The current research is devoted to studying the forced convection inside a microchannel incorporated with micro fin structures within the Re number range of 80 - 250. A finite volume based methodology is employed to model the hydrodynamic and thermodynamic behaviour of fluid flow. A comparative analysis of different fin structures (conical, circular, square and triangular) is done to find the superior fin shape. The comparisons showed that the conical micro fin shows a relatively higher convective heat transfer argumentation when compared to the other fin structures. Further, the present study is extended to find the optimize design parameters of conical fins using Non Dominated Sorting Genetic Algorithm (NSGA-II). An optimal trade off curve between two objective functions (Nu and ΔP) is obtained for 50 populations at the 20^th generation. 10 out of 50 optimized design parameter solutions are presented. It is demonstrated that the staggered fin arrangement shows a higher overall thermal performance (TP) value than the inline fin arrangement.