Designing an effective parallel microchannel heat sink (PMCHS) is necessary for addressing the cooling challenges of high heat-dissipating electronics. This paper presents a shape optimization of PMCHS to minimize the thermal resistance and pressure drop for each U, I, and Z-type inlet/outlet manifold configuration with vertical intake and coolant delivery. The performance of PMCHS influencing design parameters, such as channel width, fin width, and channel height, is designed using the response surface methodology (RSM). In the present communications adopting the Artificial Neural Network (ANN) coupled NSGA-II method, a three-dimensional numerical simulation is executed to minimize the pressure drop and thermal resistance. Numerical simulation is performed using the finite volume method; the computational domain is taken as the entire microchannel system including the inlet/outlet plenum area, ports and microchannels. The overall analysis demonstrated that the pareto optimal design point has better hydraulic and thermal performances than the predefined design. The optimized design showed benchmark thermal resistance of 0.0306 ˚C/W, 0.0315 ˚C/W, 0.0316 ˚C/W and pressure drop of 3.1 kPa, 3.2 kPa, 3.19 kPa for U, I, Z configurations respectively.