We have presented several contributions on the collision detection optimization centered on hardware performance. We focus on the first step (Broad-phase) and propose three new ways of parallelization of the well-known Sweep and Prune algorithm. We first developed a multi-core model takes into account the number of available cores. Multi-core architecture enables us to distribute geometric computations with use of multi-threading. Critical writing section and threads idling have been minimized by introducing new data structures for each thread. Programming with directives, like OpenMP, appears to be a good compromise for code portability. We then proposed a new GPU-based algorithm also based on the "Sweep and Prune" that has been adapted to multi-GPU architectures. Our technique is based on a spatial subdivision method used to distribute computations among GPUs. Results show that significant speed-up can be obtained by passing from 1 to 4 GPUs in a large-scale environment.