Particle swarm optimization (PSO) has previously been parallelized primarily by distributing the computation corresponding to particles across multiple processors. In this thesis we present a speculative approach to the parallelization of PSO that we refer to as SEPSO. In our approach, we refactor PSO such that the computation needed for iteration t+1 can be done concurrently with the computation needed for iteration t. Thus we can perform two iterations of PSO at once. Even with some amount of wasted computation, we show that this approach to parallelization in PSO often outperforms the standard parallelization of simply adding particles to the swarm. SEPSO produces results that are exactly equivalent to PSO; this is not a new algorithm or variant, only a new method of parallelization. However, given this new parallelization model we can relax the requirement of exactly reproducing PSO in an attempt to produce better results. We present several such relaxations, including keeping the best speculative position evaluated instead of the one corresponding to the standard behavior of PSO, and speculating several iterations ahead instead of just one. We show that these methods dramatically improve the performance of parallel PSO in many cases, giving speed ups of up to six times compared to previous parallelization techniques.