A liquid flow manifold microchannel heat sink is optimized with the help of 3-D numerical analysis, a surrogate method, and a multiobjective evolutionary algorithm. The performance of the manifold microchannel heat sink is optimized for the overall thermal resistance and the pumping power required for driving the coolant. The design variables related to the width of the microchannel, depth of the microchannel, width of fins, length of the nozzles, and height of the nozzles, which contribute to objective functions, are identified and optimized for minimum thermal resistance and pumping power. A Latin hypercube sampling method is used to exploit the design space. The numerical solutions obtained at these design points are utilized to construct a surrogate model, i.e., response surface approximation. The Navier-Stokes and energy equations for laminar flow and conjugate heat transfer are solved using a finite-volume solver. A hybrid multi objective evolutionary algorithm coupled with a surrogate model is applied to find out global Pareto-optimal designs (PODs). Trade-off analysis is performed in view of the conflicting nature of the two objectives, which yields PODs with low thermal resistance at various pumping powers. The ratio of the microchannel width to the microchannel height and that of the nozzle height to the microchannel height are found to be more Pareto-optimal sensitive (sensitive along the Pareto-optimal front) than others. In contrast, the ratio of the fin width to the microchannel height and that of the nozzle length to the microchannel width are found to be less Pareto-optimal sensitive than other design variables. The PODs showed lower thermal resistance and pumping power than the reference designs at various mass flow rates.