In this study, computational fluid dynamics (CFD) analysis is utilized in order to determine the convective heat transfer coefficient of an engine air-cooling system in different air velocity conditions. Various models with different geometric configurations are considered. Based on the CFD results, two formulas are proposed to approximate the values of convective heat transfer coefficients in zero and non-zero air velocities. Finally, two conflicting objective functions including volume of the required material for construction of the finned cylinder and heat release per unit temperature difference are considered. Multi-objective optimization using genetic algorithm is utilized, which generates a multiple set of solutions, each of which is a trade-off between two objectives. The user can select each of the optimal geometric configurations based on the project's requirements. In other words, considering the desired thermal design, designer is able to find the minimum volume of the required material for construction of the finned cylinder, which in turn leads to the least possible capital cost.