In this work, we study partial neighborhood local search (PNLS) techniques, which consist of adaptive walks where moves are chosen in a random subset of the current solution neighborhood. PNLSs balance between intensification and diversification is mainly determined by its single parameter λ designing the subset size. We analyze and discuss three PNLSs variants, using the abstraction of several combinatorial optimization problems into fitness landscapes: NK landscapes, Unconstrained Binary Quadratic Programming, Flow-shop scheduling, and Quadratic Assignment. Our empirical study first analyses the structure of these landscapes through indicators. Then, we perform a parameter study of PNLSs for two computational budgets to study the impact of the sample size on the balance between intensification and diversification on different landscapes. Moreover, these experiments allow us to set an appropriate parameter value to compare the ability of PNLSs to reach good-quality solutions accurately. Finally, we compare PNLS variants with two classical metaheuristics, identifying links between landscape characteristics and algorithms behavior.