The present study deals with three-dimensional fluid flow and heat transfer in a ribbed microchannel heat sink. The design variables affecting the heat transfer performance have been studied in the light of thermal resistance and pumping power and surrogate-based optimization is performed using radial basis neural network. The decrease of the thermal resistance is observed with increase of mass flow rate at the expense of higher pumping power due to rib structures. The difference between thermal resistance of ribbed microchannel and smooth microchannel reduces with increase of pumping power. The ratio of the rib width-to-height is found to be more sensitive than the other two design variables related to rib height, pitch and microchannel width.