A good quality in Electron Beam Welding (EBW) process is obtained by optimizing the process parameters because evolutionary techniques like Genetic Algorithm (GA) play an important role in deciding the weld parameters. In this work an attempt made for multi objective optimization task with the use of genetic algorithm for Inconel 718 alloy material using the EBW process. The desired weld quality is determined on the basis of the welding input parameters, and the experiments are conducted based on Response Surface Methodology (RSM). From study welding current (Iw); focus current (If) and the speed (s) are selected as the input parameters. Depth of penetration (DP) and Bead width (BW) were selected as output response for quality targets. The experimental results indicated that bead width 4.8 and depth of penetration 7.6 for the optimum values at 70mA, 530mA, and 23mm/s respectively. Grey Relational Analysis (GRA) was used for the optimization of the input parameter concurrently with the consideration of the two responses. Analysis of variance (ANOVA) method was utilized in the assessment of the importance of factors on the overall weld quality. The optimal welding parameters for minimum Bead width were found to be Iw1If3S2 and for maximum Depth of Penetration was Iw2If3S1. The outcomes of this work is compared for proposed GRA and GA algorithms by precision and welding speed and are explained. The metallurgical characteristics validate the outcome of the response characteristics for best grade value.