A methodology dedicated to the optimization of the transmutation of minor actinides (MAs) in dedicated blankets is discussed here. This methodology relies on recently developed optimization tools. In the so-called heterogeneous transmutation approach, MAs are loaded into specific assemblies located at the periphery of a fast reactor core. Thus, the resulting perturbation of the core behavior is limited and the management of MAs is entirely decoupled from standard fuel management. This also allows greater flexibility in the blanket design, in terms of material, volume fraction, and neutron spectrum to be used. On the other hand, the low neutron flux level experienced at the periphery of the core slows down the transmutation process. If this effect can be compensated for by an increase of the MA fraction loaded in the blankets, this also strongly increases their decay heat and neutron source level, which complicates spent fuel reprocessing and handling. An optimization is carried out with regard to the neutron spectrum and americium concentration in the blankets, with the dual objective of maximizing the transmuted MA mass while minimizing the total MA inventory in the fuel cycle by limiting the cooling time of such blankets. Artificial neural networks are coupled with a genetic algorithm to reduce the total calculation time. It is shown here that regardless of the MA mass to be loaded, a slightly moderated neutron spectrum is the most promising option for heterogeneous transmutation. This result is confirmed by full-core calculations. An analysis of the irradiation time is also performed, and it is shown that maximization of the irradiation time should be sought in the specific case studied here. It is concluded that from a purely physical point of view, no breakthrough can be obtained for heterogeneous transmutation.