This paper presents a comparative study of neural network (NN) training. The trained NNs are used as adaptive beamformers of antenna arrays. The training is performed either by a recently developed method called Mutated Boolean PSO (MBPSO) or by a well known beamforming method called Minimum Variance Distortionless Response (MVDR). The training procedure starts by applying the MBPSO and the MVDR to a set of random cases where a linear antenna array receives a signal of interest (SOI) and several interference signals at random directions of arrival (DOA) different from each other in the presence of additive Gaussian noise. For each case, the MBPSO and the MVDR are independently applied to estimate respective excitation weights that make the array steer the main lobe towards the DOA of the SOI and form nulls towards the DOA of the interference signals. The lowest possible value of side lobe level (SLL) is additionally required. The weights extracted by the MBPSO and the weights extracted by the MVDR are used to train respectively two different NNs. Then, the two trained NNs are independently applied to a new set of cases, where random DOA are chosen for the SOI and the interference signals. Finally, the radiation patterns extracted by the two NNs are compared to each other regarding the steering ability of the main lobe and the nulls as well as the side lobe level. The comparison exhibits the superiority of the NN trained by the MBPSO.