In this paper, two different configurations of multiple microchannel heat sinks, with fluid flow, are investigated for heat removal: straight and U-shaped channel designs. Numerical models are utilized to study the multiphysics behavior in the microchannels and these are validated by comparisons with experimental results. The main focus of this work is on the design and optimization of these systems and to outline the methodology that may be used for other similar thermal systems. Three responses, including thermal resistance, pressure drop, and maximum temperature, are parametrically modeled with respect to various design variables and operating conditions such as dimensions of the channels, total number of channels, and flow rate. Multi-objective optimization problems, which minimize the thermal resistance and the pressure drop simultaneously, are formulated and studied. Physical constraints in terms of channel height, maximum temperature, and pressure are further investigated. The Pareto frontiers are studied and the trade-off behavior between the thermal resistance and the pressure drop are discussed. Characteristic results are presented and discussed.