For the sake of software compatibility, simulations are often parallelized without much code rewriting. Performances can be further improved by optimizing codes so that to use the maximum power offered by parallel architectures. While this approach can provide some speed-up, performance of parallelized codes can be strongly limited a priori because traditional algorithms have been designed for sequential technologies. Thus, additional increase of performance should ultimately rely on some redesign of algorithms. Here, we redesign an algorithm that has traditionally been used to simulate the folding proper- ties of polymers. We address the issue of performance in the context of biological applications, more particularly in the active field of chromosome modelling. Due to the strong confinement of chromosomes in the cells, simulation of their motion is slowed down by the laborious search for the next valid states to progress. Our redesign, that we call the Possible Futures Algorithm (PFA), relies on the parallel computation of possible evolutions of the same state, which effectively increases the probability to obtain a valid state at each step. We apply PFA on a GPU-based architecture, allowing us to optimally reduce the latency induced by the computation overhead of possible futures. We show that compared to the initial sequential model the acceptance rate of new states significantly increases without impacting the execution time. In particular, the stronger the confinement of the chromosome, the more efficient PFA becomes, making our approach appealing for biological applications. While most of our results were obtained using Fermi architecture GPUs from NVIDIA, we highlight improved performance on the cutting-edge Kepler architecture K20 GPUs.