In this paper we present and investigate partial neighborhood local searches, which only explore a sample of the neighborhood at each step of the search. We particularly focus on establishing link between the structure of optimization problems and the efficiency of such local search algorithms. In our experiments we compare partial neighborhood local searches to state-of-the-art tabu search and iterated local search and perform a parameter sensitivity analysis by observing the efficiency of partial neighborhood local searches with different size of neighborhood sample. In order to facilitate the extraction of links between instances structure and search algorithm behavior we restrain the scope to binary fitness landscapes, such as NK landscapes and landscapes derived from UBQP.