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Optimization problems are more and more complex and their resource requirements are ever increasing. Although metaheuristics allow to significantly reduce the computational complexity of the search process, the latter remains time-consuming for many problems in diverse domains of application. As a result, the use of GPU has been recently revealed as an efficient way to speed up the search. In this paper, we provide a new methodology to design and implement efficiently local search methods on GPU. The work has been experimented on the permuted perceptron problem and the experimental results show that the approach is very efficient especially for large problem instances.