In this paper, we propose a pioneering framework called ParadisEO-MO-GPU for the reusable design and implementation of parallel local search metaheuristics (S- Metaheuristics) on Graphics Processing Units (GPU). We revisit the ParadisEO-MO software framework to allow its utilization on GPU accelerators focusing on the parallel iteration-level model, the major parallel model for S- Metaheuristics. It consists in the parallel exploration of the neighborhood of a problem solution. The challenge is on the one hand to rethink the design and implementation of this model optimizing the data transfer between the CPU and the GPU. On the other hand, the objective is to make the GPU as transparent as possible for the user minimizing his or her involvement in its management. In this paper, we propose solutions to this challenge as an extension of the ParadisEO framework. The first release of the new GPU-based ParadisEO framework has been experimented on the permuted perceptron problem. The preliminary results are convincing, both in terms of flexibility and easiness of reuse at implementation, and in terms of efficiency at execution on GPU.