Preliminary studies on field emission (FE) arrays comprised of carbon nanotubes (CNT) as an electron source for electric propulsion system show remarkably promising results. Design parameters for a carbon nanotube (CNT) field-emission device operating on triode configuration were numerically simulated and optimized in order to enhance the e-beam focusing quality. An additional focus gate (FG) was integrated to the device to control the profile of the emitted e-beam. An axisymmetric finite element model was developed to calculate the electric field distribution on the vacuum region and a modified Fowler- Nordheim (FN) equation was used to evaluate the current density emission and the effective emitter area. Afterward, a FE simulation was employed in order to calculate the trajectory of the emitted electrons and define the electron-optical properties of the e-beam. The integration of the FG was fully investigated via computational intelligence techniques. The best performance device according to our simulations presents a collimated e-beam profile that suits well for field emission displays, magnetic field detection and electron microscopy. The automated computational design tool presented in this study strongly benefits the robust design of integrated electron-optical systems for vacuum field emission applications, including electrodynamic tethering and electric propulsion systems.