Machinability of engineering materials is crucial for industrial manufacturing processes since it affects all the essential aspects involved, e.g. work­load, resources, surface integrity and part quality. Two basic ma­chin­ability para­meters are the surface roughness, closely associated with the functional and tribological performance of components, and the cutting forces acting on the tool. Knowledge of the cutting forces is needed for estimation of power re­quirements and for the design of machine tool elements, tool-holders and fix­tures, adequately rigid and free from vibration. This work in­ve­stigates the in­flu­ence of cutting conditions on machinability indicators such as the main cutting force Fc and surface roughness parameters Ra and Rt when longitudinally turning CuZn39Pb3 brass alloy. Full quadratic regression models were de­veloped to correlate the machining conditions with the imparted machinability characteristics. Further on, an advanced artificial grey wolf optimization algorithm was implemented to optimize the aforementioned responses with great success in finding the final optimal values of the turning parameters.