Surface roughness is one of the most important requirements of the finished products in machining process. The determination of optimal cutting parameters is very important to minimize the surface roughness of a product. This article describes the development process of a surface roughness model in high-speed ball-end milling using response surface methodology based on design of experiment. Composite desirability function and teaching-learning-based optimization algorithm have been used for determining optimal cutting process parameters. The experiments have been planned and conducted using rotatable central composite design under dry condition. Mathematical model for surface roughness has been developed in terms of cutting speed, feed per tooth, axial depth of cut and radial depth of cut as the cutting process parameters. Analysis of variance has been performed for analysing the effect of cutting parameters on surface roughness. A second-order full quadratic model is used for mathematical modelling. The analysis of the results shows that the developed model is adequate enough and good to be accepted. Analysis of variance for the individual terms revealed that surface roughness is mostly affected by the cutting speed with a percentage contribution of 47.18% followed by axial depth of cut by 10.83%. The optimum values of cutting process parameters obtained through teaching-learning-based optimization are feed per tooth (f_z) = 0.06 mm, axial depth of cut (A_p) = 0.74 mm, cutting speed (V_c) = 145.8 m/min, and radial depth of cut (A_e) = 0.38 mm. The optimum value of surface roughness at the optimum parametric setting is 1.11 µm and has been validated by confirmation experiments.