Bead-on-plate welds were carried out on aluminum plates Al-1100 using an electron beam welding machine. The weld runs were conducted as per central composite design. Regression analysis was then carried out to establish input-output relationships of the process. The weldment area was minimized, after satisfying the condition of maximum bead penetration. The above constrained optimization problem was solved utilizing a genetic algorithm (GA) with a penalty function approach. The GA was able to determine optimal weld-bead geometry and recommend the necessary process parameters for the same. An attempt was also made to model the complicated dagger-like profile of electron-beam welded material by utilizing three third-order curves. The profiles were predicted by utilizing both back-propagation trained and GA-tuned neural networks. The latter was able to yield better predictions compared to the former.