 0.7. The effect of varying the spacing and the tip cap boundary condition is investigated. In the last part of the study, it is shown that the optimal spacing between the pin fins can be correlated following the same theoretical arguments derived in the previous investigations that used simpler geometries.