Local search algorithms are powerful heuristics for solving computationally hard problems in science and industry. In these methods, designing neighborhood operators to explore large promising regions of the search space may improve the quality of the obtained solutions at the expense of a high computation process. As a consequence, the use of GPU computing provides an efficient way to speed up the search. However, designing applications on GPU is still complex and many issues have to be faced. We provide a methodology to design and implement different neighborhood structures for LS algorithms on GPU. The work has been evaluated for binary problems and the obtained results are convincing both in terms of efficiency, quality and robustness of the provided solutions at run time.