The aim of this study is to find optimum values of design parameters of a heat sink having hexagonal aluminum honeycomb fins by using the Response Surface Method (RSM) and the Pareto based multi-objective optimization. In this context, fin height (H), fin thickness (t), longitudinal pitch (S-y), angle of attack (theta) and Reynolds number (Re) are selected as design variables while Nusselt number (Nu) and friction factor (f) are chosen as objective functions. Firstly, the RSM with the face centered central composite design (FCCCD) has been employed to construct mathematical models required in multi-objective optimization problem definition. In the next step, accuracy and validity of these mathematical models are proved both statistically and experimentally. Finally, a Pareto based multi-objective optimization study has been conducted to determine optimum values of the design parameters that maximize Nu and minimize f. It is concluded that Pareto solution set obtained provides important insights into the design parameters and allows designers freedom to make a selection among the optimal solutions. (C) 2016 Elsevier Ltd. All rights reserved.