A beamsteering (BS) technique applied on antenna arrays is proposed. The technique is based on neural networks (NNs) and aims at estimating the array excitation weights that produce a main lobe towards every desired signal and achieve low side lobe level (SLL). Initially, the Mutated Boolean particle swarm optimization (MBPSO) is applied to a set of random directions of incoming signals in order to estimate the excitation weights that make a uniform linear array (ULA) produce one or more main lobes towards the respective incoming signals and achieve a SLL equal to or less than a desired value. The estimated weights are then used to train a NN efficiently. The trained NN is applied to a new set of random directions of incoming signals and the derived radiation patterns are compared to respective patterns derived by the MBPSO, a differential evolution based BS technique and the maximum likelihood method. The above comparisons were performed for various SLLs and for one or two desired signals received by a ULA. In the problem, the presence of additive zero-mean Gaussian noise was assumed. The comparative results show the advantages of the proposed BS technique.