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Multiobjective local search algorithms are efficient methods to solve complex problems in science and industry. Even if these heuristics allow to significantly reduce the computational time of the solution search space exploration, this latter cost remains exorbitant when very large problem instances are to be solved. As a result, the use of graphics processing units (GPU) has been recently revealed as an efficient way to accelerate the search process. This paper presents a new methodology to design and implement efficiently GPU-based multiobjective local search algorithms. The experimental results show that the approach is promising especially for large problem instances.