A systematic read on evaluating the machining characteristics of wire cut electrical discharge machining (WEDM) using analysis of variance (ANOVA) and multilinear regression model based multi objective optimization is provided during this analysis article. The current work explores, the surface roughness of copper metal matrix composite (MMCs) is minimized by optimizing the process parameters like spark on time, spark off time, peak current and wire feed. Taguchi's L9 orthogonal array has been used to conduct the experiments for two samples having a different composition to measure the surface roughness. The order of significance of parameters on surface roughness (Ra) for sample 1 and 2 MMCs were found using ANOVA and a multilinear regression model (MLRM) was developed to predict the Ra value. The new contribution in the present work is that, the coefficients of MLRM were optimized using artificial immune system algorithm with the objective of minimizing the mean absolute percentage error. Finally, the optimum process parameters were obtained to minimize the surface roughness and reported that the reduced value of Ra for 2.5% and 5% WC Copper MMCs were 0.9 lm and 1.1 lm, respectively later which were established by confirmation experiments.