One of sheet severe plastic deformation (SPD) operation, namely constrained groove pressing (CGP), is investigated here in order to specify the optimum values for geometrical variables of this process on pure aluminium sheets. With this regard, two different objective functions, i.e. the uniformity in the effective strain distribution and the necessary force per unit weight of the specimen, are selected to be minimized. To examine the effects of the sheet thickness, die groove angle and the die-tooth number on these objective functions, several finite-element (FE) analyses of the operation are carried out. Using the values of objective functions attained via these numerical simulations, an artificial neural network (ANN) is trained with good regression fitness. Employing a two-objective genetic algorithm (GA), a series of optimum conditions is obtained as a Pareto front diagram. The best optimum point in this diagram is the closest one to the origin which, at the same time, makes both the objective functions smallest. With this regard, a sheet thickness of 2 mm, a groove angle of and an 8-tooth die are found to be an appropriate optimal condition for performing a CGP process. The finite-element simulation with these enhanced geometrical variables is conducted and the values of the objective functions gained from the numerical analysis is found to be in good agreement with those obtained from the genetic algorithm optimization.