In this study, fluid flow and conjugate heat transfer in a micro-channel heat sink (MCHS) is simulated with ANSYS-Fluent and optimized with multi objective genetic algorithm known as elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) coded in MATLAB. Single phase, steady and fully developed liquid flow in the range of the inlet Reynolds number 500-1000 through a 3D micro-channel is solved by the laminar flow solver. The coolant fluid is considered as deionized water with dynamic viscosity depending on temperature. The geometric variables (channel width and height) of the micro-channel related to the channel's cross section and the inlet Reynolds number related to the flow rate are selected as design variables for the optimization. Two normalized objective functions of the Nusselt number and pumping power are chosen to assess the hydrodynamic and thermal performances of the MCHS. The optimization is performed for 20 generations with a number of population of 30. Optimal Pareto Front representing the trade-off between the objective functions is obtained, which provides useful results for the design of MCHS. The final generation of the optimization process reveals that in most of the design variable sets, the design points are identified as uniform distribution for the inlet Reynolds number within the limits and 0.29 mm for the micro-channel's width. However, the microchannel's height was suggested in the range of 0.50-0.67 mm in most optimum cases. (C) 2019 Elsevier Ltd. All rights reserved.