A liquid flow microchannel heat sink has been studied with the help of three-dimensional numerical analysis for mixed (electroosmotic and pressure-driven) flow. The optimization of the microchannel heat sink has been performed with the help of surrogate method coupled with multi-objective evolutionary algorithms. The effects of ionic concentration represented by the zeta potential and Debye thickness are studied at various levels of externally applied electric potential. Temperature dependent coolant properties are considered to take into account the micro-scale effects for accurately predicting the thermal performance of the microchannel heat sink. Higher value of zeta potential leads to higher flow-rate and lower thermal resistance which consequently reduced the temperature of the microprocessor chip and load of micro-pump used to supply the coolant to the microchannels. Two design variables are selected related to the microchannel width, depth and fin width and design space is explored through four-level full factorial design. The channel width-to-depth ratio is found to be higher Pareto-sensitive (sensitivity along the Pareto-optimal front) than the other design variable. The trade-off between objective functions and Pareto-sensitivity of the design variables can be utilized to economically design the microchannel heat sinks. In view of the limiting pumping power available at the micro-level the application of the electroosmosis along with the commonly used pumping source can greatly enhance the performance of the microchannel heat sink.