With the widespread application of Inconel alloys in manufacturing industries especially in the automobile as well as aerospace industries leads to manufacturers to pay more attention towards the understanding of machinability aspects of these alloys. Attributable to the need for large-scale manufacturing of Inconel machined components, the optimization of machining process variables become crucial to produce quality products economically by means of enhancing process performance. In common, several process parameters namely depth of cut, feed rate, and spindle speed influence the performance of turning operation in their own way. Concurrently, in the machining of Inconel alloys, the important performance indices are Material Removal Rate (MRR), surface roughness, and cutting force. This work deals with the assessment of process performance of Inconel 825 alloy amid turning operation. For the optimization of multiple responses, grey relation analysis has been employed that transforms the multiple responses into a corresponding single response known as overall grey relation index (OGI). Based on OGI, as a function of selected process variables, formulation of a non-linear regression model has been done and considered as the fitness function. To conclude, two evolutionary techniques, Teaching-Learning-Based Optimization, well famous as TLBO, and JAYA algorithm have been considered for optimization.