Decentralized sensor networks are collections of individual local sensors that observe a common phenomenon, quantize their observations, and send this quantized information to a central processor (fusion center) which then makes a global decision about the phenomenon. Most of the existing literature in this field consider only the data fusion aspect of this problem, i.e., the statisticalhypothesis testing and optimal combining of the information obtained by the local sensors. In this paper, we propose a Parallel Genetic Algorithm (PGA) for optimizing the probability of global detection error performance of a parallel decentralized sensor network. Specifically, we use the PGA to simultaneously optimize both the fusion rule and the local decision rules. We show that our approach provides results comparable to those obtained by using a GA and gradient-based algorithm from previous work by Aldosari and Moura, with reduced complexity. We considerboth the cases of identical (homogeneous) and non-identical (heterogeneous) sensors and demonstrate that our algorithm converges to the same optimal solution in both cases. We alsodiscuss the effect of the quality of the initial solution on the convergence of the PGA.