In this study, a new technique which uses Multi-Objective Genetic Algorithm method (NSGA-II) coupled with a Monte-Carlo based reactor physics code (MCNP) was proposed to shape the beams of neutron sources. The method was applied for the beam of Piercing Beam Port of the Istanbul Technical University TRIGA Mark II Research and Training Reactor. The beam was shaped according to the requirements of the Boron Capture Neutron Therapy (BNCT) application as described by IAEA technical documents. A set of optimized patterns, consisting of the spectrum shifter, filtering, and collimator sub-patterns, were obtained. Epithermal neutrons were considered for BNCT.