We present a novel algorithm to compute collision-free trajectories in dynamic environments. Our approach is general and makes no assumption about the obstacles or their motion. We use a replanning framework that interleaves optimization-based planning with execution. Furthermore, we describe a parallel formulation that exploits high number of cores on commodity graphics processors (GPUs) to compute a high-quality path in a given time interval. Overall, we show that search in configuration spaces can be significantly accelerated by using GPU parallelism.