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This paper is a major step towards a pioneering software framework for the reusable design and implementation of parallel metaheuristics on Graphics Processing Units (GPU). The objective is to revisit the ParadisEO framework to allow its utilization on GPU accelerators. The focus is on local search metaheuristics and the parallel exploration of their neighborhood. The challenge is to make the GPU as transparent as possible for the user. The first release of the new GPU-based ParadisEO framework has been experimented on the Quadratic Assignment Problem (QAP). 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.