The present work deals with a numerical procedure for optimizing a cooling channel with staggered elliptic dimples to enhance heat transfer and also to reduce the pressure loss. Three-dimensional Reynolds-averaged Navier-Stokes analysis is employed in conjunction with the SST model for predicting the turbulent flow and heat transfer. Three non-dimensional geometric design variables, such as the elliptic dimple diameter ratio, ratio of the dimple depth to average diameter, and ratio of the streamwise distance to spanwise distance between dimples are considered for the optimization. Twenty-one design points within the design space are selected by Latin hypercube sampling. Each objective-function value at these points is evaluated by RANS analysis to construct a surrogate model using the Kriging approach. A hybrid evolutionary multi-objective algorithm has been employed to find optimized designs considering the heat transfer and friction loss. Two extreme optimum designs on the Pareto-optimal front with regard to the heat transfer and pressure loss, respectively, have spanwise and streamwise elliptic dimple shapes, respectively, which increase the heat-transfer rate by 32.8% and decrease the pressure loss by 34.6%, respectively, compared to the reference design. (C) 2011 Elsevier Ltd. All rights reserved.