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The effect of numerous process variables has been explored for surface roughness and material removal rate during the magnetic abrasive finishing process. A hybrid approach was used in which the Taguchi technique is used in conjunction with grey relational analysis to reach the optimum combination of input variables. The L16 orthogonal array design was used to get a different combination of parameters. It was found that spindle speed of 200 rpm, the quantity of magnetic abrasives of 5 mg, mesh number of 270, and machining time 60 min caused minimum surface roughness of 0.066 µm during magnetic abrasive finishing of the brass plate. The percentage contribution of input parameters has been reported. Subsequently, the optimum results were obtained using multi-objective optimization techniques of grey relational analysis, and results were also validated using experimentation.