Hyper-heuristics are powerful search methodologies that can adapt to different kinds of problems. One element of paramount importance, however, is the selection module that they incorporate. Traditional approaches define a set of features for characterizing a problem and, thus, define how to best solve it. However, some features may vary nonlinearly as the solver progresses, requiring higher resolution in specific areas of the feature domain. This work focuses on assessing the advantage of using feature transformations to improve the given resolution and, as a consequence, to improve the overall performance of a hyper-heuristic. We provide evidence that using feature transformations may result in a better discrimination of the problem instance and, as consequence, a better performance of the hyper-heuristics. The feature transformation strategy was applied to an evolutionary-based hyper-heuristic model taken from the literature and tested on constraint satisfaction problems The proposed strategy increased the median success rate of hyper-heuristics by more than 13% and reduced its standard deviation in about 7%, while reducing the median number of adjusted consistency checks by almost 30%.