Bead-on-plate welds were carried out on austenitic stainless steel plates using an electron beam welding machine. Experimental data were collected as per central composite design and regression analysis was conducted to establish input–output relationships of the process. An attempt was made to minimize the weldment area, after satisfying the condition of maximum bead penetration. Thus, it was posed as a constrained optimization problem and solved utilizing a Genetic Algorithm with a penalty function approach. The Genetic Algorithm was able to determine optimal weld-bead geometry and recommend the necessary process parameters for the same.