The Optimal solutions of the design variables in internally finned tubes have been obtained for three-dimensional periodically fully developed turbulent flow and heat transfer. For a trapezoidal fin profile, performances of the heat exchanger are determined by considering the heat transfer rate and pressure drop, simultaneously, that are interdependent quantities. Therefore, Pareto frontier sets of a heat exchanger can be acquired by integrating CFD and a multi-objective optimization technique. The optimal values of fin widths $(d_1,;d_2)$, fin height(h) and helix angle$(gamma)$ are numerical1y obtained by minimizing the pressure loss and maximizing the heat transfer rate within ranges of $d_1=0.5sim1.5mm$, $d_2=0.5sim1.5mm$, $h=0.5sim1.5mm$, and $gamma=0sim20^{circ}$. For this, a general CFD code and a global genetic algorithm(GA) are used. The Pareto sets of the optimal solutions can be acquired after $30^{th}$ generation.