The sequential optimization strategy for design of an experimental and artificial neural network (ANN) linked genetic algorithm (GA) were applied to evaluate and optimize media component for L-asparaginase production by Aspergillus terreus MTCC 1782 in submerged fermentation. The significant media components identified by Plackett-Burman design (PBD) were fitted into a second order polynomial model ($R^2$ = 0.910) and optimized for maximum L-asparaginase production using a five-level central composite design (CCD). A nonlinear model describing the effect of variables on L-asparaginase production was developed ($R^2$ = 0.995) and optimized by a back propagation NN linked GA. Ground nut oil cake (GNOC) flour 3.99% (w/v), sodium nitrate ($NaNO_3$) 1.04%, L-asparagine 1.84%, and sucrose 0.64% were found to be the optimum concentration with a maximum predicted L-asparaginase activity of 36.64 IU/mL using a back propagation NN linked GA. The experimental activity of 36.97 IU/mL obtained using the optimum concentration of media components is close to the predicted L-asparaginase activity of the ANN linked GA.